how does ftl travel violate causality

Special Relativity/Faster than light signals, causality and Special Relativity

It is popularly imagined that Special Relativity forbids travel faster than the speed of light or the propagation of signals faster than the speed of light. However, the actual theory does not contain this assumption. The original theory, framed by Einstein in 1905, states that the speed of light in free space is constant in all inertial frames of reference so how did people in general come to believe that this implies a speed limit? The idea of a speed limit comes from two predictions of the theory, that inertia increases towards infinite as velocity approaches light speed and that causality, the succession of cause and effect, is violated if we could signal at speeds above the speed of light.

The inertial constraint does not apply to particles without a rest mass, such as the photon, or to particles that might oscillate between massless and massive forms. The possibility that causality would be violated if signals could travel faster than the speed of light is a more interesting problem however. The relationship between Faster than Light signal speeds and causality will be considered and it will be shown that if a Faster than Light signal were ever discovered then either Special Relativity or Causality will be false.

Special Relativity, faster than light signals and causality [ edit | edit source ]

Prior to the twentieth century physicists believed that sending signals from one observer to another was straightforward. They believed that light was always transmitted from a transmitter to a receiver where the transmitter was earlier than the receiver (the red line in the diagram below) and that signals might be transmitted instantaneously (the blue and purple lines in the diagram). In this pre-relativistic scenario the two observers in the diagram, Bill and Bertha, have total freedom to transmit signals at any rate up to an infinite velocity. Prior to Special Relativity there was no theory for how signals might be sent backwards in time and such a possibility was discounted.

Special Relativity leads to different predictions about the behaviour of signals. In the section of this book on simultaneity it was shown that Special Relativity predicts that clocks on two relatively moving observers will go progressively out of phase with distance along a common x-axis. This effect is shown in the diagram below.

The x' axis on the diagram is all those points that Jim considers to be NOW, events that exist at the present moment. Jim's NOW differs from Bill's NOW. The two observers read the same time at the origin of the graph but clocks differ with distance from the origin. This means that if Jim were able to send a message instantaneously from one place to another, so that it was transmitted and received at the same time, Bill would see the signal to be spanning two different times. The signal would appear to go backwards or forwards in time. This is shown in the diagram below in which Bertha sees the signal begin at one time (point B) and end at another time (point A).

Notice that if Bertha asks Jane to send an instantaneous signal to Jim then Bill, who is right next to Jim when the signal arrives, will register this signal as arriving at an earlier time than the time it was started by Bertha. If it is possible to signal instantaneously then it is possible to transmit messages backwards through time! This transfer of information back through time would apply to any signal that could be sent at a speed faster than the speed of light.

If signals could be sent at faster than light speed then Bertha and Bill could work together to become rich. Bertha could ask Jane and Jim to signal the result of a race or the price of a stock back to Bill then Bill could send this result back to Bertha at a time before the race. Bertha could then place a bet to win a fortune.. This sequence of events is shown in the diagram below, Bertha sees the result of the race at point B, signals this back to Bill at point A, using Jane and Jim to send the signal, then Bill signals back to Bertha how she should bet before the race begins.

This sequence of events might be held to be impossible in physics because it violates the principle of Causality . Causes precede effects according to the principle of Causality but if faster than light signals are possible then effects could precede causes. Notice that the violation of causality would actually be quite limited and would only apply to "space-like" separated events, these are events that are so recent that it would require a signal travelling faster than the speed of light to observe them now. Even if Bill and Jim were as far away as the moon they would only be able to peek a little over a second into Bertha's future if instantaneous signals were possible (the moon is less than 2 light seconds away).

It is well known that weakly interacting, free particles which cannot be observed because they are "space-like" separated from observation are described by the probabilistic predictions of Quantum Theory so it would not be altogether shocking, though certainly surprising, if causality were violated in these circumstances.

Why time-traveling tachyons probably don't exist

clock icon and blue abstract motion background

Tachyons are hypothetical particles that always travel faster than the speed of light. Einstein showed that such particles would allow for communication back in time, which opens up all sorts of problems with a fundamental rule of the universe. While physicists haven't proved that tachyons can't exist, there's good reason to believe they don't.

The barrier that nothing with mass can travel at the speed of light isn't just an expression of the limitation of engineering or a representation of a failure of imagination. It's baked into the very laws of the universe, as expressed by Einstein's theory of special relativity .

Let's say you want to start traveling faster than the speed of light. You start from rest and give yourself a little nudge. Because you have mass, your nudge has to overcome a bit of inertia to get you going, but you eventually get going. You light up a rocket, for example, and you blast off.

Related: Why is the speed of light the way it is?

But once you're off the launchpad, you don't stop. You have some superadvanced engine that allows you to keep pushing, causing you to continue accelerating. At speeds much lower than the speed of light, everything makes sense: For every second you fire your engines, you get the same amount of acceleration and the same boost in your velocity.

But as you approach the speed of light, something funny starts to happen. The same amount of energy put into your engines starts giving you less and less acceleration, so you get less velocity bang for your buck. Despite working your engines to the extreme, you find yourself inching closer to the speed of light but never reaching it. At some point, you realize that to achieve light speed, you need to put an infinite amount of energy into your engines — which you don't have.

The problem here is that energy is mass, as given by E = mc^2. The faster you move, the more kinetic energy you have, which means you are literally heavier the faster you go. As you approach the speed of light, your mass goes to infinity, so it takes an infinite amount of rocket power to make it to the speed of light.

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The tachyon workaround

But those rules apply to objects with mass starting below the speed of light. Massless objects, like light itself, automatically travel at light speed, never slowing down or speeding up. In 1967, building on work going back decades, physicist Gerald Feinberg proposed a new class of particle: objects with "imaginary mass." ("Imaginary" here refers to the mathematical term for the square root of -1.) These particles, which he called tachyons , would never travel slower than the speed of light. In fact, they would be forced to always go above light speed and would have just as much difficulty slowing down to light speed as we do trying to accelerate to it.

Feinberg wasn't the first to consider faster-than-light particles, but he was the one to coin our word for them. Einstein toyed with the idea but found that such particles violated a central rule of the universe: causality.

Causality is so fundamental that it underlies everything we understand about the workings of the universe. Put simply, causality states that causes must come before effects. I have to text you before your phone beeps, I have to put a piece of cheese in my mouth before I can eat it, and so on.

Causing trouble

But tachyons are capable of violating causality. To see how, let's set up a little thought experiment. I'm sitting on Earth while you're having some grand adventure out in the universe. I want to send you a signal with tachyons, so I fire up my tachyon transmitter and beam off a message.

From my perspective, the tachyons race away from me at faster than the speed of light in your direction. So far, so good.

If you're standing perfectly still, then eventually, the tachyon will reach you in less time than it would take for light to get there. You wouldn't be able to see the tachyon coming until it already passed you, which is still no big deal. If you had a telescope pointed at me, you would receive the tachyon before seeing the image of me pressing the button to send it. Curious, but still no huge problem.

— How does time work?

— 3 ways fundamental particles travel at (nearly) the speed of light

— The 'twin paradox' shows us what it really means for time to be relative

The issue comes if you start moving. In relativity, from your perspective, you are standing still while Earth appears to be receding. This introduces time dilation: From your perspective, everything in the universe — including the action of me pressing the button — slows down. In fact, if you're traveling fast enough, you could receive my tachyon and send a reply before I even hit the button in the first place; you can send a signal back in time.

Once you allow for sending signals back in time, you can play many fun games that create contradictions. You can have a message sent back to prevent your grandparents from meeting, which means you would never exist — but you need to exist to go back in time to prevent your grandparents from meeting. You can trigger an explosion that destroys the tachyon emitter before it receives your message. You can even destroy yourself in your own past.

And because we don't live in a universe where these contradictions and violations of causality happen, it seems unlikely that tachyons exist.

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Paul M. Sutter is an astrophysicist at SUNY Stony Brook and the Flatiron Institute in New York City. Paul received his PhD in Physics from the University of Illinois at Urbana-Champaign in 2011, and spent three years at the Paris Institute of Astrophysics, followed by a research fellowship in Trieste, Italy, His research focuses on many diverse topics, from the emptiest regions of the universe to the earliest moments of the Big Bang to the hunt for the first stars. As an "Agent to the Stars," Paul has passionately engaged the public in science outreach for several years. He is the host of the popular "Ask a Spaceman!" podcast, author of "Your Place in the Universe" and "How to Die in Space" and he frequently appears on TV — including on The Weather Channel, for which he serves as Official Space Specialist.

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Pentcho Valev These are all conclusions deduced, validly or invalidly, from Einstein's 1905 constant-speed-of-light postulate stating that the speed of light is independent of the speed of the light source. Actually, the speed of light does depend on the speed of the source, as posited by Newton's theory. Einstein "borrowed" the false constancy from the nonexistent ether: Einstein: "I introduced the principle of the constancy of the velocity of light, which I borrowed from H. A. Lorentz's theory of the stationary luminiferous ether..." Quoted in Wikipedia Reply
Robert Lucien Howe Was expecting the article to fall into one of Special Relativities catch pits, but everything said looks correct. It still has to be said though (and its not said often enough) that all predictions made by the theory about physics above the speed of light are still basically speculation. There is a disjunction at the speed of light so that the current mathematical rules we know may apply or may not. I have worked on imaginary numbers (within computational logic) and believe that imaginary values might always add up to net zero. - From that photons could be described pretty accurately as having imaginary & net zero mass. Zero mass gives you zero inertia which equates to infinite speed and in reality limits at what we know as the speed of light. My own prediction is that taychons carrying reverse causality enter or exist in our STL universe all the time but they are quantum objects and don't generally carry useful information. Dark matter for instance might have an imaginary or negative mass.. Reply
rod "And because we don't live in a universe where these contradictions and violations of causality happen, it seems unlikely that tachyons exist." What? consider other reports on physical law and QM stuff on space.com. Does consciousness explain quantum mechanics? | Space.com Forums It does seem that there should be no causality to the universe today, quantum or macro level. Everything should just be random chaos starting from an area smaller than an electron where everything we see today, evolved from. Reply
rod Another observation after pondering this article a bit more. In BB cosmology, all redshifts 1.4 or larger are explained where 4D space is expanding faster than c velocity (comoving radial distances) and the inflation period where space expands some 10^20 or 10^21 faster than c velocity. Apparently, there is no causality violation here, a fundamental rule of the universe, yet the BB cosmology does not explain how causality was created or even when. So, in the methodology, I can rule out tachyons, but accept 4D space expanding much faster than light speed today in cosmology. Cool :) Here is something from the early part of this report. "Tachyons are hypothetical particles that always travel faster than the speed of light." The cosmological redshift answer for larger redshifts requires *travel faster than the speed of light* too. Reply
rod "And because we don't live in a universe where these contradictions and violations of causality happen, it seems unlikely that tachyons exist." Does this thinking apply to 4D space expanding faster than c velocity used in BB cosmology (and inflation) too? Reply
grigor60 I do not understand, why every time when we talk about the speed of light it is tightly coupled to time. As well, as I do not understand this statement > The issue comes if you start moving. In relativity, from your perspective, you are standing still while Earth appears to be receding. Maybe because of a lack of knowledge. Is there any good reason to think that the speed of photons differs from that of other objects? I see only one reason for this kind of statement, that we do not have the ability to measure processes faster than the speed of light, because right now we don have the ability to do measurements or collect information from observation faster than the speed of light, People cannot observe faster than the speed of light, moreover, we cannot measure the process of movement of something faster than the speed of light just because humans can't retrieve information faster than the speed of light. And so we believe that the speed of light is related to time, But it is connected only with time, where a starting point is a person, not the universe. I don’t understand why the fact that we can’t do something, due to purely technical limitations, becomes a postulate about how the universe works. Reply
Ian The argument around causality is broadly applicable to anything that permits superluminal travel or communication. Causality itself is not a principle that can be derived from either General Relativity or quantum theory- it is simple a phenomenon we observe in our everyday experience, and as such may be an illusion derived from the way we perceive reality. Even if causality is taken to be a real physical principle it doesn't preclude the existence of tachyons, since causality issues only arise if it's also possible to somehow use them to exchange information with the slower-than-light world. Quantum entanglement also creates issues with time because observing the spin of one entangled particle instantly determines that of the other one, in all reference frames. It doesn't create a causality problem though, because the phenomenon can't be used to exchange information. Reply

grigor60 said: I do not understand, why every time when we talk about the speed of light it is tightly coupled to time. As well, as I do not understand this statement > The issue comes if you start moving. In relativity, from your perspective, you are standing still while Earth appears to be receding. Maybe because of a lack of knowledge. Is there any good reason to think that the speed of photons differs from that of other objects? I see only one reason for this kind of statement, that we do not have the ability to measure processes faster than the speed of light, because right now we don have the ability to do measurements or collect information from observation faster than the speed of light, People cannot observe faster than the speed of light, moreover, we cannot measure the process of movement of something faster than the speed of light just because humans can't retrieve information faster than the speed of light. And so we believe that the speed of light is related to time, But it is connected only with time, where a starting point is a person, not the universe. I don’t understand why the fact that we can’t do something, due to purely technical limitations, becomes a postulate about how the universe works.

Hotseflats Uhm, surely sending the Tachyon back from your moving point of view will make it seem from your perspective that the Tachyon will reach Earth before the button is pushed. In reality, time on Earth is still moving forward, whilst the Tachyon is travelling however fast it goes, as long as it is not infinity. And from Earth's perspective the Tachyon will arrive at a future point in time, leaving causality in tact. I really think the world of physics is having a collective brain fart, starting with mister Einstein. Reply
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4.7: Tachyons and Faster-than-Light (FTL)

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Benjamin Crowell
Fullerton College

Learning Objectives

Explain faster-than-light ( FTL , superluminal) motion in relativity

A Defense in Depth

Let’s summarize some ideas about faster-than-light ( FTL , superluminal) motion in relativity:

Superluminal transmission of information would violate causality, since it would allow a causal relationship between events that were spacelike in relation to one another, and the timeordering of such events is different according to different observers. Since we never seem to observe causality to be violated, we suspect that superluminal transmission of information is impossible. This leads us to interpret the metric in relativity as being fundamentally a statement of possible cause and effect relationships between events.
We observe the invariant mass defined by $m^2 = E^2 - p^2$ to be a fixed property of all objects. Therefore we suspect that it is not possible for an object to change from having $|E| > |p|$ to having $|E| < |p|$.
No continuous process of acceleration can bring an observer from $v < c$ to $v > c$ (see section 3.3). Since it’s possible to build an observer out of material objects, it seems that it’s impossible to get a material object past $c$ by a continuous process of acceleration.
If superluminal motion were possible, then one might also expect superluminal observers to be possible. But FTL frames of reference are kinematically impossible in $3 + 1$ dimensions ( section 3.8).

Thus special relativity seems to have a defense in depth against superluminal motion.

