information on time travel

Is Time Travel Possible?

We all travel in time! We travel one year in time between birthdays, for example. And we are all traveling in time at approximately the same speed: 1 second per second.

We typically experience time at one second per second. Credit: NASA/JPL-Caltech

NASA's space telescopes also give us a way to look back in time. Telescopes help us see stars and galaxies that are very far away . It takes a long time for the light from faraway galaxies to reach us. So, when we look into the sky with a telescope, we are seeing what those stars and galaxies looked like a very long time ago.

However, when we think of the phrase "time travel," we are usually thinking of traveling faster than 1 second per second. That kind of time travel sounds like something you'd only see in movies or science fiction books. Could it be real? Science says yes!

Image of galaxies, taken by the Hubble Space Telescope.

This image from the Hubble Space Telescope shows galaxies that are very far away as they existed a very long time ago. Credit: NASA, ESA and R. Thompson (Univ. Arizona)

How do we know that time travel is possible?

More than 100 years ago, a famous scientist named Albert Einstein came up with an idea about how time works. He called it relativity. This theory says that time and space are linked together. Einstein also said our universe has a speed limit: nothing can travel faster than the speed of light (186,000 miles per second).

Einstein's theory of relativity says that space and time are linked together. Credit: NASA/JPL-Caltech

What does this mean for time travel? Well, according to this theory, the faster you travel, the slower you experience time. Scientists have done some experiments to show that this is true.

For example, there was an experiment that used two clocks set to the exact same time. One clock stayed on Earth, while the other flew in an airplane (going in the same direction Earth rotates).

After the airplane flew around the world, scientists compared the two clocks. The clock on the fast-moving airplane was slightly behind the clock on the ground. So, the clock on the airplane was traveling slightly slower in time than 1 second per second.

Credit: NASA/JPL-Caltech

Can we use time travel in everyday life?

We can't use a time machine to travel hundreds of years into the past or future. That kind of time travel only happens in books and movies. But the math of time travel does affect the things we use every day.

For example, we use GPS satellites to help us figure out how to get to new places. (Check out our video about how GPS satellites work .) NASA scientists also use a high-accuracy version of GPS to keep track of where satellites are in space. But did you know that GPS relies on time-travel calculations to help you get around town?

GPS satellites orbit around Earth very quickly at about 8,700 miles (14,000 kilometers) per hour. This slows down GPS satellite clocks by a small fraction of a second (similar to the airplane example above).

Illustration of GPS satellites orbiting around Earth

GPS satellites orbit around Earth at about 8,700 miles (14,000 kilometers) per hour. Credit: GPS.gov

However, the satellites are also orbiting Earth about 12,550 miles (20,200 km) above the surface. This actually speeds up GPS satellite clocks by a slighter larger fraction of a second.

Here's how: Einstein's theory also says that gravity curves space and time, causing the passage of time to slow down. High up where the satellites orbit, Earth's gravity is much weaker. This causes the clocks on GPS satellites to run faster than clocks on the ground.

The combined result is that the clocks on GPS satellites experience time at a rate slightly faster than 1 second per second. Luckily, scientists can use math to correct these differences in time.

Illustration of a hand holding a phone with a maps application active.

If scientists didn't correct the GPS clocks, there would be big problems. GPS satellites wouldn't be able to correctly calculate their position or yours. The errors would add up to a few miles each day, which is a big deal. GPS maps might think your home is nowhere near where it actually is!

In Summary:

Yes, time travel is indeed a real thing. But it's not quite what you've probably seen in the movies. Under certain conditions, it is possible to experience time passing at a different rate than 1 second per second. And there are important reasons why we need to understand this real-world form of time travel.

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April 26, 2023

Is Time Travel Possible?

The laws of physics allow time travel. So why haven’t people become chronological hoppers?

By Sarah Scoles

yuanyuan yan/Getty Images

In the movies, time travelers typically step inside a machine and—poof—disappear. They then reappear instantaneously among cowboys, knights or dinosaurs. What these films show is basically time teleportation .

Scientists don’t think this conception is likely in the real world, but they also don’t relegate time travel to the crackpot realm. In fact, the laws of physics might allow chronological hopping, but the devil is in the details.

Time traveling to the near future is easy: you’re doing it right now at a rate of one second per second, and physicists say that rate can change. According to Einstein’s special theory of relativity, time’s flow depends on how fast you’re moving. The quicker you travel, the slower seconds pass. And according to Einstein’s general theory of relativity , gravity also affects clocks: the more forceful the gravity nearby, the slower time goes.

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“Near massive bodies—near the surface of neutron stars or even at the surface of the Earth, although it’s a tiny effect—time runs slower than it does far away,” says Dave Goldberg, a cosmologist at Drexel University.

If a person were to hang out near the edge of a black hole , where gravity is prodigious, Goldberg says, only a few hours might pass for them while 1,000 years went by for someone on Earth. If the person who was near the black hole returned to this planet, they would have effectively traveled to the future. “That is a real effect,” he says. “That is completely uncontroversial.”

Going backward in time gets thorny, though (thornier than getting ripped to shreds inside a black hole). Scientists have come up with a few ways it might be possible, and they have been aware of time travel paradoxes in general relativity for decades. Fabio Costa, a physicist at the Nordic Institute for Theoretical Physics, notes that an early solution with time travel began with a scenario written in the 1920s. That idea involved massive long cylinder that spun fast in the manner of straw rolled between your palms and that twisted spacetime along with it. The understanding that this object could act as a time machine allowing one to travel to the past only happened in the 1970s, a few decades after scientists had discovered a phenomenon called “closed timelike curves.”

“A closed timelike curve describes the trajectory of a hypothetical observer that, while always traveling forward in time from their own perspective, at some point finds themselves at the same place and time where they started, creating a loop,” Costa says. “This is possible in a region of spacetime that, warped by gravity, loops into itself.”

“Einstein read [about closed timelike curves] and was very disturbed by this idea,” he adds. The phenomenon nevertheless spurred later research.

Science began to take time travel seriously in the 1980s. In 1990, for instance, Russian physicist Igor Novikov and American physicist Kip Thorne collaborated on a research paper about closed time-like curves. “They started to study not only how one could try to build a time machine but also how it would work,” Costa says.

Just as importantly, though, they investigated the problems with time travel. What if, for instance, you tossed a billiard ball into a time machine, and it traveled to the past and then collided with its past self in a way that meant its present self could never enter the time machine? “That looks like a paradox,” Costa says.

Since the 1990s, he says, there’s been on-and-off interest in the topic yet no big breakthrough. The field isn’t very active today, in part because every proposed model of a time machine has problems. “It has some attractive features, possibly some potential, but then when one starts to sort of unravel the details, there ends up being some kind of a roadblock,” says Gaurav Khanna of the University of Rhode Island.

For instance, most time travel models require negative mass —and hence negative energy because, as Albert Einstein revealed when he discovered E = mc 2 , mass and energy are one and the same. In theory, at least, just as an electric charge can be positive or negative, so can mass—though no one’s ever found an example of negative mass. Why does time travel depend on such exotic matter? In many cases, it is needed to hold open a wormhole—a tunnel in spacetime predicted by general relativity that connects one point in the cosmos to another.

Without negative mass, gravity would cause this tunnel to collapse. “You can think of it as counteracting the positive mass or energy that wants to traverse the wormhole,” Goldberg says.

Khanna and Goldberg concur that it’s unlikely matter with negative mass even exists, although Khanna notes that some quantum phenomena show promise, for instance, for negative energy on very small scales. But that would be “nowhere close to the scale that would be needed” for a realistic time machine, he says.

These challenges explain why Khanna initially discouraged Caroline Mallary, then his graduate student at the University of Massachusetts Dartmouth, from doing a time travel project. Mallary and Khanna went forward anyway and came up with a theoretical time machine that didn’t require negative mass. In its simplistic form, Mallary’s idea involves two parallel cars, each made of regular matter. If you leave one parked and zoom the other with extreme acceleration, a closed timelike curve will form between them.

Easy, right? But while Mallary’s model gets rid of the need for negative matter, it adds another hurdle: it requires infinite density inside the cars for them to affect spacetime in a way that would be useful for time travel. Infinite density can be found inside a black hole, where gravity is so intense that it squishes matter into a mind-bogglingly small space called a singularity. In the model, each of the cars needs to contain such a singularity. “One of the reasons that there's not a lot of active research on this sort of thing is because of these constraints,” Mallary says.

Other researchers have created models of time travel that involve a wormhole, or a tunnel in spacetime from one point in the cosmos to another. “It's sort of a shortcut through the universe,” Goldberg says. Imagine accelerating one end of the wormhole to near the speed of light and then sending it back to where it came from. “Those two sides are no longer synced,” he says. “One is in the past; one is in the future.” Walk between them, and you’re time traveling.

You could accomplish something similar by moving one end of the wormhole near a big gravitational field—such as a black hole—while keeping the other end near a smaller gravitational force. In that way, time would slow down on the big gravity side, essentially allowing a particle or some other chunk of mass to reside in the past relative to the other side of the wormhole.

Making a wormhole requires pesky negative mass and energy, however. A wormhole created from normal mass would collapse because of gravity. “Most designs tend to have some similar sorts of issues,” Goldberg says. They’re theoretically possible, but there’s currently no feasible way to make them, kind of like a good-tasting pizza with no calories.

And maybe the problem is not just that we don’t know how to make time travel machines but also that it’s not possible to do so except on microscopic scales—a belief held by the late physicist Stephen Hawking. He proposed the chronology protection conjecture: The universe doesn’t allow time travel because it doesn’t allow alterations to the past. “It seems there is a chronology protection agency, which prevents the appearance of closed timelike curves and so makes the universe safe for historians,” Hawking wrote in a 1992 paper in Physical Review D .

Part of his reasoning involved the paradoxes time travel would create such as the aforementioned situation with a billiard ball and its more famous counterpart, the grandfather paradox : If you go back in time and kill your grandfather before he has children, you can’t be born, and therefore you can’t time travel, and therefore you couldn’t have killed your grandfather. And yet there you are.

Those complications are what interests Massachusetts Institute of Technology philosopher Agustin Rayo, however, because the paradoxes don’t just call causality and chronology into question. They also make free will seem suspect. If physics says you can go back in time, then why can’t you kill your grandfather? “What stops you?” he says. Are you not free?

Rayo suspects that time travel is consistent with free will, though. “What’s past is past,” he says. “So if, in fact, my grandfather survived long enough to have children, traveling back in time isn’t going to change that. Why will I fail if I try? I don’t know because I don’t have enough information about the past. What I do know is that I’ll fail somehow.”

If you went to kill your grandfather, in other words, you’d perhaps slip on a banana en route or miss the bus. “It's not like you would find some special force compelling you not to do it,” Costa says. “You would fail to do it for perfectly mundane reasons.”

In 2020 Costa worked with Germain Tobar, then his undergraduate student at the University of Queensland in Australia, on the math that would underlie a similar idea: that time travel is possible without paradoxes and with freedom of choice.

Goldberg agrees with them in a way. “I definitely fall into the category of [thinking that] if there is time travel, it will be constructed in such a way that it produces one self-consistent view of history,” he says. “Because that seems to be the way that all the rest of our physical laws are constructed.”

No one knows what the future of time travel to the past will hold. And so far, no time travelers have come to tell us about it.

Is time travel possible? Why one scientist says we 'cannot ignore the possibility.'

A common theme in science-fiction media , time travel is captivating. It’s defined by the late philosopher David Lewis in his essay “The Paradoxes of Time Travel” as “[involving] a discrepancy between time and space time. Any traveler departs and then arrives at his destination; the time elapsed from departure to arrival … is the duration of the journey.”

Time travel is usually understood by most as going back to a bygone era or jumping forward to a point far in the future . But how much of the idea is based in reality? Is it possible to travel through time?

Is time travel possible?

According to NASA, time travel is possible , just not in the way you might expect. Albert Einstein’s theory of relativity says time and motion are relative to each other, and nothing can go faster than the speed of light , which is 186,000 miles per second. Time travel happens through what’s called “time dilation.”

Time dilation , according to Live Science, is how one’s perception of time is different to another's, depending on their motion or where they are. Hence, time being relative.

Learn more: Best travel insurance

Dr. Ana Alonso-Serrano, a postdoctoral researcher at the Max Planck Institute for Gravitational Physics in Germany, explained the possibility of time travel and how researchers test theories.

Space and time are not absolute values, Alonso-Serrano said. And what makes this all more complex is that you are able to carve space-time .

“In the moment that you carve the space-time, you can play with that curvature to make the time come in a circle and make a time machine,” Alonso-Serrano told USA TODAY.

She explained how, theoretically, time travel is possible. The mathematics behind creating curvature of space-time are solid, but trying to re-create the strict physical conditions needed to prove these theories can be challenging.

“The tricky point of that is if you can find a physical, realistic, way to do it,” she said.

Alonso-Serrano said wormholes and warp drives are tools that are used to create this curvature. The matter needed to achieve curving space-time via a wormhole is exotic matter , which hasn’t been done successfully. Researchers don’t even know if this type of matter exists, she said.

“It's something that we work on because it's theoretically possible, and because it's a very nice way to test our theory, to look for possible paradoxes,” Alonso-Serrano added.

“I could not say that nothing is possible, but I cannot ignore the possibility,” she said.

She also mentioned the anecdote of Stephen Hawking’s Champagne party for time travelers . Hawking had a GPS-specific location for the party. He didn’t send out invites until the party had already happened, so only people who could travel to the past would be able to attend. No one showed up, and Hawking referred to this event as "experimental evidence" that time travel wasn't possible.

What did Albert Einstein invent?: Discoveries that changed the world

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Time travel: Is it possible?

Science says time travel is possible, but probably not in the way you're thinking.

time travel graphic illustration of a tunnel with a clock face swirling through the tunnel.

Albert Einstein's theory

General relativity and GPS
Wormhole travel
Alternate theories

Science fiction

Is time travel possible? Short answer: Yes, and you're doing it right now — hurtling into the future at the impressive rate of one second per second.

You're pretty much always moving through time at the same speed, whether you're watching paint dry or wishing you had more hours to visit with a friend from out of town.

But this isn't the kind of time travel that's captivated countless science fiction writers, or spurred a genre so extensive that Wikipedia lists over 400 titles in the category "Movies about Time Travel." In franchises like " Doctor Who ," " Star Trek ," and "Back to the Future" characters climb into some wild vehicle to blast into the past or spin into the future. Once the characters have traveled through time, they grapple with what happens if you change the past or present based on information from the future (which is where time travel stories intersect with the idea of parallel universes or alternate timelines).

Related: The best sci-fi time machines ever

Although many people are fascinated by the idea of changing the past or seeing the future before it's due, no person has ever demonstrated the kind of back-and-forth time travel seen in science fiction or proposed a method of sending a person through significant periods of time that wouldn't destroy them on the way. And, as physicist Stephen Hawking pointed out in his book " Black Holes and Baby Universes" (Bantam, 1994), "The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future."

Science does support some amount of time-bending, though. For example, physicist Albert Einstein 's theory of special relativity proposes that time is an illusion that moves relative to an observer. An observer traveling near the speed of light will experience time, with all its aftereffects (boredom, aging, etc.) much more slowly than an observer at rest. That's why astronaut Scott Kelly aged ever so slightly less over the course of a year in orbit than his twin brother who stayed here on Earth.

Related: Controversially, physicist argues that time is real

There are other scientific theories about time travel, including some weird physics that arise around wormholes , black holes and string theory . For the most part, though, time travel remains the domain of an ever-growing array of science fiction books, movies, television shows, comics, video games and more.

Scott and Mark Kelly sit side by side wearing a blue NASA jacket and jeans

Einstein developed his theory of special relativity in 1905. Along with his later expansion, the theory of general relativity , it has become one of the foundational tenets of modern physics. Special relativity describes the relationship between space and time for objects moving at constant speeds in a straight line.

The short version of the theory is deceptively simple. First, all things are measured in relation to something else — that is to say, there is no "absolute" frame of reference. Second, the speed of light is constant. It stays the same no matter what, and no matter where it's measured from. And third, nothing can go faster than the speed of light.

From those simple tenets unfolds actual, real-life time travel. An observer traveling at high velocity will experience time at a slower rate than an observer who isn't speeding through space.

While we don't accelerate humans to near-light-speed, we do send them swinging around the planet at 17,500 mph (28,160 km/h) aboard the International Space Station . Astronaut Scott Kelly was born after his twin brother, and fellow astronaut, Mark Kelly . Scott Kelly spent 520 days in orbit, while Mark logged 54 days in space. The difference in the speed at which they experienced time over the course of their lifetimes has actually widened the age gap between the two men.

"So, where[as] I used to be just 6 minutes older, now I am 6 minutes and 5 milliseconds older," Mark Kelly said in a panel discussion on July 12, 2020, Space.com previously reported . "Now I've got that over his head."

General relativity and GPS time travel

Graphic showing the path of GPS satellites around Earth at the center of the image.

The difference that low earth orbit makes in an astronaut's life span may be negligible — better suited for jokes among siblings than actual life extension or visiting the distant future — but the dilation in time between people on Earth and GPS satellites flying through space does make a difference.

Can wormholes take us back in time?

General relativity might also provide scenarios that could allow travelers to go back in time, according to NASA . But the physical reality of those time-travel methods is no piece of cake.

Wormholes are theoretical "tunnels" through the fabric of space-time that could connect different moments or locations in reality to others. Also known as Einstein-Rosen bridges or white holes, as opposed to black holes, speculation about wormholes abounds. But despite taking up a lot of space (or space-time) in science fiction, no wormholes of any kind have been identified in real life.

Related: Best time travel movies

"The whole thing is very hypothetical at this point," Stephen Hsu, a professor of theoretical physics at the University of Oregon, told Space.com sister site Live Science . "No one thinks we're going to find a wormhole anytime soon."

Primordial wormholes are predicted to be just 10^-34 inches (10^-33 centimeters) at the tunnel's "mouth". Previously, they were expected to be too unstable for anything to be able to travel through them. However, a study claims that this is not the case, Live Science reported .

The theory, which suggests that wormholes could work as viable space-time shortcuts, was described by physicist Pascal Koiran. As part of the study, Koiran used the Eddington-Finkelstein metric, as opposed to the Schwarzschild metric which has been used in the majority of previous analyses.

In the past, the path of a particle could not be traced through a hypothetical wormhole. However, using the Eddington-Finkelstein metric, the physicist was able to achieve just that.

Koiran's paper was described in October 2021, in the preprint database arXiv , before being published in the Journal of Modern Physics D.

Alternate time travel theories

While Einstein's theories appear to make time travel difficult, some researchers have proposed other solutions that could allow jumps back and forth in time. These alternate theories share one major flaw: As far as scientists can tell, there's no way a person could survive the kind of gravitational pulling and pushing that each solution requires.

Infinite cylinder theory

Astronomer Frank Tipler proposed a mechanism (sometimes known as a Tipler Cylinder ) where one could take matter that is 10 times the sun's mass, then roll it into a very long, but very dense cylinder. The Anderson Institute , a time travel research organization, described the cylinder as "a black hole that has passed through a spaghetti factory."

