superpower of time travel

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The Strongest Time-Traveling Superheroes, Ranked

Superheroes have all sorts of powers, from flight to being bulletproof, but there's one superpower many would argue to be the very best of them all: the ability to travel through time. Throughout the years, there have been a ton of superheroes who have this ability. Some acquired it naturally, while others learned how to manipulate the space-time continuum through the use of some insane technology.

Let's face it: it's not easy to break out of one time and enter into another, but there are some who have done it. Leaving the obvious villains like Doctor Doom aside, the superheroes of Marvel, DC, Image, and other comic book universes have figured out time travel and have used it to help achieve their goals. Not everyone who jumps about in time ends up mucking it up and creating events like the Flash, but there are those who travel through time without creating much of a fuss.

Here is a list of popular superheroes that can control time, but it's up to you to determine who is the best! Whether you prefer Marvel's time travel stories or prefer the ones form DC, make your voice heard. Vote up your favorites and see which superhero jumps to the top as the greatest time-traveling superhero of them all!

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Doctor Strange

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Green Lantern

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Doctor Manhattan

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Franklin Richards

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Booster Gold

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Iris West Allen

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Ranking comic book characters by their powers, strength, physical traits, affiliations, and other features, like how just goshdarn super they are.

Top 10 Most Powerful Superheroes Who Can Travel Through Time

Time travel is one of the most powerful abilities a superhero can possess, and these ten comic book heroes all showcase this awesome ability.

Traveling through time is the ultimate ace in the hole when it comes down to superhero battles and plenty of DC and Marvel super-powered beings, including some anti-heroes, are gifted with this powerful ability.

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In some cases, these heroes' time-manipulating skills are the side effects of talents that, in and of themselves, have nothing to do with journeying to the past or the future, like super-speed for example. Any damage taken or mistakes that were made are irrelevant in the presence of these ten powerful superheroes who can defeat their enemies and right their wrongs by going forward and backward through time.

The fastest man in the DC universe, Barry Allen —  The Flash is so quick that he is capable of traveling through time. That gives him the power to alter timelines  just like in the Flashpoint story in order to restore the world to its normal state. Furthermore, he can even go beyond that and travel across what is known as hypertime — the stream of multiple timelines, which allows visitors to hop from one reality on to another.

9 Doctor Strange

The Doctor doesn't really need the Time Stone as shown in the MCU in order to time travel. The Master of the Mystic Arts is capable of manipulating time without it, in a variety of ways through his formidable magical capabilities . Strange is able to stop time, slow it down or he can just travel to the past or the future. Despite his remarkable skills, he still requires a significant amount of concentration in order to pull this particular trick off.

Young Superman , back in the Silver Age of comics, was able to travel through time. His later, more grounded version, was deprived of that skill probably so that his opponents can be more of a threat to him.

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The less experienced Clark Kent, however, known as Superboy during the Pre-Crisis period was just a casual time-traveler who could simply move faster than light, affect his past and future self and occasionally, take people with him for the ride.

Rina Patel discovered her one and only power by accident, which started her on an adventure that led the unsuspecting college student to the New Warriors. Timeslip can travel to the future or the past and manipulate time in basically every other way. If Patel wants to be faster than a foe, she slows time down. If she wants to fast-forward to a moment in the future, Rina simply speeds it up. This ability also allows her to be super fast (in the eyes of others).

Nathan Summers can manipulate timelines through his psionic powers. Cable is able to transport himself as well as other individuals to any point in time and he can stay there temporarily (from a few minutes to years).

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Summers is also capable of going through this special type of travel in his astral form (his spirit detached from his body). Although Nathan used the ability once and it was extremely difficult, there is no certain proof that he is incapable of doing it again.

Nathaniel Richards (Iron Lad) from Marvel's Other Earth (Earth - 6311) brought peace to this particular version of the planet and its history after arriving through time-travel. His armor is quite similar to Tony Stark's and shares many of his Iron Man suit's features . The one difference is that Iron Lad's armor allows him to create temporal divergences, which let him manipulate time and travel through it. Richards also has a ship featuring that same ability.

DC's Godspeed can travel through time with the assistance of Barry Allen's Cosmic Treadmill. The device allows August Heart to jump into the timestream and move to whatever point in the past or the future he prefers. All of that is possible because of his Speed Force connection that grants him a number of other superhuman abilities such as enhanced stamina, strength, reflexes, healing and dimensional travel.

Bishop is a mutant of considerable talents and he is a master of energy absorption but one other very special ability of his is time travel. The member of the X-men is a capable time-traveler because of the Forge cybernetic arm that Bishop claimed as a replacement of his lost limb.

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The prosthetic is equipped with a technology, which allows Lucas to time-jump and move so quickly that he appears to be super-fast to the individuals that surround him.

2 Booster Gold

This particular DC superhero doesn't have any special powers of his own - his strength is derived from the artifacts that he stole from a future museum. Gold's power suit makes him quite a formidable being. One of its many uses is the so-called Time-travel circuitry or Chronokinesis, which is more or less the upgraded version of time travel since it also allows the user to manipulate the timestream from a distance.

1 Green Lantern

The Green Lantern Power Ring grants the wearer with many abilities but one of the most powerful and yet, somehow less popular ones is time travel. Naturally, more willpower is required for farther trips into the future. Hal Jordan, in particular, has definitely proved his mental toughness and spiritual resilience since he has successfully explored as far as the 70th century. Also, the Power Ring allows the Lantern to communicate with other individuals that are from a different point in time.

NEXT: DC: 10 Superheroes Who Were Given Their Powers  

The Top 10 Time-Travelers in the Marvel Universe

The past, present, and future have nothing on these characters who have rewritten the rules of time.

You may think of time as a one-way boulevard or a two-way express lane, but the Marvel Universe’s definition is quite different. Our concept of time is like a highway jam-packed with commuters, all shifting back and forth throughout the continuum of spacetime and the Multiverse itself.

While it seems like just about every major character has made a journey to the past (or future), several visitors from various Marvel timelines have traveled to Earth-616 and made a major impact. Here’s our roundup on the Marvel time-travelers who have left a mark on the prime Marvel Universe!

TWO-GUN KID

Since the beginning, the House of Ideas has made space for a variety of genres, including the fan-favorite Western. Series TWO-GUN KID originally saddled up in 1948 and came out sporadically for the next decade-plus showcasing Clay Harder's masked adventures. And, in 1962’s TWO-GUN KID #60 , the title's status quo got upended by introducing Matt Hawk who trained in the ways of the gunfighter and took the name Two-Gun Kid from dime store novels he read (presumably starring Clay Harder). He then went on to have his own adventures, becoming one of the Wild West's most prominent do-gooders.

He and other Western heroes were stunned to find their era visited by Kang the Conqueror , Immortus , Thor , and Moondragon in AVENGERS (1963) #141-144 . After helping the future heroes, Two-Gun asked them to bring him to the future, which they did. Becoming an Avengers reservist, he and Hawkeye: Clint Barton palled around together, but he returned to his home time in AVENGERS #175 after being kidnapped by the Collector .

Back in the Wild West, he assisted an offshoot of his old squad in WEST COAST AVENGERS (1985) #18-23 , dealt with Kang's forces again in AVENGERS FOREVER (1998) , and fought Loki with King T'Challa in BLACK PANTHER (1998) #46-48 . Then, in SHE-HULK (2005) #4 , he returned to the present when She-Hulk requested the Time Variance Authority free him from Limbo. He kicked around for quite a while after that, even getting involved in the first Super Hero Civil War .

THE (ORIGINAL) GUARDIANS OF THE GALAXY

Today the Guardians of the Galaxy might be well-known for members like Star-Lord , Gamora , Groot , and Rocket , but when the original squad debuted in MARVEL SUPER-HEROES (1967) #18 , the team looked totally different. That issue introduced the world to Charlie-27 , Martinex , Yondu and “ Major Victory ” Vance Astrovik. The quartet came together in the year 3007 on Earth-691 to combat the Brotherhood of the Badoon invasion of the United Lands of Earth.

While they would eventually go on to star in their own self-titled series that spanned 62 issues , the Guardians made a variety of guest appearances. Having met Captain America , the Thing , and Agent 13: Sharon Carter in MARVEL TWO-IN-ONE (1974) #5 , they appeared in the present in GIANT-SIZE DEFENDERS (1974) #5 . In addition to helping the title team deal with Eelar, a young Vance Astrovik met the team he would eventually join, including his future self!

The Guardians continued to appear in DEFENDERS (1972) #26-29 , though Doctor Strange noted that the coexistence of Vance's younger and older selves was causing problems in the timestream. To fix the issue and help their new companions, the Defenders transported the Guardians to their home time and helped them free the humans to defeat the Badoon on Earth.