Based on 2, FTL motion would be a property of an exotic form of matter built out of hypothetical particles with imaginary mass. Such particles are called tachyons. An imaginary mass is not absurd on its face, because experiments directly measure $E$ and $p$, not $m$. E.g., if we put a tachyon on a scale and weighed it, we would be measuring its mass-energy $E$.

The weakest of these arguments is 1, since as described in section 2.1, we have no strong reasons for believing in causality as an overarching principle of physics. It would be exciting if we could detect tachyons in particle accelerator experiments or as naturally occurring radiation. Perhaps we could even learn to transmit and receive tachyon signals artificially, allowing us to send ourselves messages from the future! This possibility was pointed out in 1917 by Tolman 1 and is referred to as the “tachyonic antitelephone.” 2

If we’re willing to let go of causality, then we just need to make sure that our tachyons comply with items 3 and 4 above. Argument 4 tells us that the laws of physics must conspire to make it impossible to build an observer out of tachyons; this is not entirely implausible, since there are other classes of particles such as photons that can’t be used to construct observers.

Experiments to search for tachyons

Experimental searches are made more difficult by conﬂicting theoretical claims as to whether tachyons should be charged or neutral, whether they should have integral or half-integral spin, and whether the normal spin-statistics relation even applies to them. 3 If charged, it is uncertain whether and under what circumstances they would emit Cerenkov radiation.

The most obvious experimental signature of tachyons would be propagation at speeds greater than $c$. Negative results were reported by Murthy and later by Clay, 4 who studied air showers generated by cosmic rays to look for precursor particles that arrived before the first photons.

One could also look for particles with $|p| > |E|$. Alvager and Erman, in a 1965 experiment, studied the beta decay of $^{170}\textrm{Tm}$, using a spectrometer to measure the momentum of charged radiation and a solid state detector to determine energy. An upper limit of one tachyon per $10^4$ beta particles was inferred.

If tachyons are neutral, then they might be difficult to detect directly, but it might be possible to infer their existence indirectly through missing energy-momentum in reactions. This is how the neutrino was first discovered. Baltay et al . 5 searched for reactions such as

\[\bar{p} + p \rightarrow \pi ^{+} + \pi ^{-} + t\]

with $t$ being a neutral tachyon, by measuring the momenta of all the other initial and final particles and looking for events in which the missing energy-momentum was spacelike. They put upper limits of $\sim 10^{-3}$ on the branching ratios of this and several other reactions leading to production of single tachyons or tachyon-antitachyon pairs.

For a long time after the discovery of the neutrino, very little was known about its mass, so it was consistent with the experimental evidence to imagine that one or more species of neutrinos were tachyons, and Chodos et al . made such speculations in 1985. A brief ﬂurry of reawakened interest in tachyons was occasioned by a 2011 debacle in which the particle-physics experiment OPERA mistakenly reported faster-than-light propagation of neutrinos; the anomaly was later found to be the result of a loose connection on a fiber-optic cable plus a miscalibrated oscillator. An experiment called KATRIN, currently nearing the start of operation at Karlsruhe, will provide the first direct measurement of the mass of the neutrino, by measuring very precisely the maximum energy of the electrons emitted in the decay of tritium, $^{3}\textrm{H} \rightarrow ^{3}\textrm{He} + e^{-} + \bar{v_e}$. Conservation of energy then allows one to determine the minimum energy of the antineutrino, which is related to its mass and momentum by $m^2 = E^2 - p^2$. Because $m^2$ appears in this equation, the experiment really measures $m^2$, not $m$, and a result of $m^2 < 0$ would bring the tachyonic neutrino back from the grave.

Tachyons and Quantum Mechanics

When we add quantum mechanics to special relativity, we get quantum field theory , which sounds scary and can be quite technical, but is governed by some very simple principles. One of these principles is that “ everything not forbidden is compulsory .” The phrase was popularized as a political satire of communism by T.H. White, but was commandeered by physicist Murray Gell-Mann to express the idea that any process not forbidden by a conservation law will in fact occur in nature at some rate. If tachyons exist, then it is possible to have two tachyons whose energy-momentum vectors add up to zero. This would seem to imply that the vacuum could spontaneously create tachyon-antitachyon pairs. Most theorists now interpret this as meaning that when tachyons pop up in the equations, it’s a sign that the assumed vacuum state is not stable, and will change into some other state that is the true state of minimum energy.

1 www.archive.org/details/theoryrelativmot00tolmrich

2 Bilaniuk et al. claimed in a 1962 paper to have found a reinterpretation that eliminated the causality violation, but their interpretation requires that rates of tachyon emission in one frame be related to rates of tachyon absorption in another frame, which in my opinion is equally problematic, since rates of absorption should depend on the environment, whereas rates of emission should depend on the emitter; the causality violation has simply been described in different words, but not eliminated. For a different critique, see Benford, Book, and Newcomb, “The tachyonic antitelephone,” Physical Review D 2 (1970) 263. Scans of the paper can be found online.

3 Feinberg, “Possibility of Faster-Than-light Particles,” Phys Rev 159 (1967) 1089, http://www.scribd.com/doc/144943457/ G-Feinberg-Possibility-of-Faster-Than-light-Particles-Phys-Rev-159-1967-1089

4 “A search for tachyons in cosmic ray showers,” Austr. J. Phys 41 (1988) 93, http://adsabs.harvard.edu/full/1988AuJPh..41...93C

5 Phys. Rev. D 1 (1970) 759

Relativity and FTL Travel

By jason w. hinson ( [email protected] ), part iv: faster than light travel--concepts and their "problems", edition: 5.1 last modified: april 8, 2003 url: http://www.physicsguy.com/ftl/ ftp (text version): ftp://ftp.cc.umanitoba.ca/startrek/relativity/.

[Physics FAQ] - [Copyright]

By Philip Gibbs, 1997, 1998.

It might be thought that special relativity provides a short negative answer to this question. In actual fact, there are many trivial ways in which things can be going faster than light (FTL) in a sense, and there may be other more genuine possibilities. On the other hand, there are also good reasons to believe that real FTL travel and communication will always be unachievable. This article is not a full answer to the question (which no doubt will continue to be discussed in the newsgroups for the foreseeable future), but it does cover some of the more common points that are repeatedly made.

It is sometimes objected that "they said no-one would ever go faster than sound and they were wrong. Now they say no-one will ever go faster than light..." Actually it is probably not true that anybody said it was impossible to go faster than sound. It was known that rifle bullets go faster than sound long before an aircraft did. The truth is that some engineers once said that controlled flight faster than sound might be impossible, and they were wrong about that. FTL travel is a very different matter. It was inevitable that someone would one day succeed in flying faster than sound, once technology got around the problems. It is not inevitable that one day technology will enable us to go faster than light. Relativity has a lot to say about this. If FTL travel or FTL communication were possible, then causality would probably be violated and some very strange situations would arise.

First we will cover the trivial ways in which things can go FTL. These points are mentioned not because they are interesting, but because they come up time and time again when FTL is being discussed, and so they are necessary to deal with. Then we will think about what we mean by non-trivial FTL travel/communication and examine some of the arguments against it. Finally, we will look at some of the more serious proposals for real FTL. Many of these things are discussed in more detail elsewhere in the FAQ and hyper-links are provided. The sections are numbered so that they can be referred to individually.

Trivial FTL Travel

1. cherenkov effect.

One way to go faster than light is to make the light slow down! Light in vacuum travels at a speed c which is a universal constant (see the FAQ entry Is the speed of light constant? ), but in a dense medium such as water or glass, light slows down to c/n where n is the refractive index of the medium (1.0003 for air, 1.4 for water). It is certainly possible for particles to travel through air or water faster than light travels in that medium, and Cherenkov radiation is produced as a result. See the FAQ entry Is there an equivalent of the sonic boom for light? .

When we discuss moving faster than light, we are really talking about exceeding the speed of light in vacuum c (299,792,458 m/s). The Cherenkov effect is thus not considered to be a real example of FTL travel.

2. Third-Party Observers

If a rocket A is travelling away from me at 0.6c in a westerly direction, and another B is travelling away from me at 0.6c in an easterly direction, then the total distance between A and B as seen in my frame of reference is increasing at 1.2c . An apparent relative speed greater than c can be observed by a third person in this way.

But this is not what is normally meant by relative speeds. The true speed of rocket A relative to rocket B is the speed at which an observer in rocket B observes his distance from A to be increasing. The two speeds must be added using the relativistic formula for addition of velocities. (See the FAQ entry How do You Add Velocities in Special Relativity? ) In this case the relative speed is actually about 0.88c , so this is not an example of FTL travel.

3. Shadows and Light Spots

Think about how fast a shadow can move. If you project the shadow of your finger using a nearby lamp onto a distant wall and then wag your finger, the shadow will move much faster than your finger. If your finger moves parallel to the wall, the shadow's speed will be multiplied by a factor D/d where d is the distance from the lamp to your finger, and D is the distance from the lamp to the wall. The speed can even be much faster than this if the wall is at an angle to your finger's motion. If the wall is very far away, the movement of the shadow will be delayed because of the time it takes light to get there, but the shadow's speed is still increased by the same ratio. The speed of a shadow is therefore not restricted to be less than the speed of light.

This behaviour of a shadow is all about the arrival of successive "pieces of light" (photons, if you will) at a screen. It is really no different to the faster-than-light speed of a spot on the Moon's surface caused by a laser that has been aimed at that surface and is being waved around on Earth. Given that the distance to the Moon is 385,000 km, try working out the speed of that spot if you wave the laser at a gentle speed. You might also like to think about a water wave arriving obliquely at a long straight beach. How fast can the point at which the wave is breaking travel along the beach?

This sort of thing turns up in Nature; for example, the beam of light from a pulsar can sweep across a dust cloud. A bright explosion emits an expanding spherical shell of light or other radiation. When this shell intersects a surface, it creates a circle of light which expands faster than light. A natural example of this has been observed when an electromagnetic pulse from a lightning flash hits an upper layer of the atmosphere.

These are all examples of "things" that seem to be moving faster than light. In reality, no object or signal is moving faster that light here. For a more prosaic example, imagine squirting water from a garden hose at a fence, and moving your aim from one end of the fence to the other. The intersection point of water stream and fence moves quickly, but of course no thing or signal is really moving along the fence. A succession of water molecules strikes the fence, but their speed of travel has nothing to do with how quickly you move the hose. It is a kind of optical illusion for us to think that the wet spot advancing along the fence is a moving object or signal. The ban in relativity against faster-than-light travel actually concerns the speed of signals (which includes material objects and waves): in a vacuum, no signal is allowed to move faster than light moves in its vicinity. Neither a moving shadow, nor a laser spot, nor a wet spot on a fence, constitute a signal that is being sent from the initial position of those spots to the final position. Since these moving spots don't constitute a signal, they are all allowed to move faster than light. This is not really what we mean by faster-than-light travel, although it shows how difficult it is to define what we really do mean by faster-than-light travel. See also the FAQ The Superluminal Scissors .

4. Rigid Bodies

If you have a long rigid stick and you hit one end, wouldn't the other end have to move immediately? Would this not provide a means of FTL communication?

Well, it would if there were such things as perfectly rigid bodies. In practice the effect of hitting one end of the stick propagates along it at the speed of sound in the material; this speed depends on the stick's elasticity and density. Relativity places an absolute limit on material rigidity in such a way that the speed of sound in the material will not be greater than c .

The same principle applies if you hold a long string or rod vertically in a gravitational field and let go of the top end. The point at which you let go will start to move immediately, but the lower end cannot move until the effect has propagated down the length. That speed of propagation depends on the nature of the material and the strength of the gravitational field.

It is difficult to formulate a general theory of elastic materials in relativity, but the general principle can be illustrated with newtonian mechanics. The equation for longitudinal motion in an ideal elastic body can be derived from Hooke's law. In terms of the mass per unit length p and Young's modulus of elasticity Y , the longitudinal displacement X satisfies a wave equation (see for example Goldstein's "Classical Mechanics"):

Plane wave solutions travel at the speed of sound s where s 2 = Y/p . This wave equation does not allow any causal effect to propagate faster than s . Relativity therefore imposes a limit on elasticity: Y < pc 2 . In practice, no known material comes anywhere near this limit. Note that even if the speed of sound is near c , the matter does not necessarily move at relativistic speeds. But how can we know that no material can possibly exceed this limit? The answer is that all materials are made of particles whose interaction are governed by the standard model of particle physics, and no influence faster than light can propagate in that model (see the section on Quantum Field Theory below).

So although there is no such thing as a rigid body, there is such a thing as rigid body motion; but this is another example in the same category as the shadows and light spots described above which do not give FTL communication. (See also the FAQ articles The Superluminal Scissors and The Rigid Rotating Disk in Relativity ).

5. Phase, Group, and Signal Velocities

Look at this wave equation:

This has solutions of the form:

These solutions are sine waves propagating with a speed

But this is faster than light, so is this the equation for a tachyon field? (See the paragraph on tachyons below ). No, it is the usual relativistic equation for an ordinary particle with mass!

Superluminal speeds such as this present no problem once we recognise three types of speed associated with wave motion: phase velocity , group velocity , and signal velocity . Phase velocity is the velocity of waves that have well-defined wavelengths, and it often varies as a function of this wavelength. We can combine ("superpose") waves of different wavelengths to build a wave packet , a blob of some specified extent over which the wave disturbance is not small. This packet does not have a well-defined wavelength, and because it usually spreads out as it travels, it doesn't have a well-defined velocity either; but it does have representative velocity, and this is called its group velocity, which will usually be less than c . Each of the packet's constituent wave trains travels with its own individual phase velocity, which in some instances will be greater than c . But it is only possible to send information with such a wave packet at the group velocity (the velocity of the blob), so the phase velocity is yet another example of a speed faster than light that cannot carry a message.

In some situations, we can build a fairly exotic wave packet whose group velocity is greater than c . Does this then constitute an example of information being sent at a speed faster than light? It turns out that for these packets, information does not travel at the group velocity; instead, it travels at the signal velocity , which has to do with the time of arrival of the initial rise of the wave front as it reaches its destination. You might not now be surprised to learn that the signal velocity turns out always to be less than c .

6. Superluminal Galaxies

If something is coming towards you at nearly the speed of light and you measure its apparent speed without taking into account the diminishing time it takes light to reach you from the object, you can get an answer that is faster than light. This is an optical illusion, and is not due to the object's moving at FTL. See the FAQ Apparent Superluminal Velocity of Galaxies .

7. Relativistic Rocket

A controller based on Earth is monitoring a space ship moving away at a speed 0.8c . According to the theory of relativity, he will observe a time dilation that slows the ship's clocks by a factor of 5/3, even after he has taken into account the Doppler shift of signals coming from the space ship. If he works out the distance moved by the ship divided by the time elapsed as measured by the onboard clocks, he will get an answer of 4/3 c . He infers from this that the ship's occupants determine themselves to be traversing the distances between stars at speeds greater than the speed of light when measured with their clocks. From the point of view of the occupants their clocks undergo no slowing; rather, they maintain that it is the distance between the stars which has contracted by a factor of 5/3. So they also agree that they are covering the known distances between stars at 4/3 c .

