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evidence: speed of light limit as a fundamental property of the relationship between space and time

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Don't stop presses yet for faster-than-light neutrinos: Science Reference Center

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Faster than Light: Science Reference Center

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the streak of light you see on Meteors

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Faster than Light: Science Reference Center

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FASTER THAN LIGHT: Science Reference Center

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The science of Star Trek: Science Reference Center

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question 4
how long? days,months,years? How long?

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Question:

"If we were able to build a spaceship that could travel at the speed of light, what would be the physical consequences? As an example, I think Alpha Centauri is about 4 light-years away, so I basically need 4 years on that spaceship to reach it. But, will my body age at the same rate when I am on the ship or will in remain the same?"

Answer:

Firstly, the physical consequence of traveling at the speed of light is that your mass becomes infinite and you slow down. According to relativity, the faster you move, the more mass you have. The same works on Earth when you're driving down the freeway. You weigh a tiny bit more driving around than you do when you're completely at rest.

So, traveling at the speed of light in the conventional way is impossible. Fortunately, nature offers us a few ways of cheating. These methods include wormholes and traveling at warp speed, among others.

As far as I know, time dilation (which is what your question is centered around) doesn't apply in any of these cases (or, at least at a much less-noticeable for things like warp where you are still in 'normal' and 'non- relativistic ' space - again, as far as I'm aware). So, I'm going to skip these and talk about traveling really fast using 'conventional' means.

Time dilation is "an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses". This is why astronauts returning from the International Space Station have 'traveled' 0.007 seconds into the future after spending 6 months in orbit. Of course, they haven't really traveled forward in time; they just aged slower relative to everyone on Earth. So, how about I use Alpha Centauri as an example. Lets assume you are able to instantly accelerate to 99.9% the speed of light, as well as instantly decelerate, without killing yourself or destroying your ship (which would probably result in your death).

Alpha Centauri is technically 4.5 light-years away, but Wolfram Alpha won't let me do that calculation, so I've set the value for 4. Traveling at 99.9c for 4 years (Earth time) means you'd experience a trip of about 2 weeks (14 days). Yes, everyone on Earth will have aged four years and you will have aged only 2 weeks. To imagine this dilation effect for this particular trip, you can think of it one of two ways; either time on the ship is moving 110 times slower than 'normal' or you're traveling a distance 110 times shorter - as far as spacetime is concerned, it's the same thing.

Of course, communication from that distance means any signal you send (assuming it was powerful enough to be heard and understood) would take 4 Earth-time years to get back to Earth, so it's probable that you'd show up in the system, do science for a year or so (likely sending some type of signal to Earth to let Mission Control know you're still alive - even if you can't transmit usable data), then return to Earth. You will have been gone for a total of 9 Earth-years and about 1.24 years your time (this is excluding the time dilation effects of not being in an Earth-like gravity well for the duration of your stay in the Centauri system).
Read more about the finicky nature of time here. Or, discover why TARDIS could actually exist here.

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Physical Consequences of Light-speed Travel:

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Question: "If we were able to build a spaceship that could travel at the speed of light, what would be the physical consequences? As an example, I think Alpha Centauri is about 4 light-years away, so I basically need 4 years on that spaceship to reach it.

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question 3
will we ever travel to other galexys?

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I can get you there fast! Craig Cormack, CC BY

Long before the Empire struck back, before the United Federation of Planets federated, Isaac Asimov created Foundation, the epic tale of the decline and fall of the Galactic Empire. Asimov's Empire comprised 25 million planets, knit together by sleek spaceships hurtling through the galaxy.

And how did these spaceships cross the vast gulf between the stars? By jumping through hyperspace, of course, as Asimov himself explains in Foundation:

Travel through ordinary space could proceed at no rate more rapid than that of ordinary light... and that would have meant years of travel between even the nearest of inhabited systems. Through hyper-space, that unimaginable region that was neither space nor time, matter nor energy, something nor nothing, one could traverse the length of the Galaxy in the interval between two neighboring instants of time.

What the heck is Asimov talking about? Did he know something about a secret theory of faster-than-light travel? Hardly. Asimov was participating in a grand science fiction tradition: when confronted with an immovable obstacle to your story, make something up.