Later, the Guardians met with a new group of Earth's Mightiest Heroes to combat Korvac , a villain from their own time period who had attained godlike powers. Throughout the “Korvac Saga” in AVENGERS #167-181 , the Guardians fought valiantly to save the past. Before heading home, they fought alongside Carol Danvers , Spider-Man , and the Thing in MS. MARVEL (1977) #23 , MARVEL TEAM-UP (1972) #86 and MARVEL TWO-IN-ONE (1974) #69 respectively.

Speaking of Korvac: This time-traveler has threatened reality on a variety of occasions! In the aforementioned “Korvac Saga,” he traveled from the future of Earth-691 to Earth-616, but before that, Michael Korvac betrayed humanity to the Badoon who later cut off his legs and fused him to a hovering computer module. Seeking revenge, he decided to take over the Badoon empire, but was first brought to the present by Elder of the Universe Grandmaster in GIANT-SIZE DEFENDERS (1974) #3 . Using his machinery’s ability to absorb energy, he syphoned off some of the Grandmaster’s power, which allowed him to travel through time on his own.

Returning to the present, Korvac visited Galactus ’ ship and managed to absorb some of the Power Cosmic, which allowed him to restore his body and take control of all things. He eventually fought the Avengers and the Guardians but took his own life when he felt that his partner Carina lost faith in him.

Korvac came back in his own time-hopping mini-crossover called “The Korvac Quest” (playing out across FANTASTIC FOUR ANNUAL #24 , THOR ANNUAL #6 , SILVER SURFER ANNUAL #4 and GUARDIANS OF THE GALAXY ANNUAL #1 ), but was ultimately turned into a baby in the future. He has returned as an adult to the present several times, including in AVENGERS ACADEMY (2010) #11-12 . Members of the team accidentally transported Carina to their base which drew Korvac's attention. When she rebuked him, it led to a huge battle with all the Avengers involved!

Planning another attack, Korvac went back to Earth-616 and began slowly dismantling time. In GUARDIANS 3000 (2014) , the original Guardians felt it in their own time and went back to discover the cause: Korvac. His plans wound up falling apart because of the Incursions leading into SECRET WARS (2015) . After reality was put back together, he appeared regularly in IRON MAN (2020) and attempted to bring peace to Earth by ending all life. Thankfully, the Armored Avenger and his allies stopped Korvac once more.

OLD MAN LOGAN

More than most super-powered groups, the X-Men are no strangers to time-travelers joining their ranks. One of the more recent additions came from Earth-21923 , a world in which the villains worked together and manipulated Wolverine into killing the X-Men before dividing up the whole nation amongst themselves. Afterwards, Logan attempted to live a normal, non-violent life, but returned to action when an older Hawkeye needed help with a mission. Wolverine ultimately killed the Red Skull of his time but returned home to discover that his wife and children had been murdered by the Hulk Gang.

This “Old Man Logan” version of Wolverine wound up in the Earth-616 present after the entire Multiverse was rewritten during 2015’s SECRET WARS. Though he began a mission of preemptive vengeance almost immediately in the pages of OLD MAN LOGAN (2015) , he slowly allowed himself to be integrated into the larger X-Men family, taking the place of his past self who had died before his arrival. This more experienced, (more tragic) James Howlett regularly appeared in his own book as well as EXTRAORDINARY X-MEN (2015) , X-MEN: GOLD (2017) , and WEAPON X (2017) .

During his time in the present, he met many of Earth’s heroes, and even participated in the Second Superhuman Civil War . In DEAD MAN LOGAN (2018) , the hero said his goodbyes in the present and returned to his future to live out the rest of his life.

KATE PRYDE (EARTH-811)

While many of the characters on this list have made several trips to the present, others managed to change the course of human history in just one journey. In the classic “Days of Future Past” story (1981’s UNCANNY X-MEN #141-142 ), readers were introduced to Earth-811, a possible future in which Senator Robert Kelly, Charles Xavier , and Moira MacTaggert were killed by mutant terrorists on Halloween 1980.

That attack prompted the government to unleash the Sentinels and create three designations for living beings: H (baseline humans), A (anomalous humans), and M (mutants). The mutants that were not killed were placed in concentration camps, but that did not destroy their hope to change the past.

Working with her fellow alternate future X-Men, Kate managed to send her consciousness back to 1980 to inhabit the body of her younger self, Kitty Pryde . She got the attention of the X-Men and explained the future to them, noting that they could fix the whole thing by going to Washington, D.C. to prevent the assassination. They did exactly that by stopping Mystique and the Brotherhood of Mutants . Not bad for a one-time time-traveler!

With origins in yet another future where mutants were rounded up and imprisoned ( Earth-1191 ), Lucas Bishop became a member of the X.S.E. (Xavier Security Enforcers) AKA the mutant police. During one mission he was chasing Trevor Fitzroy , a rebel-turned-criminal mutant whose powers allowed him to travel through time. Bishop wound up in the present as seen in UNCANNY X-MEN #282-283 , and although both of his X.S.E. partners were killed, he succeeded in sending his quarry Fitzroy back to the future. Though initially uneasy of the X-Men, Bishop decided to stick around with the team in hopes of stopping the event that triggers his future.

During his time in the present, Bishop went on scores of missions with the X-Men, but he became incredibly important during the AGE OF APOCALYPSE event as the catalyst for returning everything to the way it had been before Charles Xavier was killed by a time-traveling Legion .

Further down the line, Bishop found himself at the heart of the “Messiah Complex” crossover which featured a variety of factions trying to track down the first mutant born since HOUSE OF M , Hope Summers . Bishop revealed that, in his timeline, this “mutant messiah” would kill one million humans. To that end, he fought against many of his old teammates—including fellow time-traveler Cable —to kill the child Hope. Bishop eventually saw the error of his ways and has since made amends with his fellow X-Men.

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On the island of Krakoa , Bishop became an inaugural member of  Kate Pryde’s  Marauders, and added Red Bishop  of the Hellfire Trading Company to his resume. He was also one of Krakoa’s  Great Captains , established by the  Quiet Council of Krakoa . Then, in  INFERNO (2021) #1 ,  Cyclops  stepped down from the position of Captain Commander, the leader of all Great Captains, and promoted Bishop to the role.

SPIDER-MAN 2099

Back in 1992 , Marvel launched a forward-looking lineup of series that took place in the year 2099, a not-so distant alternate future of Earth-616. Miguel O’Hara was 2099’s Wall-Crawler, carrying on Peter Parker's legacy of arachnid heroics in SPIDER-MAN 2099 (1992) . Though there were a few meetings between the 2099 and Earth-616 Spidey, Miguel did not travel back to the prime reality for a long period of time until SUPERIOR SPIDER-MAN (2013) #17 . During that time, Miguel was not only stranded in the past , but encountered Otto Octavius in the body of Spider-Man!

Taking on the identity of Michael “Mike” O’Mara, Miguel began working for Alchemax, the company that were a critical part in his life circa 2099. Down the line, Spider-Man 2099 has played major roles in the multiversal SPIDER-VERSE and SPIDER-GEDDON events, helping to save not just the present reality, but countless others too.

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THE GOD(S) OF THUNDER

To battle the threat of Gorr the God Butcher , God of Thunder Thor needed all the help he could acquire in fan-favorite series THOR: GOD OF THUNDER (2012) . So, who better to recruit than versions of himself?

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To cut off the source of Gorr’s universal god-killer “the Godbomb,” the past’s “Young Thor” and the future’s “King Thor” collaborated with the present Odinson. These three cross-time Thors were also assisted by King Thor’s granddaughters Frigg , Ellisiv and Atli all of whom worked together to save godhood.

The three goddesses would later travel back via Time Diamonds to meet the legendary Jane Foster after her initial stint as Thor . Though they took her flying, they did not tell her about the epic story ahead in the WAR OF THE REALMS event, at the end of which the Fantastic Four used Doctor Doom’s Time Platform to recruit King Thor and Young Thor to end the conflict. WAR OF THE REALMS also resurrected Jane as Thor once more.

THE ENTIRE SUMMERS FAMILY

Warning: The Summers-Grey kids know how to alter a timeline.

Thor and his selves get around the time stream regularly, but not nearly as much as the Summers’ mutant family. Dad Cyclops alone has traipsed through time on a variety of occasions, so let’s start with that. As a kid, he and his fellow original X-Men traveled to the present as versions of their younger selves in ALL-NEW X-MEN (2012) . And don't forget about the time that he and his wife Jean Grey took a trip several thousand years into the future in ADVENTURES OF CYCLOPS & PHOENIX (1994) to save Scott’s son Nathan Summers, AKA Cable.