This is a real effect which in principle could be used by space travellers to cover very large distances in their lifetimes. If they accelerate at a constant acceleration equal to the acceleration due to gravity on Earth, they would not only have a perfect artificial gravity on their ship, but would also be able to cross the galaxy in only about 12 years of their own "proper time": that is, they would age 12 years during the journey. See the FAQ What are the Equations for the Relativistic Rocket?

Nevertheless, this is not true FTL travel. The effective speed calculated used the distance in one reference frame and the time in another. This is no way to calculate a speed. Only the occupants of the ship benefit from this effective speed. The controller will not measure them to be travelling large distances in his own lifetime.

8. Speed of Gravity

Some people have argued that the speed of gravity in a gravitationally bound system is much greater than c or even infinite. In fact, gravitational effects and gravitational waves travel at the speed of light c . See the articles Does Gravity Travel at the Speed of Light? and What is Gravitational Radiation? for the explanation.

9. EPR Paradox

In 1935 Einstein, Podolsky, and Rosen published a thought experiment that seemed to produce a paradox in quantum mechanics, as well as demonstrating that it was incomplete. Their argument used the fact that there can be an apparent instantaneous interaction in the measurement of two separated particles that have been prepared in a certain "entangled" manner. Einstein called it "spooky action at a distance". It has been shown by Eberhard that no information can be passed using this effect; so there is no FTL communication, but the paradox is still very controversial. See the FAQ article The EPR Paradox and Bell's Inequality for more details.

10. Virtual Photons

In quantum field theory forces are mediated by "virtual particles". The Heisenberg Uncertainty Principle allows these virtual particles to move faster than light. But virtual particles are not called "virtual" for nothing. They are only part of a convenient mathematical notation, and once again, no real FTL travel or communication is possible. See the FAQ Virtual Particles .

11. Quantum Tunnelling

Quantum Tunnelling is the quantum mechanical effect that permits a particle to pass through a barrier when it does not have enough energy to do so classically. You can do a calculation of the time it takes a particle to tunnel through such a barrier. The answer you get can come out less than the time it takes light to cover the distance at speed c . Does this provide a means of FTL communication? Ref: T. E. Hartman, J. Appl. Phys. 33 , 3427 (1962).

The answer must surely be "No!"—otherwise our understanding of QED is very suspect. Yet a group of physicists have performed experiments that seem to suggest that FTL communication by quantum tunneling is possible. They claim to have transmitted Mozart's 40th Symphony through a barrier 11.4cm wide at a speed of 4.7 c . Their interpretation is, of course, very controversial. Most physicists say this is a quantum effect where no information can actually be passed at FTL speeds. If the effect is real it is difficult to see why it should not be possible to transmit signals into the past by placing the apparatus in a fast-moving frame of reference. Refs: W. Heitmann and G. Nimtz, Phys. Lett. A196 , 154 (1994); A. Enders and G. Nimtz, Phys. Rev. E48 , 632 (1993).

Terence Tao has pointed out that apparent FTL transmission of an audio signal over such a short distance is not very impressive. The signal takes less than 0.4 ns to travel the 11.4 cm at light speed, but it is quite easy to anticipate an audio signal ahead of time by up to 1000 ns simply by extrapolating the signal waveform. Although this is not what is being done in the above experiments, it does illustrate that the experimenters will need to use a much higher frequency random signal, or transmit over much larger distances, if they are to demonstrate FTL information transfer convincingly.

The likely conclusion is that there is no real FTL communication taking place, and that the effect is another manifestation of the Heisenberg Uncertainty Principle.

12. Casimir Effect

The Casimir Effect describes the fact that a very small but measurable force exists between two uncharged conducting plates when they are very close together. It is due to the existence of vacuum energy (see the FAQ article on the Casimir Effect ). A surprising calculation by Scharnhorst suggests that photons travelling across the gap between the plates in the Casimir Effect must go faster than c by a very very small amount (at best 1 part in 10 24 for a 1 nanometre gap.) It has been suggested that in certain cosmological situations, such as in the vicinity of cosmic strings if they exist, the effect could be much more pronounced. Even so, further theoretical investigations have shown that, once again, there is no possibility of FTL communication using this effect. Refs: K. Scharnhorst, Physics Letters B236 , 354 (1990) S. Ben-Menahem, Physics Letters B250 , 133 (1990) Andrew Gould (Princeton, Inst. Advanced Study). IASSNS-AST-90-25 Barton & Scharnhorst, J. Phys. A26 , 2037 (1993).

13. Expansion of the Universe

According to Hubble's Law, two galaxies that are a distance D apart are moving away from each other at a speed HD , where H is Hubble's constant. So this interpretation of Hubble's Law implies that two galaxies separated by a distance greater than c/H must be moving away from each other faster than light. Actually, the modern viewpoint describes this situation differently: general relativity takes the galaxies as being at rest relative to one another, while the space between them is expanding. In that sense, the galaxies are not moving away from each other faster than light; they are not moving away from each other at all! This change of viewpoint is not arbitrary; rather, it's in accord with the different but very fruitful view of the universe that general relativity provides. So the distance between two objects can be increasing faster than light because of the expansion of the universe, but this does not mean, in fact, that their relative speed is faster than light.

As was mentioned above, in special relativity it is possible for two objects to be moving apart by speeds up to twice the speed of light as measured by an observer in a third frame of reference. In general relativity even this limit can be surpassed, but it will not then be possible to observe both objects at the same time. Again, this is not real faster-than-light travel; it will not help anyone to travel across the galaxy faster than light. All that is happening is that the distance between two objects is increasing faster when taken in some cosmological reference frame.

14. The Moon revolves round my head faster than light!

Stand up in a clear space and spin round. It is not too difficult to turn at one revolution each two seconds. Suppose the Moon is on the horizon. How fast is it spinning round your head? It is about 385,000 km away, so the answer is 1.21 million km/s, which is more than four times the speed of light! It might sound ridiculous to say that the Moon is going round your head when really it is you who is turning, but according to general relativity all co-ordinate systems are equally valid, including rotating ones. So isn't the Moon going faster than light?

What it comes down to is the fact that velocities in different places cannot be compared directly in general relativity. Notice that the Moon is not overtaking any light in its own locality. The speed of the Moon can only be compared to the speeds of other objects in its own locality. Indeed, the concept of speed is not a very useful one in general relativity, and this makes it difficult to define what "faster than light" means. Even the statement that "the speed of light is constant" is open to interpretation in general relativity. Einstein himself, on page 76 of his book "Relativity: the Special and the General Theory", wrote that the statement cannot claim unlimited validity. When there is no absolute definition of time and distance it is not so clear how speeds should be determined.

Nevertheless, the modern interpretation is that the speed of light is constant in general relativity and this statement is a tautology given that standard units of distance and time are tied together using the speed of light. The Moon is given to be moving slower than light because it remains within the "future light cone" propagating from its position at any instant.

Relativity Arguments Against FTL Travel

15. what does "faster than light" mean.

The cases given so far only demonstrate how difficult it is to pin down exactly what we mean by FTL travel or communication. If we do not include things such as moving shadows, then what exactly do we mean by FTL?

In relativity there is no such thing as absolute velocity, only relative velocity; but there is a clear distinction between "world lines" that are "timelike", "lightlike", and "spacelike". By "world line" we mean a curve traced out in the four dimensions of space-time. Such a curve is the set of all events that make up the history of a particle. If a world line is spacelike then it describes something moving faster than light. So there is a clear meaning of what is meant by a "faster-than-light" speed which does not depend on the existence of third-party observers.

But what do we mean by an "object" if we don't want to include shadows? We could define an object to be anything that carries energy, charge, spin, or information; or perhaps just that it must be made of atoms, but there are technical problems in each case. In general relativity energy cannot be localised, so we had better avoid using energy in our definition. Charge and spin can be localised, but not every object need have charge or spin. Using the concept of information is better but tricky to define, and sending information faster than light is really just FTL communication—not FTL travel. Another difficulty is knowing whether an object seen at A is the same as the one that was earlier seen at B when we claim that it has travelled across the gap faster than light. Could it not be a duplicate? It could even be argued that FTL communication makes FTL travel possible, because you can send the blueprint for an object FTL as advance information, and then reconstruct the object—although not everyone would accept such teleportation as FTL travel.

The problems of specifying just what we mean by FTL are more difficult in general relativity. A valid form of FTL travel may mean distorting space-time (e.g. making a worm hole) to get from A to B without going on a spacelike curve locally. There is a distinction between going faster than light locally and getting from A to B faster than light globally . When a gravitational lens bends the light coming from a distant galaxy asymmetrically, the light coming round the galaxy on one side reaches us later than light that left at the same time and went round the other side. We must avoid a definition of FTL travel that says a particle going from A to B gets there before light that has made the same journey along a lightlike geodesic. This makes it very difficult, perhaps impossible, to define global FTL travel unambiguously.

If you were expecting me to finish this section with a precise definition of what is meant by FTL travel and FTL communication, I am afraid I must disappoint you! The above difficulties are insurmountable. Nonetheless, you will probably recognise the real thing when confronted with it now that I have given some examples of what would not be FTL travel.

16. The Infinite-Energy Argument

When Einstein wrote down his postulates for special relativity, he did not include the statement that you cannot travel faster than light. There is a misconception that it is possible to derive it as a consequence of the postulates he did give. Incidentally, it was Henri Poincare who said "Perhaps we must construct a new mechanics [...] in which the speed of light would become an impassable limit." That was in an address to the International Congress of Arts and Science in 1904—before Einstein announced special relativity in 1905.

It is a consequence of relativity that the energy of a particle of rest mass m moving with speed v is given by

As the speed approaches the speed of light, the particle's energy approaches infinity. Hence it should be impossible to accelerate an object with rest mass to the speed of light; also, particles with zero rest mass must always move at exactly the speed of light, since otherwise they would have no energy. This is sometimes called the "light speed barrier", but it is very different from the "sound speed barrier". As an aircraft approaches the speed of sound it starts to feel pressure waves which indicate that it is moving close to the speed of sound, and before the existence and effects of these waves were well understood, they destroyed several aircraft in the mid 20th century; hence the old name of sound "barrier". In fact, with more thrust and the right aerodynamics, an aircraft can certainly pass through the sound barrier.

The situation is different for light. As the light speed barrier is approached (in a perfect vacuum) there are no such waves according to relativity (destructive or otherwise). Moving at 0.999 c is just like standing still with everything rushing past you at −0.999 c . Particles are routinely pushed to these speeds and beyond in accelerators, so the theory is well established. Trying to attain the speed of light in this way is a matter of chasing something that is forever just out of your reach.

This explains why it is not possible to exceed the speed of light by ordinary mechanical means. But it does not in itself rule out FTL travel. It is really just one way in which things cannot be made to go faster than light, rather than a proof that there is no way to do so. Particles are known to decay instantly into other particles which fly off at high speed. It is not necessary to think in terms of the particles' having been accelerated, so how could we say that they could not go faster than light? What about the possibility of particles that might always have been moving faster than light, and which might be used to send information if they can be detected without ever slowing down to less than the speed of light? Even if such "tachyons" don't exist (and we don't believe that they do exist), there may be ways of moving matter from A to B faster than light is able to travel from A to B by the usual route, but without anything having to go at a FTL speed locally. See the paragraph on tachyons below .

17. Quantum Field Theory

Except for gravity, all physical phenomena are observed to comply with the "Standard Model" of particle physics. The Standard Model is a relativistic quantum field theory which incorporates the nuclear and electromagnetic forces as well as all the observed particles. In this theory, any pair of operators corresponding to physical observables at space-time events separated by a spacelike interval "commute" (i.e. their order can be reversed). In principle, this implies that effects cannot propagate faster than light in the standard model, and it can be regarded as the quantum field theory equivalent of the infinite energy argument.

But no completely rigorous proofs of anything exist in the quantum field theory of the Standard Model, since no one has yet succeeded in showing that the theory is completely self consistent; and in fact, most likely it is not! In any case, there is no guarantee that there are not other undiscovered particles and forces that disobey the no-FTL rule. Nor is there any generalisation that takes gravity and general relativity into account. Many physicists working on quantum gravity doubt that such simplistic expressions of causality and locality will be generalised. All told, there is no guarantee that light speed will be meaningful as a speed limit in a more complete theory that might arise in the future.

18. Grandfather Paradox

A better argument against FTL travel is the Grandfather Paradox. In special relativity, a particle moving FTL in one frame of reference will be travelling back in time in another. FTL travel or communication should therefore also give the possibility of travelling back in time or sending messages into the past. If such time travel is possible, you would be able to go back in time and change the course of history by killing your own grandfather. This is a very strong argument against FTL travel, but it leaves open the perhaps-unlikely possibility that we may be able to make limited journeys at FTL speed that did not allow us to come back. Or it may be that time travel is possible and causality breaks down in some consistent fashion when FTL travel is achieved. That is not very likely either, but if we are discussing FTL then we had better keep an open mind.

Conversely, if we could travel back in time we might also claim the ability to travel FTL, because we can go back in time and then travel at a slow speed to arrive somewhere before light got there by the usual route. See the FAQ article on Time Travel for more on this subject.

Open Possibilities for FTL Travel

In this last section I give a few of the speculative but serious suggestions for possible faster-than-light travel. These are not the kinds of thing usually included in the FAQ because they raise more questions than answers. They are included merely to make the point that serious research is being done in this direction. Only a brief introduction to each topic is given; more information can be found all over the Internet (and should, like almost everything on the Internet, be taken with a huge grain of salt!).

19. Tachyons

Tachyons are hypothetical particles that travel faster than light locally. Their mass must take on imaginary values (i.e. to do with the square root of −1) to be able to do so, but they have real-valued energy and momentum. Sometimes people imagine that such FTL particles would be impossible to detect, but there is no reason to think so. Shadows and spotlights suffice to show that there is no logic in this suggestion, because they can certainly go FTL and still be seen.

No tachyons have definitely been found and most physicists doubt their existence. There has been a claim that experiments to measure neutrino mass in tritium beta decay indicated that the neutrinos were tachyonic. ; while this is very doubtful, it is not entirely ruled out. Tachyon theories have problems because, apart from the possibility of causality violations, they destabilise the vacuum. It may be possible to get around such difficulties—but then we would not be able to use tachyons for the kind of FTL communication that we would like.

The truth is that most physicists consider tachyons to be a sign of pathological behaviour in field theories, and the interest in them among the wider public stems mostly from the fact that they are used so often in science fiction. See the FAQ article on Tachyons .

20. Worm Holes

A famous proposition for global FTL travel is to use "worm holes". Worm holes are shortcuts through space-time from one place in the universe to another which would permit you to go from one end to the other in a shorter time than it would take light passing by the usual route. Worm holes are a feature of classical general relativity, but to create them you have to change the topology of space-time. That might be possible within a theory of quantum gravity.