After spinning this black hole spaghetti a few billion revolutions per minute, a spaceship nearby — following a very precise spiral around the cylinder — could travel backward in time on a "closed, time-like curve," according to the Anderson Institute.

The major problem is that in order for the Tipler Cylinder to become reality, the cylinder would need to be infinitely long or be made of some unknown kind of matter. At least for the foreseeable future, endless interstellar pasta is beyond our reach.

Time donuts

Theoretical physicist Amos Ori at the Technion-Israel Institute of Technology in Haifa, Israel, proposed a model for a time machine made out of curved space-time — a donut-shaped vacuum surrounded by a sphere of normal matter.

"The machine is space-time itself," Ori told Live Science . "If we were to create an area with a warp like this in space that would enable time lines to close on themselves, it might enable future generations to return to visit our time."

Amos Ori is a theoretical physicist at the Technion-Israel Institute of Technology in Haifa, Israel. His research interests and publications span the fields of general relativity, black holes, gravitational waves and closed time lines.

There are a few caveats to Ori's time machine. First, visitors to the past wouldn't be able to travel to times earlier than the invention and construction of the time donut. Second, and more importantly, the invention and construction of this machine would depend on our ability to manipulate gravitational fields at will — a feat that may be theoretically possible but is certainly beyond our immediate reach.

Graphic illustration of the TARDIS (Time and Relative Dimensions in Space) traveling through space, surrounded by stars.

Time travel has long occupied a significant place in fiction. Since as early as the "Mahabharata," an ancient Sanskrit epic poem compiled around 400 B.C., humans have dreamed of warping time, Lisa Yaszek, a professor of science fiction studies at the Georgia Institute of Technology in Atlanta, told Live Science .

Every work of time-travel fiction creates its own version of space-time, glossing over one or more scientific hurdles and paradoxes to achieve its plot requirements.

Some make a nod to research and physics, like " Interstellar ," a 2014 film directed by Christopher Nolan. In the movie, a character played by Matthew McConaughey spends a few hours on a planet orbiting a supermassive black hole, but because of time dilation, observers on Earth experience those hours as a matter of decades.

Others take a more whimsical approach, like the "Doctor Who" television series. The series features the Doctor, an extraterrestrial "Time Lord" who travels in a spaceship resembling a blue British police box. "People assume," the Doctor explained in the show, "that time is a strict progression from cause to effect, but actually from a non-linear, non-subjective viewpoint, it's more like a big ball of wibbly-wobbly, timey-wimey stuff."

Long-standing franchises like the "Star Trek" movies and television series, as well as comic universes like DC and Marvel Comics, revisit the idea of time travel over and over.

Related: Marvel movies in order: chronological & release order

Here is an incomplete (and deeply subjective) list of some influential or notable works of time travel fiction:

Books about time travel:

A sketch from the Christmas Carol shows a cloaked figure on the left and a person kneeling and clutching their head with their hands.

Rip Van Winkle (Cornelius S. Van Winkle, 1819) by Washington Irving
A Christmas Carol (Chapman & Hall, 1843) by Charles Dickens
The Time Machine (William Heinemann, 1895) by H. G. Wells
A Connecticut Yankee in King Arthur's Court (Charles L. Webster and Co., 1889) by Mark Twain
The Restaurant at the End of the Universe (Pan Books, 1980) by Douglas Adams
A Tale of Time City (Methuen, 1987) by Diana Wynn Jones
The Outlander series (Delacorte Press, 1991-present) by Diana Gabaldon
Harry Potter and the Prisoner of Azkaban (Bloomsbury/Scholastic, 1999) by J. K. Rowling
Thief of Time (Doubleday, 2001) by Terry Pratchett
The Time Traveler's Wife (MacAdam/Cage, 2003) by Audrey Niffenegger
All You Need is Kill (Shueisha, 2004) by Hiroshi Sakurazaka

Movies about time travel:

Planet of the Apes (1968)
Superman (1978)
Time Bandits (1981)
The Terminator (1984)
Back to the Future series (1985, 1989, 1990)
Star Trek IV: The Voyage Home (1986)
Bill & Ted's Excellent Adventure (1989)
Groundhog Day (1993)
Galaxy Quest (1999)
The Butterfly Effect (2004)
13 Going on 30 (2004)
The Lake House (2006)
Meet the Robinsons (2007)
Hot Tub Time Machine (2010)
Midnight in Paris (2011)
Looper (2012)
X-Men: Days of Future Past (2014)
Edge of Tomorrow (2014)
Interstellar (2014)
Doctor Strange (2016)
A Wrinkle in Time (2018)
The Last Sharknado: It's About Time (2018)
Avengers: Endgame (2019)
Tenet (2020)
Palm Springs (2020)
Zach Snyder's Justice League (2021)
The Tomorrow War (2021)

Television about time travel:

Image of the Star Trek spaceship USS Enterprise

Doctor Who (1963-present)
The Twilight Zone (1959-1964) (multiple episodes)
Star Trek (multiple series, multiple episodes)
Samurai Jack (2001-2004)
Lost (2004-2010)
Phil of the Future (2004-2006)
Steins;Gate (2011)
Outlander (2014-2023)
Loki (2021-present)

Games about time travel:

Chrono Trigger (1995)
TimeSplitters (2000-2005)
Kingdom Hearts (2002-2019)
Prince of Persia: Sands of Time (2003)
God of War II (2007)
Ratchet and Clank Future: A Crack In Time (2009)
Sly Cooper: Thieves in Time (2013)
Dishonored 2 (2016)
Titanfall 2 (2016)
Outer Wilds (2019)

Additional resources

Explore physicist Peter Millington's thoughts about Stephen Hawking's time travel theories at The Conversation . Check out a kid-friendly explanation of real-world time travel from NASA's Space Place . For an overview of time travel in fiction and the collective consciousness, read " Time Travel: A History " (Pantheon, 2016) by James Gleik.

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

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Ailsa is a staff writer for How It Works magazine, where she writes science, technology, space, history and environment features. Based in the U.K., she graduated from the University of Stirling with a BA (Hons) journalism degree. Previously, Ailsa has written for Cardiff Times magazine, Psychology Now and numerous science bookazines.

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Will it ever be possible for time travel to occur? – Alana C., age 12, Queens, New York

Have you ever dreamed of traveling through time, like characters do in science fiction movies? For centuries, the concept of time travel has captivated people’s imaginations. Time travel is the concept of moving between different points in time, just like you move between different places. In movies, you might have seen characters using special machines, magical devices or even hopping into a futuristic car to travel backward or forward in time.

But is this just a fun idea for movies, or could it really happen?

The question of whether time is reversible remains one of the biggest unresolved questions in science. If the universe follows the laws of thermodynamics , it may not be possible. The second law of thermodynamics states that things in the universe can either remain the same or become more disordered over time.

It’s a bit like saying you can’t unscramble eggs once they’ve been cooked. According to this law, the universe can never go back exactly to how it was before. Time can only go forward, like a one-way street.

Time is relative

However, physicist Albert Einstein’s theory of special relativity suggests that time passes at different rates for different people. Someone speeding along on a spaceship moving close to the speed of light – 671 million miles per hour! – will experience time slower than a person on Earth.

Related: The speed of light, explained

People have yet to build spaceships that can move at speeds anywhere near as fast as light, but astronauts who visit the International Space Station orbit around the Earth at speeds close to 17,500 mph. Astronaut Scott Kelly has spent 520 days at the International Space Station, and as a result has aged a little more slowly than his twin brother – and fellow astronaut – Mark Kelly. Scott used to be 6 minutes younger than his twin brother. Now, because Scott was traveling so much faster than Mark and for so many days, he is 6 minutes and 5 milliseconds younger .

Some scientists are exploring other ideas that could theoretically allow time travel. One concept involves wormholes , or hypothetical tunnels in space that could create shortcuts for journeys across the universe. If someone could build a wormhole and then figure out a way to move one end at close to the speed of light – like the hypothetical spaceship mentioned above – the moving end would age more slowly than the stationary end. Someone who entered the moving end and exited the wormhole through the stationary end would come out in their past.

However, wormholes remain theoretical : Scientists have yet to spot one. It also looks like it would be incredibly challenging to send humans through a wormhole space tunnel.

Time travel paradoxes and failed dinner parties

There are also paradoxes associated with time travel. The famous “ grandfather paradox ” is a hypothetical problem that could arise if someone traveled back in time and accidentally prevented their grandparents from meeting. This would create a paradox where you were never born, which raises the question: How could you have traveled back in time in the first place? It’s a mind-boggling puzzle that adds to the mystery of time travel.

Famously, physicist Stephen Hawking tested the possibility of time travel by throwing a dinner party where invitations noting the date, time and coordinates were not sent out until after it had happened. His hope was that his invitation would be read by someone living in the future, who had capabilities to travel back in time. But no one showed up.

As he pointed out : “The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future.”

Telescopes are time machines

Interestingly, astrophysicists armed with powerful telescopes possess a unique form of time travel. As they peer into the vast expanse of the cosmos, they gaze into the past universe. Light from all galaxies and stars takes time to travel, and these beams of light carry information from the distant past. When astrophysicists observe a star or a galaxy through a telescope, they are not seeing it as it is in the present, but as it existed when the light began its journey to Earth millions to billions of years ago.

NASA’s newest space telescope, the James Webb Space Telescope , is peering at galaxies that were formed at the very beginning of the Big Bang, about 13.7 billion years ago.

While we aren’t likely to have time machines like the ones in movies anytime soon, scientists are actively researching and exploring new ideas. But for now, we’ll have to enjoy the idea of time travel in our favorite books, movies and dreams.

This article first appeared on the Conversation. You can read the original here .

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Paradox-Free Time Travel Is Theoretically Possible, Researchers Say

Matthew S. Schwartz

A dog dressed as Marty McFly from Back to the Future attends the Tompkins Square Halloween Dog Parade in 2015. New research says time travel might be possible without the problems McFly encountered. Timothy A. Clary/AFP via Getty Images hide caption

A dog dressed as Marty McFly from Back to the Future attends the Tompkins Square Halloween Dog Parade in 2015. New research says time travel might be possible without the problems McFly encountered.

"The past is obdurate," Stephen King wrote in his book about a man who goes back in time to prevent the Kennedy assassination. "It doesn't want to be changed."

Turns out, King might have been on to something.

Countless science fiction tales have explored the paradox of what would happen if you went back in time and did something in the past that endangered the future. Perhaps one of the most famous pop culture examples is in Back to the Future , when Marty McFly goes back in time and accidentally stops his parents from meeting, putting his own existence in jeopardy.

But maybe McFly wasn't in much danger after all. According a new paper from researchers at the University of Queensland, even if time travel were possible, the paradox couldn't actually exist.

Researchers ran the numbers and determined that even if you made a change in the past, the timeline would essentially self-correct, ensuring that whatever happened to send you back in time would still happen.

"Say you traveled in time in an attempt to stop COVID-19's patient zero from being exposed to the virus," University of Queensland scientist Fabio Costa told the university's news service .

"However, if you stopped that individual from becoming infected, that would eliminate the motivation for you to go back and stop the pandemic in the first place," said Costa, who co-authored the paper with honors undergraduate student Germain Tobar.

"This is a paradox — an inconsistency that often leads people to think that time travel cannot occur in our universe."

A variation is known as the "grandfather paradox" — in which a time traveler kills their own grandfather, in the process preventing the time traveler's birth.

The logical paradox has given researchers a headache, in part because according to Einstein's theory of general relativity, "closed timelike curves" are possible, theoretically allowing an observer to travel back in time and interact with their past self — potentially endangering their own existence.

But these researchers say that such a paradox wouldn't necessarily exist, because events would adjust themselves.

Take the coronavirus patient zero example. "You might try and stop patient zero from becoming infected, but in doing so, you would catch the virus and become patient zero, or someone else would," Tobar told the university's news service.

In other words, a time traveler could make changes, but the original outcome would still find a way to happen — maybe not the same way it happened in the first timeline but close enough so that the time traveler would still exist and would still be motivated to go back in time.

"No matter what you did, the salient events would just recalibrate around you," Tobar said.

The paper, "Reversible dynamics with closed time-like curves and freedom of choice," was published last week in the peer-reviewed journal Classical and Quantum Gravity . The findings seem consistent with another time travel study published this summer in the peer-reviewed journal Physical Review Letters. That study found that changes made in the past won't drastically alter the future.

Bestselling science fiction author Blake Crouch, who has written extensively about time travel, said the new study seems to support what certain time travel tropes have posited all along.

"The universe is deterministic and attempts to alter Past Event X are destined to be the forces which bring Past Event X into being," Crouch told NPR via email. "So the future can affect the past. Or maybe time is just an illusion. But I guess it's cool that the math checks out."

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Is time travel even possible? An astrophysicist explains the science behind the science fiction

Published: Nov 13, 2023

By: Magazine Editor

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Written by Adi Foord , assistant professor of physics , UMBC

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Will it ever be possible for time travel to occur? – Alana C., age 12, Queens, New York

But is this just a fun idea for movies, or could it really happen?

Time is relative

However, wormholes remain theoretical: Scientists have yet to spot one. It also looks like it would be incredibly challenging to send humans through a wormhole space tunnel.

Paradoxes and failed dinner parties

As he pointed out : “The best evidence we have that time travel is not possible, and never will be, is that we have not been invaded by hordes of tourists from the future.”

Telescopes are time machines

NASA’s newest space telescope, the James Webb Space Telescope , is peering at galaxies that were formed at the very beginning of the Big Bang, about 13.7 billion years ago.

This article is republished from The Conversation under a Creative Commons license. Read the original article and see more than 250 UMBC articles available in The Conversation.

Tags: CNMS , Physics , The Conversation

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How Time Travel Works

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From millennium-skipping Victorians to phone booth-hopping time traveler teenagers, the term time travel often summons our most fantastic visions of what it means to move through the fourth dimension. But of course you don't need a time machine or a fancy wormhole to jaunt through the years.

As you've probably noticed, we're all constantly engaged in the act of time travel. At its most basic level, time is the rate of change in the universe -- and like it or not, we are constantly undergoing change. We age, the planets move around the sun, and things fall apart.

We measure the passage of time in seconds, minutes, hours and years, but this doesn't mean time flows at a constant rate. In fact Einstein's theory of relativity determines that time is not universal. Just as the water in a river rushes or slows depending on the size of the channel, time flows at different rates in different places. In other words, time is relative.

But what causes this fluctuation along our one-way trek from the cradle to the grave? It all comes down to the relationship between time and space. Human beings frolic about in the three spatial dimensions of length, width and depth. Time joins the party as that most crucial fourth dimension . Time can't exist without space, and space can't exist without time. The two exist as one: the space time continuum . Any event that occurs in the universe has to involve both space and time.

In this article, we'll look at the real-life, everyday methods of time travel in our universe, as well as some of the more far-fetched methods of dancing through the fourth dimension.

Did you know your GPS devices rely on time-travel calculations to help you navigate around town? It's true! GPS satellite clocks are about 3 8 seconds longer per day than a clock closer to earth due to the gravitational frequency shift. They make up for this discrepancy by using time travel calculations or they could be way off from your current location and time.

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Time Travel and Modern Physics

Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently paradoxical. The most famous paradox is the grandfather paradox: you travel back in time and kill your grandfather, thereby preventing your own existence. To avoid inconsistency some circumstance will have to occur which makes you fail in this attempt to kill your grandfather. Doesn’t this require some implausible constraint on otherwise unrelated circumstances? We examine such worries in the context of modern physics.

1. Paradoxes Lost?

2. topology and constraints, 3. the general possibility of time travel in general relativity, 4. two toy models, 5. slightly more realistic models of time travel, 6. the possibility of time travel redux, 7. even if there are constraints, so what, 8. computational models, 9. quantum mechanics to the rescue, 10. conclusions, other internet resources, related entries.

Supplement: Remarks and Limitations on the Toy Models

Modern physics strips away many aspects of the manifest image of time. Time as it appears in the equations of classical mechanics has no need for a distinguished present moment, for example. Relativity theory leads to even sharper contrasts. It replaces absolute simultaneity, according to which it is possible to unambiguously determine the time order of distant events, with relative simultaneity: extending an “instant of time” throughout space is not unique, but depends on the state of motion of an observer. More dramatically, in general relativity the mathematical properties of time (or better, of spacetime)—its topology and geometry—depend upon how matter is arranged rather than being fixed once and for all. So physics can be, and indeed has to be, formulated without treating time as a universal, fixed background structure. Since general relativity represents gravity through spacetime geometry, the allowed geometries must be as varied as the ways in which matter can be arranged. Alongside geometrical models used to describe the solar system, black holes, and much else, the scope of variation extends to include some exotic structures unlike anything astrophysicists have observed. In particular, there are spacetime geometries with curves that loop back on themselves: closed timelike curves (CTCs), which describe the possible trajectory of an observer who returns exactly back to their earlier state—without any funny business, such as going faster than the speed of light. These geometries satisfy the relevant physical laws, the equations of general relativity, and in that sense time travel is physically possible.

Yet circular time generates paradoxes, familiar from science fiction stories featuring time travel: [ 1 ]

Consistency: Kurt plans to murder his own grandfather Adolph, by traveling along a CTC to an appropriate moment in the past. He is an able marksman, and waits until he has a clear shot at grandpa. Normally he would not miss. Yet if he succeeds, there is no way that he will then exist to plan and carry out the mission. Kurt pulls the trigger: what can happen?
Underdetermination: Suppose that Kurt first travels back in order to give his earlier self a copy of How to Build a Time Machine. This is the same book that allows him to build a time machine, which he then carries with him on his journey to the past. Who wrote the book?
Easy Knowledge: A fan of classical music enhances their computer with a circuit that exploits a CTC. This machine efficiently solves problems at a higher level of computational complexity than conventional computers, leading (among other things) to finding the smallest circuits that can generate Bach’s oeuvre—and to compose new pieces in the same style. Such easy knowledge is at odds with our understanding of our epistemic predicament. (This third paradox has not drawn as much attention.)

The first two paradoxes were once routinely taken to show that solutions with CTCs should be rejected—with charges varying from violating logic, to being “physically unreasonable”, to undermining the notion of free will. Closer analysis of the paradoxes has largely reversed this consensus. Physicists have discovered many solutions with CTCs and have explored their properties in pursuing foundational questions, such as whether physics is compatible with the idea of objective temporal passage (starting with Gödel 1949). Philosophers have also used time travel scenarios to probe questions about, among other things, causation, modality, free will, and identity (see, e.g., Earman 1972 and Lewis’s seminal 1976 paper).