Oh, and remember Kate Pryde from the “Days of Future Past” timeline? Well, she's not the only one from that future who came to the present. Kate was followed by Rachel Grey/Summers —the daughter of that era's Scott Summers and Jean Grey—who had telepathic powers like her mother, but had been turned into a mutant-hunting Hound following the destruction of Xavier’s School for Gifted Youngsters. After Kate’s mission to the past, Rachel eventually made contact with the Phoenix Force which allowed her to physically, not just mentally, travel to the present of Earth-616 in UNCANNY X-MEN #184 . Since then, Rachel has allied herself with Xavier's other students and teams, defending the denizens of the present for years, now under the codename Prestige.

But it’s son of Cyclops, Cable—whose mother is Madelyne Pryor , a Mister Sinister -created clone of Jean Grey—that has made his way through time more often than even his half-brother X-Man . Following Nathan’s birth in UNCANNY X-MEN #201 , Apocalypse infected the infant with a techno-organic virus that threatened his life ( X-FACTOR #65-68 ). To save his son, Cyclops agreed to let Sister Askani, a member of a religious anti-Apocalypse cult, take the child to the far future where they could better manage baby Cable’s affliction.

The Clan Askani saved Nathan's life but could not fully cure him of the virus. When he was still a child, the mysterious “Slym and Redd” stepped in to raise him. Though Cable didn’t know it at the time, this couple was a temporally displaced Scott and Jean. While Scott and Jean returned to their present in ADVENTURES OF CYCLOPS & PHOENIX #4 , the boy grew to become an incredibly resourceful soldier of the future. Though a younger version of him did come to the present in X-FORCE (2018) , the most well-known version of the man known as Cable debuted in NEW MUTANTS (1983) #87 , though he would not reveal his history, or connection to the Summers family, for some time.

Since then, Cable has been involved in just about every major X-event. He was at the forefront of defeating his own time-traveling clone Stryfe in the “X-Cutioner's Song” storyline , and also ensured Hope Summers’ survival during “Messiah Complex” and throughout CABLE (2008) . Hope Summers not only represents the reinvigoration of the mutant race, but as a member of The Five , she's an integral part of the mutant resurrection process, making her one of the most important beings in the continuation of Krakoa.

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KANG…ALL OF THEM

If you had to take notes to keep track of some of these temporally adventurous individuals, now's the time to break out the cork board, red string, and pushpins because Kang’s got them all beat! Born to Earth-6311, a reality in which humanity evolved to the point where peace reigned supreme, a man named Nathaniel Richards—related to either present-day Reed Richards or Doctor Doom —grew bored and desired conquest.

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To that end the conquering Nathaniel built his own time ship which was stocked with future tech and traveled to Ancient Egypt where he took on the identity of Pharoah Rama-Tut in FANTASTIC FOUR (1961) #19 . While in that era, he encountered many heroes traveling from Earth-616’s present. However, after surviving a time storm, “Rama-Tut” decided to switch things up by becoming the Scarlet Centurion ! Those attempts to destroy Earth's Mightiest Heroes early in their tenure—as seen in AVENGERS ANNUAL (1967) #2 —proved a failure.

Leaving that identity behind, Richards became Rama-Tut once more, but overshot his home in the 30th century and wound up in the far more dangerous 40th century where he took on the name Kang the Conqueror , the character who debuted in AVENGERS (1963) #8 . Thus began Kang’s recurring attempts to defeat the heroes of the present. Though he has come close several times—like during the “Kang War” story in AVENGERS (1998) #38-55 —the Conqueror has never truly lived up to his name, though it appears that he never stops trying just like the interminable march of time.

But not all Kangs are bad. (And thanks to parallel and offshoot timelines there are plenty.) In one unusual blip of the timestream, a teen version of Kang, Iron Lad , traveled back to the present and became a founding member of the Young Avengers . He even succeeded in killing his older self, but that led to a time storm of epic proportions, so much so that Iron Lad undid the murder and returned to his proper period, knowing he’d eventually become the corrupted Kang.

But as readers have learned over the years, “Kang” isn't even this character's endpoint. The Lord Immortus —who first appeared in AVENGERS #10 —pops up from time to time to mix it up not only with the heroes of the present, but also with Kang himself. (As seen in tales like “ Celestial Madonna ” and “ Destiny War .”) You'd be surprised how many times Kang has tussled with himself and the wild results—but that doesn't stop the Kangs from interfering with each other’s intricate plots for power!

Regardless of which variant of Kang we’re talking about, no character has traversed time as often and as freely. And while these stories take place across the expansive Marvel Multiverse including all of time and space, they can all be read in one place: the Marvel Unlimited app !

To read your Marvel comics digitally, download the  Marvel Unlimited app  for  iOS  and  Android  devices. Gain an expansive catalog of 30,000+ comics spanning Marvel Comics history, plus access your entire digital library including comics redeemed from print.  

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Have Powers, Will (Time) Travel: Superheroes and the Urge to Change the Past

Eileen Gonzalez

Eileen's primary literary love is comic books, but she’s always on the lookout for her next literary adventure no matter what form it takes. She has a Bachelor's in media studies, a Master's in digital communication, a smattering of published short stories, and a seriously cute dog. Follow her on Bluesky .

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In Alex Segura’s YA novel Ara ñ a and Spider-Man 2099: Dark Tomorrow , Anya/Araña is on the trail of a stolen artifact when said artifact unexpectedly blasts her into the early 22nd century. There, she meets Miguel, the former Spider-Man 2099, who is no stranger to time travel. But Miguel gave up being a hero after traumatic personal losses, and it will take the gravest crisis imaginable to convince him to put on his costume and be a hero one more time.

Since time travel is integral to the plot, reading this novel got me thinking about the different ways time travel has appeared in superhero stories — some good, some bad. Along the way, Segura was kind enough to answer my questions about Dark Tomorrow and time travel stories in general. If you care about spoilers, read freely: there are none here — at least, none for Dark Tomorrow .

Just a Jump to the Left…

Time travel stories predate comics by at least several decades. Encyclopedia Britannica cites books like H.G. Wells’s The Time Machine and even Charles Dickens’s A Christmas Carol as early classics in the genre. The Time Machine was adapted as a comic book in the Classics Illustrated series, which Segura cited to me as a story that resonated with him as a young reader.

“I love [time travel stories], honestly,” he said. “The idea of hopping around time has always been of interest”

It has also been a part of the superhero experience since the early days. In the 1940s, Batman traveled back in time to pal around with D’Artagnan and the Three Musketeers in Batman #32 and into the near future to show what the world might be like if the Nazis were to win World War II in Batman #15. (Granted, this last one was less a story and more an attempt to scare the audience into buying war bonds.)

Time travel became a common plot device in the 1950s and ’60s, when stringent self-censorship precluded more violent kinds of stories. That’s how we got nonsense like Action Comics #148, in which Superman travels back in time to cheat Indigenous people out of the land Metropolis sits on, and Green Lantern #8, in which Hal Jordan is drafted into fighting villains in the 58th century because humans of the future are too pathetic to do it themselves (but not too pathetic to kidnap a 20th-century man and give him amnesia).

But there were more serious stories too. In the poignant yet retroactively hilarious Avengers #56, Captain America traveled back to the 1940s to convince himself that his sidekick Bucky was really dead. (Bucky was not, in fact, dead.)

This versatility is part of what draws Segura to time travel stories: they “can range from the funny to the painfully emotional,” he told me, “and I love the idea of affecting your own future or going back in time to see what things were like. The story possibilities are endless.”

As superheroes made their way into other genres, they took their tales of time travel with them. An episode of Freakazoid! has the titular hero prevent the Pearl Harbor attack, which somehow results in Rush Limbaugh becoming a decent person. In his 1978 film, Superman reverses the Earth’s rotation, which also reverses time and allows him another chance to save Lois Lane. (It goes without saying that that’s not how science works , but okay, fine.)

And then there’s the star of The CW’s The Flash , Barry Allen. Oh, Barry. Damn it, Barry .

With Great Power Comes Great Irresponsibility

The Flash may be more closely associated with time travel than any other hero (which I’m sure upsets Booster Gold, a 25th century ne’er-do-well who traveled to our time to become a heroic gloryhound). Early on, he learned he could travel through time by running on the Cosmic Treadmill. Some of his biggest foes — Reverse-Flash and Abra Kadabra — and his closest allies — his wife Iris West and their grandson Bart Allen — come from the future. Barry would later abuse his ability to time travel in both the comic Flashpoint and the TV show The Flash , when he rewrote all of reality to bring his murdered mom back to life.

This storyline is where I started to view time travel tales differently. Even more than Ray Bradbury’s A Sound of Thunder , this is the story that made me realize the ethical pitfalls of time travel.

Unlike Eckels, the hapless protagonist of Bradbury’s classic story — or even grief-stricken Superman impulsively reversing the Earth’s rotation by a couple of minutes — Barry Allen makes a conscious decision to change the past. As Reverse-Flash gleefully puts it, “You traded the life of your mother for the rest of the world!”