To keep a worm hole open, regions of negative energy would be needed. Misner and Thorne have suggested using the Casimir Effect on a grand scale to generate the negative energy, while Visser has proposed a solution involving cosmic strings. These are very speculative ideas which may simply not be possible. Exotic matter with negative energy may not exist in the form required.

Thorne has found that if worm holes can be created, then they can be used to construct closed timelike loops in space-time which would imply the possibility of time travel. It has been suggested that the "multiverse" interpretation of quantum mechanics (many universes co-existing) gets you out of trouble by allowing time to evolve differently if you succeed in going back to a previous time. But multiverses are entirely out of keeping with the Ockham's Razor approach to doing science, and constitute more of a popular interpretation of quantum mechanics than a serious physical theory. Hawking says that worm holes would simply be unstable and therefore unusable. The subject remains a fertile area for thought experiments that help clarify what is and what is not possible according to known and suggested laws of physics. Refs: W. G. Morris and K. S. Thorne, American Journal of Physics 56 , 395–412 (1988) W. G. Morris, K. S. Thorne, and U. Yurtsever, Phys. Rev. Letters 61 , 1446–9 (1988) Matt Visser, Physical Review D39 , 3182–4 (1989) See also "Black Holes and Time Warps", Kip Thorne, Norton & co. (1994) For an explanation of the multiverse see "The Fabric of Reality" David Deutsch, Penguin Press.

21. Warp Drives

A "warp drive" such as used in the Star Trek science fiction series would be a mechanism for warping space-time in such a way that an object could move faster than light. Miguel Alcubierre made himself famous by working out a space-time geometry which describes such a warp drive. The warp in space-time makes it possible for an object to go FTL while remaining on a timelike curve. The main catch is the same one that may stop us making large worm holes. To make such a warp, you would need exotic matter with negative energy density. Even if such exotic matter can exist, it is not clear how it could be deployed to make the warp drive work. Ref. M. Alcubierre, Classical and Quantum Gravity, 11 , L73–L77, (1994). Ref. S. Finazzi, S. Liberati, C. Barcel�, Semiclassical instability of dynamical warp drives at arxiv.org.

To begin with, it is rather difficult to define exactly what is really meant by FTL travel and FTL communication. Many things such as shadows can go FTL, but not in a useful way that can carry information.
There are several serious possibilities for real FTL which have been proposed in the scientific literature, but these always come with technical difficulties.
The Heisenberg Uncertainty Principle tends to stop the use of apparent FTL quantum effects for sending information or matter.
In general relativity there are potential means of FTL travel, but they may be impossible to make work. It is thought highly unlikely that engineers will be building space ships with FTL drives in the foreseeable future, if ever, but it is curious that theoretical physics as we presently understand it seems to leave the door open to the possibility.
FTL travel of the sort science fiction writers would like is almost certainly impossible. For physicists the interesting question is "why is it impossible and what can we learn from that?"

8.2 How FTL Travel Implies Violation of Causality

Description.

This article is from the Relativity and FTL Travel FAQ , by Jason W. Hinson [email protected] with numerous contributions by others.

I refer you back to Diagram 2-9 (reproduced below as Diagram 8-1) so that I can demonstrate the causality problem involved with FTL travel. There you see two observers passing by one another. Diagram 8-1 (Copy of Diagram 2-9) t t' | / + / | / __--x' + / __C'- |/__-- -+---+---+-__o---+---+---+- x * __-- /| __-- / + -- / | / + / | The origin marks the place and time where the two observers are right next to one another. The x' and t' axes are said to represent the frame of reference of O' (I'll use Op--for O-prime--so that I can easily indicate the possessive form of O as O's and the possessive form of O' as Op's). The x and t axes are then the reference frame of the O observer. We consider the O system to be our rest system, while the Op observer passes by O at a relativistic speed. As you can see from the two coordinate systems, the two observers measure space and time in different ways. Now, consider again the event marked "*". Cover up the x and t axis and look only at the Op system. In this system, the event is above the x' axis. If the Op observer at the origin could look left and right and see all the way down his space axis instantaneously, then he would have to wait a while for the event "*" to occur. Now cover up the Op system and look only at the O system. In this system, the event is below the x axis. So to O, the event has already occurred by the time the two observers are passing one another. Normally, this fact gives us no trouble. If you draw a light cone (as discussed in Section 2.8) through the origin, then the event will be outside of the light cone. As long as no signal can travel faster than the speed of light, then it will be impossible for either observer to know about or influence the event. So even though it is in one observer's past, he cannot know about it, and even though it is in the other observer's future, he cannot have an effect on it. This is how relativity saves its own self from violating causality. However, consider the prospect of FTL travel with this diagram in mind. As O and Op pass by one another, the event "*" has not happened yet in Op's frame of reference. Thus, if he can send an FTL signal fast enough, then he should be able to send a signal (from the origin) which could effect "*". However, in O's frame, "*" has already occurred by the time O and Op pass by one another. This means that the event "Op sends out the signal which effects *" occurs after the event which it effects, "*", in O's frame. For O, The effect precedes the cause. Thus, the signal which travels FTL in Op's frame violates causality for O's frame. Similarly, since "*" has already occurred in O's frame when O and Op pass one another, then in his frame an FTL signal could be sent out from "*" which could reach O and tell him about the event as the two observer's past. However, for Op, the event "O learns about * as O and Op pass one another" comes before * itself. Thus, the signal which is FTL in O's frame violates causality in Op's frame. In short, for any signal sent FTL in one frame of reference, another frame of reference can be found in which that signal actually traveled backwards in time, thus violating causality in that frame. Notice that in this example I never mentioned anything about how the signal gets between the origin and *. I didn't even require that the signal be "in our universe" when it was "traveling" (remember our definition of FTL travel in Section 6.1). The only things I required were that (1) the signal's "sending" and "receiving" were events in our universe and (2) the space-time between the origin and "*" is flat (i.e. it is correctly described by special relativity diagrams). Some FTL ideas may invalidate the second assumption, but we will consider them a bit later. We will find, however, that violation of causality still follows from all the FTL travel concepts.

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Q: Hyperspace, warp drives, and faster than light travel: why not?

Physicist : Firstly: no. But, if you’re really set on it: maybe. The essential problems are that moving faster than light (FTL) requires impossible acceleration (not difficult but impossible in a “doesn’t make sense to talk about” kind of way), and FTL violates causality in some weird ways (for example, it allows travel backward in time).

This needs a little background, so pack a lunch.

Differently moving observers see events happen in different places. For example, if you’re in a car, everything you do seems to be happening in more or less the same place, while for someone on the side of the road all the things that you do are strung out along the car’s route.

Perspectives that are moving with respect to each other are said to be in different “frames”. So everyone in the car are in one frame, everyone waiting at a bus stop are in another frame, and everyone in an airplane overhead are in yet another frame. There’s nothing more to frames than that. So, something like “move to a different frame” just means “change speed”.

Alice (red) and Bob (blue) are moving with respect to each other. For no particularly good reason Alice sets off two firecrackers (green crosses). In Alice's frame (left) the explosions happen in the same place, one after the other. In Bob's frame (right) the explosions happen in different places. In all of the diagrams in this post, time is up and space is right/left.

Galileo (the famous one) recognized that in different frames the same events happen in different places (picture above). More than that, he realized that all of the physics that he knew of worked the same regardless of the frame (moving / not moving), and with remarkable humility he named that realization “Galilean Equivalence”.

In 1905 the ‘Stein introduced a theory about relative movement that took Galilean Equivalence (physical laws are the same in all frames) and added invariance of light speed in all frames. This is the corner-stone of relativity, and it’s called the “Einstein Equivalence Principle”. The first big result of the EEP, is that not only do different frames disagree on where events happen, but also when . It’s a bit much to go into, so if you’re interested in why, there’s an “explanation” in this post .

Different frames (red and blue) disagree on, among other things, what "now" is. The time that an event occurs, and even the order of events, can be changed by moving from one frame to another. The dashed lines are a single moment in time, (which are different) from each frame's perspective.

In the world according to Galileo (pre-relativity) any event could be moved relative to any other just by moving very fast. For example if two events happen in the same place, but one hour apart according to Alice, then Bob can make the second event happen 60 miles away from the first by moving at 60 miles per hour relative to Alice. Sadly, questions about “who’s right?” aren’t valid. The universe has no “preferred frame”.

In Galileo’s old-timey world view there are some restrictions to how events can be rearranged from one frame to another. Namely, the time when an event occurs never changes, and the future is always the future, and the past is always the past.

With the advent of relativity that was no longer the case, however, new restrictions popped up. A pair of events can be separated in three ways: timelike, lightlike, and spacelike.

For a given event (center, black) all other events fall into one of three categories: timelike, lightlike, or spacelike separated. The yellow lines represent the path that light takes through the given event. The spacelike event can move around in its area on the right (even allowing it to occur before or after the center event), and the timelike event can move around in its area on the top.

Timelike separation means that there’s some frame in which the two events happen in the same place. That is, if you move fast enough (slower than light) you can be present at both. Timelike separated events always happen in an order: no matter what frame you’re in, everyone will agree which event happened first and which happened second. Every event you’ve ever personally experienced has been “timelike separated” from every other.

Lightlike separation means that to be present at both events you’d have to be traveling at light speed.

Spacelike separated means that there’s no way to be present at both events, even travelling at the speed of light. Things that are happening in Alpha Centauri “right now” are spacelike separated from us (right now). There is always some frame in which spacelike separated events happen at the same time, but never in the same place. Even weirder, spacelike separated events don’t have an order . Different frames will disagree on which happens first.

So, finally: here’s the issue. If you accelerate like crazy, get a huge rocket or whatever, the highest speed you can get up to is almost the speed of light. The “start” and “stop” events of your journey will always be timelike separated, regardless of how high your acceleration, or how long you accelerate for. Traveling faster than light means that your start and stop events are spacelike separated, and there is no physically real acceleration that can get you to move like that. Most people are willing to forgive that, and say: “Dude, wormholes and warp drives! S’cool!”. But those brave souls still need to contend with the second issue: causality.

A ship with some kind of FTL drive races a beam of light. Left: The ship engages the drive (green cross), simply moves faster than light for a while, then disengages the drive (red cross). Right: The exact same situation as viewed from a different frame.

Say you’ve got the Enterprise ( NCC-1701 ) and it works just like you’d expect: it cruises around at sub-light speeds until it engages its warp drive, which allows it to move at FTL speeds. It moves from one star system to another, then eventually disengages the drive and “drops out of warp”, no harm no foul. However! When viewed from a different frame, the same situation can be very strange.

The engage and disengage events are spacelike separated, so they don’t actually have an order. From (any one of) the proper frames, the disengage event can happen first (right half of the image above). When that’s the case you find that:

-First there’s one ship, traveling slower than light.

-Then suddenly, and without cause of any kind, two new copies of the ship appear at a place some distance away. One is traveling faster than light, and the other is traveling slower. This event corresponds with the drive being shut down.

-The FTL version travels backward until it contacts the original ship, at which point they both disappear at the moment that the original engages its drive.

Now, sure, ships coming into existence and popping out again may seem bad enough, but the big problem is that FTL travel opens the door to backward time travel (forward is fine: you’re doing it now).

By taking a couple spacelike paths that end earlier than they started you can zig-zag back in time and find yourself in the same place you started, but earlier than the time when you originally left (in the example on the right side of the picture above the route gets you back to before you left, but in a different location).

Time traveling zig-zag: If you can get into the past somewhere else once, then why not do it twice and get into your own past?

There are a lot of problems with time travel (see: “Time Cop” and “Back to the Future”). But, paradoxes and amazing one-liners aside, it seems to be very impossible. There is no indication, direct or indirect, that the future can affect the past at all ( except for psychics , obviously ), let alone that anything can physically move from the future to the past. So; case closed. As long as the future follows the past, nothing can travel faster than light.

Spacetime diagrams for some sci-fi ideas about FTL (from left to right, then top to bottom): Star Trek or Star Wars, Battlestar Galactica, Babylon 5, and Dr. Who. Dashed lines are connections, not traversed distance. Click to enlarge.

But wait! Despite their romantic prospects, physicists are consummate, rarely-say-die, optimists. In that vein they’ve come up with several scenarios that (if real) would allow for FTL travel, but circumvent the whole time-travel thing.

The quickest way is to alter one of the basic assumptions of relativity; namely that all frames are equivalent. Just declare that FTL travel is possible, but only in one direction. That prevents things from zig-zagging into the past, but it also makes space travel kinda boring. Sure you can explore stuff, but you can never get home.

Alternatively, you can declare that there exists one unique frame such that no paths into the past are possible. Although other frames still get weird effects (disappearing ships, and causeless events, and whatnot), nothing can to loop back into its own past. I think this is the idea that most sci-fi shows and books are working with, but that’s meeting them more than half way.

21 Responses to Q: Hyperspace, warp drives, and faster than light travel: why not?

Relating to the “fictional universe” thing, can you elaborate on the last paragraph a little? If I understand right, basically what you’re saying is if you had a universe that did possess a preferred frame of reference, then this aspect of FTL wouldn’t exist?

You wouldn’t have to worry in general about things going into their own past (which is what causes problems and paradoxes). In a nutshell, the last paragraph is about establishing an absolute ordering of the events that any object can experience. That is, if you see an “effect” at some point, there’s no way that you can travel such that later (for you) you’ll see the “cause”. I’m not sure that be-clears or be-murkys.

I remember reading in some book that logically considered the physics in Star Trek and explained the impossibilities and circumventions, and there was something that I *probably* didn’t understand properly, but seems relevant here.

The author did a bit of work describing that, while it would need an astronomical amount of energy, it’s still physically possible to travel distances faster than light would, by shrinking the space between you and the destination. Your ship never moves faster than light, and you still arrive a thousand years faster than you normally would.

I was worrying about that. That’s why I was careful to talk about “starting” and “ending” events while ignoring everything in between. The exact method used to get from one place to another isn’t terribly important. In Star Trek the warp drive makes the acceleration “real”, but the “causality problems” remain. So, while locally , the ship never moves faster than light it does still move faster than light globally , and that’s what causes problems. Confused readers should read about the “ Alcubierre Drive ” which is (frankly) the result of a physicist watching too much Star Trek.

Have you seen the experiment on light that moves faster than light by moving backwards? http://rochester.edu/news/show.php?id=2544

It’s not as exciting as it sounds (unfortunately). They’re basically doing this again.

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Are there really causality problems with FTL?? My understanding of the equations for time v. speed is that time isn’t negative with FTL, but complex. I tend to think that is fundamentally different.

Mass is the same way. Sure, C is impossible for anything with mass, but close to it on either side isn’t. Given the interesting reports on neutrinos lately (still unconfirmed) I wasn’t all that shocked! In fact, I had generally wondered why anything with mass would consistently travel near the speed of light for any reasonable length of time. However, if they are traveling faster than light, it makes perfect sense! They can never slow down to the speed of light because of the infinite mass problem.