We begin below with Consistency , turning to the other paradoxes in later sections. A standard, stone-walling response is to insist that the past cannot be changed, as a matter of logic, even by a time traveler (e.g., Gödel 1949, Clarke 1977, Horwich 1987). Adolph cannot both die and survive, as a matter of logic, so any scheme to alter the past must fail. In many of the best time travel fictions, the actions of a time traveler are constrained in novel and unexpected ways. Attempts to change the past fail, and they fail, often tragically, in just such a way that they set the stage for the time traveler’s self-defeating journey. The first question is whether there is an analog of the consistent story when it comes to physics in the presence of CTCs. As we will see, there is a remarkable general argument establishing the existence of consistent solutions. Yet a second question persists: why can’t time-traveling Kurt kill his own grandfather? Doesn’t the necessity of failures to change the past put unusual and unexpected constraints on time travelers, or objects that move along CTCs? The same argument shows that there are in fact no constraints imposed by the existence of CTCs, in some cases. After discussing this line of argument, we will turn to the palatability and further implications of such constraints if they are required, and then turn to the implications of quantum mechanics.

Wheeler and Feynman (1949) were the first to claim that the fact that nature is continuous could be used to argue that causal influences from later events to earlier events, as are made possible by time travel, will not lead to paradox without the need for any constraints. Maudlin (1990) showed how to make their argument precise and more general, and argued that nonetheless it was not completely general.

Imagine the following set-up. We start off having a camera with a black and white film ready to take a picture of whatever comes out of the time machine. An object, in fact a developed film, comes out of the time machine. We photograph it, and develop the film. The developed film is subsequently put in the time machine, and set to come out of the time machine at the time the picture is taken. This surely will create a paradox: the developed film will have the opposite distribution of black, white, and shades of gray, from the object that comes out of the time machine. For developed black and white films (i.e., negatives) have the opposite shades of gray from the objects they are pictures of. But since the object that comes out of the time machine is the developed film itself it we surely have a paradox.

However, it does not take much thought to realize that there is no paradox here. What will happen is that a uniformly gray picture will emerge, which produces a developed film that has exactly the same uniform shade of gray. No matter what the sensitivity of the film is, as long as the dependence of the brightness of the developed film depends in a continuous manner on the brightness of the object being photographed, there will be a shade of gray that, when photographed, will produce exactly the same shade of gray on the developed film. This is the essence of Wheeler and Feynman’s idea. Let us first be a bit more precise and then a bit more general.

For simplicity let us suppose that the film is always a uniform shade of gray (i.e., at any time the shade of gray does not vary by location on the film). The possible shades of gray of the film can then be represented by the (real) numbers from 0, representing pure black, to 1, representing pure white.

Let us now distinguish various stages in the chronological order of the life of the film. In stage $S_1$ the film is young; it has just been placed in the camera and is ready to be exposed. It is then exposed to the object that comes out of the time machine. (That object in fact is a later stage of the film itself). By the time we come to stage $S_2$ of the life of the film, it has been developed and is about to enter the time machine. Stage $S_3$ occurs just after it exits the time machine and just before it is photographed. Stage $S_4$ occurs after it has been photographed and before it starts fading away. Let us assume that the film starts out in stage $S_1$ in some uniform shade of gray, and that the only significant change in the shade of gray of the film occurs between stages $S_1$ and $S_2$. During that period it acquires a shade of gray that depends on the shade of gray of the object that was photographed. In other words, the shade of gray that the film acquires at stage $S_2$ depends on the shade of gray it has at stage $S_3$. The influence of the shade of gray of the film at stage $S_3$, on the shade of gray of the film at stage $S_2$, can be represented as a mapping, or function, from the real numbers between 0 and 1 (inclusive), to the real numbers between 0 and 1 (inclusive). Let us suppose that the process of photography is such that if one imagines varying the shade of gray of an object in a smooth, continuous manner then the shade of gray of the developed picture of that object will also vary in a smooth, continuous manner. This implies that the function in question will be a continuous function. Now any continuous function from the real numbers between 0 and 1 (inclusive) to the real numbers between 0 and 1 (inclusive) must map at least one number to itself. One can quickly convince oneself of this by graphing such functions. For one will quickly see that any continuous function $f$ from $[0,1]$ to $[0,1]$ must intersect the line $x=y$ somewhere, and thus there must be at least one point $x$ such that $f(x)=x$. Such points are called fixed points of the function. Now let us think about what such a fixed point represents. It represents a shade of gray such that, when photographed, it will produce a developed film with exactly that same shade of gray. The existence of such a fixed point implies a solution to the apparent paradox.

Let us now be more general and allow color photography. One can represent each possible color of an object (of uniform color) by the proportions of blue, green and red that make up that color. (This is why television screens can produce all possible colors.) Thus one can represent all possible colors of an object by three points on three orthogonal lines $x, y$ and $z$, that is to say, by a point in a three-dimensional cube. This cube is also known as the “Cartesian product” of the three line segments. Now, one can also show that any continuous map from such a cube to itself must have at least one fixed point. So color photography can not be used to create time travel paradoxes either!

Even more generally, consider some system $P$ which, as in the above example, has the following life. It starts in some state $S_1$, it interacts with an object that comes out of a time machine (which happens to be its older self), it travels back in time, it interacts with some object (which happens to be its younger self), and finally it grows old and dies. Let us assume that the set of possible states of $P$ can be represented by a Cartesian product of $n$ closed intervals of the reals, i.e., let us assume that the topology of the state-space of $P$ is isomorphic to a finite Cartesian product of closed intervals of the reals. Let us further assume that the development of $P$ in time, and the dependence of that development on the state of objects that it interacts with, is continuous. Then, by a well-known fixed point theorem in topology (see, e.g., Hocking & Young 1961: 273), no matter what the nature of the interaction is, and no matter what the initial state of the object is, there will be at least one state $S_3$ of the older system (as it emerges from the time travel machine) that will influence the initial state $S_1$ of the younger system (when it encounters the older system) so that, as the younger system becomes older, it develops exactly into state $S_3$. Thus without imposing any constraints on the initial state $S_1$ of the system $P$, we have shown that there will always be perfectly ordinary, non-paradoxical, solutions, in which everything that happens, happens according to the usual laws of development. Of course, there is looped causation, hence presumably also looped explanation, but what do you expect if there is looped time?

Unfortunately, for the fan of time travel, a little reflection suggests that there are systems for which the needed fixed point theorem does not hold. Imagine, for instance, that we have a dial that can only rotate in a plane. We are going to put the dial in the time machine. Indeed we have decided that if we see the later stage of the dial come out of the time machine set at angle $x$, then we will set the dial to $x+90$, and throw it into the time machine. Now it seems we have a paradox, since the mapping that consists of a rotation of all points in a circular state-space by 90 degrees does not have a fixed point. And why wouldn’t some state-spaces have the topology of a circle?

However, we have so far not used another continuity assumption which is also a reasonable assumption. So far we have only made the following demand: the state the dial is in at stage $S_2$ must be a continuous function of the state of the dial at stage $S_3$. But, the state of the dial at stage $S_2$ is arrived at by taking the state of the dial at stage $S_1$, and rotating it over some angle. It is not merely the case that the effect of the interaction, namely the state of the dial at stage $S_2$, should be a continuous function of the cause, namely the state of the dial at stage $S_3$. It is additionally the case that path taken to get there, the way the dial is rotated between stages $S_1$ and $S_2$ must be a continuous function of the state at stage $S_3$. And, rather surprisingly, it turns out that this can not be done. Let us illustrate what the problem is before going to a more general demonstration that there must be a fixed point solution in the dial case.

Forget time travel for the moment. Suppose that you and I each have a watch with a single dial neither of which is running. My watch is set at 12. You are going to announce what your watch is set at. My task is going to be to adjust my watch to yours no matter what announcement you make. And my actions should have a continuous (single valued) dependence on the time that you announce. Surprisingly, this is not possible! For instance, suppose that if you announce “12”, then I achieve that setting on my watch by doing nothing. Now imagine slowly and continuously increasing the announced times, starting at 12. By continuity, I must achieve each of those settings by rotating my dial to the right. If at some point I switch and achieve the announced goal by a rotation of my dial to the left, I will have introduced a discontinuity in my actions, a discontinuity in the actions that I take as a function of the announced angle. So I will be forced, by continuity, to achieve every announcement by rotating the dial to the right. But, this rotation to the right will have to be abruptly discontinued as the announcements grow larger and I eventually approach 12 again, since I achieved 12 by not rotating the dial at all. So, there will be a discontinuity at 12 at the latest. In general, continuity of my actions as a function of announced times can not be maintained throughout if I am to be able to replicate all possible settings. Another way to see the problem is that one can similarly reason that, as one starts with 12, and imagines continuously making the announced times earlier, one will be forced, by continuity, to achieve the announced times by rotating the dial to the left. But the conclusions drawn from the assumption of continuous increases and the assumption of continuous decreases are inconsistent. So we have an inconsistency following from the assumption of continuity and the assumption that I always manage to set my watch to your watch. So, a dial developing according to a continuous dynamics from a given initial state, can not be set up so as to react to a second dial, with which it interacts, in such a way that it is guaranteed to always end up set at the same angle as the second dial. Similarly, it can not be set up so that it is guaranteed to always end up set at 90 degrees to the setting of the second dial. All of this has nothing to do with time travel. However, the impossibility of such set ups is what prevents us from enacting the rotation by 90 degrees that would create paradox in the time travel setting.

Let us now give the positive result that with such dials there will always be fixed point solutions, as long as the dynamics is continuous. Let us call the state of the dial before it interacts with its older self the initial state of the dial. And let us call the state of the dial after it emerges from the time machine the final state of the dial. There is also an intermediate state of the dial, after it interacts with its older self and before it is put into the time machine. We can represent the initial or intermediate states of the dial, before it goes into the time machine, as an angle $x$ in the horizontal plane and the final state of the dial, after it comes out of the time machine, as an angle $y$ in the vertical plane. All possible $\langle x,y\rangle$ pairs can thus be visualized as a torus with each $x$ value picking out a vertical circular cross-section and each $y$ picking out a point on that cross-section. See figure 1 .

Figure 1 [An extended description of figure 1 is in the supplement.]

Suppose that the dial starts at angle $i$ which picks out vertical circle $I$ on the torus. The initial angle $i$ that the dial is at before it encounters its older self, and the set of all possible final angles that the dial can have when it emerges from the time machine is represented by the circle $I$ on the torus (see figure 1 ). Given any possible angle of the emerging dial, the dial initially at angle $i$ will develop to some other angle. One can picture this development by rotating each point on $I$ in the horizontal direction by the relevant amount. Since the rotation has to depend continuously on the angle of the emerging dial, circle $I$ during this development will deform into some loop $L$ on the torus. Loop $L$ thus represents all possible intermediate angles $x$ that the dial is at when it is thrown into the time machine, given that it started at angle $i$ and then encountered a dial (its older self) which was at angle $y$ when it emerged from the time machine. We therefore have consistency if $x=y$ for some $x$ and $y$ on loop $L$. Now, let loop $C$ be the loop which consists of all the points on the torus for which $x=y$. Ring $I$ intersects $C$ at point $\langle i,i\rangle$. Obviously any continuous deformation of $I$ must still intersect $C$ somewhere. So $L$ must intersect $C$ somewhere, say at $\langle j,j\rangle$. But that means that no matter how the development of the dial starting at $I$ depends on the angle of the emerging dial, there will be some angle for the emerging dial such that the dial will develop exactly into that angle (by the time it enters the time machine) under the influence of that emerging dial. This is so no matter what angle one starts with, and no matter how the development depends on the angle of the emerging dial. Thus even for a circular state-space there are no constraints needed other than continuity.

Unfortunately there are state-spaces that escape even this argument. Consider for instance a pointer that can be set to all values between 0 and 1, where 0 and 1 are not possible values. That is, suppose that we have a state-space that is isomorphic to an open set of real numbers. Now suppose that we have a machine that sets the pointer to half the value that the pointer is set at when it emerges from the time machine.

Figure 2 [An extended description of figure 2 is in the supplement.]

Suppose the pointer starts at value $I$. As before we can represent the combination of this initial position and all possible final positions by the line $I$. Under the influence of the pointer coming out of the time machine the pointer value will develop to a value that equals half the value of the final value that it encountered. We can represent this development as the continuous deformation of line $I$ into line $L$, which is indicated by the arrows in figure 2 . This development is fully continuous. Points $\langle x,y\rangle$ on line $I$ represent the initial position $x=I$ of the (young) pointer, and the position $y$ of the older pointer as it emerges from the time machine. Points $\langle x,y\rangle$ on line $L$ represent the position $x$ that the younger pointer should develop into, given that it encountered the older pointer emerging from the time machine set at position $y$. Since the pointer is designed to develop to half the value of the pointer that it encounters, the line $L$ corresponds to $x=1/2 y$. We have consistency if there is some point such that it develops into that point, if it encounters that point. Thus, we have consistency if there is some point $\langle x,y\rangle$ on line $L$ such that $x=y$. However, there is no such point: lines $L$ and $C$ do not intersect. Thus there is no consistent solution, despite the fact that the dynamics is fully continuous.

Of course if 0 were a possible value, $L$ and $C$ would intersect at 0. This is surprising and strange: adding one point to the set of possible values of a quantity here makes the difference between paradox and peace. One might be tempted to just add the extra point to the state-space in order to avoid problems. After all, one might say, surely no measurements could ever tell us whether the set of possible values includes that exact point or not. Unfortunately there can be good theoretical reasons for supposing that some quantity has a state-space that is open: the set of all possible speeds of massive objects in special relativity surely is an open set, since it includes all speeds up to, but not including, the speed of light. Quantities that have possible values that are not bounded also lead to counter examples to the presented fixed point argument. And it is not obvious to us why one should exclude such possibilities. So the argument that no constraints are needed is not fully general.

An interesting question of course is: exactly for which state-spaces must there be such fixed points? The arguments above depend on a well-known fixed point theorem (due to Schauder) that guarantees the existence of a fixed point for compact, convex state spaces. We do not know what subsequent extensions of this result imply regarding fixed points for a wider variety of systems, or whether there are other general results along these lines. (See Kutach 2003 for more on this issue.)

A further interesting question is whether this line of argument is sufficient to resolve Consistency (see also Dowe 2007). When they apply, these results establish the existence of a solution, such as the shade of uniform gray in the first example. But physicists routinely demand more than merely the existence of a solution, namely that solutions to the equations are stable—such that “small” changes of the initial state lead to “small” changes of the resulting trajectory. (Clarifying the two senses of “small” in this statement requires further work, specifying the relevant topology.) Stability in this sense underwrites the possibility of applying equations to real systems given our inability to fix initial states with indefinite precision. (See Fletcher 2020 for further discussion.) The fixed point theorems guarantee that for an initial state $S_1$ there is a solution, but this solution may not be “close” to the solution for a nearby initial state, $S'$. We are not aware of any proofs that the solutions guaranteed to exist by the fixed point theorems are also stable in this sense.

Time travel has recently been discussed quite extensively in the context of general relativity. General relativity places few constraints on the global structure of space and time. This flexibility leads to a possibility first described in print by Hermann Weyl:

Every world-point is the origin of the double-cone of the active future and the passive past [i.e., the two lobes of the light cone]. Whereas in the special theory of relativity these two portions are separated by an intervening region, it is certainly possible in the present case [i.e., general relativity] for the cone of the active future to overlap with that of the passive past; so that, in principle, it is possible to experience events now that will in part be an effect of my future resolves and actions. Moreover, it is not impossible for a world-line (in particular, that of my body), although it has a timelike direction at every point, to return to the neighborhood of a point which it has already once passed through. (Weyl 1918/1920 [1952: 274])

A time-like curve is simply a space-time trajectory such that the speed of light is never equaled or exceeded along this trajectory. Time-like curves represent possible trajectories of ordinary objects. In general relativity a curve that is everywhere timelike locally can nonetheless loop back on itself, forming a CTC. Weyl makes the point vividly in terms of the light cones: along such a curve, the future lobe of the light cone (the “active future”) intersects the past lobe of the light cone (the “passive past”). Traveling along such a curve one would never exceed the speed of light, and yet after a certain amount of (proper) time one would return to a point in space-time that one previously visited. Or, by staying close to such a CTC, one could come arbitrarily close to a point in space-time that one previously visited. General relativity, in a straightforward sense, allows time travel: there appear to be many space-times compatible with the fundamental equations of general relativity in which there are CTC’s. Space-time, for instance, could have a Minkowski metric everywhere, and yet have CTC’s everywhere by having the temporal dimension (topologically) rolled up as a circle. Or, one can have wormhole connections between different parts of space-time which allow one to enter “mouth $A$” of such a wormhole connection, travel through the wormhole, exit the wormhole at “mouth $B$” and re-enter “mouth $A$” again. CTCs can even arise when the spacetime is topologically $\mathbb{R}^4$, due to the “tilting” of light cones produced by rotating matter (as in Gödel 1949’s spacetime).

General relativity thus appears to provide ample opportunity for time travel. Note that just because there are CTC’s in a space-time, this does not mean that one can get from any point in the space-time to any other point by following some future directed timelike curve—there may be insurmountable practical obstacles. In Gödel’s spacetime, it is the case that there are CTCs passing through every point in the spacetime. Yet these CTCs are not geodesics, so traversing them requires acceleration. Calculations of the minimal fuel required to travel along the appropriate curve should discourage any would-be time travelers (Malament 1984, 1985; Manchak 2011). But more generally CTCs may be confined to smaller regions; some parts of space-time can have CTC’s while other parts do not. Let us call the part of a space-time that has CTC’s the “time travel region” of that space-time, while calling the rest of that space-time the “normal region”. More precisely, the “time travel region” consists of all the space-time points $p$ such that there exists a (non-zero length) timelike curve that starts at $p$ and returns to $p$. Now let us turn to examining space-times with CTC’s a bit more closely for potential problems.

In order to get a feeling for the sorts of implications that closed timelike curves can have, it may be useful to consider two simple models. In space-times with closed timelike curves the traditional initial value problem cannot be framed in the usual way. For it presupposes the existence of Cauchy surfaces, and if there are CTCs then no Cauchy surface exists. (A Cauchy surface is a spacelike surface such that every inextendable timelike curve crosses it exactly once. One normally specifies initial conditions by giving the conditions on such a surface.) Nonetheless, if the topological complexities of the manifold are appropriately localized, we can come quite close. Let us call an edgeless spacelike surface $S$ a quasi-Cauchy surface if it divides the rest of the manifold into two parts such that

every point in the manifold can be connected by a timelike curve to $S$, and
any timelike curve which connects a point in one region to a point in the other region intersects $S$ exactly once.

It is obvious that a quasi-Cauchy surface must entirely inhabit the normal region of the space-time; if any point $p$ of $S$ is in the time travel region, then any timelike curve which intersects $p$ can be extended to a timelike curve which intersects $S$ near $p$ again. In extreme cases of time travel, a model may have no normal region at all (e.g., Minkowski space-time rolled up like a cylinder in a time-like direction), in which case our usual notions of temporal precedence will not apply. But temporal anomalies like wormholes (and time machines) can be sufficiently localized to permit the existence of quasi-Cauchy surfaces.