And Barry’s action is not without consequences. In both the comic and the TV show, the lives of Barry’s friends turn out vastly different — and sometimes worse — than how they were before.

As Segura points out, consequences are another reason that time travel makes for such a fascinating subject. In particular, he cited the “emotional stakes” — the inevitability of revisiting painful events or dead loved ones, or of seeing future events you may not like — as being especially high and therefore especially interesting. I can certainly agree, but personally, I have trouble sympathizing with a supposedly heroic character who willingly (and, in the TV show, more than once) messes with something as dangerous as time because he can’t handle being sad or accept his mistakes.

Obviously, Barry has the right to be upset over his mother’s death, even years after the fact. But you don’t get to ruin countless lives just because you can (it seems unlikely that Barry’s friends are the only ones who got screwed over, out of all the billions of people in the world). He allows his grief to make him selfish, even villainous. Who else but a villain tries to remake the world as they see fit? Go to therapy like the rest of us, bud.

Fortunately, Dark Tomorrow is more judicious in its use of time travel: Anya doesn’t do it on purpose, and Miguel only did so when the world was in danger. But Segura acknowledges that Miguel’s pain, much like Barry Allen’s, could have driven him down a darker path.

“[I]t’d be weird if he wasn’t” tempted to go back in time and prevent his personal tragedies from occurring, Segura says. “But I think one of the lessons Miguel learned early on was the fragility of time travel, and how the timeline tends to right itself or protect itself against major attempts to alter it….At his heart, Miguel is a scientist, and has probably grappled with these questions regularly when caught up in his time travel adventures!”

In other words, the heroes of Dark Tomorrow are not trying to remake the world in their image, so to speak. They’re just trying to save it, and in the process of doing so, they could end up changing a few things — probably for the better, but who knows what tomorrow will bring?

In the Not-Too-Distant Future…

So why do we still like all these time travel tales? Or, in my case, all of these tales except for those starring Barry Allen?

I think it’s a combination of everything I’ve covered: it’s high-stakes, it’s emotional, and it’s just plain fun. The appeals and temptations of time travel may be stronger for a superhero than for your average character, making for even richer storytelling. Righting wrongs is the superhero’s main reason for existing. If presented with the chance to use time travel to fix past mistakes, they’re sure to feel pressure to do so — and, in some cases, succumb to that pressure.

In Dark Tomorrow , the time travel is in part a simple necessity: Araña and Spider-Man 2099 exist a century apart, so the only way that they — Marvel’s two Latine Spider-people — could go adventuring together is through time travel shenanigans. But Segura believes it serves another purpose: to compare two very different worlds with surprisingly similar problems.

“Miguel’s Nueva York might seem shinier and more convenient than our New York, but as we dig deeper, we see some of the same problems crop up — and some of the same class issues and social situations,” Segura says. “It really helps hammer home the theme that you can be a hero whenever you are, and it takes the same kind of passion, dedication, and sacrifice.”

By opening a door to the past — or the future — time travel stories don’t just entertain us: they teach us the critical lesson that people are people, no matter where or when they were born.

For more time travelin’ superheroes, check out these lists about heroes wrecking the timestream and getting stuck in the past !

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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.

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 time . You do it whether you want to or not, at a steady rate of one second per second. You may think there's no similarity to traveling in one of the three spatial dimensions at, say, one foot per second. But according to Einstein 's theory of relativity , we live in a four-dimensional continuum — space-time — in which space and time are interchangeable.

Einstein found that the faster you move through space, the slower you move through time — you age more slowly, in other words. One of the key ideas in relativity is that nothing can travel faster than the speed of light — about 186,000 miles per second (300,000 kilometers per second), or one light-year per year). But you can get very close to it. If a spaceship were to fly at 99% of the speed of light, you'd see it travel a light-year of distance in just over a year of time. 

That's obvious enough, but now comes the weird part. For astronauts onboard that spaceship, the journey would take a mere seven weeks. It's a consequence of relativity called time dilation , and in effect, it means the astronauts have jumped about 10 months into the future. 

Traveling at high speed isn't the only way to produce time dilation. Einstein showed that gravitational fields produce a similar effect — even the relatively weak field here on the surface of Earth . We don't notice it, because we spend all our lives here, but more than 12,400 miles (20,000 kilometers) higher up gravity is measurably weaker— and time passes more quickly, by about 45 microseconds per day. That's more significant than you might think, because it's the altitude at which GPS satellites orbit Earth, and their clocks need to be precisely synchronized with ground-based ones for the system to work properly. 

The satellites have to compensate for time dilation effects due both to their higher altitude and their faster speed. So whenever you use the GPS feature on your smartphone or your car's satnav, there's a tiny element of time travel involved. You and the satellites are traveling into the future at very slightly different rates.

But for more dramatic effects, we need to look at much stronger gravitational fields, such as those around black holes , which can distort space-time so much that it folds back on itself. The result is a so-called wormhole, a concept that's familiar from sci-fi movies, but actually originates in Einstein's theory of relativity. In effect, a wormhole is a shortcut from one point in space-time to another. You enter one black hole, and emerge from another one somewhere else. Unfortunately, it's not as practical a means of transport as Hollywood makes it look. That's because the black hole's gravity would tear you to pieces as you approached it, but it really is possible in theory. And because we're talking about space-time, not just space, the wormhole's exit could be at an earlier time than its entrance; that means you would end up in the past rather than the future.

Trajectories in space-time that loop back into the past are given the technical name "closed timelike curves." If you search through serious academic journals, you'll find plenty of references to them — far more than you'll find to "time travel." But in effect, that's exactly what closed timelike curves are all about — time travel

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There's another way to produce a closed timelike curve that doesn't involve anything quite so exotic as a black hole or wormhole: You just need a simple rotating cylinder made of super-dense material. This so-called Tipler cylinder is the closest that real-world physics can get to an actual, genuine time machine. But it will likely never be built in the real world, so like a wormhole, it's more of an academic curiosity than a viable engineering design.

Yet as far-fetched as these things are in practical terms, there's no fundamental scientific reason — that we currently know of — that says they are impossible. That's a thought-provoking situation, because as the physicist Michio Kaku is fond of saying, "Everything not forbidden is compulsory" (borrowed from T.H. White's novel, "The Once And Future King"). He doesn't mean time travel has to happen everywhere all the time, but Kaku is suggesting that the universe is so vast it ought to happen somewhere at least occasionally. Maybe some super-advanced civilization in another galaxy knows how to build a working time machine, or perhaps closed timelike curves can even occur naturally under certain rare conditions.

This raises problems of a different kind — not in science or engineering, but in basic logic. If time travel is allowed by the laws of physics, then it's possible to envision a whole range of paradoxical scenarios . Some of these appear so illogical that it's difficult to imagine that they could ever occur. But if they can't, what's stopping them? 

Thoughts like these prompted Stephen Hawking , who was always skeptical about the idea of time travel into the past, to come up with his "chronology protection conjecture" — the notion that some as-yet-unknown law of physics prevents closed timelike curves from happening. But that conjecture is only an educated guess, and until it is supported by hard evidence, we can come to only one conclusion: Time travel is possible.

A party for time travelers 

Hawking was skeptical about the feasibility of time travel into the past, not because he had disproved it, but because he was bothered by the logical paradoxes it created. In his chronology protection conjecture, he surmised that physicists would eventually discover a flaw in the theory of closed timelike curves that made them impossible. 

In 2009, he came up with an amusing way to test this conjecture. Hawking held a champagne party (shown in his Discovery Channel program), but he only advertised it after it had happened. His reasoning was that, if time machines eventually become practical, someone in the future might read about the party and travel back to attend it. But no one did — Hawking sat through the whole evening on his own. This doesn't prove time travel is impossible, but it does suggest that it never becomes a commonplace occurrence here on Earth.

The arrow of time 

One of the distinctive things about time is that it has a direction — from past to future. A cup of hot coffee left at room temperature always cools down; it never heats up. Your cellphone loses battery charge when you use it; it never gains charge. These are examples of entropy , essentially a measure of the amount of "useless" as opposed to "useful" energy. The entropy of a closed system always increases, and it's the key factor determining the arrow of time.

It turns out that entropy is the only thing that makes a distinction between past and future. In other branches of physics, like relativity or quantum theory, time doesn't have a preferred direction. No one knows where time's arrow comes from. It may be that it only applies to large, complex systems, in which case subatomic particles may not experience the arrow of time.

Time travel paradox 

If it's possible to travel back into the past — even theoretically — it raises a number of brain-twisting paradoxes — such as the grandfather paradox — that even scientists and philosophers find extremely perplexing.

Killing Hitler

A time traveler might decide to go back and kill him in his infancy. If they succeeded, future history books wouldn't even mention Hitler — so what motivation would the time traveler have for going back in time and killing him?