Fair enough! That’s why I was careful not to talk too much about how the FTL object experiences time, and just tried to stick to where/when it ends up from the perspective of other reference frames, which is where the real problems crop up.

By complex, I meant that it was in the form of a mathematically complex number, that is a+bi and not a straight forward negative number.

Also, another error that I think many people make is to think that if it were actually a straight forward negative number, that would mean that they would travel backwards in the time of a stationary observer. In reality, It would mean they age in a negative direction to include the causality issue of arriving at there destination at the age of 20years old prior to deciding to leave for it at the age of 40.

If it can be shown that neutrinos, or anything for that matter, do travel FTL(I’m not saying that they do. I’m going to wait for the experimental data to come in..), we are definitely going to have to wrap our minds around what a+bi actually implies in terms of relativity.

Doesn’t hurt to get a head start…alas though, it makes my brain hurt. uhg! lol I hate complex numbers!

$L^2 = ct^2-x^2-y^2-z^2$

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Traveling faster than light means that your start and stop events are space-like separated? I thought you said traveling at light-speed means that the start and stop events are light-like separated. Could you mean that light like separation is infinite (since one’s mass would become infinite at light-speed), faster than light would be the causality problem due to individuals in different frames (people on a starship in normal space would be perceiving a space-like separation start-stop event occurring in random locations, while the people on board the trans-light vessel would be perceiving it as if it were them going to their destination? I’m trying to wrap my head around this but say an anti-gravity flux between star cores aided in the directional accuracy at which a starship “jumped” along a theoretical jump “line” of anti-gravitational flux? Thus it could use the stars as way-points, and the jump-points at these anti-gravity wells in various locations within star systems (getting into fiction a bit I know, but I’m trying to come up with a legitimate explanation for rapid interstellar travel involving other dimensions coiled up and the effects of anti-gravity and anti-matter have on these dimensions. :P)

FTL with equations:

http://www.shankaranarayanan.com/special-general-space-spatial-hyperspatial-time-relativity-hyperspace-hyper-hyperspatial-theory-faster-than-light-travel-to-stars/

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Well, entropic arrow of time aside, it seems to me that there’s nothing that privileges the past over the future in terms of information flow–past events cause future events, to be sure, but future events can also be extrapolated into past events, so causality can be said to be subjective. Hence, going back in time can be possible as long as causality doesn’t mind pairs of objects appearing out of nowhere. However, we know that causality does , in fact, allow pairs of objects to appear out of nowhere–this is the basis of Hawking radiation, after all. Also, it turns out that antimatter is exactly equivalent to matter with its reactions reversed in time (and also space–specifically, chirality/spin–I think), meaning that the best interpretation of Hawking radiation is particles which escape a black hole by spontaneously exceeding the speed of light–that is, going back in time. Extrapolating from there, a FTL/retrotemporal ship would be observed as a mirror-image ship traveling in reverse with negative mass that was spontaneously generated along with a ship at its destination, and eventually annhilated a younger version of the same ship. Of course, this is probably not practical on a large scale. In any case, quantum effects also smooth over paradoxical situations–for example, the grandfather paradox is resolved as being, and having always been, a superposition of one universe where a guy decides to go back in time and kill his grandfather, and another universe where a time-traveler appears and shoots a man before he can become a grandfather. (I heard that some computer simulation discovered that, given a ball fired into a wormhole that opens in the past in such a way that it will knock its past self away from said wormhole, there is always a solution for which the ball emerges from a wormhole at an angle and alters its trajectory so that it enters the wormhole at the same angle. Finding such solutions is likely much easier if superpositions are allowed.)

Considering you’re technically a scientist it’s stunning that you pose the question: “Hyperspace, warp drives, and faster than light travel: why not?” then proceed to answer as if they’re all the same thing. They are absolutely – no ambiguity – not.

It’s mind boggling that articles like this and on other science related sites need to educate themselves on what FTL is and isn’t. Having a spaceship that can travel interstellar distances in a short amount of time does not mean its travelling faster than light. Frankly it’s embarrassing that this has to be said.

FTL violates the laws of physics, period – travelling using warp or some other variation of wormhole does not.

As of right now we know – and feel free to ask the next physicist you meet that’s not you – that creating a wormhole or a warp bubble or enclosure or whatever you want to call it – does NOT violate the laws of physics. Two years ago Alcubierre published his work and while it has been modified and been written about extensively it has not been shown to violate physics as we know them.

Yes, there are problems such as exotic material which may or may not be possible to create and when the theory was first published it required fuel quantities about the size of a large gas giant but in less than a year another physicist made a modification to the equations that reduced that to the size of a minivan.

You simply cannot say that in fifty or a hundred or five hundred years we will not be able to solve these obstacles. That would be incredibly arrogant and history is littered with the forgotten names of those that said “can’t” in the world of science.

Again, FTL is impossible without rewriting the laws of physics – yeah, we get that. Other ways around interstellar distances such as warp, wormholes or variants of such are not impossible and do not violate the laws of physics. That can can be said empirically.

@Paul Davis – while it’s true that Alcubierre’s concept by itself doesn’t permit backward-in-time travel, and thereby causality paradoxes…apparently there are ways to exploit a pair of warp drives to create a true causality paradox. Allen Everett published a paper about it in 1995, which can be found here: http://exvacuo.free.fr/div/Sciences/Dossiers/Time/A%20E%20Everett%20-%20Warp%20drive%20and%20causality%20-%20prd950914.pdf

Honestly it’s such an incredibly tedious read that I gave up on it (a few diagrams would’ve been nice, Dr. Everett). But I plan on getting back to it sometime. Because most of the writing I’ve seen on this subject strikes me as rather unconvincing, and it’s crucial to know for certain if warp field propulsion necessarily yields real, rather than apparent, causality violations.

For example, one “proof” of a warp field causality violation that I read recently described a canine traveler moving at 4C wrt an observer on the Earth, flying past the Earth and grabbing a water balloon, then striking a cat at some distance from the Earth. The cat is struck by the water balloon before it sees the canine acquire the balloon at the Earth. But this is merely an apparent causality violation from the cat’s POR. The wet cat could then watch a time-reversed image of its assailant moving backward toward the Earth, where the water balloon was acquired, and realize that the tool of its misery had been acquired in the past in a region formerly outside of its perception. No real causality violation has occurred, because if the doused cat had killed the passing canine, it wouldn’t prevent the rascally dog’s prank from transpiring. In fact I’ve yet to see a rigorous and compelling proof that superluminal travel yields actual paradoxes rather than illusory ones – perhaps Everett’s paper will convince me.

Because I can hold out hope that a deeper understanding of dark energy, or a sensible model of the cosmic inflation mechanism, may one day allow us to circumnavigate the warp field requirement for (imaginary) negative mass. But a genuine causality violation seems like a deal breaker, unless there’s another dimension of time (per Dr. Itzah Bars’ work on 2T physics).

It’s interesting that Einstein concluded that FTL causality paradoxes offer no logical objections, but he felt that their absence from our observations of the world sufficed to prove them untenable. Because absence of evidence is not evidence for absence – if superluminal travel requires conditions that can only be produced artificially, like we see in today’s metamaterials for example, then we should expect to observe new phenomena as our technological capabilities expand in the centuries and millennia ahead.

My thanks to The Physicist for providing a fun article on this subject. I just don’t find the argument convincing because I don’t see an explicit treatment here describing how FTL travel can return a voyager to the same space at an earlier time. Alcubierre’s metric maintains synchronized proper time and coordinate time, so simple warp field FTL travel forbids backwards travel through time, contrary to the “Time-traveling zig-zag” diagram above.

To avoid apparent time travel at FTL speeds would require:

1. A technologically feasible means of said speed.

2. A new relativity to describe the properties of the reconfigured spacetime that allows FTL speed.

What is nice about the new relativity theory is that it wouldn’t have to supercede the current theory. Instead, you would simply have two versions, call them subluminal and superluminal.

In the case of wormholes, you wouldn’t even need a new relativity.