Given a timelike orientation, a quasi-Cauchy surface unproblematically divides the manifold into its past (i.e., all points that can be reached by past-directed timelike curves from $S)$ and its future (ditto mutatis mutandis ). If the whole past of $S$ is in the normal region of the manifold, then $S$ is a partial Cauchy surface : every inextendable timelike curve which exists to the past of $S$ intersects $S$ exactly once, but (if there is time travel in the future) not every inextendable timelike curve which exists to the future of $S$ intersects $S$. Now we can ask a particularly clear question: consider a manifold which contains a time travel region, but also has a partial Cauchy surface $S$, such that all of the temporal funny business is to the future of $S$. If all you could see were $S$ and its past, you would not know that the space-time had any time travel at all. The question is: are there any constraints on the sort of data which can be put on $S$ and continued to a global solution of the dynamics which are different from the constraints (if any) on the data which can be put on a Cauchy surface in a simply connected manifold and continued to a global solution? If there is time travel to our future, might we we able to tell this now, because of some implied oddity in the arrangement of present things?

It is not at all surprising that there might be constraints on the data which can be put on a locally space-like surface which passes through the time travel region: after all, we never think we can freely specify what happens on a space-like surface and on another such surface to its future, but in this case the surface at issue lies to its own future. But if there were particular constraints for data on a partial Cauchy surface then we would apparently need to have to rule out some sorts of otherwise acceptable states on $S$ if there is to be time travel to the future of $S$. We then might be able to establish that there will be no time travel in the future by simple inspection of the present state of the universe. As we will see, there is reason to suspect that such constraints on the partial Cauchy surface are non-generic. But we are getting ahead of ourselves: first let’s consider the effect of time travel on a very simple dynamics.

The simplest possible example is the Newtonian theory of perfectly elastic collisions among equally massive particles in one spatial dimension. The space-time is two-dimensional, so we can represent it initially as the Euclidean plane, and the dynamics is completely specified by two conditions. When particles are traveling freely, their world lines are straight lines in the space-time, and when two particles collide, they exchange momenta, so the collision looks like an “$X$” in space-time, with each particle changing its momentum at the impact. [ 2 ] The dynamics is purely local, in that one can check that a set of world-lines constitutes a model of the dynamics by checking that the dynamics is obeyed in every arbitrarily small region. It is also trivial to generate solutions from arbitrary initial data if there are no CTCs: given the initial positions and momenta of a set of particles, one simply draws a straight line from each particle in the appropriate direction and continues it indefinitely. Once all the lines are drawn, the worldline of each particle can be traced from collision to collision. The boundary value problem for this dynamics is obviously well-posed: any set of data at an instant yields a unique global solution, constructed by the method sketched above.

What happens if we change the topology of the space-time by hand to produce CTCs? The simplest way to do this is depicted in figure 3 : we cut and paste the space-time so it is no longer simply connected by identifying the line $L-$ with the line $L+$. Particles “going in” to $L+$ from below “emerge” from $L-$ , and particles “going in” to $L-$ from below “emerge” from $L+$.

Figure 3: Inserting CTCs by Cut and Paste. [An extended description of figure 3 is in the supplement.]

How is the boundary-value problem changed by this alteration in the space-time? Before the cut and paste, we can put arbitrary data on the simultaneity slice $S$ and continue it to a unique solution. After the change in topology, $S$ is no longer a Cauchy surface, since a CTC will never intersect it, but it is a partial Cauchy surface. So we can ask two questions. First, can arbitrary data on $S$ always be continued to a global solution? Second, is that solution unique? If the answer to the first question is $no$, then we have a backward-temporal constraint: the existence of the region with CTCs places constraints on what can happen on $S$ even though that region lies completely to the future of $S$. If the answer to the second question is $no$, then we have an odd sort of indeterminism, analogous to the unwritten book: the complete physical state on $S$ does not determine the physical state in the future, even though the local dynamics is perfectly deterministic and even though there is no other past edge to the space-time region in $S$’s future (i.e., there is nowhere else for boundary values to come from which could influence the state of the region).

In this case the answer to the first question is yes and to the second is no : there are no constraints on the data which can be put on $S$, but those data are always consistent with an infinitude of different global solutions. The easy way to see that there always is a solution is to construct the minimal solution in the following way. Start drawing straight lines from $S$ as required by the initial data. If a line hits $L-$ from the bottom, just continue it coming out of the top of $L+$ in the appropriate place, and if a line hits $L+$ from the bottom, continue it emerging from $L-$ at the appropriate place. Figure 4 represents the minimal solution for a single particle which enters the time-travel region from the left:

Figure 4: The Minimal Solution. [An extended description of figure 4 is in the supplement.]

The particle “travels back in time” three times. It is obvious that this minimal solution is a global solution, since the particle always travels inertially.

But the same initial state on $S$ is also consistent with other global solutions. The new requirement imposed by the topology is just that the data going into $L+$ from the bottom match the data coming out of $L-$ from the top, and the data going into $L-$ from the bottom match the data coming out of $L+$ from the top. So we can add any number of vertical lines connecting $L-$ and $L+$ to a solution and still have a solution. For example, adding a few such lines to the minimal solution yields:

Figure 5: A Non-Minimal Solution. [An extended description of figure 5 is in the supplement.]

The particle now collides with itself twice: first before it reaches $L+$ for the first time, and again shortly before it exits the CTC region. From the particle’s point of view, it is traveling to the right at a constant speed until it hits an older version of itself and comes to rest. It remains at rest until it is hit from the right by a younger version of itself, and then continues moving off, and the same process repeats later. It is clear that this is a global model of the dynamics, and that any number of distinct models could be generating by varying the number and placement of vertical lines.

Knowing the data on $S$, then, gives us only incomplete information about how things will go for the particle. We know that the particle will enter the CTC region, and will reach $L+$, we know that it will be the only particle in the universe, we know exactly where and with what speed it will exit the CTC region. But we cannot determine how many collisions the particle will undergo (if any), nor how long (in proper time) it will stay in the CTC region. If the particle were a clock, we could not predict what time it would indicate when exiting the region. Furthermore, the dynamics gives us no handle on what to think of the various possibilities: there are no probabilities assigned to the various distinct possible outcomes.

Changing the topology has changed the mathematics of the situation in two ways, which tend to pull in opposite directions. On the one hand, $S$ is no longer a Cauchy surface, so it is perhaps not surprising that data on $S$ do not suffice to fix a unique global solution. But on the other hand, there is an added constraint: data “coming out” of $L-$ must exactly match data “going in” to $L+$, even though what comes out of $L-$ helps to determine what goes into $L+$. This added consistency constraint tends to cut down on solutions, although in this case the additional constraint is more than outweighed by the freedom to consider various sorts of data on ${L+}/{L-}$.

The fact that the extra freedom outweighs the extra constraint also points up one unexpected way that the supposed paradoxes of time travel may be overcome. Let’s try to set up a paradoxical situation using the little closed time loop above. If we send a single particle into the loop from the left and do nothing else, we know exactly where it will exit the right side of the time travel region. Now suppose we station someone at the other side of the region with the following charge: if the particle should come out on the right side, the person is to do something to prevent the particle from going in on the left in the first place. In fact, this is quite easy to do: if we send a particle in from the right, it seems that it can exit on the left and deflect the incoming left-hand particle.

Carrying on our reflection in this way, we further realize that if the particle comes out on the right, we might as well send it back in order to deflect itself from entering in the first place. So all we really need to do is the following: set up a perfectly reflecting particle mirror on the right-hand side of the time travel region, and launch the particle from the left so that— if nothing interferes with it —it will just barely hit $L+$. Our paradox is now apparently complete. If, on the one hand, nothing interferes with the particle it will enter the time-travel region on the left, exit on the right, be reflected from the mirror, re-enter from the right, and come out on the left to prevent itself from ever entering. So if it enters, it gets deflected and never enters. On the other hand, if it never enters then nothing goes in on the left, so nothing comes out on the right, so nothing is reflected back, and there is nothing to deflect it from entering. So if it doesn’t enter, then there is nothing to deflect it and it enters. If it enters, then it is deflected and doesn’t enter; if it doesn’t enter then there is nothing to deflect it and it enters: paradox complete.

But at least one solution to the supposed paradox is easy to construct: just follow the recipe for constructing the minimal solution, continuing the initial trajectory of the particle (reflecting it the mirror in the obvious way) and then read of the number and trajectories of the particles from the resulting diagram. We get the result of figure 6 :

Figure 6: Resolving the “Paradox”. [An extended description of figure 6 is in the supplement.]

As we can see, the particle approaching from the left never reaches $L+$: it is deflected first by a particle which emerges from $L-$. But it is not deflected by itself , as the paradox suggests, it is deflected by another particle. Indeed, there are now four particles in the diagram: the original particle and three particles which are confined to closed time-like curves. It is not the leftmost particle which is reflected by the mirror, nor even the particle which deflects the leftmost particle; it is another particle altogether.

The paradox gets it traction from an incorrect presupposition. If there is only one particle in the world at $S$ then there is only one particle which could participate in an interaction in the time travel region: the single particle would have to interact with its earlier (or later) self. But there is no telling what might come out of $L-$: the only requirement is that whatever comes out must match what goes in at $L+$. So if you go to the trouble of constructing a working time machine, you should be prepared for a different kind of disappointment when you attempt to go back and kill yourself: you may be prevented from entering the machine in the first place by some completely unpredictable entity which emerges from it. And once again a peculiar sort of indeterminism appears: if there are many self-consistent things which could prevent you from entering, there is no telling which is even likely to materialize. This is just like the case of the unwritten book: the book is never written, so nothing determines what fills its pages.

So when the freedom to put data on $L-$ outweighs the constraint that the same data go into $L+$, instead of paradox we get an embarrassment of riches: many solution consistent with the data on $S$, or many possible books. To see a case where the constraint “outweighs” the freedom, we need to construct a very particular, and frankly artificial, dynamics and topology. Consider the space of all linear dynamics for a scalar field on a lattice. (The lattice can be though of as a simple discrete space-time.) We will depict the space-time lattice as a directed graph. There is to be a scalar field defined at every node of the graph, whose value at a given node depends linearly on the values of the field at nodes which have arrows which lead to it. Each edge of the graph can be assigned a weighting factor which determines how much the field at the input node contributes to the field at the output node. If we name the nodes by the letters a , b , c , etc., and the edges by their endpoints in the obvious way, then we can label the weighting factors by the edges they are associated with in an equally obvious way.

Suppose that the graph of the space-time lattice is acyclic , as in figure 7 . (A graph is Acyclic if one can not travel in the direction of the arrows and go in a loop.)

Figure 7: An Acyclic Lattice. [An extended description of figure 7 is in the supplement.]

It is easy to regard a set of nodes as the analog of a Cauchy surface, e.g., the set $\{a, b, c\}$, and it is obvious if arbitrary data are put on those nodes the data will generate a unique solution in the future. [ 3 ] If the value of the field at node $a$ is 3 and at node $b$ is 7, then its value at node $d$ will be $3W_{ad}$ and its value at node $e$ will be $3W_{ae} + 7W_{be}$. By varying the weighting factors we can adjust the dynamics, but in an acyclic graph the future evolution of the field will always be unique.

Let us now again artificially alter the topology of the lattice to admit CTCs, so that the graph now is cyclic. One of the simplest such graphs is depicted in figure 8 : there are now paths which lead from $z$ back to itself, e.g., $z$ to $y$ to $z$.

Figure 8: Time Travel on a Lattice. [An extended description of figure 8 is in the supplement.]

Can we now put arbitrary data on $v$ and $w$, and continue that data to a global solution? Will the solution be unique?

In the generic case, there will be a solution and the solution will be unique. The equations for the value of the field at $x, y$, and $z$ are:

Solving these equations for $z$ yields

which gives a unique value for $z$ in the generic case. But looking at the space of all possible dynamics for this lattice (i.e., the space of all possible weighting factors), we find a singularity in the case where $1-W_{zx}W_{xz} - W_{zy}W_{yz} = 0$. If we choose weighting factors in just this way, then arbitrary data at $v$ and $w$ cannot be continued to a global solution. Indeed, if the scalar field is everywhere non-negative, then this particular choice of dynamics puts ironclad constraints on the value of the field at $v$ and $w$: the field there must be zero (assuming $W_{vx}$ and $W_{wy}$ to be non-zero), and similarly all nodes in their past must have field value zero. If the field can take negative values, then the values at $v$ and $w$ must be so chosen that $vW_{vx}W_{xz} = -wW_{wy}W_{yz}$. In either case, the field values at $v$ and $w$ are severely constrained by the existence of the CTC region even though these nodes lie completely to the past of that region. It is this sort of constraint which we find to be unlike anything which appears in standard physics.

Our toy models suggest three things. The first is that it may be impossible to prove in complete generality that arbitrary data on a partial Cauchy surface can always be continued to a global solution: our artificial case provides an example where it cannot. The second is that such odd constraints are not likely to be generic: we had to delicately fine-tune the dynamics to get a problem. The third is that the opposite problem, namely data on a partial Cauchy surface being consistent with many different global solutions, is likely to be generic: we did not have to do any fine-tuning to get this result.

This third point leads to a peculiar sort of indeterminism, illustrated by the case of the unwritten book: the entire state on $S$ does not determine what will happen in the future even though the local dynamics is deterministic and there are no other “edges” to space-time from which data could influence the result. What happens in the time travel region is constrained but not determined by what happens on $S$, and the dynamics does not even supply any probabilities for the various possibilities. The example of the photographic negative discussed in section 2, then, seems likely to be unusual, for in that case there is a unique fixed point for the dynamics, and the set-up plus the dynamical laws determine the outcome. In the generic case one would rather expect multiple fixed points, with no room for anything to influence, even probabilistically, which would be realized. (See the supplement on

Remarks and Limitations on the Toy Models .

It is ironic that time travel should lead generically not to contradictions or to constraints (in the normal region) but to underdetermination of what happens in the time travel region by what happens everywhere else (an underdetermination tied neither to a probabilistic dynamics nor to a free edge to space-time). The traditional objection to time travel is that it leads to contradictions: there is no consistent way to complete an arbitrarily constructed story about how the time traveler intends to act. Instead, though, it appears that the more significant problem is underdetermination: the story can be consistently completed in many different ways.

Echeverria, Klinkhammer, and Thorne (1991) considered the case of 3-dimensional single hard spherical ball that can go through a single time travel wormhole so as to collide with its younger self.

Figure 9 [An extended description of figure 9 is in the supplement.]

The threat of paradox in this case arises in the following form. Consider the initial trajectory of a ball as it approaches the time travel region. For some initial trajectories, the ball does not undergo a collision before reaching mouth 1, but upon exiting mouth 2 it will collide with its earlier self. This leads to a contradiction if the collision is strong enough to knock the ball off its trajectory and deflect it from entering mouth 1. Of course, the Wheeler-Feynman strategy is to look for a “glancing blow” solution: a collision which will produce exactly the (small) deviation in trajectory of the earlier ball that produces exactly that collision. Are there always such solutions? [ 4 ]

Echeverria, Klinkhammer & Thorne found a large class of initial trajectories that have consistent “glancing blow” continuations, and found none that do not (but their search was not completely general). They did not produce a rigorous proof that every initial trajectory has a consistent continuation, but suggested that it is very plausible that every initial trajectory has a consistent continuation. That is to say, they have made it very plausible that, in the billiard ball wormhole case, the time travel structure of such a wormhole space-time does not result in constraints on states on spacelike surfaces in the non-time travel region.

In fact, as one might expect from our discussion in the previous section, they found the opposite problem from that of inconsistency: they found underdetermination. For a large class of initial trajectories there are multiple different consistent “glancing blow” continuations of that trajectory (many of which involve multiple wormhole traversals). For example, if one initially has a ball that is traveling on a trajectory aimed straight between the two mouths, then one obvious solution is that the ball passes between the two mouths and never time travels. But another solution is that the younger ball gets knocked into mouth 1 exactly so as to come out of mouth 2 and produce that collision. Echeverria et al. do not note the possibility (which we pointed out in the previous section) of the existence of additional balls in the time travel region. We conjecture (but have no proof) that for every initial trajectory of $A$ there are some, and generically many, multiple-ball continuations.

Friedman, Morris, et al. (1990) examined the case of source-free non-self-interacting scalar fields traveling through such a time travel wormhole and found that no constraints on initial conditions in the non-time travel region are imposed by the existence of such time travel wormholes. In general there appear to be no known counter examples to the claim that in “somewhat realistic” time-travel space-times with a partial Cauchy surface there are no constraints imposed on the state on such a partial Cauchy surface by the existence of CTC’s. (See, e.g., Friedman & Morris 1991; Thorne 1994; Earman 1995; Earman, Smeenk, & Wüthrich 2009; and Dowe 2007.)

How about the issue of constraints in the time travel region $T$? Prima facie , constraints in such a region would not appear to be surprising. But one might still expect that there should be no constraints on states on a spacelike surface, provided one keeps the surface “small enough”. In the physics literature the following question has been asked: for any point $p$ in $T$, and any space-like surface $S$ that includes $p$ is there a neighborhood $E$ of $p$ in $S$ such that any solution on $E$ can be extended to a solution on the whole space-time? With respect to this question, there are some simple models in which one has this kind of extendability of local solutions to global ones, and some simple models in which one does not have such extendability, with no clear general pattern. The technical mathematical problems are amplified by the more conceptual problem of what it might mean to say that one could create a situation which forces the creation of closed timelike curves. (See, e.g., Yurtsever 1990; Friedman, Morris, et al. 1990; Novikov 1992; Earman 1995; and Earman, Smeenk, & Wüthrich 2009). What are we to think of all of this?

The toy models above all treat billiard balls, fields, and other objects propagating through a background spacetime with CTCs. Even if we can show that a consistent solution exists, there is a further question: what kind of matter and dynamics could generate CTCs to begin with? There are various solutions of Einstein’s equations with CTCs, but how do these exotic spacetimes relate to the models actually used in describing the world? In other words, what positive reasons might we have to take CTCs seriously as a feature of the actual universe, rather than an exotic possibility of primarily mathematical interest?

We should distinguish two different kinds of “possibility” that we might have in mind in posing such questions (following Stein 1970). First, we can consider a solution as a candidate cosmological model, describing the (large-scale gravitational degrees of freedom of the) entire universe. The case for ruling out spacetimes with CTCs as potential cosmological models strikes us as, surprisingly, fairly weak. Physicists used to simply rule out solutions with CTCs as unreasonable by fiat, due to the threat of paradoxes, which we have dismantled above. But it is also challenging to make an observational case. Observations tell us very little about global features, such as the existence of CTCs, because signals can only reach an observer from a limited region of spacetime, called the past light cone. Our past light cone—and indeed the collection of all the past light cones for possible observers in a given spacetime—can be embedded in spacetimes with quite different global features (Malament 1977, Manchak 2009). This undercuts the possibility of using observations to constrain global topology, including (among other things) ruling out the existence of CTCs.

Yet the case in favor of taking cosmological models with CTCs seriously is also not particularly strong. Some solutions used to describe black holes, which are clearly relevant in a variety of astrophysical contexts, include CTCs. But the question of whether the CTCs themselves play an essential representational role is subtle: the CTCs arise in the maximal extensions of these solutions, and can plausibly be regarded as extraneous to successful applications. Furthermore, many of the known solutions with CTCs have symmetries, raising the possibility that CTCs are not a stable or robust feature. Slight departures from symmetry may lead to a solution without CTCs, suggesting that the CTCs may be an artifact of an idealized model.