Killing your grandfather

Instead of killing a young Hitler, you might, by accident, kill one of your own ancestors when they were very young. But then you would never be born, so you couldn't travel back in time to kill them, so you would be born after all, and so on … 

A closed loop

Suppose the plans for a time machine suddenly appear from thin air on your desk. You spend a few days building it, then use it to send the plans back to your earlier self. But where did those plans originate? Nowhere — they are just looping round and round in time.

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24 Reasons Time Travel is the Ultimate Superpower

March 5, 2019 by Roy Huff

Hollywood has finally caught on with the Flash, Timeless, Frequency, and DC’s Legends of Tomorrow, but they’re only scratching the surface.

It took confronting a rabid pit bull in middle school to understand the awesomeness of superpowers and how not having them sucks when you’re in a bind.

Imagine staring down a beast foaming at the mouth, not knowing if it would chase you down and infect you with an insidious disease that drives you mad until you succumb to a horrible death. Fortunately, in this case, the only superpower I needed was patience to wait for animal control.

But all superpowers aren’t created equal. With all due respect to Scientologists’ who revere powers like  auditing  and the ability to hold one’s need to use the restroom, time travel is in a league of its own.

I don’t mean the limited power depicted in most fiction. I’m talking about time travel that avoids the nonsense of the paradox and encompasses slowing time, freezing time, looping time, and moving backward and forward through time at will.

And don’t let some content editor block you with a mysterious force that prevents you from changing too much just because he thinks it’s bad fiction or gives the protagonist too much power. It’s all or nothing, baby. Yes, it’s totally awesome, and you know it. In case you’re not convinced, try these reasons on for size.

Kill Hitler (or Any Other Ruthless Dictator) and See What Happens

Screw the consequences. And don’t tell me Hitler made the world a better place for some sick, twisted reason. Yes, the world would be totally different, but I’d bet it would be a very interesting and good different. Why not find out?

Cream the Kid Who Picked on You in School

If you’ve ever been bullied, you’ll appreciate this one. A few time loops will make you poetic with your jabs and punches, or you could just have a little fun and put them in an awkward position when time resumes at normal speed.

Ace Any Test

If you can’t get an A with the ultimate cheat sheet, it’s time to move on.

Try Out Different Lines on a Prospective Date Until One Works

50 First Dates  comes to mind, as does  Groundhog Day  (my personal favorite). But there’s so much to work with. Who wouldn’t want to know the most beautiful thing to say to that perfect person they’ve always wanted to impress?

Make a Ton of Cash

It’s so obvious, yet so many time travel stories don’t bother to make the most of this storyline. If you controlled time, how would you make a ton of cash? So many possibilities here:

Win the lottery, a hand at poker, or name your gambling vice. Play the stock market. Invest in real estate. Discover hidden loot, buried trinkets, lost relics, and sunken ships. The list is endless.

Invent Gadgets From the Future

Another personal favorite, but I digress. Why not accelerate things a bit? For the environmentally conscious, here’s an excellent way to make alternative energy a cheap efficient reality. Or invent a way to upload information to your brain. While you’re at it, throw in a holodeck and some replicators.

Save Books From the Library of Alexandria (Then Read Them All)

Bibliophiles rejoice! Even lovers of poetry and literary fiction should jump on the sci-fi bandwagon for this one,  seriously ! You’ll need to bring a translator, or at least a souped up version of Google Translate. The payoff would be enormous.

Rip Mega Hits From the Future

You may not sound as good, but then again, talent is overrated. It’s not stealing if it hasn’t been invented yet, so ignore the naysayers who complain about the ethics. If it’s fame you desire, this option is a must.

Find out if Your Significant Other is a Cheater

If you have suspicions, they probably are. But if you’ve just started dating, save yourself the headaches and skip ahead.

Buy the Perfect Gift

If you’ve found that perfect love, you know finding the perfect gift can be equally as hard. Those initial facial expressions don’t lie.

See What Happens to Your Kids

For maximum impact, foresight is necessary. Maybe your kid should study art. Find out now if that safe career path makes them miserable or that speed takes them to the Olympics  or prison .

Prevent the Death of Millions Before Natural Disasters

Even time travel stories constrained by the paradox should jump on this one. The butterfly effect may change most things, but natural disasters will outlast most storms of change. What could be better than saving thousands of lives from earthquakes and tsunamis?

Get the Appreciation you Know you Deserve

It’s okay to indulge every once in a while. Who wouldn’t want to know what those accolades from your boss, friends, or significant other will look like? It will save a heck of a lot of time if you discover you need to move on. Just make sure your clicker doesn’t share the same memory feature as Adam Sandler’s.

Change the Outcome of Elections

Whether you’re a Democrat, Republican, Tory, or Liberal, I’m sure there’ve been winners you’d like to see get crushed. Time travel takes opponent research to the next level. Have fun with it.

Visit Your Own funeral

Avoiding death is obvious, but a more practical reason is discovering who attends your funeral. Don’t waste any more time caring what people think if they don’t bother to show up. Life’s too short.

Visit the End of Civilization (if it Ever Comes)

Call me an optimist. I’m still planning on hopping into a cryo chamber by the  Alcor Life Extension Foundation  and hitching a ride to the future. Therapeutic cloning, gene modification, and singularity may extend life well beyond the realms of modern science. 

If we’ve survived this long, what’s a few more billion years? Yes, maybe we’ll all look like Lady Cassandra from  Doctor Who , but I think mankind will survive longer than most envision,  Skynet  be damned.

Visit the Death of the Universe

Our universe will eventually die. Everything down to the subatomic particles will be ripped apart as the expansion of the universe throttles at breakneck speeds. It may be boring to watch, but why not?

Prevent the Death of the Universe

If you can visit, why not stop it? You could do it the hard way by changing the laws of physics, like the Q in  Star Trek TNG . Or, you could do it the “easy” way by creating a stable wormhole to a parallel universe and hitching a ride.

Accelerate the Progress of Scientific Theories

Don’t know how to make a stable wormhole? No worries! A few hundred thousand time loops will do the trick, or you could just jump a century or two in the future and read the Cliff notes version.

Prove Once and for all What Happened in the Beginning of Time

After you’ve visited the end, take a trip to the beginning.

Hang Out With Jesus

I’m sure hanging out with JC would be a lot cooler than most people realize. Besides, good friends are hard to come by.

Empty Your Netflix Queue

I saved the best for last. I remember when this didn’t take that long, but since the advent of original content and A+ acquisitions, there’s never enough screen time.  

Originally posted on Geeks Media

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The Science of Mental Time Travel and Why Our Ability to Imagine the Future Is Essential to Our Humanity

By maria popova.

Lewis Carroll’s Alice in Wonderland remains one of my all-time favorite books , largely because Carroll taps his training as a logician to imbue the whimsical story with an allegorical dimension that blends the poetic with the philosophical. To wit: The Red Queen remembers the future instead of the past — an absurd proposition so long as we think of time as linear and memory as beholden to the past, and yet a prescient one given how quantum physics (coincidentally, a perfect allegorical exploration of Wonderland ) conceives of time and what modern cognitive science tells us about how elastic our experience of time is . As it turns out, the Red Queen is far more representative of how human memory actually works than we dare believe.

“To be human,” writes Dan Falk in In Search of Time: The History, Physics, and Philosophy of Time ( public library ), “is to be aware of the passage of time; no concept lies closer to the core of our consciousness” — something evidenced by our millennia-old quest to map this invisible dimension . One of the most remarkable and evolutionarily essential elements of experiencing time through human consciousness is something psychologists and cognitive scientists call mental time travel — a potent bi-directional projection that combines episodic memory , which allows us to draw on our autobiographical experience and call up events, experiences, and emotions that occurred in the past, with the ability to imagine and anticipate future events. Falk puts it unambiguously:

Without it, there would be no planning, no building, no culture; without an imagined picture of the future, our civilization would not exist.

As it turns out, episodic memory — a term coined in the early 1970s by Canadian neuroscientist Endel Tulving, author of the seminal book Elements of Episodic Memory — is central to our capacity for mental time travel and, according to many scientists, fairly unique to humans. Unlike other facets of memory, such as the acquisition of new skills, which are rooted in the here-and-now, Falk points out that episodic memory allows us “to peer back across time, using our imagination to revisit just about any event that we choose.” This mental reliving of the past may be the root of some distinct human maladies — take the wistful reminiscence over a lost love, for instance — but it is also central to our evolutionary survival, allowing us to anticipate future outcomes based on past ones and thus to plan better and be more prepared for what tomorrow may bring. (The dark side of this evolutionarily beneficial faculty is that our over-planning often ends up shortchanging our happiness .)