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Q: Does quantum mechanics really say that there’s some probability that objects will suddenly start moving or that things can suddenly “shift” to the other side of the universe?
Q: Using modern technology, are we any closer to turning lead into gold than alchemists were hundreds of years ago?
Q: How do you turn/change directions in space?
Q: If a man hangs on an un-insulated wire using both his hands what will happen and why?
Learning intro number theory
Q: Is the Alcubierre warp drive really possible? How close are we to actually building one and going faster than light?
Q: Is darkness a wave the way light is a wave? What is the speed of dark?
Q: Is it a coincidence that a circles circumference is the derivative of its area, as well as the volume of a sphere being the antiderivative of its surface area? What is the explanation for this?
Q: If hot air rises, why is it generally colder at higher elevations?
Q: What is quantum teleportation? Why can’t we use it to communicate faster than light?
Q: Since all particles display wave-like characteristics, does that imply that one could use destructive wave interference to destroy or at least drastically change a particle?
Q: How does the Oberth Effect work, and where does the extra energy come from? Why is it better for a rocket to fire at the lowest point in its orbit?
Q: How do lenses that concentrate light not violate the second law of thermodynamics? If you use a magnifying glass to burn ants, aren’t you making a point hotter than the ambient temperature without losing energy?
Q: What makes natural logarithms natural? What’s so special about the number e?
Q: If the world were to stop spinning, would the people and everything on it be considered ‘lighter’ or ‘heavier’? Would any change take place? And does centrifugal force have an effect on gravity?
Q: Two entangled particles approach a black hole, one falls in and the other escapes. Do they remain entangled? What about after the black hole evaporates?
Q: If there are 10 dimensions, then why don’t we notice them?
Q: Will the world end tomorrow?
Q: In an infinite universe, does everything that’s possible have to happen somewhere?
Q: Which of Earth’s life forms could survive on each planet of the Solar System?
Q: What are fractional dimensions? Can space have a fractional dimension?
Q: Are shadows 2-dimensional? Are there any real examples of 2-dimensional things in the universe?
Q: Is it possible to experience different rates of time? If time were to speed up, slow down, or stop, what would you experience?
Q: How many theorems are there?
Q: How much of a direct effect do planets and stars have on us? Is astrology reasonable or plausable?
Q: Why are scientists looking for life in space by looking for water? How can they be sure that all life uses water?
Q: If energy is neither created nor destroyed, what happens to the energy within our bodies and brains when we die?
Q: Could Kurt Vonnegut’s “Ice-9 catastrophe” happen?
Q: How accurately do we need to know π? Is there a reason to know it out to billions of digits?
My bad: If fusion in the Sun suddenly stopped, what would happen?
Q: If fusion in the Sun suddenly stopped, what would happen?
Q: Does opening a refrigerator cool down the room?
Q: What is the probability of an outcome after it’s already happened?
Q: How do you answer a question scientifically?
Q: Why are the days still longer than nights, until a few days after the fall equinox?
Q: What is a Fourier transform? What is it used for?
Q: What are singularities? Do they exist in nature?
Q: Is it likely that there are atoms in my body that have traveled from the other side of the planet, solar system, galaxy, or universe?
Q: Is there a number set that is “above” complex numbers?
Q: Are the brain and consciousness quantum mechanical in nature?
Q: How are voltage and current related to battery life? What is the difference between batteries with the same voltage, but different shapes or sizes? What about capacitors?
Q: What are virtual particles?
Q: Would it be possible to create an antimatter weapon by “harvesting” enough antimatter, containing it in an electro-magnetic field and placing that in a projectile?
Q: If Earth was flat, would there be a horizon? If so, what would it look like? If the Earth was flat and had infinite area, would that change the answer?
Q: Is there an experiment which could provide conclusive evidence for either the Many Worlds or Copenhagen interpretations of quantum physics?
Q: If you could drill a tunnel through the whole planet and then jumped down this tunnel, how would you fall?
Q: How many people riding bicycle generators would be needed, in an 8-hour working day, to equal or surpass the energy generated by an average nuclear power plant?
Q: Why is hitting water from a great height like hitting concrete?
Q: How does instantaneous communication violate causality?
Q: What is the “False Vacuum” and are we living in it?
Q: How would the universe be different if π = 3?
Q: Is it possible for an artificial black hole to be created, or something that has the same effects? If so, how small could it be made?
Q: Do colors exist?
Q: How can we see the early universe and the Big Bang? Shouldn’t the light have already passed us?
Q: Are beautiful, elegant or simple equations more likely to be true?
Q: If quantum mechanics says everything is random, then how can it also be the most accurate theory ever?
Q: Why do wet stones look darker, more colorful, and polished?
Q: What would the universe be like with additional temporal dimensions?
The 2012 Venus transit
Q: Why haven’t we discovered Earth-like planets yet?
Q: Is quantum randomness ever large enough to be noticed?
Q: How is radiometric dating reliable? Why is it that one random thing is unpredictable, but many random things together are predictable?
Q: Is the final step in evolution an ascension into an energy-based lifeform?
Q: What would life be like in higher dimensions?
Q: How much does fire weigh?
Q: Since the real-world does all kinds of crazy calculations in no time, can we use physics to calculate stuff?
Q: Is there some way to actually play quidditch?
Q: Can you poke something that’s far away with a stick faster than it would take light to get there?
Q: Does how you deal cards affect how random they are?
Q: Will CERN awaken the Elder Gods?
Q: The information contained in a big system isn’t the same as the amount of information in its parts. Why?
Q: Is the quantum zeno effect a real thing?
Q: Is there an intuitive proof for the chain rule?
Q: How do you write algorithms to enycrypt things?
Q: Satellites experience less time because they’re moving fast, but more time because they’re so high. Is there an orbit where the effects cancel out? Is that useful?
Q: Is it possible to objectively quantify the amount of information a sentence contains?
Q: What would happen if a black hole passed through our solar system?
Q: If you are talking to a distant alien, how would you tell them which way is left and which way is right?
Q: Would it be possible in the distant future to directly convert matter into energy?
Q: What’s the difference between anti-matter and negative-matter?
Q: Why does gravity make some things orbit and some things fall?
Q: Do you need faith to believe in science?
Q: What keeps spinning tops upright?
Q: Do time and distance exist in a completely empty universe?
Q: Why is it that photographs of wire mesh things, like window screens and grates, have waves in them?
Q: How does quantum physics affect electron configurations and spectral lines?
Q: Is it possible for an atomic orbital to exist beyond the s, p, f and d orbitals they taught about in school? Like could there be a (other letter) orbital beyond that?
Q: Will the world end in 2012?
Q: How do you find the height of a rocket using trigonometry?
Q: What are chaos and chaos theory? How can you talk about chaos?
Q: What is the Riemann Hypothesis? Why is it so important?
Q: Why does the entropy of the universe always increase, and what is the heat death of the universe?
Q: Could God have existed forever? Is it actually feasibly possibly for some ‘being’ to have just existed, infinitely?
Q: How can wormholes be used for time travel?
Q: If gravity suddenly increased would airplanes fall out of the sky, or would it compress the air in such a way that airplanes could keep flying?
Entanglement omnibus!
Q: How are imaginary exponents defined?
Q: Why do nuclear weapons cause EMPs (electromagnetic pulses)?
Q: How does the expansion of space affect the things that inhabit that space? Are atoms, people, stars, and everything else getting bigger too?
Q: What would Earth be like if it didn’t turn?
Q: According to the Many Worlds Interpretation, every event creates new universes. Where does the energy and matter for the new universes come from?
Q: Can wind chill make things “feel” colder than absolute zero?
Q: What is “spin” in particle physics? Why is it different from just ordinary rotation?
Q: What is Bayes’ rule and how do I use it to improve my life?
Q: Are there universal truths?
Q: What’s the difference between black holes and worm holes? Could black holes take you to other universes?
Q: Is there an equation that determines whether a question gets answered on ask a mathematician/physicist?
Q: If you could hear through space as though it were filled with air, what would you hear?
Q: What is the three body problem?
Q: How are fractals made?
Q: CERN’s faster than light neutrino thing: WTF?
Q: What’s the point of purely theoretical research?
Q: Why does lightning flash, but thunder rolls?
Burning Man 2011
Q: If light slows down in different materials, then how can it be a universal speed?
Q: What is mass?
Q: How much of physics can be deduced from previous equations/axioms?
Q: If God were all-seeing and all-knowing, the double-slit experiment wouldn’t work, would it? Wouldn’t God’s observation of the location of the photon collapse its probability wave function?
Q: How do those “executive ball clicker” things work?
Q: Why is cold fusion so difficult?
Q: Why does light choose the “path of least time”?
Q: Does light experience time?
Q: Would it be possible for humans to terraform mars?
Q: Can light be used to transfer energy instead of power lines?
Particle physics, neutrinos, and chirality too!
Q: What are integral transforms and how do they work?
Q: How does reflection work?
Q: What does a measurement in quantum mechanics do?
Q: If you stood in the beam of a particle accelerator, what would happen?
Q: What exactly is the vacuum catastrophe and what effects does this have upon our understanding of the universe?
Q: What is a “measurement” in quantum mechanics?
Q: How close is Jupiter to being a star? What would happen to us if it were?
Q: Can you fix the “1/0 problem” by defining 1/0 as a new number?
Q: How can we have any idea what a 4D hypercube or any n-D object “looks like”? What is the process of developing a picture of a higher dimensional object?
Q: Is it possible to destroy a black hole?
Q: Why does the Earth orbit the Sun?
Q: If you suddenly replaced all the water drops in a rainbow with same-sized spheres of polished diamond, what would happen to the rainbow? How do you calculate the size of a rainbow?
Q: If we meet aliens, will they have the same math and physics that we do?
Q: Is 0.9999… repeating really equal to 1?
Q: What would Earth be like to us if it were a cube instead of spherical? Is this even possible?
Q: How do velocities add? If I’m riding a beam of light and I throw a ball, why doesn’t the ball go faster than light?
Q: What is the universe expanding into? What’s outside the universe?
Cheap experiments and demonstrations for kids.
Q: How do I estimate the probability that God exists?
Q: How do you calculate 6/2(1+2) or 48/2(9+3)? What’s the deal with this orders of operation business?
Q: Is there a single equation that proves black holes are real?
Q: Is the edge of a circle with an infinite radius curved or straight?
Q: As a consequence of relativity, objects becomes more massive when they’re moving fast. What is it about matter that causes that to happen?
Q: What is the evidence for the Big Bang?
Q: Is there a formula to find the Nth term in the Fibonacci sequence?
Q: Why is the integral/antiderivative the area under a function?
Mathematical proof of the existence of God.
Video: Getting Computers to Learn
Q: What is going on in a nuclear reactor, and what happens during a meltdown?
Q: How do I find the love of my life? (a Mathematician’s perspective)
Q: Are all atoms radioactive?
Q: How do you talk about the size of infinity? How can one infinity be bigger than another?
Q: Why does E=MC 2 ?
Q: What are the equations of electromagnetism? What all do they describe to us?
Q: What is the entropy of nothing?
Q: How can quantum computers break encryption?
Q: How does quantum computing work?
Q: What causes buoyancy?
My bad: If atoms are mostly made up of empty space, why do things feel solid?
Q: How many mathematicians/physicists does it take to screw in a light bulb?
Q: Why is it that (if you exclude 2 & 3) the difference between the squares of any two prime numbers is divisible by 12?
Q: Why does relativistic length contraction (Lorentz contraction) happen?
Q: Why does Lorentz contraction only act in the direction of motion?
Q: If atoms are mostly made up of empty space, why do things feel solid?
Q: Can we build a planet?
Q: How does a scientist turn ideas into math?
Q: Is Santa real?
Q: Why isn’t the shortest day of the year also the day with the earliest sunset?
Q: Why does “curved space-time” cause gravity?: A better answer.
Q: According to relativity, two moving observers always see the other moving through time slower. Isn’t that a contradiction? Doesn’t one have to be faster?
Q: What does 0^0 (zero raised to the zeroth power) equal? Why do mathematicians and high school teachers disagree?
Q: Can you do the double slit experiment with a cat cannon?
Q: How is the “Weak nuclear force” a force? What does it do?
Q: Does Gödel’s Incompleteness Theorem imply that it’s impossible to be logical?
Q: If accelerating charges radiate, and everything is full of charges, then why don’t I radiate every time I move?
Q: If you zoom in far enough, what do particles look like?
Q: What would you experience if you were going the speed of light?
Q: Why is pi not a definite number?
Q: What came before the big bang?
Q: How do “Numerology Math Tricks” work? (adding digits and tricks with nines)
Q: What is a magnetic field?
Q: What is the probability that two randomly chosen people will have been born on the same day?
Q: Which is a better approach to quantum mechanics: Copenhagen or Many Worlds?
Q: Why is our vision blurred underwater?
Q: In the NEC “faster than light” experiment, did they really make something go faster than light?
Q: How does a Tesla coil work?
Q: What are Feynman diagrams, how are they used (theoretically & practically), and are there alternative/competing diagrams to Feynman’s?
Q: Does the 2nd law of thermodynamics imply that everything must eventually die, regardless of the ultimate fate of the universe?
Q: What is The Golden Ratio? How is it used in Mathematics?
Q: Why can’t you have an atom made entirely out of neutrons?
Q: What is the physical meaning of “symmetries”? Why is there one-to-one correspondence between laws of conservation and symmetries? Why is it important that there is such correspondence?
Q: Why does energy have to be positive (and real)?
Q: How does the Twin Paradox work?
Q: How can photons have energy and momentum, but no mass?
Q: If you were on the inside of the Sun falling in, the matter closer to the surface doesn’t affect your acceleration, but the matter closer to the core does. Why is that?
Q: How do surge protectors work?
Relativity and Quantum Mechanics: the elevator pitch
Q: Why are orbits elliptical? Why is the Sun in one focus, and what’s in the other?
Q: What would happen if everyone in the world jumped at the same time?
Q: How can electrons “jump” between places without covering the intervening distance?
Q: Why do we only see one rainbow at a time?
Q: Why does putting spin on a ball change how it moves through the air?
Quantum mech, choices, and time travel too!
Q: Why is the speed of light finite?
Q: Why is the speed of light the fastest speed? Why is light so special?
Q: Will we ever overcome the Heisenberg uncertainty principle?
Q: If gravity is the reaction matter has on space, in that it warps space, why do physicist’s look for a gravity particle? Wouldn’t gravity be just a bi-product of what matter does to space?
Q: Is it possible to beat the laws of physics?
Q: What’s the chance of getting a run of K or more successes (heads) in a row in N Bernoulli trials (coin flips)? Why use approximations when the exact answer is known?
Q: Aren’t physicists just doing experiments to confirm their theories? Couldn’t they “prove” anything they want?
Q: What’s up with that “bowling ball creates a dip in a sheet” analogy of spacetime? Isn’t it gravity that makes the dip in the first place?
Q: If we find a “Theory of Everything” will we be done?
Q: Is it possible to say if the Earth is moving or sitting still without going into space?
Q: Will there always be things that will not or cannot be known?
Q: If you could see through the Earth, how big would Australia look from the other side?
Q: How is it that Bell’s Theorem proves that there are no “hidden variables” in quantum mechanics? How do we know that God really does play dice with the universe?
Q: Does an electric field have mass? Does it take energy to move an electric field?
Q: What would the consequenses for our universe be if the speed of light was only about one hundred miles per hour?
Q: Do virtual particles violate the laws that energy can be created or destroyed? Have virtual particles ever been observed? In any other instance can energy ever be destroyed or created?
Video: How do we know that 1+1=2? A journey into the foundations of math.
Q: Would it be possible to generate power from artificial lightning?
Q: What is the optimum spectrum to visualize things with? Theoretically, which type of vision would be the best to see things with?
Q: What causes iron, nickel, and cobalt to be attracted to magnets, but not other metals?
Q: Is it possible to fill a black hole? If you were to continuously throw galaxies worth of matter into a black hole, would it ever fill up? And what would theoretically happen if all the matter in the universe was thrown into a single black hole?
Q: Can math and science make you better at gambling?
Q: Spectroscopy?
Q: Is it possible to breach the center of a nebula?
Q: How does a gravitational sling shot actually speed things up?
Q: If energy is quantized, what is the least amount of energy possible? And how did they measure it?
Q: How did Lord Kelvin come up with the absolute temperature? I mean, how could he say surely that it was 273.15 C below zero?
Q: What do complex numbers really mean or represent?
Q: Is it odd that the universe’s constants are all so perfectly conducive to life?
Q: How/when will the world end?
Q: What would happen if an unstoppable force met with an unmovable, impenetrable object?
My bad: Have aliens ever visited Earth?
Q: How do Bell pairs (entangled particles) behave experimentally?
Video: What your Spiritual Guru Never Told you about Quantum Mechanics
Q: How big does an object have to be to gravitationally attract a Human or have a molten core?
Video: The Scientific Investigation of Aliens – Evidence Examined
Q: How do I count the number of ways of picking/choosing/taking k items from a list/group/set of n items when order does/doesn’t matter?
Q: Who would win in a fight: Gödel or Feynman?
Q: How hard would it be to make a list of products of primes that could beat public key encryption?
Q: What are complex numbers used for?
Q: Can one truly create something from nothing? If matter formed from energy (as in the Big Bang expansion), where did the energy come from?
Q: Why does wind make you colder, but re-entry makes you hotter?
Q: Are explosions more or less powerful in space?
Q: What is infinity? (A brief introduction to infinite sets, infinite limits, and infinite numbers)
Q: Are there physical limits in the universe other than the speed of light?
Q: Is it of any coincidence that mathematics is able to describe physical reality – given that both are inventions of the human mind?
Q: If you were to break down an average human body into its individual atoms, and then laid the atoms out in a single straight line, how far would it stretch?
Q: What’s it like when you travel at the speed of light?
Q: Is there a real life example where two negatives make a positive?
Q: Do the “laws” of physics and math exist? If so, where? Are they discovered or invented/created by humans?
Q: Do we have free will?
Q: How did mathematicians calculate trig functions and numbers like pi before calculators?
Q: How can planes fly upside-down?
Q: A flurry of blackhole questions!
Q: Why does going fast or being lower make time slow down?
Q: What’s so special about the Gaussian distribution (i.e. the normal distribution / bell curve)??
Q: Is the universe infinitely old?
Q: Have aliens ever visited Earth?
Q: Why is the sky blue?
Q: Is there a formula for how much water will splash, most importantly how high, and in what direction from the toilet bowl when you *ehem* take a dump in it ?
Q: What is the meaning of the term “random”? Can thinking affect the future?
Q: Is it possible to choose an item from an infinite set of items such that each one has an equal chance of being selected?
Q: Do aliens exist?
Q: Is it true that all matter is simply condensed energy?
Q: Which is better: Math or Physics?
Q: Why is the number 1 not considered a prime number?
Q: If the universe is expanding and all the galaxies are moving away from one another, how is it possible for galaxies to collide?
Q: What happens when you fall into a blackhole?
Q: Is the total complexity of the universe growing, shrinking or staying the same?
Q: If two trains move towards each other at certain velocities, and a fly flies between them at a certain constant speed, how much distance will the fly cover before they crash?
Q: Why does oxygen necessarily indicate the presence of life?
Q: What’s the relationship between entropy in the information-theory sense and the thermodynamics sense?
Q: Would it be possible to kill ALL of Earth’s life with nuclear bombs?
Q: Will black holes ever release their energy and will we be able to tell what had gone into them?
Q: What are the Intersecting Chord and Power of a Point Theorems?
Q: How far away is the edge of the universe?
Q: Why do superconductors have to be cold?
Q: Why does the leading digit 1 appear more often than other digits in all sorts of numbers? What’s the deal with Benford’s Law?
Q: How does the Monty Hall Problem work?
Q: How/Why are Quantum Mechanics and Relativity incompatible?
Q: What the heck are imaginary numbers, how are they useful, and do they really exist?
Q: What’s that third hole in electrical outlets for?
Q: Do physicists really believe in true randomness?
Q: Could a simple cup of coffee be heated by a hand held device designed to not only mix but heat the water through friction, and is that more efficient than heating on a stove and then mixing?
Q: What did Einstein mean by: “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”
Q: Why does saliva boil in the vacuum of space?
Q: Can things really be in two places at the same time?
Q: Why do weird things happen so much?
Q: Will CERN create a black hole?
Q: What’s the highest population growth rate that the Earth can support?
Q: What is time?
Q: What is “Dark Matter”?
Q: Why do heavy objects bend space and what is it they are bending?
Q: Why does math work so well at modeling the world around us?
Q: Why is it that when you multiply a positive number with a negative number you get a negative number?
Q: What is the best way to understand relativity theory? Why is it so counter intuitive?
Q: Will we ever go faster than light?
Q: If you were on a space station, would you be able to tell the difference between centrifugal force and normal gravity?
Q: Is teleportation possible?
Q: If black holes are “rips” in the fabric of our universe, does it mean they lead to other universes? If so, then did time begin in that universe at the inception of the black hole? Could we be in a black hole?
Q: Since pi is infinite, do its digits contain all finite sequences of numbers?
Q: What is the connection between quantum physics and consciousness?
Q: What is the probability that in a group of 31 people, none of them have birthdays in February or August?
Q: What is the meaning of life?
Q: Why is e to the i pi equal to -1?
Q: How does a refrigerator work?
Q: How do I find the love of my life?
Q: Why does “curved space-time” cause gravity?
Q: What is monotony?
Q: How do we know if science is right?
Q: How plausible is it that the laws of physics may actually function differently in other parts of the universe?
Q: Are there an infinite number of prime numbers?
Q: How can we prove that 2+2 always equals 4?

Sharp Blue: Relativity, FTL and causality

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About This Article

Richard Baker September 12, 2003 Physics Science comments

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Italicised articles are old and unrevised.