The second sense of possibility regards whether “reasonable” initial conditions can be shown to lead to, or not to lead to, the formation of CTCs. As with the toy models above, suppose that we have a partial Cauchy surface $S$, such that all the temporal funny business lies to the future. Rather than simply assuming that there is a region with CTCs to the future, we can ask instead whether it is possible to create CTCs by manipulating matter in the initial, well-behaved region—that is, whether it is possible to build a time machine. Several physicists have pursued “chronology protection theorems” aiming to show that the dynamics of general relativity (or some other aspects of physics) rules this out, and to clarify why this is the case. The proof of such a theorem would justify neglecting solutions with CTCs as a source of insight into the nature of time in the actual world. But as of yet there are several partial results that do not fully settle the question. One further intriguing possibility is that even if general relativity by itself does protect chronology, it may not be possible to formulate a sensible theory describing matter and fields in solutions with CTCs. (See SEP entry on Time Machines; Smeenk and Wüthrich 2011 for more.)

There is a different question regarding the limitations of these toy models. The toy models and related examples show that there are consistent solutions for simple systems in the presence of CTCs. As usual we have made the analysis tractable by building toy models, selecting only a few dynamical degrees of freedom and tracking their evolution. But there is a large gap between the systems we have described and the time travel stories they evoke, with Kurt traveling along a CTC with murderous intentions. In particular, many features of the manifest image of time are tied to the thermodynamical properties of macroscopic systems. Rovelli (unpublished) considers a extremely simple system to illustrate the problem: can a clock move along a CTC? A clock consists of something in periodic motion, such as a pendulum bob, and something that counts the oscillations, such as an escapement mechanism. The escapement mechanism cannot work without friction; this requires dissipation and increasing entropy. For a clock that counts oscillations as it moves along a time-like trajectory, the entropy must be a monotonically increasing function. But that is obviously incompatible with the clock returning to precisely the same state at some future time as it completes a loop. The point generalizes, obviously, to imply that anything like a human, with memory and agency, cannot move along a CTC.

Since it is not obvious that one can rid oneself of all constraints in realistic models, let us examine the argument that time travel is implausible, and we should think it unlikely to exist in our world, in so far as it implies such constraints. The argument goes something like the following. In order to satisfy such constraints one needs some pre-established divine harmony between the global (time travel) structure of space-time and the distribution of particles and fields on space-like surfaces in it. But it is not plausible that the actual world, or any world even remotely like ours, is constructed with divine harmony as part of the plan. In fact, one might argue, we have empirical evidence that conditions in any spatial region can vary quite arbitrarily. So we have evidence that such constraints, whatever they are, do not in fact exist in our world. So we have evidence that there are no closed time-like lines in our world or one remotely like it. We will now examine this argument in more detail by presenting four possible responses, with counterresponses, to this argument.

Response 1. There is nothing implausible or new about such constraints. For instance, if the universe is spatially closed, there has to be enough matter to produce the needed curvature, and this puts constraints on the matter distribution on a space-like hypersurface. Thus global space-time structure can quite unproblematically constrain matter distributions on space-like hypersurfaces in it. Moreover we have no realistic idea what these constraints look like, so we hardly can be said to have evidence that they do not obtain.

Counterresponse 1. Of course there are constraining relations between the global structure of space-time and the matter in it. The Einstein equations relate curvature of the manifold to the matter distribution in it. But what is so strange and implausible about the constraints imposed by the existence of closed time-like curves is that these constraints in essence have nothing to do with the Einstein equations. When investigating such constraints one typically treats the particles and/or field in question as test particles and/or fields in a given space-time, i.e., they are assumed not to affect the metric of space-time in any way. In typical space-times without closed time-like curves this means that one has, in essence, complete freedom of matter distribution on a space-like hypersurface. (See response 2 for some more discussion of this issue). The constraints imposed by the possibility of time travel have a quite different origin and are implausible. In the ordinary case there is a causal interaction between matter and space-time that results in relations between global structure of space-time and the matter distribution in it. In the time travel case there is no such causal story to be told: there simply has to be some pre-established harmony between the global space-time structure and the matter distribution on some space-like surfaces. This is implausible.

Response 2. Constraints upon matter distributions are nothing new. For instance, Maxwell’s equations constrain electric fields $\boldsymbol{E}$ on an initial surface to be related to the (simultaneous) charge density distribution $\varrho$ by the equation $\varrho = \text{div}(\boldsymbol{E})$. (If we assume that the $E$ field is generated solely by the charge distribution, this conditions amounts to requiring that the $E$ field at any point in space simply be the one generated by the charge distribution according to Coulomb’s inverse square law of electrostatics.) This is not implausible divine harmony. Such constraints can hold as a matter of physical law. Moreover, if we had inferred from the apparent free variation of conditions on spatial regions that there could be no such constraints we would have mistakenly inferred that $\varrho = \text{div}(\boldsymbol{E})$ could not be a law of nature.

Counterresponse 2. The constraints imposed by the existence of closed time-like lines are of quite a different character from the constraint imposed by $\varrho = \text{div}(\boldsymbol{E})$. The constraints imposed by $\varrho = \text{div}(\boldsymbol{E})$ on the state on a space-like hypersurface are:

local constraints (i.e., to check whether the constraint holds in a region you just need to see whether it holds at each point in the region),
quite independent of the global space-time structure,
quite independent of how the space-like surface in question is embedded in a given space-time, and
very simply and generally stateable.

On the other hand, the consistency constraints imposed by the existence of closed time-like curves (i) are not local, (ii) are dependent on the global structure of space-time, (iii) depend on the location of the space-like surface in question in a given space-time, and (iv) appear not to be simply stateable other than as the demand that the state on that space-like surface embedded in such and such a way in a given space-time, do not lead to inconsistency. On some views of laws (e.g., David Lewis’ view) this plausibly implies that such constraints, even if they hold, could not possibly be laws. But even if one does not accept such a view of laws, one could claim that the bizarre features of such constraints imply that it is implausible that such constraints hold in our world or in any world remotely like ours.

Response 3. It would be strange if there are constraints in the non-time travel region. It is not strange if there are constraints in the time travel region. They should be explained in terms of the strange, self-interactive, character of time travel regions. In this region there are time-like trajectories from points to themselves. Thus the state at such a point, in such a region, will, in a sense, interact with itself. It is a well-known fact that systems that interact with themselves will develop into an equilibrium state, if there is such an equilibrium state, or else will develop towards some singularity. Normally, of course, self-interaction isn’t true instantaneous self-interaction, but consists of a feed-back mechanism that takes time. But in time travel regions something like true instantaneous self-interaction occurs. This explains why constraints on states occur in such time travel regions: the states “ ab initio ” have to be “equilibrium states”. Indeed in a way this also provides some picture of why indeterminism occurs in time travel regions: at the onset of self-interaction states can fork into different equi-possible equilibrium states.

Counterresponse 3. This is explanation by woolly analogy. It all goes to show that time travel leads to such bizarre consequences that it is unlikely that it occurs in a world remotely like ours.

Response 4. All of the previous discussion completely misses the point. So far we have been taking the space-time structure as given, and asked the question whether a given time travel space-time structure imposes constraints on states on (parts of) space-like surfaces. However, space-time and matter interact. Suppose that one is in a space-time with closed time-like lines, such that certain counterfactual distributions of matter on some neighborhood of a point $p$ are ruled out if one holds that space-time structure fixed. One might then ask

Why does the actual state near $p$ in fact satisfy these constraints? By what divine luck or plan is this local state compatible with the global space-time structure? What if conditions near $p$ had been slightly different?

And one might take it that the lack of normal answers to these questions indicates that it is very implausible that our world, or any remotely like it, is such a time travel universe. However the proper response to these question is the following. There are no constraints in any significant sense. If they hold they hold as a matter of accidental fact, not of law. There is no more explanation of them possible than there is of any contingent fact. Had conditions in a neighborhood of $p$ been otherwise, the global structure of space-time would have been different. So what? The only question relevant to the issue of constraints is whether an arbitrary state on an arbitrary spatial surface $S$ can always be embedded into a space-time such that that state on $S$ consistently extends to a solution on the entire space-time.

But we know the answer to that question. A well-known theorem in general relativity says the following: any initial data set on a three dimensional manifold $S$ with positive definite metric has a unique embedding into a maximal space-time in which $S$ is a Cauchy surface (see, e.g., Geroch & Horowitz 1979: 284 for more detail), i.e., there is a unique largest space-time which has $S$ as a Cauchy surface and contains a consistent evolution of the initial value data on $S$. Now since $S$ is a Cauchy surface this space-time does not have closed time like curves. But it may have extensions (in which $S$ is not a Cauchy surface) which include closed timelike curves, indeed it may be that any maximal extension of it would include closed timelike curves. (This appears to be the case for extensions of states on certain surfaces of Taub-NUT space-times. See Earman, Smeenk, & Wüthrich 2009). But these extensions, of course, will be consistent. So properly speaking, there are no constraints on states on space-like surfaces. Nonetheless the space-time in which these are embedded may or may not include closed time-like curves.

Counterresponse 4. This, in essence, is the stonewalling answer which we indicated in section 1. However, whether or not you call the constraints imposed by a given space-time on distributions of matter on certain space-like surfaces “genuine constraints”, whether or not they can be considered lawlike, and whether or not they need to be explained, the existence of such constraints can still be used to argue that time travel worlds are so bizarre that it is implausible that our world or any world remotely like ours is a time travel world.

Suppose that one is in a time travel world. Suppose that given the global space-time structure of this world, there are constraints imposed upon, say, the state of motion of a ball on some space-like surface when it is treated as a test particle, i.e., when it is assumed that the ball does not affect the metric properties of the space-time it is in. (There is lots of other matter that, via the Einstein equation, corresponds exactly to the curvature that there is everywhere in this time travel worlds.) Now a real ball of course does have some effect on the metric of the space-time it is in. But let us consider a ball that is so small that its effect on the metric is negligible. Presumably it will still be the case that certain states of this ball on that space-like surface are not compatible with the global time travel structure of this universe.

This means that the actual distribution of matter on such a space-like surface can be extended into a space-time with closed time-like lines, but that certain counterfactual distributions of matter on this space-like surface can not be extended into the same space-time. But note that the changes made in the matter distribution (when going from the actual to the counterfactual distribution) do not in any non-negligible way affect the metric properties of the space-time. (Recall that the changes only effect test particles.) Thus the reason why the global time travel properties of the counterfactual space-time have to be significantly different from the actual space-time is not that there are problems with metric singularities or alterations in the metric that force significant global changes when we go to the counterfactual matter distribution. The reason that the counterfactual space-time has to be different is that in the counterfactual world the ball’s initial state of motion starting on the space-like surface, could not “meet up” in a consistent way with its earlier self (could not be consistently extended) if we were to let the global structure of the counterfactual space-time be the same as that of the actual space-time. Now, it is not bizarre or implausible that there is a counterfactual dependence of manifold structure, even of its topology, on matter distributions on spacelike surfaces. For instance, certain matter distributions may lead to singularities, others may not. We may indeed in some sense have causal power over the topology of the space-time we live in. But this power normally comes via the Einstein equations. But it is bizarre to think that there could be a counterfactual dependence of global space-time structure on the arrangement of certain tiny bits of matter on some space-like surface, where changes in that arrangement by assumption do not affect the metric anywhere in space-time in any significant way . It is implausible that we live in such a world, or that a world even remotely like ours is like that.

Let us illustrate this argument in a different way by assuming that wormhole time travel imposes constraints upon the states of people prior to such time travel, where the people have so little mass/energy that they have negligible effect, via the Einstein equation, on the local metric properties of space-time. Do you think it more plausible that we live in a world where wormhole time travel occurs but it only occurs when people’s states are such that these local states happen to combine with time travel in such a way that nobody ever succeeds in killing their younger self, or do you think it more plausible that we are not in a wormhole time travel world? [ 5 ]

An alternative approach to time travel (initiated by Deutsch 1991) abstracts away from the idealized toy models described above. [ 6 ] This computational approach considers instead the evolution of bits (simple physical systems with two discrete states) through a network of interactions, which can be represented by a circuit diagram with gates corresponding to the interactions. Motivated by the possibility of CTCs, Deutsch proposed adding a new kind of channel that connects the output of a given gate back to its input —in essence, a backwards-time step. More concretely, given a gate that takes $n$ bits as input, we can imagine taking some number $i \lt n$ of these bits through a channel that loops back and then do double-duty as inputs. Consistency requires that the state of these $i$ bits is the same for output and input. (We will consider an illustration of this kind of system in the next section.) Working through examples of circuit diagrams with a CTC channel leads to similar treatments of Consistency and Underdetermination as the discussion above (see, e.g., Wallace 2012: § 10.6). But the approach offers two new insights (both originally due to Deutsch): the Easy Knowledge paradox, and a particularly clear extension to time travel in quantum mechanics.

A computer equipped with a CTC channel can exploit the need to find consistent evolution to solve remarkably hard problems. (This is quite different than the first idea that comes to mind to enhance computational power: namely to just devote more time to a computation, and then send the result back on the CTC to an earlier state.) The gate in a circuit incorporating a CTC implements a function from the input bits to the output bits, under the constraint that the output and input match the i bits going through the CTC channel. This requires, in effect, finding the fixed point of the relevant function. Given the generality of the model, there are few limits on the functions that could be implemented on the CTC circuit. Nature has to solve a hard computational problem just to ensure consistent evolution. This can then be extended to other complex computational problems—leading, more precisely, to solutions of NP -complete problems in polynomial time (see Aaronson 2013: Chapter 20 for an overview and further references). The limits imposed by computational complexity are an essential part of our epistemic situation, and computers with CTCs would radically change this.

We now turn to the application of the computational approach to the quantum physics of time travel (see Deutsch 1991; Deutsch & Lockwood 1994). By contrast with the earlier discussions of constraints in classical systems, they claim to show that time travel never imposes any constraints on the pre-time travel state of quantum systems. The essence of this account is as follows. [ 7 ]

A quantum system starts in state $S_1$, interacts with its older self, after the interaction is in state $S_2$, time travels while developing into state $S_3$, then interacts with its younger self, and ends in state $S_4$ (see figure 10 ).

Figure 10 [An extended description of figure 10 is in the supplement.]

Deutsch assumes that the set of possible states of this system are the mixed states, i.e., are represented by the density matrices over the Hilbert space of that system. Deutsch then shows that for any initial state $S_1$, any unitary interaction between the older and younger self, and any unitary development during time travel, there is a consistent solution, i.e., there is at least one pair of states $S_2$ and $S_3$ such that when $S_1$ interacts with $S_3$ it will change to state $S_2$ and $S_2$ will then develop into $S_3$. The states $S_2, S_3$ and $S_4$ will typically be not be pure states, i.e., will be non-trivial mixed states, even if $S_1$ is pure. In order to understand how this leads to interpretational problems let us give an example. Consider a system that has a two dimensional Hilbert space with as a basis the states $\vc{+}$ and $\vc{-}$. Let us suppose that when state $\vc{+}$ of the young system encounters state $\vc{+}$ of the older system, they interact and the young system develops into state $\vc{-}$ and the old system remains in state $\vc{+}$. In obvious notation:

Similarly, suppose that:

Let us furthermore assume that there is no development of the state of the system during time travel, i.e., that $\vc{+}_2$ develops into $\vc{+}_3$, and that $\vc{-}_2$ develops into $\vc{-}_3$.

Now, if the only possible states of the system were $\vc{+}$ and $\vc{-}$ (i.e., if there were no superpositions or mixtures of these states), then there is a constraint on initial states: initial state $\vc{+}_1$ is impossible. For if $\vc{+}_1$ interacts with $\vc{+}_3$ then it will develop into $\vc{-}_2$, which, during time travel, will develop into $\vc{-}_3$, which inconsistent with the assumed state $\vc{+}_3$. Similarly if $\vc{+}_1$ interacts with $\vc{-}_3$ it will develop into $\vc{+}_2$, which will then develop into $\vc{+}_3$ which is also inconsistent. Thus the system can not start in state $\vc{+}_1$.

But, says Deutsch, in quantum mechanics such a system can also be in any mixture of the states $\vc{+}$ and $\vc{-}$. Suppose that the older system, prior to the interaction, is in a state $S_3$ which is an equal mixture of 50% $\vc{+}_3$ and 50% $\vc{-}_3$. Then the younger system during the interaction will develop into a mixture of 50% $\vc{+}_2$ and 50% $\vc{-}_2$, which will then develop into a mixture of 50% $\vc{+}_3$ and 50% $\vc{-}_3$, which is consistent! More generally Deutsch uses a fixed point theorem to show that no matter what the unitary development during interaction is, and no matter what the unitary development during time travel is, for any state $S_1$ there is always a state $S_3$ (which typically is not a pure state) which causes $S_1$ to develop into a state $S_2$ which develops into that state $S_3$. Thus quantum mechanics comes to the rescue: it shows in all generality that no constraints on initial states are needed!

One might wonder why Deutsch appeals to mixed states: will superpositions of states $\vc{+}$ and $\vc{-}$ not suffice? Unfortunately such an idea does not work. Suppose again that the initial state is $\vc{+}_1$. One might suggest that that if state $S_3$ is

one will obtain a consistent development. For one might think that when initial state $\vc{+}_1$ encounters the superposition

it will develop into superposition

and that this in turn will develop into

as desired. However this is not correct. For initial state $\vc{+}_1$ when it encounters

will develop into the entangled state

In so far as one can speak of the state of the young system after this interaction, it is in the mixture of 50% $\vc{+}_2$ and 50% $\vc{-}_2$, not in the superposition

So Deutsch does need his recourse to mixed states.

This clarification of why Deutsch needs his mixtures does however indicate a serious worry about the simplifications that are part of Deutsch’s account. After the interaction the old and young system will (typically) be in an entangled state. Although for purposes of a measurement on one of the two systems one can say that this system is in a mixed state, one can not represent the full state of the two systems by specifying the mixed state of each separate part, as there are correlations between observables of the two systems that are not represented by these two mixed states, but are represented in the joint entangled state. But if there really is an entangled state of the old and young systems directly after the interaction, how is one to represent the subsequent development of this entangled state? Will the state of the younger system remain entangled with the state of the older system as the younger system time travels and the older system moves on into the future? On what space-like surfaces are we to imagine this total entangled state to be? At this point it becomes clear that there is no obvious and simple way to extend elementary non-relativistic quantum mechanics to space-times with closed time-like curves: we apparently need to characterize not just the entanglement between two systems, but entanglement relative to specific spacetime descriptions.

How does Deutsch avoid these complications? Deutsch assumes a mixed state $S_3$ of the older system prior to the interaction with the younger system. He lets it interact with an arbitrary pure state $S_1$ younger system. After this interaction there is an entangled state $S'$ of the two systems. Deutsch computes the mixed state $S_2$ of the younger system which is implied by this entangled state $S'$. His demand for consistency then is just that this mixed state $S_2$ develops into the mixed state $S_3$. Now it is not at all clear that this is a legitimate way to simplify the problem of time travel in quantum mechanics. But even if we grant him this simplification there is a problem: how are we to understand these mixtures?