And yet the benefits outweigh the costs, in evolutionary terms. Falk explains:

The capacity for mental time travel gave our ancestors an invaluable edge in the struggle for survival. They believe there is a profound link between remembering the past and imagining the future. The very act of remembering, they argue, gives one the “raw material” needed to construct plausible scenarios of future events and act accordingly. Mental time travel “provides increased behavioral flexibility to act in the present to increase future survival chances.” If this argument is correct, then mental time travel into the past — remembering — “is subsidiary to our ability to imagine future scenarios.” Tulving agrees: “What is the benefit of knowing what has happened in the past? Why do you care? The importance is that you’ve learned a lesson,” he says. “Perhaps the evolutionary advantage has to do with the future rather than the past.” Modern neuroscience appears to confirm that line of reasoning: as far as your brain is concerned, the act of remembering is indeed very similar to the act of imagining the future.

Though we might not be able to “remember” the future, as the Red Queen does, we do envision it in ways strikingly similar to how we picture events from the past — Falk notes that fMRI studies indicate we use similar regions in the brain’s frontal and temporal lobes when thinking about events in either direction of time. What’s more, psychologists have found that much like it’s harder for us to remember an event in the distant past than a recent one, it’s harder for us to imagine an event in the distant future than one expected to take place soon. This hints at the massively misguided way in which we think of and evaluate memory, which we falsely depict as a recording device , versus foresight. Falk writes:

When we imagine the future, we know what we picture is really just an educated guess; we may be right in the broad brushstrokes, but we are almost certainly wrong in the details. We hold memory to a higher standard. We feel — most of the time — that our memories are more than guesses, that they reflect what really happened. When confronted with a conflicting account of how last week’s party unfolded, we cling to our beliefs: He must be mistaken; I know what I saw.

Falk cites the Harvard psychologist Daniel Schacter:

[The brain is] a fundamentally prospective organ that is designed to use information from the past and the present to generate predictions about the future. Memory can be thought of as a tool used by the prospective brain to generate simulations of possible future events… We tend to think of memory as having primarily to do with the past… And maybe one reason we have it is so that we can have a warm feeling when we reminisce, and so on. But I think the thing that has been neglected is its role in allowing us to predict and simulate the future.

In order to mentally time-travel into the future, the brain has to accomplish a couple of things at once — we activate our “semantic memory,” which encompasses our basic knowledge of facts about the world and thus helps paint a backdrop for the imagined scene, and we call on our episodic memory, which pulls on our autobiographical library of remembered experiences to fill in specific details for this general scene. Curiously, episodic memory tends to be rather flawed but, according to two scientists Falk quotes, that’s okay since its core purpose is to provide “a more general toolbox that allowed us to escape from the present and develop foresight, and perhaps create a sense of personal identity.”

To be sure, just like elsewhere in cognitive science , human exceptionalism may be misplaced here — scientists have found that other species are also capable of varying degrees of mental time travel. Falk cites one of the most intriguing experiments, involving scrub jays. He writes:

Psychologist Nicola Clayton and her colleagues housed the birds on alternate days in two different compartments — one in which the jays always received “breakfast,” and one in which they did not. Then the birds were unexpectedly given extra food in the evening, at a location where they could access either compartment. The jays promptly cached their surplus — and they preferentially cached it in the “no breakfast” compartment. Because the birds were not hungry at the time of the caching, the researchers claim that the birds truly anticipated the hunger they would experience the next morning.

Still, the fact that humans are capable of remarkably elaborate and detailed mental time travel reveals something unique about our evolution and the development of such hallmarks of humanity as language and theory of mind. Falk writes:

In all likelihood, the capacity for mental time travel did not develop in isolation but rather alongside other crucial cognitive abilities. “To entertain a future event one needs some kind of imagination,” [the prominent psychologists Thomas] Suddendorf and [Michael] Corballis write, “some kind of representational space in our mind for the imaginary performance.” Language could also play an important role. Our language skills embrace mental time travel by the use of tenses and recursive thinking; when we say “A year from now, he will have retired,” we’re imagining a future time in which some event — which has not yet happened — will lie in the past… Mental time travel may have been “a pre-requisite to the evolution of language itself.” If mental time travel is indeed unique to humans, it may help us understand why complex language is also, apparently, unique.

In fact, the development of mental time travel may even be how the concept of time itself came into existence — according to Suddendorf and Corballis, our species emerged victorious in “an extraordinary evolutionary arms race” largely due to our growing capacity for foresight and sophisticated language, which not only gave us culture and “coordinated aggression” but also, for the first time in evolutionary history, enabled us to understand the concepts of “past” and “future.” The mental reconstruction of what has been and the imagining of what could be, they argue, created the concept of time and enabled us to understand the continuity between the past and the future. Falk, once again, puts it succinctly:

Mental time travel may indeed be the cognitive rudder that allows our brains to navigate the river of time.

In Search of Time is a fantastic read in its entirety, covering such facets of life’s most intricate dimension as how the calendar was born, why illusion and reality aren’t always so discernible from one another, and what the ultimate fate of the universe might be. Complement it with these seven excellent books on time and a fascinating read on how our memory works .

— Published July 1, 2014 — https://www.themarginalian.org/2014/07/01/mental-time-travel-dan-falk/ —

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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!

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).

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.

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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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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• Lloyd, Seth, Lorenzo Maccone, Raul Garcia-Patron, Vittorio Giovannetti, and Yutaka Shikano, 2011, “Quantum Mechanics of Time Travel through Post-Selected Teleportation”, Physical Review D , 84(2): 025007. doi:10.1103/PhysRevD.84.025007
• Malament, David B., 1977, “Observationally Indistinguishable Spacetimes: Comments on Glymour’s Paper”, in Foundations of Space-Time Theories , John Earman, Clark N. Glymour, and John J. Stachel (eds.), (Minnesota Studies in the Philosophy of Science 8), Minneapolis, MN: University of Minnesota Press, 61–80.
• –––, 1984, “‘Time Travel’ in the Gödel Universe”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , 1984(2): 91–100. doi:10.1086/psaprocbienmeetp.1984.2.192497
• –––, 1985, “Minimal Acceleration Requirements for ‘Time Travel’, in Gödel Space‐time”, Journal of Mathematical Physics , 26(4): 774–777. doi:10.1063/1.526566
• Manchak, John Byron, 2009, “Can We Know the Global Structure of Spacetime?”, Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics , 40(1): 53–56. doi:10.1016/j.shpsb.2008.07.004
• –––, 2011, “On Efficient ‘Time Travel’ in Gödel Spacetime”, General Relativity and Gravitation , 43(1): 51–60. doi:10.1007/s10714-010-1068-3
• Maudlin, Tim, 1990, “Time-Travel and Topology”, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , 1990(1): 303–315. doi:10.1086/psaprocbienmeetp.1990.1.192712
• Novikov, I. D., 1992, “Time Machine and Self-Consistent Evolution in Problems with Self-Interaction”, Physical Review D , 45(6): 1989–1994. doi:10.1103/PhysRevD.45.1989
• Smeenk, Chris and Christian Wüthrich, 2011, “Time Travel and Time Machines”, in the Oxford Handbook on Time , Craig Callender (ed.), Oxford: Oxford University Press, 577–630..
• Stein, Howard, 1970, “On the Paradoxical Time-Structures of Gödel”, Philosophy of Science , 37(4): 589–601. doi:10.1086/288328
• Thorne, Kip S., 1994, Black Holes and Time Warps: Einstein’s Outrageous Legacy , (Commonwealth Fund Book Program), New York: W.W. Norton.
• Verch, Rainer, 2020, “The D-CTC Condition in Quantum Field Theory”, in Progress and Visions in Quantum Theory in View of Gravity , Felix Finster, Domenico Giulini, Johannes Kleiner, and Jürgen Tolksdorf (eds.), Cham: Springer International Publishing, 221–232. doi:10.1007/978-3-030-38941-3_9
• Wallace, David, 2012, The Emergent Multiverse: Quantum Theory According to the Everett Interpretation , Oxford: Oxford University Press. doi:10.1093/acprof:oso/9780199546961.001.0001
• Wasserman, Ryan, 2018, Paradoxes of Time Travel , Oxford: Oxford University Press. doi:10.1093/oso/9780198793335.001.0001
• Weyl, Hermann, 1918/1920 [1922/1952], Raum, Zeit, Materie , Berlin: Springer; fourth edition 1920. Translated as Space—Time—Matter , Henry Leopold Brose (trans.), New York: Dutton, 1922. Reprinted 1952, New York: Dover Publications.
• Wheeler, John Archibald and Richard Phillips Feynman, 1949, “Classical Electrodynamics in Terms of Direct Interparticle Action”, Reviews of Modern Physics , 21(3): 425–433. doi:10.1103/RevModPhys.21.425
• Yurtsever, Ulvi, 1990, “Test Fields on Compact Space‐times”, Journal of Mathematical Physics , 31(12): 3064–3078. doi:10.1063/1.528960

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.