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<< Previous in Series: “Absolute Future and Absolute Past”

A brief note to my recent visitors: If you’ve arrived here from sites with highly misleading blurbs and expect to find a discussion of how faster-than-light travel is possible, I’m afraid you will be disappointed. This article outlines an argument commonly accepted by physicists which demonstrates that in special relativity faster-than-light travel is not possible.

( This article forms a companion piece of sorts to the first half of the section on Special Relativity in my Very Brief History of Time , so it might make more sense if you read that first. If that doesn’t make sense, try reading the earlier parts too! )

One of the most striking aspects of special relativity is that faster than light travel is equivalent to time travel. This is also one of the most widely understood aspects of the theory, and almost every explanation I’ve seen of the effects of superluminal travel on causality has been badly garbled. In this article, I will try to explain it more clearly.

The paths of light rays in a special relativistic spacetime (a so-called Minkowski spacetime ) act like a causal grain running through the spacetime. The outgoing light rays from an event form a surface in spacetime called the event’s future light cone . The light rays converging on an event form a surface called the event’s past light cone . For any event P (where P is a label for something happening at a given place at a given time), the events within P’s future light cone make up its absolute future and those within its past light cone make up its absolute past : the former are the events that P can influence and the latter are the events that can influence P. Unlike the situation in classical mechanics, there are also events outside both light cones of P that can neither influence nor be influenced by P (at least in the absence of faster than light travel or communication). These concepts are summarised in figure 1 (where, as usual in such spacetime diagrams, I’ve suppressed two spatial dimensions):

To understand this causal structure a little better, we’ll have to look more closely at how different observers see spacetime. In the following, we’ll be exclusively concerned with observers at rest in inertial frames , which are collections of coordinate systems moving at uniform velocity with respect to one another. Special relativity is founded on two postulates (and a lot of experimental evidence supporting its conclusions, of course):

The laws of physics look the same to all observers in inertial reference frames. This is the “Principle of Relativity” that lets us perform calculations relative to any inertial frame we like and be assured that we will get the same values for all physically meaningful quantities. This postulate holds in classical mechanics too.
The speed of light is the same in all directions in all inertial frames. It is this postulate that gives rise to all the strange consequences of special relativity, including those discussed here.

The constancy of the speed of light in all frames means that different observers must slice spacetime into space and time in different ways. This is quite unlike the situation in classical mechanics, in which everyone can agree on what is space and what is time. In particular, from the point of view of a stationary observer, an observer moving at constant velocity has a coordinate frame whose space and time axes are “tilted” towards the light cone. By the relativity postulate, this situation must be symmetric - the second observer will consider herself stationary and the first observer’s frame “tilted”. From this sort of reasoning and a little bit of mathematical sophistication, we can cook up a recipe for translating the coordinates assigned to events between inertial frames. Each such translation is known as a Lorentz transformation . Let’s look at one more closely:

In this diagram, we can see the seeds of our strategy for violating causality using faster than light signals. Looking at events P and Q, we see that P occurs after Q according to the observer in the white frame, but to the observer in the blue frame P happens first. This situation is enshrined in the lore of relativity under the name “ relativity of simultaneity ”, because different observers will have different ideas about which events take place simultaneously. For events within the light cones, though, all observers agree on temporal ordering. It’s not possible to tilt the coordinate frame enough to make events in P’s absolute future appear to be in P’s past. That’s why it’s called the absolute future in the first place!

All of the foregoing may be quite odd to those unfamiliar with relativity, but all will be well for causality provided that there are no superluminal causal influences. If we have faster than light effects then it’s rather easy to make paradoxical causality violations. For the sake of concreteness, I’ll consider a pair of “ansibles” - superluminal transmitters whose signals are received simultaneously with their transmission when both the transmitter and receiver share an inertial frame. The same sort of argument applies to faster than light effects that are not instantaneous, and to signals carried by faster than light spacecraft. I’ve just chosen this case because it makes the diagrams easier to draw and easier to understand. Let’s look at a single use of our ansible:

By itself, this single use of the ansible doesn’t create a causality violation. If Bob transmits a signal back towards Alice using a conventional light-speed transmitter, she receives it a later time than when she signalled to Bob. Even if Bob re-transmits with his ansible, Alice receives the reply just a little after she sent out her signal. The problems arise when we bring another inertial frame into play. Let’s suppose that we have another pair of inertial observers, Carol and Dave, who are moving with respect to Alice and Bob, and who have a pair of ansibles of their own. As Carol flies past Bob at event Q, Bob gives her the message from Alice and she transmits it to Dave as soon in the diagram (in which I’ve not drawn any coordinate grids to reduce clutter):

Now causality is in real trouble, as we can see if we consider the pair of transmissions (from Alice to Bob, then from Carol to Dave):

Notice that we’ve arranged for Dave to receive the signal from Carol as he’s flying past Alice. Notice too that he receives it before Alice has sent her first signal! This means that Alice can transmit information into her own past by way of Bob, Carol, Dave, some spaceships, and two pairs of ansibles. And that’s why faster than light travel or communication, special relativity and causality cannot coexist.

Next in Series: “Time Dilation” >>

Ars Lykaion
The Observatory

Why does FTL travel = Time Travel?

Thread starter Mr. Smith
Start date Mar 1, 2011

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Ars tribunus militum.

Mar 1, 2011
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Ars Tribunus Angusticlavius

The concept of time travel with faster than light traveling objects comes from some of the cute math that comes from it. Generally speaking, all subatomic particles that are theoretically FTL are classified as "tachyons" and you can read all about them on wikipedia . Skim through that and then ask your questions, imo.

Ars Legatus Legionis

I did a write up of this a couple of years ago when the Observatory started. Imagine the following: Bob and Alice make a bet about who will get to Alpha Centari first. On year 1, Alice builds a ship that can travel nearly the speed of light. So much near, that after she's done her instantaneous acceleration, one day to her dilates to 1 year to Bob. Therefore, it's only going to take 4 years to get to Alpha Centari (and to her, 4 days). On year 2, Bob develops instantaneous teleportation and decides to jump over to Alice to brag. He does so. Now, when is he? From Alice's standpoint, only a few minutes have passed on the Earth since she left (after all, time dilation works both ways). So, now Bon offers to take Alice back to Earth using his device. But, who's reference frame do we use? If we use Bob's original reference frame, Alice gets to jump 2 years into the future. If we use Alice's frame, Bob gets to jump back in time 2 years. There are lots of good pictures, but to really understand everything, the math is what describes it.

Wise, Aged Ars Veteran

The Bob and Alice example makes no sense... you are forgetting that the time it takes to explain the process and offer to take her back lodges him more or less in sync with her time reference, but at the same time he has never left his own frame. Also she hasn't even left his frame. She traveled 1 day from her perspective and 1 year from Bob's. If the ship was to stop instantly, besides turning both Alice and Bob into chunky salsa from the deceleration it would still be 1 day from her perspective and 1 year from his. That would not change those are constants from their points of view. Using the device to travel back to earth ignoring the continuing dilation from being on the accelerating ship, which would only be weeks or months of real time change vs. ship time depending of course on how long the conversation takes, instantaneous teleportation drops Alice back on earth one year after she left (+ months or weeks) but her passage of time due to dilation is 1 day (+ however long the conversation took) The hardest part of this is over thinking the problem she is actually biologically younger but that is the twin paradox in practice. up until the space ship is built that can travel that fast we have no real test of the boundaries of this, but thus far the space shuttle has proved time differences due to acceleration and gravitation time differential in atomic clocks, in practice making shuttle crews a few nano seconds younger than the rest of us poor earth bound slugs.

Mar 2, 2011

We have proven time dilation. It is used daily in research labs. Read my example again. Alice doesn't need to stop -- she's still traveling relative to Earth.

There may be something correct going on in Lord Firth's post, but if so I'm having trouble locating it (maybe find and repost the post you had in mind from the old thread, rather than paraphrasing from memory?). The simplest correct thought experiment to show that FTL implies time travel is this: You have a faster than light (lets say instantaneous) transmitter and receiver, separated in space. Lets say they're in the same reference frame. In their reference frame, transmission and reception of a signal are simultaneous events. However, in a reference frame that is moving away from the transmitter, towards the receiver, messages are received before they are sent. (If you want to understand why events that are simultaneous in one reference frame are not in another start your reading at the wiki entry for relativity of simultaneity ) Getting a signal to your own past is also doable (or rather not doable, but would be if there was FTL), but more complicated. Some people convince themselves that the above "isn't really time travel" or is a technicality, so if you're one of those people it's worth it to wade into that more complicated explanation. Here's a decent explanation of that one. (Actually that guy has a whole series of bite sized special relativity explanations that are pretty good, with minkowski diagrams and everything, worth exploring from the top if you're new to the subject)

Well-known member

I can understand that once the ship reaches B, that if they were to look back through some telescope, it would appear as if the ship were still en route (assuming a ship traveling at superluminal velocity can be "seen" -- but whatever). But this would be incorrect -- right? Just a matter (pun!) of the information catching up with the reference frame/"reality" at B? Click to expand...

Gravitomagnetic arguments also predict that a flexible or fluid toroidal mass undergoing minor axis rotation ("smoke ring" rotation) will tend to pull matter through the throat (a case of rotational frame dragging, acting through the throat). In theory, this configuration might be used for accelerating objects (through the throat) without such objects experiencing any g-forces.[12] Click to expand...

vishnu":gox211d8 said: There may be something correct going on in Lord Firth's post, but if so I'm having trouble locating it (maybe find and repost the post you had in mind from the old thread, rather than paraphrasing from memory?). Click to expand...

If observer A is traveling at some velocity w.r.t. observer B, A will see B's clock go slower, and B will see A's clock go slower. If you now have A send an FTL signal to B, and then B sends the FTL back to A, the signal from B to A could arrive before A sent the signal to begin with, and this is how you set up a paradox. Basically, A and B synchronize clocks as they pass in the night, so they both agree on time 0. At A-time=100, A observes B's clock as time=10. So A sends a FTL communication to B to tell him "Hey, fix your clock!". B receives this communication at time 10, but he sees A's clock as reading time=1, so he responds, "No! You fix your clock!" So, A now receives this message at time=1, which is 99 units before he sent the "first" message. Click to expand...

LordFrith":1uc1gxrv said: If we use Bob's original reference frame, Alice gets to jump 2 years into the future. If we use Alice's frame, Bob gets to jump back in time 2 years. Click to expand...

Ok but what if FTL travel is possible but instantaneous FTL travel/communication is not possible? Ie in the case of traversible wormholes current theory IIRC is that it will still take a non-trivial amount of time (1 year again IIRC) to traverse the wormhole. Is it still possible to create a causality violation when FTL takes a year?

Hat Monster

troymclure":3f6624sg said: Ok but what if FTL travel is possible but instantaneous FTL travel/communication is not possible? Ie in the case of traversible wormholes current theory IIRC is that it will still take a non-trivial amount of time (1 year again IIRC) to traverse the wormhole. Is it still possible to create a causality violation when FTL takes a year? Click to expand...

OK then as per the OP... how and why? I can get the causality violations happen when travelling faster then the speed of light through space. But how can it be a causality violation when you're travelling via say a wormhole. Ie. I leave here at 1.1.2000 (/shrug). I travel thru a wormhole to other side of the galaxy. spend 10 years there including 2 years of travel time. arrive back on 2010. In addition lets say my destination was chosen because it is running at the same inertial reference frame (or close enough) to earth. So i should not be affected by time dilation. How does the fact that I can beat a lightbeam there affect anything? and the laws of thermodynamics?

A couple of points: 1) you can use FTL travel and not be forced to travel back in time. 2) With time travel, you now have a conservation of energy problem -- in the closed system containing your trip, there are now two of you. So, you've created energy. There is a way (sort of) around this that relies on some pretty rough theorhetical definitions of antimatter.

Ok well actually I don't believe in time travel. (figure if it was possible for someone to travel backwards in time and change the past then they would have already done so^^). So 2. /shrug right on. no worries there. Also... alternative to wormholes... say you use a warp-drive (can't remember official name) to travel through space. Is your inertial reference frame still the same as the earths or whatever reference frame you had when you activated the warp-drive? Cause you're not moving through space-time any different you're just getting space-time to move you. So would you be affected by time dilation when using a warp-drive or something similar?

I can get the causality violations happen when travelling faster then the speed of light through space. But how can it be a causality violation when you're travelling via say a wormhole. Click to expand...

And, one of the first things that comes to my mind when all of these discussions are made is, "Well, the problem is crossing inertial frames! So, just don't allow that and everything's fine!" Well, no. It's pretty easy to imagine a system of "beacons" al set up in the same inertial frame that spaceships communicate to as they fly by. Furthermore, you could then imagine different beacon system being in different inertial frames. And, at that point, you merely need to use plain-old light communication to pass data from one frame to another as the beacons pass each other in space... and voila, same problem.

Ars Praefectus

If observer A is traveling at some velocity w.r.t. observer B, A will see B's clock go slower, and B will see A's clock go slower. Click to expand...

jgtg32a":1xzz33pa said: If observer A is traveling at some velocity w.r.t. observer B, A will see B's clock go slower, and B will see A's clock go slower. Click to expand...

samantha_cs

Ok, let me take a shot at this: Suppose there are three planets in a row, A, B and C, such that the distance from the central planet to each outer planet is the same. The citizens of the central planet, B, have secretly planted planet-destroying bombs on the other two planets. They send out a light-speed signal to detonate the bombs. Now, the two outer planets are allies, and as soon as one of them blows up, they will immediately send one of their FTL courier ships to the other outer planet to warn them to disable the bomb. In the reference frame in which all three planets are at rest, it's quite obvious that the central planet's dastardly scheme will succeed in destroying both outer planets. The light-speed signal will arrive simultaneously at both planets, and there will be no chance to send word from A to C or vice versa to stop the bomb. Now, consider the events as they unfold from the perspective of a standard (less than light speed) traveler going from C to A. In their reference frame, they are stationary, and all three planets are moving. Since they are moving, and since the speed of light is constant in all inertial reference frames, planet A will 'run into' the light speed signal sent by planet B before that signal has a chance to 'catch up' to planet C. Planet A is now destroyed before planet B; planet A's FTL courier ship in orbit immediately takes off and arrives at Planet C in time to stop the bomb. This is, of course, a completely symmetric problem, though. A traveler who was on a trip from A to C would see the opposite. Planet C would blow up first, giving their orbiting courier time to warn Planet A. This is how FTL travel breaks causality. If we limit the speed of the courier to the speed of light, then it's obvious that there is no way planet A's signal to planet C can beat the detonation signal or vice versa. No matter what reference frame you are in, both Planet A and Planet C are doomed, although there may be differences in the precise order of events. Adding an FTL mechanism causes this scenario to become paradoxical. Now we must determine which of the reference frames is the 'real' one in order to determine which planet explodes, something relativity tells us we can not do. Click to expand...

This is, of course, a completely symmetric problem, though. A traveler who was on a trip from A to C would see the opposite. Planet C would blow up first, giving their orbiting courier time to warn Planet A. Click to expand...