If we take an ignorance interpretation of mixtures we run into trouble. For suppose that we assume that in each individual case each older system is either in state $\vc{+}_3$ or in state $\vc{-}_3$ prior to the interaction. Then we regain our paradox. Deutsch instead recommends the following, many worlds, picture of mixtures. Suppose we start with state $\vc{+}_1$ in all worlds. In some of the many worlds the older system will be in the $\vc{+}_3$ state, let us call them A -worlds, and in some worlds, B -worlds, it will be in the $\vc{-}_3$ state. Thus in A -worlds after interaction we will have state $\vc{-}_2$ , and in B -worlds we will have state $\vc{+}_2$. During time travel the $\vc{-}_2$ state will remain the same, i.e., turn into state $\vc{-}_3$, but the systems in question will travel from A -worlds to B -worlds. Similarly the $\vc{+}$ $_2$ states will travel from the B -worlds to the A -worlds, thus preserving consistency.

Now whatever one thinks of the merits of many worlds interpretations, and of this understanding of it applied to mixtures, in the end one does not obtain genuine time travel in Deutsch’s account. The systems in question travel from one time in one world to another time in another world, but no system travels to an earlier time in the same world. (This is so at least in the normal sense of the word “world”, the sense that one means when, for instance, one says “there was, and will be, only one Elvis Presley in this world.”) Thus, even if it were a reasonable view, it is not quite as interesting as it may have initially seemed. (See Wallace 2012 for a more sympathetic treatment, that explores several further implications of accepting time travel in conjunction with the many worlds interpretation.)

We close by acknowledging that Deutsch’s starting point—the claim that this computational model captures the essential features of quantum systems in a spacetime with CTCs—has been the subject of some debate. Several physicists have pursued a quite different treatment of evolution of quantum systems through CTC’s, based on considering the “post-selected” state (see Lloyd et al. 2011). Their motivations for implementing the consistency condition in terms of the post-selected state reflects a different stance towards quantum foundations. A different line of argument aims to determine whether Deutsch’s treatment holds as an appropriate limiting case of a more rigorous treatment, such as quantum field theory in curved spacetimes. For example, Verch (2020) establishes several results challenging the assumption that Deutsch’s treatment is tied to the presence of CTC’s, or that it is compatible with the entanglement structure of quantum fields.

What remains of the grandfather paradox in general relativistic time travel worlds is the fact that in some cases the states on edgeless spacelike surfaces are “overconstrained”, so that one has less than the usual freedom in specifying conditions on such a surface, given the time-travel structure, and in some cases such states are “underconstrained”, so that states on edgeless space-like surfaces do not determine what happens elsewhere in the way that they usually do, given the time travel structure. There can also be mixtures of those two types of cases. The extent to which states are overconstrained and/or underconstrained in realistic models is as yet unclear, though it would be very surprising if neither obtained. The extant literature has primarily focused on the problem of overconstraint, since that, often, either is regarded as a metaphysical obstacle to the possibility time travel, or as an epistemological obstacle to the plausibility of time travel in our world. While it is true that our world would be quite different from the way we normally think it is if states were overconstrained, underconstraint seems at least as bizarre as overconstraint. Nonetheless, neither directly rules out the possibility of time travel.

If time travel entailed contradictions then the issue would be settled. And indeed, most of the stories employing time travel in popular culture are logically incoherent: one cannot “change” the past to be different from what it was, since the past (like the present and the future) only occurs once. But if the only requirement demanded is logical coherence, then it seems all too easy. A clever author can devise a coherent time-travel scenario in which everything happens just once and in a consistent way. This is just too cheap: logical coherence is a very weak condition, and many things we take to be metaphysically impossible are logically coherent. For example, it involves no logical contradiction to suppose that water is not molecular, but if both chemistry and Kripke are right it is a metaphysical impossibility. We have been interested not in logical possibility but in physical possibility. But even so, our conditions have been relatively weak: we have asked only whether time-travel is consistent with the universal validity of certain fundamental physical laws and with the notion that the physical state on a surface prior to the time travel region be unconstrained. It is perfectly possible that the physical laws obey this condition, but still that time travel is not metaphysically possible because of the nature of time itself. Consider an analogy. Aristotle believed that water is homoiomerous and infinitely divisible: any bit of water could be subdivided, in principle, into smaller bits of water. Aristotle’s view contains no logical contradiction. It was certainly consistent with Aristotle’s conception of water that it be homoiomerous, so this was, for him, a conceptual possibility. But if chemistry is right, Aristotle was wrong both about what water is like and what is possible for it. It can’t be infinitely divided, even though no logical or conceptual analysis would reveal that.

Similarly, even if all of our consistency conditions can be met, it does not follow that time travel is physically possible, only that some specific physical considerations cannot rule it out. The only serious proof of the possibility of time travel would be a demonstration of its actuality. For if we agree that there is no actual time travel in our universe, the supposition that there might have been involves postulating a substantial difference from actuality, a difference unlike in kind from anything we could know if firsthand. It is unclear to us exactly what the content of possible would be if one were to either maintain or deny the possibility of time travel in these circumstances, unless one merely meant that the possibility is not ruled out by some delineated set of constraints. As the example of Aristotle’s theory of water shows, conceptual and logical “possibility” do not entail possibility in a full-blooded sense. What exactly such a full-blooded sense would be in case of time travel, and whether one could have reason to believe it to obtain, remain to us obscure.

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How to cite this entry . Preview the PDF version of this entry at the Friends of the SEP Society . Look up topics and thinkers related to this entry at the Internet Philosophy Ontology Project (InPhO). Enhanced bibliography for this entry at PhilPapers , with links to its database.

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Time travel could be possible, but only with parallel timelines

Assistant Professor, Physics, Brock University

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Barak Shoshany does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

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Have you ever made a mistake that you wish you could undo? Correcting past mistakes is one of the reasons we find the concept of time travel so fascinating. As often portrayed in science fiction, with a time machine, nothing is permanent anymore — you can always go back and change it. But is time travel really possible in our universe , or is it just science fiction?

Read more: Curious Kids: is time travel possible for humans?

Our modern understanding of time and causality comes from general relativity . Theoretical physicist Albert Einstein’s theory combines space and time into a single entity — “spacetime” — and provides a remarkably intricate explanation of how they both work, at a level unmatched by any other established theory. This theory has existed for more than 100 years, and has been experimentally verified to extremely high precision, so physicists are fairly certain it provides an accurate description of the causal structure of our universe.

For decades, physicists have been trying to use general relativity to figure out if time travel is possible . It turns out that you can write down equations that describe time travel and are fully compatible and consistent with relativity. But physics is not mathematics, and equations are meaningless if they do not correspond to anything in reality.

Arguments against time travel

There are two main issues which make us think these equations may be unrealistic. The first issue is a practical one: building a time machine seems to require exotic matter , which is matter with negative energy. All the matter we see in our daily lives has positive energy — matter with negative energy is not something you can just find lying around. From quantum mechanics, we know that such matter can theoretically be created, but in too small quantities and for too short times .

However, there is no proof that it is impossible to create exotic matter in sufficient quantities. Furthermore, other equations may be discovered that allow time travel without requiring exotic matter. Therefore, this issue may just be a limitation of our current technology or understanding of quantum mechanics.

an illustration of a person standing in a barren landscape underneath a clock

The other main issue is less practical, but more significant: it is the observation that time travel seems to contradict logic, in the form of time travel paradoxes . There are several types of such paradoxes, but the most problematic are consistency paradoxes .

A popular trope in science fiction, consistency paradoxes happen whenever there is a certain event that leads to changing the past, but the change itself prevents this event from happening in the first place.

For example, consider a scenario where I enter my time machine, use it to go back in time five minutes, and destroy the machine as soon as I get to the past. Now that I destroyed the time machine, it would be impossible for me to use it five minutes later.

But if I cannot use the time machine, then I cannot go back in time and destroy it. Therefore, it is not destroyed, so I can go back in time and destroy it. In other words, the time machine is destroyed if and only if it is not destroyed. Since it cannot be both destroyed and not destroyed simultaneously, this scenario is inconsistent and paradoxical.

Eliminating the paradoxes

There’s a common misconception in science fiction that paradoxes can be “created.” Time travellers are usually warned not to make significant changes to the past and to avoid meeting their past selves for this exact reason. Examples of this may be found in many time travel movies, such as the Back to the Future trilogy.

But in physics, a paradox is not an event that can actually happen — it is a purely theoretical concept that points towards an inconsistency in the theory itself. In other words, consistency paradoxes don’t merely imply time travel is a dangerous endeavour, they imply it simply cannot be possible.

This was one of the motivations for theoretical physicist Stephen Hawking to formulate his chronology protection conjecture , which states that time travel should be impossible. However, this conjecture so far remains unproven. Furthermore, the universe would be a much more interesting place if instead of eliminating time travel due to paradoxes, we could just eliminate the paradoxes themselves.

One attempt at resolving time travel paradoxes is theoretical physicist Igor Dmitriyevich Novikov’s self-consistency conjecture , which essentially states that you can travel to the past, but you cannot change it.

According to Novikov, if I tried to destroy my time machine five minutes in the past, I would find that it is impossible to do so. The laws of physics would somehow conspire to preserve consistency.

Introducing multiple histories

But what’s the point of going back in time if you cannot change the past? My recent work, together with my students Jacob Hauser and Jared Wogan, shows that there are time travel paradoxes that Novikov’s conjecture cannot resolve. This takes us back to square one, since if even just one paradox cannot be eliminated, time travel remains logically impossible.

So, is this the final nail in the coffin of time travel? Not quite. We showed that allowing for multiple histories (or in more familiar terms, parallel timelines) can resolve the paradoxes that Novikov’s conjecture cannot. In fact, it can resolve any paradox you throw at it.

The idea is very simple. When I exit the time machine, I exit into a different timeline. In that timeline, I can do whatever I want, including destroying the time machine, without changing anything in the original timeline I came from. Since I cannot destroy the time machine in the original timeline, which is the one I actually used to travel back in time, there is no paradox.

After working on time travel paradoxes for the last three years , I have become increasingly convinced that time travel could be possible, but only if our universe can allow multiple histories to coexist. So, can it?

Quantum mechanics certainly seems to imply so, at least if you subscribe to Everett’s “many-worlds” interpretation , where one history can “split” into multiple histories, one for each possible measurement outcome – for example, whether Schrödinger’s cat is alive or dead, or whether or not I arrived in the past.

But these are just speculations. My students and I are currently working on finding a concrete theory of time travel with multiple histories that is fully compatible with general relativity. Of course, even if we manage to find such a theory, this would not be sufficient to prove that time travel is possible, but it would at least mean that time travel is not ruled out by consistency paradoxes.

Time travel and parallel timelines almost always go hand-in-hand in science fiction, but now we have proof that they must go hand-in-hand in real science as well. General relativity and quantum mechanics tell us that time travel might be possible, but if it is, then multiple histories must also be possible.

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Where Does the Concept of Time Travel Come From?

Time; he's waiting in the wings.

Wormholes have been proposed as one possible means of traveling through time.

The dream of traveling through time is both ancient and universal. But where did humanity's fascination with time travel begin, and why is the idea so appealing?

The concept of time travel — moving through time the way we move through three-dimensional space — may in fact be hardwired into our perception of time . Linguists have recognized that we are essentially incapable of talking about temporal matters without referencing spatial ones. "In language — any language — no two domains are more intimately linked than space and time," wrote Israeli linguist Guy Deutscher in his 2005 book "The Unfolding of Language." "Even if we are not always aware of it, we invariably speak of time in terms of space, and this reflects the fact that we think of time in terms of space."

Deutscher reminds us that when we plan to meet a friend "around" lunchtime, we are using a metaphor, since lunchtime doesn't have any physical sides. He similarly points out that time can not literally be "long" or "short" like a stick, nor "pass" like a train, or even go "forward" or "backward" any more than it goes sideways, diagonal or down.

Related: Why Does Time Fly When You're Having Fun?

Perhaps because of this connection between space and time, the possibility that time can be experienced in different ways and traveled through has surprisingly early roots. One of the first known examples of time travel appears in the Mahabharata, an ancient Sanskrit epic poem compiled around 400 B.C., Lisa Yaszek, a professor of science fiction studies at the Georgia Institute of Technology in Atlanta, told Live Science

In the Mahabharata is a story about King Kakudmi, who lived millions of years ago and sought a suitable husband for his beautiful and accomplished daughter, Revati. The two travel to the home of the creator god Brahma to ask for advice. But while in Brahma's plane of existence, they must wait as the god listens to a 20-minute song, after which Brahma explains that time moves differently in the heavens than on Earth. It turned out that "27 chatur-yugas" had passed, or more than 116 million years, according to an online summary , and so everyone Kakudmi and Revati had ever known, including family members and potential suitors, was dead. After this shock, the story closes on a somewhat happy ending in that Revati is betrothed to Balarama, twin brother of the deity Krishna.

Time is fleeting

To Yaszek, the tale provides an example of what we now call time dilation , in which different observers measure different lengths of time based on their relative frames of reference, a part of Einstein's theory of relativity.

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Such time-slip stories are widespread throughout the world, Yaszek said, citing a Middle Eastern tale from the first century BCE about a Jewish miracle worker who sleeps beneath a newly-planted carob tree and wakes up 70 years later to find it has now matured and borne fruit (carob trees are notorious for how long they take to produce their first harvest). Another instance can be found in an eighth-century Japanese fable about a fisherman named Urashima Tarō who travels to an undersea palace and falls in love with a princess. Tarō finds that, when he returns home, 100 years have passed, according to a translation of the tale published online by the University of South Florida .

In the early-modern era of the 1700 and 1800s, the sleep-story version of time travel grew more popular, Yaszek said. Examples include the classic tale of Rip Van Winkle, as well as books like Edward Belamy's utopian 1888 novel "Looking Backwards," in which a man wakes up in the year 2000, and the H.G. Wells 1899 novel "The Sleeper Awakes," about a man who slumbers for centuries and wakes to a completely transformed London.

Related: Science Fiction or Fact: Is Time Travel Possible ?

In other stories from this period, people also start to be able to move backward in time. In Mark Twain’s 1889 satire "A Connecticut Yankee in King Arthur's Court," a blow to the head propels an engineer back to the reign of the legendary British monarch. Objects that can send someone through time begin to appear as well, mainly clocks, such as in Edward Page Mitchell's 1881 story "The Clock that Went Backwards" or Lewis Carrol's 1889 children's fantasy "Sylvie and Bruno," where the characters possess a watch that is a type of time machine .

The explosion of such stories during this era might come from the fact that people were "beginning to standardize time, and orient themselves to clocks more frequently," Yaszek said.

Time after time

Wells provided one of the most enduring time-travel plots in his 1895 novella "The Time Machine," which included the innovation of a craft that can move forward and backward through long spans of time. "This is when we’re getting steam engines and trains and the first automobiles," Yaszek said. "I think it’s no surprise that Wells suddenly thinks: 'Hey, maybe we can use a vehicle to travel through time.'"

Because it is such a rich visual icon, many beloved time-travel stories written after this have included a striking time machine, Yaszek said, referencing The Doctor's blue police box — the TARDIS — in the long-running BBC series "Doctor Who," and "Back to the Future"'s silver luxury speedster, the DeLorean .

More recently, time travel has been used to examine our relationship with the past, Yaszek said, in particular in pieces written by women and people of color. Octavia Butler's 1979 novel "Kindred" about a modern woman who visits her pre-Civil-War ancestors is "a marvelous story that really asks us to rethink black and white relations through history," she said. And a contemporary web series called " Send Me " involves an African-American psychic who can guide people back to antebellum times and witness slavery.

"I'm really excited about stories like that," Yaszek said. "They help us re-see history from new perspectives."

Time travel has found a home in a wide variety of genres and media, including comedies such as "Groundhog Day" and "Bill and Ted's Excellent Adventure" as well as video games like Nintendo's "The Legend of Zelda: Majora's Mask" and the indie game "Braid."

Yaszek suggested that this malleability and ubiquity speaks to time travel tales' ability to offer an escape from our normal reality. "They let us imagine that we can break free from the grip of linear time," she said. "And somehow get a new perspective on the human experience, either our own or humanity as a whole, and I think that feels so exciting to us."

That modern people are often drawn to time-machine stories in particular might reflect the fact that we live in a technological world, she added. Yet time travel's appeal certainly has deeper roots, interwoven into the very fabric of our language and appearing in some of our earliest imaginings.

"I think it's a way to make sense of the otherwise intangible and inexplicable, because it's hard to grasp time," Yaszek said. "But this is one of the final frontiers, the frontier of time, of life and death. And we're all moving forward, we're all traveling through time."

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Can Animals Tell Time?
Why Does Time Sometimes Fly When You're NOT Having Fun?

Originally published on Live Science .

Adam Mann is a freelance journalist with over a decade of experience, specializing in astronomy and physics stories. He has a bachelor's degree in astrophysics from UC Berkeley. His work has appeared in the New Yorker, New York Times, National Geographic, Wall Street Journal, Wired, Nature, Science, and many other places. He lives in Oakland, California, where he enjoys riding his bike.

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Time travel is theoretically possible, calculations show. But that doesn't mean you could change the past.

Time travel is possible based on the laws of physics, according to researchers.
But time-travelers wouldn't be able to alter the past in a measurable way, they say.
And the future would essentially stay the same, according to the reseachers.

Imagine you could hop into a time machine, press a button, and journey back to 2019, before the novel coronavirus made the leap from animals to humans.

What if you could find and isolate patient zero? Theoretically, the COVID-19 pandemic wouldn't happen, right?

Not quite, because then future-you wouldn't have decided to time travel in the first place.

For decades, physicists have been studying and debating versions of this paradox: If we could travel back in time and change the past, what would happen to the future?

A 2020 study offered a potential answer: Nothing.

"Events readjust around anything that could cause a paradox, so the paradox does not happen," Germain Tobar, the study's author previously told IFLScience .

Tobar's work, published in the peer-reviewed journal Classical and Quantum Gravity in September 2020, suggests that according to the rules of theoretical physics, anything you tried to change in the past would be corrected by subsequent events.

The grandfather paradox

Physicists have considered time travel to be theoretically possible since Albert Einstein came up with his theory of relativity. Einstein's calculations suggest it's possible for an object in our universe to travel through space and time in a circular direction, eventually ending up at a point on its journey where it's been before – a path called a closed time-like curve.

Still, physicists continue to struggle with scenarios like the coronavirus example above, in which time-travelers alter events that already happened. The most famous example is known as the grandfather paradox: Say a time-traveler goes back to the past and kills a younger version of his or her grandfather. The grandfather then wouldn't have any children, erasing the time-traveler's parents and, of course, the time-traveler, too. But then who would kill Grandpa?