• Adlam, Emily, unpublished, “ Is There Causation in Fundamental Physics? New Insights from Process Matrices and Quantum Causal Modelling ”, 2022, arXiv: 2208.02721. doi:10.48550/ARXIV.2208.02721
• Rovelli, Carlo, unpublished, “ Can We Travel to the Past? Irreversible Physics along Closed Timelike Curves ”, arXiv: 1912.04702. doi:10.48550/ARXIV.1912.04702

causation: backward | determinism: causal | quantum mechanics | quantum mechanics: retrocausality | space and time: being and becoming in modern physics | time machines | time travel

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Astrophysicist says he has cracked the code for time travel

C an you imagine going back in time to visit a lost loved one? This heartwrenching desire is what propelled astrophysicist Professor Ron Mallett on a lifelong quest to build a time machine. After years of research, Professor Mallett claims to have finally developed the revolutionary equation for time travel.

The idea of bending time to our will – revisiting the past, altering history, or glimpsing into the future – has been a staple of science fiction for over a century. But could it move from fantasy to reality?

The inspiration: A father's love and a classic novel

Professor Mallett's obsession with time travel and its equation has its roots in a shattering childhood experience. When he was just ten years old, his father, a television repairman who fostered his son's love of science, tragically passed away from a heart attack.

Devastated, the young Mallett sought solace in books. It was H.G. Wells' The Time Machine that sparked a lifelong fascination.

Wells' opening lines became his mantra: "Scientific people know very well that Time is only a kind of Space. And why cannot we move in Time as we move about in the other dimensions of Space?"

This profound question ignited Mallett's scientific journey. He dedicated himself to understanding the nature of time, determined to find a way to revisit the past and see his beloved father once more.

Time travel equation in the hospital

Decades of research into black holes and Einstein's theories of relativity led to the time travel equation.

While hospitalized for a heart condition, Mallett had a revelation. "It turns out that black holes can create a gravitational field that could lead to the creation of time loops that could allow us to go back in time," he explained.

Imagine the fabric of spacetime as a river. While time usually flows in one direction, Mallett theorizes that the immense gravity of a spinning black hole can create whirlpools, where time twists back on itself.

The time machine blueprint

Mallett's vision for a time machine centers on what he calls "an intense and continuous rotating beam of light" to manipulate gravity. His device would use a ring of lasers to mimic the spacetime-distorting effects of a black hole.

"Let's say you have a cup of coffee in front of you. Start stirring the coffee with the spoon. It started to spin, right? That's what a spinning black hole does," explained Mallett.

"In Einstein's theory, space and time are related to each other. That's why it's called space-time. So when the black hole spins, it will actually cause time to shift."

"Eventually, a rotating beam of laser lights can be used as a kind of time machine and cause a time warp that will allow us to go back to the past," said Mallett. Perhaps, what began as a son's wish to see his father one last time might one day transform our understanding of time itself.

Challenges and limitations

The obstacles on the path from time travel equation to machine are immense. Mallett acknowledges the "galactic amounts of energy" needed to power such a device – energy levels far beyond our current capabilities.

The sheer size of a theoretical time machine is also unknown. While Mallett optimistically states, "I figured out how to do it. In theory, it is possible," the reality is that he may not live to see the machine built.

Furthermore, Mallett's theory comes with a significant constraint. "You can send information back, but you can only send it back to the point where you started operating the device."

In this sense, the time machine is like a one-way message service to the past. You can't travel to a point before the machine existed.

Mallet's lifetime of dedication to time travel

Despite the daunting challenges, Mallett's remarkable journey is a testament to the human spirit. Alongside his time travel research, he's led a distinguished academic career, teaching physics at the University of Connecticut .

Now in his seventies, his work has been propelled by an unwavering belief in the possibility of the seemingly impossible.

Equation vs. reality of time travel

Whether Mallett's time machine will ever transcend the realm of theory is uncertain. Skeptics point to the vast technological hurdles and potential paradoxes raised by tampering with time.

Yet, the mere possibility that science might one day unlock the secrets of temporal travel is enough to ignite the imagination. Could we rewrite our regrets, learn from past mistakes, or witness historical events firsthand?

Perhaps Professor Mallett's greatest legacy won't be a time travel equation itself, but the inspiration he provides – a reminder that audacious dreams and unrelenting curiosity have the power to push the boundaries of what we believe is possible.

Read more about Professor Mallett's work here .

More about space-time

As discussed above, space-time, a concept that feels as vast and complex as the universe itself, forms the backbone of our cosmic understanding.

At its core, it blends the dimensions of space and time into a single four-dimensional continuum, challenging our perceptions of reality. This intertwined nature of space and time underpins everything from the motion of planets to the flow of time itself.

Einstein's groundbreaking contribution

Albert Einstein, with his theory of relativity, revolutionized our understanding of space-time. He posited that space and time are not separate entities but are connected in a dynamic relationship affected by mass and energy.

This relationship implies that the presence of a massive object, like a planet or a star, can warp the fabric of space-time around it. It's a concept that turns the notion of a flat, unchanging universe on its head, suggesting that the very structure of the cosmos is malleable.

The warp and weft of the cosmos

Imagine space-time as a vast sheet of fabric. When a heavy object sits on this fabric, it creates a dip or curve. This curvature is what we perceive as gravity.

Planets orbit stars not because they are being "pulled" in a straight line towards them, but because they are following the curved space-time geometry that these massive objects create.

This curvature of space-time is not just a theoretical concept; it's observable and measurable, especially in the presence of extremely massive and dense objects, like black holes.

Gravitational waves: Echoes of cosmic events

One of the most compelling pieces of evidence for the theory of relativity and the dynamic nature of space-time comes from the detection of gravitational waves.

These waves are ripples in the fabric of space-time, generated by some of the most violent and energetic processes in the universe, such as colliding black holes.

Their discovery not only confirmed Einstein's predictions but also opened a new window into observing cosmic events that were previously invisible to us.

Practical impact of space-time

While these concepts might seem distant from daily life, they have real-world applications, particularly in technology. The Global Positioning System (GPS), a technology integral to modern navigation, relies on an understanding of space-time.

Satellites orbiting Earth need to account for the effects of gravitational time dilation -- a consequence of the curvature of space-time -- to provide accurate location data to users on the ground.

In summary, space-time is a framework that shapes our understanding of the universe. From guiding the planets in their orbits to enabling precise navigation on Earth, its effects are both profoundly cosmic and surprisingly practical.

As we continue to explore and understand the intricacies of space-time, we edge closer to unraveling the mysteries of the cosmos, one gravitational wave at a time.

How black holes are linked to time travel

Playing a major role in Dr. Mallett's time machine, black holes exert a gravitational pull so immense that not even light can escape their grasp. This intense gravity fundamentally alters the fabric of space-time around the black hole.

The stronger the gravity, the more pronounced these effects become, leading to what scientists call gravitational time dilation -- a phenomenon where time itself warps, slowing down relative to an observer far from the gravitational pull.

Time dilation explained

At the heart of this phenomenon lies Albert Einstein's theory of General Relativity, which posits that gravity is the result of masses warping the space-time around them.

In the vicinity of a black hole, this warping becomes so extreme that it significantly affects the flow of time.

An observer standing at a safe distance would perceive time to pass much slower for someone closer to the black hole.

This effect intensifies as one approaches the event horizon, the point of no return beyond which the gravitational pull becomes inescapable.

Boundary between time zones

The event horizon of a black hole marks a stark boundary in the universe, where time as we understand it undergoes a dramatic transformation.

To an external observer, objects approaching the event horizon appear to slow down and almost freeze in time, never quite crossing the threshold.

This illusion results from the light from those objects taking longer and longer to reach the observer as the objects move closer to the event horizon, due to the extreme gravitational pull affecting the light's path.

Theoretical implications and observations

This warping of time around black holes is not just a theoretical curiosity. As Dr. Mallett explained previously in this article, it has practical implications for our understanding of the universe. For instance, it plays a crucial role in the behavior of binary systems where one star orbits a black hole.

Moreover, advancements in technology, such as precise atomic clocks and observations from space telescopes, have allowed scientists to measure these effects, further confirming the predictions of General Relativity.

In summary, black holes serve as natural laboratories for testing the limits of our understanding of physics, offering insights into the complex interplay between gravity and the fabric of space-time.

The phenomenon of time dilation near these cosmic behemoths challenges our notions of time and space, inviting us to explore beyond the boundaries of our current knowledge.

As we continue to observe and study these fascinating objects, we inch closer to unraveling the mysteries of the universe.

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Iran missile and drone attack on Israel – what we know so far

Israel’s military has reported minor damage after Iran launched dozens of drones and missiles towards it late on Saturday

• Iran attack on Israel – live updates
• Full report: Iran launches drones and cruise missiles against Israel

Iran launched hundreds of drones as well as cruise missiles towards Israel , in the Islamic Republic’s first ever direct attack on the Jewish state, in response to the 1 April strike on an Iranian diplomatic building in the Syrian capital, Damascus, which killed a senior figure in Iran’s Islamic Revolutionary Guards and eight other officers.