*Everything* travels through space/time at c (c = speed of light). You either travel through TIME or you travel through SPACE, but you *always* travel through SPACETIME. From a photon's point of view (for the sake of argument), 0 time passes for it from the moment it is emitted, to the moment it is absorbed. The BANG/SPLAT approach to photons. It can travel billions of lightyears, and for -it- zero time elapsed, but it traveled a long long way. From our frame of reference, it took billions of years to travel those billions of lightyears. If the photon went faster than c, it would appear to travel those billions of lightyears from its own frame of reference, and arrive -before- it left (negative amount of time). which is of course, impossible Click to expand...

Emkorial":3veikju1 said: The most you can (thoeretically) do is throw all the energy on one side of the equation, which makes the other side 0 . There's no way to go less than 0. Click to expand...

Garet Jax":3k9ouqir said: This is my response to one of the earlier times this question was asked. I'm not sure it's a "time travel" example as much as it is a "breaks causality" example. Ok, let me take a shot at this: Suppose there are three planets in a row, A, B and C, such that the distance from the central planet to each outer planet is the same. The citizens of the central planet, B, have secretly planted planet-destroying bombs on the other two planets. They send out a light-speed signal to detonate the bombs. Now, the two outer planets are allies, and as soon as one of them blows up, they will immediately send one of their FTL courier ships to the other outer planet to warn them to disable the bomb. In the reference frame in which all three planets are at rest, it's quite obvious that the central planet's dastardly scheme will succeed in destroying both outer planets. The light-speed signal will arrive simultaneously at both planets, and there will be no chance to send word from A to C or vice versa to stop the bomb. Now, consider the events as they unfold from the perspective of a standard (less than light speed) traveler going from C to A. In their reference frame, they are stationary, and all three planets are moving. Since they are moving, and since the speed of light is constant in all inertial reference frames, planet A will 'run into' the light speed signal sent by planet B before that signal has a chance to 'catch up' to planet C. Planet A is now destroyed before planet B; planet A's FTL courier ship in orbit immediately takes off and arrives at Planet C in time to stop the bomb. This is, of course, a completely symmetric problem, though. A traveler who was on a trip from A to C would see the opposite. Planet C would blow up first, giving their orbiting courier time to warn Planet A. This is how FTL travel breaks causality. If we limit the speed of the courier to the speed of light, then it's obvious that there is no way planet A's signal to planet C can beat the detonation signal or vice versa. No matter what reference frame you are in, both Planet A and Planet C are doomed, although there may be differences in the precise order of events. Adding an FTL mechanism causes this scenario to become paradoxical. Now we must determine which of the reference frames is the 'real' one in order to determine which planet explodes, something relativity tells us we can not do. Click to expand...

No, the relative simultaneity phenomena is real and not simply a matter of perception. According to special relativity, events which are separated by more space than time (as defined by the speed of light) can occur in different orders in different inertial reference frames. This can be shown mathematically for the kind of theoretical omni-present observer I implicitly invoke in my example. I don't know nearly enough about the physics of wormholes to speculate with much confidence about wormhole travel. Edit: To clarify, the fact that an event occurs cannot be different in different reference frames. So either the planets blow up or they don't. That can't depend on the frame. But the precise timing of the events can be different in different frames, and for 'spacelike' events, even the order of events can be different.

Ars Scholae Palatinae

*I've read some stuff on this before but i had thought it was like when a person sees a fast object shrinking the faster it goes(approaching c), it doesn't actually shrink it's just an artefact of lights interactions with objects moving very quickly. Click to expand...

QuantumET":cessgagl said: *I've read some stuff on this before but i had thought it was like when a person sees a fast object shrinking the faster it goes(approaching c), it doesn't actually shrink it's just an artefact of lights interactions with objects moving very quickly. Click to expand...

Excession":xjifk54x said: Apparently, you can use lasers to provide temperatures measured in the -negative- Kelvins (Kelvin 0 is "absolute" 0, one of those 0's you can't possibly break, right?), the negative Kelvin is offset by the higher energy in the interation, I can't explain it (IANAP), but Wiki has a crack at it : Click to expand...

troymclure":3r02jgli said: The fact that someone observes something different doesn't make it in reality different does it? Ie from planet A's reference frame they see the speed of light signal coming from planet B at c. same as planet C. And if they're all travelling at the same speed (same inertial frame) time is the same for all of them. What a person sees happening * is just about when the light from the events actually got to them... isn't it? Click to expand...

Mar 3, 2011

QuantumET":1r5mc46m said: *I've read some stuff on this before but i had thought it was like when a person sees a fast object shrinking the faster it goes(approaching c), it doesn't actually shrink it's just an artefact of lights interactions with objects moving very quickly. Click to expand...

troymclure":3ctcm98l said: Isn't that physically impossible? Ie what would happen if we did that in real life? As in fact it should be possible to do with known physics... Click to expand...

I assume you're asking if the barn can't break and the ship can't break, what happens? I'll preface this by saying there's no such thing as a truly rigid object in relativity: Lets choose the reference frame of the rocket right before it hits the back door, and stay in that reference frame (the rocket will be accelerating so it's frame is no good). The rocket is clearly too long to fit in the barn, but the back end of the rocket doesn't "know" the front has hit anything yet, so it keeps going. The rocket compresses and the back end of the rocket makes it through the front door of the barn. Then the front door closes. The rocket stays compressed, unable to expand through the doors. The "T and U paradox" or "detonator paradox" is another good length contraction thought experiment to read up on, once you've wrapped your brain around this one. At the bottom of a U-shaped structure there is a button for a bomb. A T-shaped structure fits inside the U but when they're both at rest it isn't quite long enough to push the button for the bomb. The T and the U come together at relativistic speed. Think about what happens from the point of view of the U, and what happens from the point of view of the T. Does the bomb go off? I've sort of given away the answer with my answer to the above, but it's worth giving it a think.

troymclure":1snnyl01 said: QuantumET":1snnyl01 said: *I've read some stuff on this before but i had thought it was like when a person sees a fast object shrinking the faster it goes(approaching c), it doesn't actually shrink it's just an artefact of lights interactions with objects moving very quickly. Click to expand...

vishnu":9fjj93tf said: I assume you're asking if the barn can't break and the ship can't break, what happens? I'll preface this by saying there's no such thing as a truly rigid object in relativity: Lets choose the reference frame of the rocket right before it hits the back door, and stay in that reference frame (the rocket will be accelerating so it's frame is no good). The rocket is clearly too long to fit in the barn, but the back end of the rocket doesn't "know" the front has hit anything yet, so it keeps going. The rocket compresses and the back end of the rocket makes it through the front door of the barn. Then the front door closes. The rocket stays compressed, unable to expand through the doors. Click to expand...

Alexandre":3n8uxf99 said: Edit: VISHNU!!! (Again!) Click to expand...

troymclure":3n8uxf99 said: ok T and U paradox. Um wouldn't it depend on which one is moving? Ie if length contracts at relativistic speeds then if the U is moving the bomb will go off, but not if it's the T that moves. I think. Click to expand...

Frustrating flight cancellations, daylong waits prompt DOT to strike deal on airline consumer complaints

The Biden administration is enlisting the help of officials in 15 states to enforce consumer-protection laws covering airline travelers , a power that by law is limited to the federal government.

The U.S. Department of Transportation said Tuesday that the states, which include California, New York and Illinois, will help ensure that government enforcement activities keep up with a current boom in air travel.

Under an agreement announced by Transportation Secretary Pete Buttigieg , state attorney general offices will be able to investigate complaints about airline service. If they believe an airline violated the law or is refusing to cooperate with investigators, the states could refer cases to the Transportation Department for enforcement.

In return, the Transportation Department, or DOT, will give the states access to its consumer-complaint system and train state employees about federal consumer laws covering airlines .

“This is a partnership that will greatly improve DOT’s capacity to hold airlines accountable and to protect passengers,” Buttigieg told reporters.

Buttigieg pointed to travelers whose flights are canceled and then must wait days for another flight or pay more to fly home on another airline. “Things like that are a violation of passenger rights, and we are seeing far too many cases of that,” he said.

Other states whose officials signed the “memorandum of understanding” with the Transportation Department are: Colorado, Connecticut, Maine, Maryland, Michigan, Nevada, New Hampshire, North Carolina, Oklahoma, Pennsylvania, Rhode Island and Wisconsin, plus the District of Columbia, the Northern Mariana Islands and the U.S. Virgin Islands.

Buttigieg, a Democrat, repeatedly cast the agreement as bipartisan, but only two of the state officials who signed on are Republicans. Buttigieg indicated his department hopes to recruit more states.

Under U.S. law, the federal government alone regulates consumer-protection laws covering airlines. The carriers are not legally required to respond to state investigations.

Consumer advocates have pushed to expand enforcement power to the states. However, both the full House and a key Senate committee declined to include that proposal in pending legislation that covers the Federal Aviation Administration, part of the Transportation Department.

“During the pandemic, we actually got more complaints about airline traffic than any other topic, and it was frustrating” because the state had no authority to investigate the complaints, Colorado Attorney General Philip Weiser said.

Weiser argued that Congress should give states power to enforce airline consumer-protection laws, “but I have to say, we didn’t wait for Congress to act.”

Consumer groups praised the agreement while saying they would rather see Congress write into law the power of states to regulate consumer-protection rules.

“This is the next best thing,” said William McGee, an aviation expert at the American Economic Liberties Project, which opposes industry consolidation. “We don’t look at this as a threat to DOT’s authority. We look at it as the states assisting DOT, which doesn’t have the staffing to handle all the complaints they get.”

Airlines for America, a trade group representing the largest U.S. carriers, said it works with state and national groups “to constantly improve the customer experience for all passengers. We appreciate the role of state attorneys general and their work on behalf of consumers, and we look forward to continue working with them.”

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IMAGES

Why FTL implies time travel
Backwards Time Travel: Can We Influence Our Casual Past?
How Does Faster Than Light Travel Violate Causality
FTL signal and causality
How Does Faster Than Light Travel Violate Causality
Solve the FTL communications causality paradox : r/paradoxes

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COMMENTS

How does faster than light travel violate causality?
8. There is a simple answer; faster than light travel does not violate causality. What faster than light travel does, is contradicts the usual axiomization of relativity; and hence allows you to derive all kinds of paradoxial 'conclusions'. But shifting the blame on causality is more fashionable convention than anything else.
Faster-than-light
Neither of these phenomena violates special relativity or creates problems with causality, and thus neither qualifies as faster-than-light as described here. In the following examples, certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.
Why FTL implies time travel
However, faster-than-light communication (which includes travel) breaks something very fundamental about physics, something that is often ignored by sci-fi, and difficult for non-physicists to understand. If you allow faster-than-light (FTL), then you break causality: you are allowing time-travel. One pithy way of saying this is: Pick two ...
Special Relativity/Faster than light signals, causality and Special
The inertial constraint does not apply to particles without a rest mass, such as the photon, or to particles that might oscillate between massless and massive forms. The possibility that causality would be violated if signals could travel faster than the speed of light is a more interesting problem however.
Why time-traveling tachyons probably don't exist
Einstein toyed with the idea of faster-than-light-particles but found that such particles violated a central rule of the universe: causality.
4.7: Tachyons and Faster-than-Light (FTL)
A Defense in Depth. Let's summarize some ideas about faster-than-light (FTL, superluminal) motion in relativity:Superluminal transmission of information would violate causality, since it would allow a causal relationship between events that were spacelike in relation to one another, and the timeordering of such events is different according to different observers.
8. The Second Problem: FTL, Causality, and Unsolvable Paradoxes
the meaning of causality and the problems of an unsolvable paradox. I will then try to show how any form of FTL travel will produce violation of the causality principle. Finally, I will explain how, without special provisions being in place, FTL travel can go further to produce an unsolvable paradox. Continue to:
Relativity and FTL Travel: Part IV
8.2 How FTL Travel Implies Violation of Causality 8.3 How We Get Unsolvable Paradoxes Chapter 9: FTL Concepts with these Problems in Mind 9.1 Tachyons (Without Special Provisions) ... One result of this is that if a charged tachyon were to exist, then because it would travel faster than light, it would give off a radiation known as Cherenkov ...
Is Faster-Than-Light Travel or Communication Possible?
If FTL travel or FTL communication were possible, then causality would probably be violated and some very strange situations would arise. First we will cover the trivial ways in which things can go FTL. These points are mentioned not because they are interesting, but because they come up time and time again when FTL is being discussed, and so ...
How Faster than Light Speed Breaks CAUSALITY and creates ...
Signup for your FREE trial to Wondrium here: http://ow.ly/f5Jw30rNLaD - Highly recommended!Explanation of light cones: https://www.youtube.com/watch?v=ZfR1Jc...
Could someone explain how FTL violates causality? : r/askscience
Which means that a quick FTL trip back and forth and you've actually time travelled within a particular reference frame. This doesn't necessarily rule out FTL travel completely. It may be possible that some quirkiness of the way FTL travel might work will prevent causality violations. However, our current understanding of relativity is ...
8.2 How FTL Travel Implies Violation of Causality
For. O, The effect precedes the cause. Thus, the signal which travels FTL in Op's. frame violates causality for O's frame. Similarly, since "*" has already. occurred in O's frame when O and Op pass one another, then in his frame an. FTL signal could be sent out from "*" which could reach O and tell him about.
ELI5: How does faster than light travel (FTL) violate the laws of
The speed of light is misleading. Light travels at the speed of causality: the fastest speed at which information (or any other massless phenomenon) can propagate through space. By definition, an object travelling faster than light moves faster than information about its travel actually propagates, theoretically allowing it to arrive at its ...
Q: Hyperspace, warp drives, and faster than light travel: why not?
Physicist: Firstly: no. But, if you're really set on it: maybe. The essential problems are that moving faster than light (FTL) requires impossible acceleration (not difficult but impossible in a "doesn't make sense to talk about" kind of way), and FTL violates causality in some weird ways (for example, it allows travel backward in time).
Why does FTL travel/information break causality? : r/askscience
Now causality means that if event A causes event B, then event A must happen before event B. Now if event A causes event B, and the affect travels faster than the speed of light, then there would be a frame of reference where event B happens before event A, even though event A is the cause of event B. Hence, causality is broken.
Sharp Blue: Relativity, FTL and causality
The only way to have both faster-than-light travel and causality is to discard relativistic spacetime and restore some nation of absolute time (which, I think, is what Chris is arguing for). ... If you are willing to violate these postulates then of course you can have FTL without causality violation. For example, in the comment above wTarasoff ...
Why does FTL travel = Time Travel?
A couple of points: 1) you can use FTL travel and not be forced to travel back in time. 2) With time travel, you now have a conservation of energy problem -- in the closed system containing your ...
Frustrating flight cancellations, daylong waits prompt DOT to strike
The Biden administration is enlisting the help of officials in 15 states to enforce consumer-protection laws covering airline travelers, a power that by law is limited to the federal government.