A take on this paradox appears in the movie "Back to the Future," when Marty McFly almost stops his parents from meeting in the past – potentially causing himself to disappear.

To address the paradox, Tobar and his supervisor, Dr. Fabio Costa, used the "billiard-ball model," which imagines cause and effect as a series of colliding billiard balls, and a circular pool table as a closed time-like curve.

Imagine a bunch of billiard balls laid out across that circular table. If you push one ball from position X, it bangs around the table, hitting others in a particular pattern.

The researchers calculated that even if you mess with the ball's pattern at some point in its journey, future interactions with other balls can correct its path, leading it to come back to the same position and speed that it would have had you not interfered.

"Regardless of the choice, the ball will fall into the same place," Dr Yasunori Nomura, a theoretical physicist at UC Berkeley, previously told Insider.

Tobar's model, in other words, says you could travel back in time, but you couldn't change how events unfolded significantly enough to alter the future, Nomura said. Applied to the grandfather paradox, then, this would mean that something would always get in the way of your attempt to kill your grandfather. Or at least by the time he did die, your grandmother would already be pregnant with your mother.

Back to the coronavirus example. Let's say you were to travel back to 2019 and intervene in patient zero's life. According to Tobar's line of thinking, the pandemic would still happen somehow.

"You might try and stop patient zero from becoming infected, but in doing so you would catch the virus and become patient zero, or someone else would," Tobar said, according to Australia's University of Queensland , where Tobar graduated from.

Nomura said that although the model is too simple to represent the full range of cause and effect in our universe, it's a good starting point for future physicists.

Watch: There are 2 types of time travel and physicists agree that one of them is possible

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Time Travel Facts

Physics of time travel.

Table of Contents

Time travel nears with new trillion-dollar ‘dual-use’ government technology. Visionary new closed timeline curves theory offers a peek into our past.

The idea of going back in time first captivated the popular imagination when H.G. Wells published his book , ‘The Time Machine’ in 1895. But today, this is no longer Star Trek pseudo-science but credible theorization incorporating standard laws of physics. That’s according to Texan, Joseph E. Olson in his article, ‘ Time Travel Tremor ,’ featured in Canada Free Press (June 7, 2010).

How is Time Travel Possible?

Joe insists time travel is infinitely more possible as theorists number-crunch two loose ends from the equations handed down to us by Albert Einstein and Godel’s solution to the ‘Field Equations’ in 1949. It seems even Einstein, himself, admitted the time travel door may be wide open to us yet.

Olson explains, “To the general public the take-home message is this: all that is necessary to complete the Einstein Theory of curved time-space is the charge and the rotation of the cosmological dust.”

The former Houston engineer explains that the two unknowns from that fateful 1949 equation were the spin of the cosmic dust and the net charge of the universal background radiation.

Olson enthuses, “To solve these equations we needed some empirical data. We needed un-disturbed cosmic dust, best collected on the moon, and advanced space-based telescopes to measure the rotation speed and the galactic radio wave radiation.”

The real-world data has painstakingly been put together at great expense as a result of the trillion-dollar space programs of rival Cold War superpowers, the United States and the former Soviet Union. Additional tweaking may now be ongoing here on Earth at the $6 billion Hadron Space Collider in Switzerland.

Top Scientists Seriously Study Time Travel

A long-time outspoken critic of the man-made theory of climate change , this insightful Texan is not shy of controversy. In pitching in with an incredible new angle to humanity’s big dream Olson expects to be labeled by some a ‘conspiracy nut.’ No less an icon of mainstream science, Stephen Hawking, a modern-day Sir Isaac Newton, has waded in to affirm that time travel is feasible in his documentary series on the ‘Discovery Channel.’

British science guru, Hawking admits he kept quiet until now for fear of “being labeled a crank.” Olson has no such fears and the Texan is blasting out on this with both barrels suggesting the public ridicule and the secrecy of successive U.S. governments simply adds fuel to his fire.

Indeed, with trillions of taxpayer dollars accumulated in related research projects with no apparent return on the investment, public speculation readily links projects such as the Hadron particle Collider with the once fanciful musings of H.G. Wells.

Dual Use Technologies

To channel vast amounts of government resources into what would otherwise be a giant cosmological white elephant, Olson identifies the need for policymakers to often couch their time travel research within the context of military defense; what he calls the incorporation of additional ‘dual use’ technologies.

An example of ‘dual use’ technical innovation was the Apollo Moon mission landings, which were seen not just as international kudos for the U.S., but a giant leap towards winning the superpowers’ arms race with the former Soviet Union. Thus the Hadron particle collider may be cloaked in another plausible cover while this hunt for the Holy Grail of science becomes ever more tantalizing.

Olson says, after decades of relentless acquisition of data, we are now about there. The great ‘Theory equation’ could finally be calculated and new technologies developed and refined to implement this new closed timeline curves theory with an actual machine that may cross the time-space curve into our history.

Russian Mathematicians Affirm Time Travel Possible

Olson expects those protective of government secrets will be quick to call him a crank but he’s not concerned. He has plenty of well-credentialed big-hitters supporting his ideas. For example, as reported in the UK’s ‘Independent’ newspaper (February 8, 2008) two Russian mathematicians, Irina Aref’eva and Igor Volovich, have spoken out in support of such a new theory.

The Russians envision the Large Hadron Collider at Cern as the most likely testbed for mankind’s first peek into the past. They suggested 2008 was the most credible “year zero” for time travel because they calculate it was the ideal location for plausible tiny “wormholes” in space that could allow some form of time travel.

Where future developments will lead we can only guess, because as Olson says, whoever seeks to exploit this technology will be guarding it very jealously and will be loathe to want to share it.

References:

Connor, S., ‘The Big Question: Is time travel possible, and is there any chance that it will ever take place?’ Science Editor, The Independent ( February 8, 2008)
Godel, K., An example of a new type of cosmological solutions of Einstein’s field equations of gravitation, (1949); Oxford University Press.
Olson, J., ‘Time Travel Tremor,’ Canada Free Press (June 7, 2010)
Overbye, D., ‘Large Hadron Collider,’ New York Times , (June 8, 2010)
Matyszczyk, C. ‘Hawking: Time Travel Will Happen,’ (May 2, 2010); Cnet News

Time Travelers Throughout History: Myth or Reality?

T he concept of time travel has long captivated humanity’s imagination, fueling countless stories, myths, and scientific speculations about the possibility of journeying through time, altering the past, or glimpsing into the future. From ancient legends and mythical tales to modern theories and technological advancements, the idea of traversing the temporal landscape has persisted across cultures, civilizations, and scientific disciplines, blurring the lines between fiction and reality. In this article, we will embark on a fascinating journey through time, exploring the intriguing tales of alleged time travelers throughout history, examining the evidence, theories, and the enduring mysteries that surround this captivating phenomenon.

Introduction to Time Travel: A Brief Overview

Time travel, the hypothetical concept of moving between different points in time, has intrigued philosophers, scientists, and storytellers for centuries, inspiring creativity, curiosity, and speculation about the nature of time, causality, and the possibilities of temporal exploration within the fabric of reality and the cosmic landscape.

Historical Context and Cultural Perceptions: Throughout history, various cultures, civilizations, and religious traditions have embraced the concept of time travel, weaving tales, myths, and narratives that explore the mysteries of time, destiny, and the human imagination’s boundless creativity.
Scientific Theories and Temporal Paradoxes: Theoretical physics, quantum mechanics, and the theory of relativity offer frameworks, equations, and principles that explore the potential for time dilation, wormholes, black holes, and the mysterious quantum phenomena that challenge our classical understanding of time’s arrow, reality, and the nature of the cosmos.

Ancient Legends, Myths, and Timeless Tales

Ancient civilizations, mythologies, and religious traditions have crafted tales, legends, and narratives that delve into the mysteries of time, destiny, and the human quest for understanding the temporal landscape, shaping our cultural perceptions, beliefs, and fascination with time travel.

Mythical Heroes, Gods, and Timeless Journeys: Ancient myths, such as the tales of King Arthur, Merlin, and the Avalon legends, the Hindu epic of Mahabharata, and the ancient Greek stories of Chronos, offer glimpses into the timeless tales of heroes, gods, and mythical journeys that transcend time, space, and the human imagination’s boundless realms.
Religious Traditions, Prophetic Visions, and Cosmic Cycles: Religious scriptures, prophecies, and spiritual traditions, including the biblical stories of Moses, Noah’s Ark, and the concept of the end times, the Hindu beliefs in cosmic cycles, rebirth, and the eternal dance of creation and destruction, and the Buddhist teachings on karma, impermanence, and the interconnectedness of all existence, reflect humanity’s quest for understanding, enlightenment, and the mysteries of time, destiny, and the timeless wisdom embedded within the fabric of reality and the cosmic landscape.

Modern Time Travelers, Urban Legends, and Scientific Speculations

In the modern era, alleged time travelers, urban legends, and scientific speculations have emerged, capturing public attention, sparking debates, and fueling the fascination with time travel, reality, and the enduring quest to unravel the mysteries of the temporal landscape.

Alleged Time Travelers and Contemporary Claims: Numerous individuals have come forward with claims of being time travelers, sharing stories, experiences, and alleged evidence of their journeys through time, inspiring curiosity, skepticism, and debate within the public, media, and scientific communities about the authenticity, credibility, and the mysteries surrounding these intriguing claims.
Scientific Theories, Quantum Mechanics, and the Possibilities of Time Travel: Theoretical physics, quantum mechanics, and the theory of relativity offer insights, equations, and principles that explore the potential for time dilation, wormholes, black holes, and the mysterious quantum phenomena that challenge our classical understanding of time’s arrow, reality, and the nature of the cosmos, revealing the intricate interplay of quantum forces, spacetime geometry, and the cosmic dynamics shaping our understanding of time travel, reality, and the mysteries of the universe.

Time travelers throughout history, whether rooted in ancient myths, modern urban legends, or scientific speculations, reflect humanity’s enduring fascination with time travel, the mysteries of the temporal landscape, and the timeless quest for understanding, enlightenment, and the boundless possibilities that lie within the fabric of reality and the cosmic tapestry.

As we explore, investigate, and unravel the intriguing tales of alleged time travelers throughout history through historical inquiry, scientific exploration, and the pursuit of knowledge, we embark on a journey of discovery, exploration, and enlightenment that transcends boundaries, deepens our understanding of human creativity, imagination, and the enduring quest for truth, meaning, and the timeless wonders that inspire wonder, curiosity, and a renewed appreciation for the grandeur, diversity, and interconnectedness of the human experience, cultural heritage, and the boundless realms of time, space, and the universe beyond.

Read More: The Goldilocks Zone: Finding Planets Just Right for Life

Time Travelers Throughout History: Myth or Reality? 2

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Air Travel Consumer Report: January 2024 Numbers

WASHINGTON – The U.S. Department of Transportation (DOT) today released its Air Travel Consumer Report (ATCR) on airline operational data compiled for the month of January 2024 for on-time performance, mishandled baggage, and mishandled wheelchairs and scooters. The ATCR is designed to assist consumers with information on the quality of services provided by airlines.

DOT expects that airlines will operate flights as scheduled and that when they do not, airlines will provide consumers the services consumers have been promised when a flight is canceled or delayed because of an airline issue. After a two-year DOT push to improve the passenger experience, the 10 largest airlines now guarantee meals and free rebooking on the same airline and nine guarantee hotel accommodations. Consumer-friendly information regarding airline commitments to their customers is available on the Department’s Airline Customer Service Dashboard at FlightRights.Gov. DOT also pushed airlines to provide fee-free family seating and rolled out a new family seating dashboard that highlights the airlines that guarantee fee-free family seating, and those of the 10 largest that do not, making it easier for parents to avoid paying junk fees to sit with their children when they fly.

In addition, DOT is improving transportation for individuals with disabilities. In July 2023, DOT finalized a rule which requires airlines to make lavatories on new, single-aisle aircraft more accessible. Then, in February 2024, DOT issued a proposal to address other barriers that Americans who use a wheelchair encounter when it comes to air travel by, among other things, mandating enhanced training for airline employees and contractors who physically assist passenger with disabilities and handle passengers’ wheelchairs.

Further, when necessary, DOT takes enforcement action against airlines and ticket agents that fail to comply with the Department’s aviation consumer protection requirements. In 2023, DOT issued the largest fines in the history of the consumer protection office. This includes a $140 million penalty against Southwest Airlines for failing passengers during the 2022 holiday meltdown. That penalty, which was in addition to over $600 million DOT already ensured was refunded by Southwest to passengers, requires Southwest to establish a $90 million compensation system for future passengers affected by significant delays and cancellations. DOT has helped return more than $3 billion in refunds to travelers since the pandemic began.

Flight Operations

The 560,352 flights operated in January 2024 were 99.56% of the 562,845 flights operated in January 2023. Operated flights in January 2024 were down 0.44% year-over-year from the 562,845 flights operated in January 2023 and down 7.18% month-over-month from 603,756 flights operated in December 2023.

"U.S. Airlines Operated Domestic Flights: January 2022-January 2024. Operated=Scheduled - Canceled"

In January 2024, the 10 marketing network carriers reported 582,425 scheduled domestic flights, 22,073 (3.8%) of which were canceled. In December 2023, airlines scheduled 606,218 domestic flights, 2,462 (1.3%) of which were canceled. In January 2023, airlines scheduled 573,877 domestic flights, 11,032 (1.9%) of which were canceled.

On January 6, 2024, the Federal Aviation Administration (FAA) ordered the grounding of Boeing 737 MAX aircraft with a mid-cabin door plug installed operated by U.S. airlines or in U.S. territory. On January 24, 2024, FAA cleared all such aircraft to return to service after each aircraft operator successfully completed a new inspection process approved by the FAA. Alaska Airlines and United Airlines have informed the DOT that the grounding of the 737 MAX9 aircraft with the mid-cabin door plug installed has impacted their on-time statistics during this reporting period.

January 2024 On-Time Arrival

In January 2024, reporting marketing carriers posted an on-time arrival rate of 72.8%, down from both 83.9% in December 2023 and from 76.2% in January 2023.

Highest Marketing Carrier On-Time Arrival Rates January 2024 (ATCR Table 1)

Delta Airlines Network – 77.8%
Allegiant Air – 75.6%
Southwest Airlines – 73.9%

Lowest Marketing Carrier On-Time Arrival Rates January 2024 (ATCR Table 1)

Alaska Airlines Network – 64.7%
JetBlue Airways – 69.5%
American Airlines Network – 70.5%

January 2024 Flight Cancellations

In January 2024, reporting marketing carriers canceled 3.8% of their scheduled domestic flights, higher than both the rate of 0.4% in December 2023 and the rate of 1.9% in January 2023.

Lowest Marketing Carrier Rates of Canceled Flights January 2024 (ATCR Table 6)

Hawaiian Airlines – 1.5%
Spirit Airlines – 1.5%
JetBlue Airways – 1.7%

Highest Marketing Carrier Rates of Canceled Flights January 2024 (ATCR Table 6)

Alaska Airlines Network – 11.9%
United Airlines Network – 6.9%
Southwest Airlines – 3.1%

Complaints About Airline Service

The release of air travel service complaint data in the Air Travel Consumer Report (ATCR) has been delayed primarily because of the continued high volume of complaints against airlines and ticket agents received by the Office of Aviation Consumer Protection (OACP) and the time needed to review and process these consumer complaints. The Department is investing in modernizing its system for handling consumer complaints with the support of a Technology Modernization Fund (TMF) investment to improve the customer experience for the tens of thousands of consumers who use the system each year and enable OACP to more effectively engage in oversight of the airline industry.

As DOT modernizes its system, given the continued high volume of air travel service complaints concerning airlines and ticket agents, DOT has revised how it processes consumer complaints received after June 1, 2023. From June 2023 until the date its system is modernized, DOT intends to revise the ATCR to display consumer submissions (complaints, inquiries, and opinions) as opposed to complaints for this period. The Department will continue to display civil rights complaints in the ATCR in a similar manner as before and anticipates publishing submission and civil rights complaint numbers in spring.

Tarmac Delays

In January 2024, airlines reported 71 tarmac delays of more than three hours on domestic flights, compared to five tarmac delays of more than three hours on domestic flights reported in December 2023. In January 2024, airlines reported six tarmac delays of more than four hours on international flights, compared to zero tarmac delays of more than four hours on international flights reported in December 2023.

Airlines are required to have and adhere to assurances that they will not allow aircraft to remain on the tarmac for more than three hours for domestic flights and four hours for international flights without providing passengers the option to deplane, subject to exceptions related to safety, security, and Air Traffic Control related reasons. An exception also exists for departure delays if the airline begins to return the aircraft to a suitable disembarkation point to deplane passengers by those times.

The Department investigates extended tarmac delays.

Mishandled Baggage

In January 2024, reporting marketing carriers handled 37.4 million bags and posted a mishandled baggage rate of 0.75%, higher than both the rate of 0.50% in December 2023 and the rate of 0.73% in January 2023.

The Department began displaying the mishandled baggage data as a percentage (i.e., per 100 bags enplaned) in January 2022. This is consistent with the manner that the mishandled wheelchairs and scooters rate is calculated and displayed. In the prior three calendar year reports (2019 to 2021), the Department calculated the mishandled baggage rate based on the number of mishandled bags per 1,000 checked bags.

Mishandled Wheelchairs and Scooters

In January 2024, reporting marketing carriers reported checking 56,659 wheelchairs and scooters and mishandling 836 for a rate of 1.48% mishandled wheelchairs and scooters, higher than the rate of 1.39% mishandled in December 2023 and lower than the rate of 1.47% mishandled in January 2023.

As described earlier, in February 2024, the Department announced its proposal to strengthen its rule implementing the Air Carrier Access Act (ACAA) to address the serious problems that individuals with disabilities using wheelchairs and scooters face when traveling by air that impact their safety and dignity, including mishandled wheelchairs and scooters and improper transfers to and from aircraft seats, aisle chairs, and personal wheelchairs. The proposed rule would require that airlines meet strict standards in accommodating passengers with disabilities by setting new standards for prompt, safe, and dignified assistance, mandating enhanced training for airline employees and contractors who physically assist passengers with disabilities and handle passengers’ wheelchairs, and outlining actions that airlines must take to protect passengers when a wheelchair is damaged during transport. The proposed rule also clarifies that damaging or delaying the return of a wheelchair is an automatic violation of the ACAA.

Bumping/Oversales

Bumping/oversales data, unlike other air carrier data, are reported quarterly rather than monthly. For the fourth quarter of 2023, the 10 U.S. reporting marketing carriers posted an involuntary denied boarding, or bumping, rate of 0.20 per 10,000 passengers, lower than both the rate of 0.35 in the third quarter of 2023 and the rate of 0.30 in the fourth quarter of 2022.

Incidents Involving Animals

As part of its IT modernization, DOT’s Office of Aviation Consumer Protection (OACP) is improving the options for covered carriers to submit their monthly and annual Reports on Incidents Involving Animals During Air Transport. While the new system is being developed, OACP is permitting covered carriers to delay submission of reports on incidents involving animals during air transport. Annual data on such incidents will be published when DOT receives carriers’ complete submissions of the 2023 data.