Benny Gantz, a member of the war cabinet, said that Israel will exact a price from Iran in response to its mass missile and drone attack when the time is right. His comments came ahead of a war cabinet meeting alongside Israel’s prime minister, Benjamin Netanyahu, and the country’s defence minister, Yoav Gallant.

Tehran has warned it will strike again with greater force if Israel or the US retaliate for the Iranian strike on Israel by more 300 drones and missiles on Saturday night. The air raids , the Islamic Republic’s first ever direct attack on the Israeli state, brought a years-long shadow war into the open and threatened to draw the region into a broader conflagration as Israel said it was considering its response.

However, the attack, mostly launched from inside Iran, caused only modest damage in Israel as most were shot down with the help of the US, Britain and Jordan. An air force base in southern Israel was hit, but continued to operate as normal and a seven-year-old child was seriously hurt by shrapnel. There were no other reports of serious damage. Israeli military spokesperson Rear Adm Daniel Hagari said that 99% of the launches had been intercepted.

Most of the Iranian drones flying over Syria’s airspace during Tehran’s strikes overnight were downed by Israeli and US jets before reaching their targets in Israel, two western intelligence sources told Reuters .

The UN security council will hold an emergency meeting on Sunday at the request of Israel’s ambassador to the UN, the council’s president said in a statement.

Iran informed Turkey in advance of its planned operation against Israel, a Turkish diplomatic source has told Reuters . The source also said that the US conveyed to Iran via Ankara that its operation must be “within certain limits”. These reports come after Iran’s foreign minister, Hossein Amirabdollahian , said in a meeting with foreign ambassadors in Tehran that Iran had informed the US that its attacks against Israel will be “limited” and for self-defence only.

John Kirby, the White House’s top national security spokesperson, told ABC’s This Week programme on Sunday that the US will continue to help Israel defend itself, but does not want war with Iran. “We don’t seek escalated tensions in the region. We don’t seek a wider conflict,” Kirby said. News outlet Axios reported that Joe Biden , the US president, had told Netanyahu that he would oppose an Israeli counterattack against Iran and that the prime minister should “take the win”.

UK Royal Air Force fighter jets and refuelling aircraft were also involved in Israel’s defence, taking off from bases in Cyprus. Their role, according to the UK Ministry of Defence, was to fill in for the US air force in the sorties against Islamic State normally carried out over Iraq and north-eastern Syria, but also to intercept Iranian drones if they came into the UK area of operations.

World leaders have condemned Iran’s attack, with regional powers including Saudi Arabia and Egypt calling for restraint. The UN secretary general, António Guterres, said: “I am deeply alarmed about the very real danger of a devastating region-wide escalation. I urge all parties to exercise maximum restraint to avoid any action that could lead to major military confrontations on multiple fronts in the Middle East.”

Jordan’s prime minister, Bisher Khasawneh , warned that any escalation in the region would lead to “dangerous paths”, joining a chorus of condemnation from world leaders to the attack. Other countries including the UK, Spain, the US, Egypt, Saudi Arabia and China, have called for restraint amid fears of a regional escalation of conflict across the Middle East. Iran’s foreign ministry has summoned the ambassadors of the UK , France , and Germany to question what it referred to as their “irresponsible stance” regarding Tehran’s retaliatory strikes on Israel, the semi-official Iranian Labour news agency reported .

Major airlines across the Middle East, including Emirates Airlines and Qatar Airways , announced they would resume some of their operations in the region after cancelling or rerouting some flights in response to Iran’s attack on Israel. Israel said it had reopened its airspace as of 7:30am local time on Sunday morning, with Beirut airport also reopening this morning. Several Iranian airports, including Tehran’s Imam Khomeini International, however, have cancelled flights until Monday.

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Screen Rant

Star trek: discovery’s biggest future mystery is finally answered.

Star Trek: Discovery season 5, episode 4's time travel finally answers one of the show's oldest questions about "Calypso" from Star Trek: Short Treks.

WARNING: Contains SPOILERS For Star Trek: Discovery season 5, episode 4, "Face the Strange." ​​​​

• Star Trek: Discovery finally connects the dots between the show and the Short Treks episode "Calypso."
• "Face the Strange" explores time loops and a Breen attack that destroys the Federation.
• Star Trek: Discovery season 5, episode 4 sets Star Trek: Short Treks' "Calypso" in an alternate future timeline.

Star Trek: Discovery finally answered one of the show's biggest mysteries about the Star Trek: Short Treks episode "Calypso." In its fifth and final season, Discovery has incorporated more references and connections to past Star Trek than any previous season. Following a classic Star Trek plot, Star Trek: Discovery season 5, episode 4 , "Face the Strange" finds Captain Michael Burnham (Sonequa Martin-Green), Commander Rayner (Callum Keith Rennie), and Commander Paul Stamets (Anthony Rapp) stuck in a time loop caused by Moll (Eve Harlow) and L'ak (Elias Toufexis) that shockingly connects to the Short Trek "Calypso."

Written by Sean Cochran and directed by Lee Rose, "Face the Strange" reflects on Star Trek: Discovery's history and how much the characters have changed since Discovery's earliest seasons . Since Burnham and Rayner were transporting just as the time jumping began, they remain aware that they are in a time loop, as does Stamets, due to his Tardigrade DNA. As Burnham, Stamets, and Rayner try to determine the cause of their time jumping, they visit Discovery's past, present, and future. In one of the jumps, Burnham and Rayner end up on the empty USS Discovery first seen in Star Trek: Short Treks season 1, episode 2, "Calypso."

9 Star Trek Characters Who Can Hide Discovery Season 5 Treasure Hunt Clues

Star trek: discovery finally answers short trek’s “calypso” mystery, captain burnham and commander rayner jump to 3218, 27 years after discovery season 5..

In Star Trek: Short Treks' "Calypso," a human soldier named Craft (Aldis Hodge) is rescued from his escape pod by the USS Discovery's sentient computer, Zora (Annabelle Wallis). Zora reveals that she has been alone for nearly a thousand years and has spent the time evolving herself. Zora falls in love with Craft, and the two connect over old movies, particularly 1957's Funny Face. Craft eventually makes the difficult decision to use Discovery's lone warp-capable shuttlecraft to attempt the long journey back to his home, unsure if the shuttle will even make it that far.

Zora shows Burnham and Rayner the wreckage of the destroyed Federation headquarters, telling them they must find a way out of the time loop to prevent this future from happening.

Star Trek: Discovery 's season 5, episode 4 finally reveals that the USS Discovery ended up abandoned in "Calypso" because of Star Trek: Trek: Deep Space Nine 's villains, the Breen . When Burnham and Rayner jump to a point about thirty years into their future, they follow the sound of old show tunes to Discovery's empty bridge. A surprised Zora reveals that, in this timeline, the Breen acquired the Progenitors' technology and used it to attack the Federation. Zora shows Burnham and Rayner the wreckage of the destroyed Federation headquarters, telling them they must find a way out of the time loop to prevent this future from happening.

Captain Burnham and Commander Rayner visit Zora in 3218, 27 years after the events of Star Trek: Discovery season 5 in 3191.

Short Trek’s “Calypso” Will Never Happen After Star Trek: Discovery Season 5

Captain burnham and her crew will ensure the breen never get the progenitor technology..

It's unlikely Star Trek: Discovery will end with the destruction of the Federation, and it's safe to assume that Captain Burnham and the USS Discovery's crew will find the Progenitors' treasure and prevent the Breen attack. This means that the Federation will not be destroyed, the Discovery crew won't be killed by the Breen, and Zora will not be abandoned for a thousand years. Star Trek: Short Treks' "Calypso," then, takes place in an alternate timeline where the Federation lost, and the events of Star Trek: Discovery season 5 will render that potential future - and "Calypso" - null and void within Star Trek 's Prime Timeline.

"Calypso" taking place in an alternate future also helps explain any discrepancies between the Short Treks episode and Star Trek: Discovery.

Star Trek has played with alternate timelines before (most notably with J.J. Abrams' Kelvin timeline Star Trek movies ). Zora and Craft will still have their moment in another reality, but one that is not part of the Prime Universe Star Trek timeline. "Face the Strange" feels like classic Star Trek in the best way, and though Discovery season 5's writers did not know about the show's cancelation, it already feels like they are tying up loose ends. Thankfully, Star Trek: Discovery finally addressed Zora and the USS Discovery's future in "Calypso." It's great to have the answer, at last, that the events of Star Trek: Discovery season 5 set Star Trek: Short Treks' "Calypso" in an alternate future.

New episodes of Star Trek: Discovery stream Thursdays on Paramount+.

Star Trek: Discovery