In January 2024, carriers reported zero incidents involving the death, injury, or loss of an animal while traveling by air, equal to the zero reports filed in both December 2023 and in January 2023.

Consumers may file air travel consumer or civil rights complaints online at https://secure.dot.gov/air-travel-complaint , or they may mail a complaint to the Office of Aviation Consumer Protection, U.S. Department of Transportation, C-70, W96-432, 1200 New Jersey Avenue, SE, Washington, DC 20590.

The ATCR and other aviation consumer matters of interest to the public can be found at https://www.transportation.gov/airconsumer .

Mindfulness

How time perspective affects travel, do you live in the past, present, or future.

Posted April 15, 2024 | Reviewed by Michelle Quirk

What Is Mindfulness?
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Understanding your own time perspective can enhance your life experience.
Our characteristic types are neither good nor bad, just different from one another.
Children are present-oriented, while adults favor the future. Seniors tend to preserve the past.

As an enjoyable vacation winds down, some of us become impatient to get home and move on to the next thing. Maybe that’s you. But, instead, you might be someone who tries to preserve, or even expand, every remaining moment. In either case, you’ll attempt to lock these precious flashes into your memory bank with mental snapshots. But without any effort, and all too quickly, the present quickly fades into the past. How we experience time is relevant to travel. Understanding your own time perspective can enhance your experience.

Stanford University Professor Emeritus Phil Zimbardo, author of The Time Paradox , notes that we are all oriented to time in one of the following characteristic ways—past, present, or future. According to his profile, I am future-oriented. What might your style be? Let’s see.

Those of us in the future category are goal-driven, focused on the future consequences of our actions, and forward-looking in general. Then there are the present-hedonic folks, the pleasure seekers who enjoy things in real-time, with less concern about tomorrow. Folks who live in the present tend to be open to experiences they didn’t necessarily plan, and they don’t need to check it off their bucket list. If this style fits, you’re probably most content with the moment-to-moment flow of your travel.

Past-oriented people make up the remaining category. This might be you if you compare current experiences with memories of past events or situations. Past-oriented folks determine the value of travel, according to Zimbardo, by assigning a pleasure quotient to the comparison—better or worse and by how much? This style is more analytic and rational, and based less on emotional factors than is true for present-focused folks. Does this sound like you?

Our characteristic types are neither good nor bad—just different from one another. Future- and past-oriented travelers provide a logical, systematic understanding of where travel fits into human experience. These styles have great evolutionary value. Our distant ancestors, who chronicled the past and predicted the future, tended to be the shaman and storytellers of the tribe. Reviewing the past and predicting the future was critical to human survival.

Present-oriented people tend to have more fun in the moment, and every society needs this type of person to keep things from getting too serious. Savoring the present is an acquired skill and is worth the effort to cultivate! Also, by expanding the present-pleasant and then reviewing a trip in the past-positive, you can have both good feelings and pleasurable memories. Since, as Zimbardo’s research indicates, we have characteristic ways of perceiving time, maintaining a present focus may require some work—if this isn’t naturally how you see the world.

Zimbardo points to another dimension of time—one that is age-related. In general, children are present-oriented while adults favor the future. Seniors tend to preserve the past. As a future-focused senior, I'm aware of the need to put my foot on the brake and try to prolong the present—particularly the pleasing moments while vacationing. This takes some work.

Regardless of the type that best explains you, here are some strategies to expand your time orientation:

If you’re naturally drawn to the past or future , notice these tendencies and gently nudge yourself toward the present moment. When you catch yourself reminiscing about the last time you were in Paris, as you sit at an outdoor café savoring your steaming latte and munching on a croissant, remind yourself that the people you see strolling by are there right now—not last time or next time. The weather is uniquely now, not needing a contrast with a warmer or sunnier last visit. The present can be pleasant without any backward reference—or simply less.
Future- oriented travelers tend to spend their present moments imagining future trips, which makes sense in planning life but can steal from the here and now. Recently, on a river cruise through Austria, I was struck by how much conversation I overheard about planning the next trip. Busily sharing these thoughts with fellow travelers, these vacationers sat by a large picture window as the ship sailed into a new city—totally missing the present moment, unnoticed outside of the window.
Again, if future is your natural mode, keep that in mind as you travel. Learn to prolong the only moment that truly exists—this one that you anticipated for months or maybe years. The first step involves gently guiding your awareness back to the present. Practicing meditation even a few minutes a day will make this process easier.

This article is based on a chapter from my book: Inward Traveler: 51 Ways to Explore the World Mindfully, 2018.

Stanford University professor emeritus, Phil Zimbardo, authored The Time Paradox, Free Press, N.Y., 2008.

Francine Toder, Ph.D. , is an emeritus faculty member of California State University, Sacramento and is a clinical psychologist retired from private practice.

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Check the estimated wait time for a nonimmigrant visa interview appointment at a U.S. Embassy or Consulate.

Note: Please check the individual Embassy or Consulate website to determine if your case is eligible for a waiver of the in-person interview.

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2024 could be the year to travel as airfare prices are declining

Last month there was a notable decline in airfare prices, with a 7.1% decrease compared to the same month last year.

A traveler pushes a cart topped with baggage in Denver International Airport.

If you've noticed that airfare prices seem a bit more affordable lately, it's because they're on a downward trend.

According to data released Tuesday by the U.S. Department of Transportation, the average domestic airfare for 2023 was $382, making it 3.1% lower than the inflation-adjusted average fare of $394 in 2022; and it's 36.4% lower than the peak fare of $600 recorded in 2000.

The news comes while costs continue to rise in most other sectors — yet the desire to travel continues to increase.

"In the first quarter 2023, passenger demand increased with U.S. airlines reporting 75.4 million originating passengers, up 138.8% from 31.6 million passengers in the fourth quarter of 2020," DOT said in the press release. "U.S. passenger airlines collected 74.2% of total operating revenue of $39.2 billion from passenger fares during the first three months of 2023, down from 88.5% in 1990."

As for the numbers for this year, Nerdwallet reports that airfares dropped by 7.1% in March compared to the same month in 2023, and since 2019 before the start of the pandemic, airfares have only gone up by 2.6%.

While the prices are a bit lower, airlines like Delta are still benefiting from the traveling boom. Delta's first-quarter earnings report highlighted a $37 million profit fueled by the strong demand, and the airline says they expect the trend to continue throughout the summer.

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This news comes as the airline shared its first-quarter earnings for this year, saying it has earned $37 million thus far.

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Kamala Harris, Traveling to Arizona, Will Slam Trump Over Abortion

The vice president is set to lean into a partywide attack on Donald Trump and fellow Republicans, who are newly on the defensive over the issue.

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Vice President Kamala Harris speaking at a lectern.

By Nicholas Nehamas , Lisa Lerer and Reid J. Epstein

Vice President Kamala Harris will travel to Arizona on Friday to assail former President Donald J. Trump over abortion restrictions, with plans to blame him for bans in the state and across the country.

In her remarks at a rally in Tucson, Ms. Harris will lean into the Biden campaign’s new attack line on laws pushed by Republicans that have cut off abortion access for millions of American women: Donald Trump did this.

She is also planning a new way to hit the former president, arguing that a second Trump administration would enforce the Comstock Act, a rarely used federal law from 1873, to circumvent Congress and ban medication abortion nationwide.

“They want to use another law from the 1800s — the Comstock Act — to ban medication abortion in all 50 states,” Ms. Harris is expected to say in Tucson, according to Biden campaign aides. “A ban that would include states where abortion is currently legal.”

Medication abortions now account for the majority of abortions nationwide, so enforcement of the Comstock Act could have a significant impact on the availability of the procedure.

While the former president has never specifically mentioned the act publicly, some of his allies have begun sketching out proposals to enforce it through executive actions . The law, once considered a constitutional relic, prohibits the mailing of “obscene, lewd, or lascivious” materials and has become part of a high-profile lawsuit seeking to halt the availability of abortion pills.

This week, Arizona became the center of the national debate on reproductive rights after a ruling by the state’s top court upheld an 1864 law banning nearly all abortions. The decision gave Democrats around the country an opportunity to focus their races on abortion rights, a strategy that has led to unexpected victories for the party over the last two years. The Biden campaign has already released two new ads this week hammering Mr. Trump on abortion.

“The overturning of Roe was a seismic event,” Ms. Harris is expected to say in Tucson, according to a copy of her prepared remarks distributed by the Biden campaign. “And this ban in Arizona is one of the biggest aftershocks yet.”

Ms. Harris’s comments on Friday may be some of the most direct and extended attacks that she has made against Mr. Trump on the issue. While she has appeared frequently at events about abortion rights, she has often done so in her official capacity, limiting her ability to criticize Republicans. The event in Tucson, however, is a campaign rally, meaning Ms. Harris can speak more freely.

“We all must understand who is to blame,” her prepared remarks say. “It is the former president, Donald Trump. It is Donald Trump who, during his campaign in 2016, said women should be punished for seeking an abortion.”

The vice president’s trip to Arizona was planned before the ruling and was originally supposed to involve an official event on student debt. But even before the court ruling, Ms. Harris insisted that abortion rights become the focus instead and that the campaign take over, according to three Democratic officials familiar with the planning.

The timing could not have been better for the Biden campaign. On Monday, Mr. Trump released a video saying that abortion restrictions should be left up to the states. The next day, the Arizona Supreme Court upheld a prestatehood law banning nearly all abortions, without exceptions for rape and incest. (The law, which Mr. Trump has since criticized , has not yet gone into effect.)

Republicans have been left on the defensive, including Kari Lake, the Trump ally running for an open Senate seat in Arizona. Two years ago, when she was running for governor, Ms. Lake called the Civil War-era abortion ban “a great law.” But on Thursday, she released a five-minute video , saying that “this total ban on abortion” was “out of line with where the people of this state are.”

“I chose life,” said Ms. Lake, who has two children, of her own pregnancies. “But I’m not every woman. I want to make sure that every woman who finds herself pregnant has more choices so that she can make that choice that I made.”

Ms. Lake’s stark shift shows how much the politics of abortion have changed since Supreme Court justices appointed by Mr. Trump ruled in favor of a Mississippi law in Dobbs v. Jackson Women’s Health Organization and abolished the constitutional right to abortion.

“This is the first presidential election since Dobbs. And it is a massively important issue because it does affect every woman in some capacity. It just does,” said Stephanie Schriock, former president of Emily’s List, the powerful organization that seeks to elect Democratic women who support abortion rights. “It crosses people’s minds because women are dealing with this stuff all the time, particularly those of reproductive age, which is a pretty big swath of all of Gen Z and millennials.”

Nicholas Nehamas is a Times political reporter covering the re-election campaign of President Biden. More about Nicholas Nehamas

Lisa Lerer is a national political reporter for The Times, based in New York. She has covered American politics for nearly two decades. More about Lisa Lerer

Reid J. Epstein covers campaigns and elections from Washington. Before joining The Times in 2019, he worked at The Wall Street Journal, Politico, Newsday and The Milwaukee Journal Sentinel. More about Reid J. Epstein

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Reporting by Dan Williams in Jerusalem, Parisa Hafezi in Dubai, Timur Azhari in Baghdad, Jeff Mason, Eric Beech and Doina Chiacu in Washington and Suleiman al-Khalidi in Amman and Lidia Kelly in Lisbon; Writing by Angus McDowall; Editing by Jonathan Oatis, Daniel Wallis, Chizu Nomiyama, Howard Goller and William Mallard

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The Biden administration said it would not renew a license set to expire early on Thursday that had broadly eased Venezuela oil sanctions, moving to reimpose punitive measures in response to President Nicolas Maduro’s failure to meet his election commitments.

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Is Time Travel Possible?
In Summary: Yes, time travel is indeed a real thing. But it's not quite what you've probably seen in the movies. Under certain conditions, it is possible to experience time passing at a different rate than 1 second per second. And there are important reasons why we need to understand this real-world form of time travel.
Time travel
The first page of The Time Machine published by Heinemann. Time travel is the hypothetical activity of traveling into the past or future.Time travel is a widely recognized concept in philosophy and fiction, particularly science fiction. In fiction, time travel is typically achieved through the use of a hypothetical device known as a time machine.The idea of a time machine was popularized by H ...
A beginner's guide to time travel
A beginner's guide to time travel. Learn exactly how Einstein's theory of relativity works, and discover how there's nothing in science that says time travel is impossible. Everyone can travel in ...
Is Time Travel Possible?
Time traveling to the near future is easy: you're doing it right now at a rate of one second per second, and physicists say that rate can change. According to Einstein's special theory of ...
Can we time travel? A theoretical physicist provides some answers
Time travel makes regular appearances in popular culture, with innumerable time travel storylines in movies, television and literature. But it is a surprisingly old idea: one can argue that the ...
Will time travel ever be possible? Science behind curving space-time
She explained how, theoretically, time travel is possible. The mathematics behind creating curvature of space-time are solid, but trying to re-create the strict physical conditions needed to prove ...
Time travel
An observer traveling at high velocity will experience time at a slower rate than an observer who isn't speeding through space. While we don't accelerate humans to near-light-speed, we do send ...
Is time travel possible? An astrophysicist explains
Time travel is the concept of moving between different points in time, just like you move between different places. In movies, you might have seen characters using special machines, magical ...
Is time travel even possible? An astrophysicist explains the science
Scientists are trying to figure out if time travel is even theoretically possible. If it is, it looks like it would take a whole lot more knowledge and resources than humans have now to do it.
Paradox-Free Time Travel Is Theoretically Possible, Researchers Say
According a new paper from researchers at the University of Queensland, even if time travel were possible, the paradox couldn't actually exist. Researchers ran the numbers and determined that even ...
Is Time Travel Even Possible? An Astrophysicist Explains The Science
Telescopes are time machines. Interestingly, astrophysicists armed with powerful telescopes possess a unique form of time travel. As they peer into the vast expanse of the cosmos, they gaze into the past universe. Light from all galaxies and stars takes time to travel, and these beams of light carry information from the distant past.
Time Travel
Time Travel. First published Thu Nov 14, 2013; substantive revision Fri Mar 22, 2024. There is an extensive literature on time travel in both philosophy and physics. Part of the great interest of the topic stems from the fact that reasons have been given both for thinking that time travel is physically possible—and for thinking that it is ...
How Time Travel Works
GPS satellite clocks are about 3 8 seconds longer per day than a clock closer to earth due to the gravitational frequency shift. They make up for this discrepancy by using time travel calculations or they could be way off from your current location and time. Time travel is a concept that has existed in science-fiction for hundreds of years ...
Time Travel and Modern Physics
Time Travel and Modern Physics. First published Thu Feb 17, 2000; substantive revision Mon Mar 6, 2023. Time travel has been a staple of science fiction. With the advent of general relativity it has been entertained by serious physicists. But, especially in the philosophy literature, there have been arguments that time travel is inherently ...
Time travel could be possible, but only with parallel timelines
Time travel appears to contradict logic. (Shutterstock) The other main issue is less practical, but more significant: it is the observation that time travel seems to contradict logic, in the form ...
Physicist Discovers 'Paradox-Free' Time Travel Is Theoretically
"The maths checks out - and the results are the stuff of science fiction," said physicist Fabio Costa from the University of Queensland, who supervised the research. Fabio Costa (left) and Germain Tobar (right). (Ho Vu) The research smoothed out the problem with another hypothesis, that time travel is possible but that time travelers would be restricted in what they did, to stop them ...
Where Does the Concept of Time Travel Come From?
One of the first known examples of time travel appears in the Mahabharata, an ancient Sanskrit epic poem compiled around 400 B.C., Lisa Yaszek, a professor of science fiction studies at the ...
The scientist trying to travel back in time
Mallett was aged 10 when his father died suddenly, of a heart attack, an event that the scientist says changed the track of his life forever. "For me, the sun rose and set on him, he was just ...
Time Travel Is Possible but Changing the Past Isn't, Study Says
Dec 31, 2022, 9:13 AM PST. Doc Brown and Marty McFly in "Back to the Future." Universal Pictures. Time travel is possible based on the laws of physics, according to researchers. But time-travelers ...
Time Travel Facts
Physics of Time Travel. Time travel nears with new trillion-dollar 'dual-use' government technology. Visionary new closed timeline curves theory offers a peek into our past. The idea of going back in time first captivated the popular imagination when H.G. Wells published his book, 'The Time Machine' in 1895.
There's One Way Time Travel Could Be Possible, According to This
One attempt at resolving time travel paradoxes is theoretical physicist Igor Dmitriyevich Novikov's self-consistency conjecture, which essentially states that you can travel to the past, but you cannot change it. According to Novikov, if I tried to destroy my time machine five minutes in the past, I would find that it is impossible to do so.
Time Travel
Time Travel. Time travel is commonly defined with David Lewis' definition: An object time travels if and only if the difference between its departure and arrival times as measured in the surrounding world does not equal the duration of the journey undergone by the object. For example, Jane is a time traveler if she travels away from home in ...
Time Travelers Throughout History: Myth or Reality?
Introduction to Time Travel: A Brief Overview. Time travel, the hypothetical concept of moving between different points in time, has intrigued philosophers, scientists, and storytellers for ...
Air Travel Consumer Report: January 2024 Numbers
WASHINGTON - The U.S. Department of Transportation (DOT) today released its Air Travel Consumer Report (ATCR) on airline operational data compiled for the month of January 2024 for on-time performance, mishandled baggage, and mishandled wheelchairs and scooters. The ATCR is designed to assist consumers with information on the quality of services provided by airlines.
How Time Perspective Affects Travel
How we experience time is relevant to travel. Understanding your own time perspective can enhance your experience. Stanford University Professor Emeritus Phil Zimbardo, author of The Time Paradox ...
Visa Appointment Wait Times
Wait Time for Interview. The estimated wait time to receive a nonimmigrant visa interview appointment at a U.S. embassy or consulate and is based on workload and staffing and can vary from week to week. The information provided is an estimate and does not guarantee the availability of an appointment. Wait Time for Interview Waiver
2024 could be the year to travel as airfare prices are declining
According to data released Tuesday by the U.S. Department of Transportation, the average domestic airfare for 2023 was $382, making it 3.1% lower than the inflation-adjusted average fare of $394 in 2022; and it's 36.4% lower than the peak fare of $600 recorded in 2000. The news comes while costs continue to rise in most other sectors — yet ...
Kamala Harris, Traveling to Arizona, Will Slam Trump Over Abortion
April 12, 2024, 5:04 a.m. ET. Vice President Kamala Harris will travel to Arizona on Friday to assail former President Donald J. Trump over abortion restrictions, with plans to blame him for bans ...
Iran launches retaliatory attack on Israel with hundreds of drones
Iran launched explosive drones and fired missiles at Israel late on Saturday in its first direct attack on Israeli territory, a retaliatory strike that raised the threat of a wider regional ...

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Time Travelers Throughout History: Myth or Reality?

Introduction to Time Travel: A Brief Overview

Ancient Legends, Myths, and Timeless Tales

Modern Time Travelers, Urban Legends, and Scientific Speculations