Bastian Hoppe, CC BY-NC-ND

You can't beat the speed of light

The problem is that as far as we know, faster-than-light travel is impossible, making galactic empires, federations, confederacies and any other cross-galaxy civilizations impossible. But that's so inconvenient. To evade the cosmic speed limit science fiction has created "warp-drives," "hyperspace," "subspace," and other tricks that have become so ingrained, fans of science fiction don't give them a second thought.

Everyone knows what the Enterprise is doing when it does this:

Or when the Millennium Falcon does this:

Or when the Jupiter 2... actually the Robinson family tried to get to Alpha Centauri without any special effects:

Lost in Space 'The Derelict'

No wonder they got lost in space.

Light sets the cosmic speed limit

Why can't we really exceed the speed of light? After all, people used to talk about a "sound barrier" up until the barrier was broken. But the speed of light is a much tougher barrier to crack. When scientists developed the theory of light back in the 19th century, it came with a special puzzle: their theory seemed to show that every observer should measure the same speed for light, about 186,000 miles per second. But that means if you try to chase a beam of light, no matter how fast you move, the light beam will still fly away from you at 186,000 miles per second. And what's even more bizarre is that if you are moving at 99% of the speed of light, and your friend is standing still, both of you will see the light moving away at exactly the same speed.

Many scientists back then didn't really believe this odd prediction, and the American physicist Albert Michelson (along with his collaborator Edward Morley) set out to measure how the speed of light would change due to the motion of the earth through space. But their famous Michelson-Morley experiment found no change at all. The speed of light seemed to be the same regardless of whether they measured it in the same direction the earth was moving, or in some other direction - a rare example of a non-discovery that turned out to be more important than a discovery!

Enter Einstein and relativity

Instead of trying to explain away this bizarreness, Albert Einstein embraced it. He built an entire theory, called special relativity, around the idea that the speed of light is the same for everyone who measures it, no matter how fast they are moving in relation to the light. In order to accommodate this behavior for light, Einstein's theory predicted that time and space would have to stretch or contract as someone traveled with increasing speed. And out of special relativity popped a cosmic speed limit: nothing could ever exceed the speed of light.

Relativity is a cornerstone of all of modern physics, and we have no reason to doubt it - no one has ever observed an object moving faster than light. There's actually a minor clarification necessary here: Einstein's speed limit is the speed of light in a vacuum. Light slows down when it moves through a material like water or glass, and then it's perfectly possible to exceed this reduced speed of light - up to its speed in a vacuum, of course. Anything moving faster than light in water or glass produces the luminous equivalent of a sonic boom, called Čerenkov radiation. It's what gives underwater nuclear reactors their attractive blue glow.

But about that warp drive...

Of all of the attempts to wiggle out of Einstein's speed limit, probably the most plausible is theoretical physicist Miguel Alcubierre's "warp drive". Alcubierre's proposal doesn't violate the cosmic speed limit - it goes around it. Try filling a greasy frying pan with water and then put a drop of soap into the pan. The grease will fly away to the sides of the pan.

Trekky0623

Alcubierre's warp drive does the same thing with space itself. Alcubierre showed that by a suitable distribution of matter, you can shrink space in front of your spaceship and stretch it behind the spaceship, creating a small bubble around the ship that moves as fast as you like. Because space is contracting in front of the ship, the ship wouldn't officially be moving faster than the speed of light. In fact, the ship would actually be at rest relative to the warp bubble, and the people inside the ship wouldn't even feel any acceleration. Talk about a smooth ride!

There's just one tiny problem.... Alcubierre's space warp can only be generated by violating something called the "weak energy condition." Scientists can't prove that the weak energy condition is always true, but any violation would produce a lot of strange things, like negative energy densities, and possible wormholes or time machines. Cool - sign me up for that! But we've never seen any actual violations of the weak energy condition. So the Alcubierre warp drive occupies a kind of physics twilight zone - not absolutely ruled out, but not very plausible, either.

So how will humanity ever reach the stars? The door marked "faster-than-light travel" has been slammed in our face and welded shut. We'll have to sneak in some other way. Get to work!

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Faster-than-light travel: are we there yet?

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Long before the Empire struck back, before the United Federation of Planets federated, Isaac Asimov created Foundation, the epic tale of the decline and fall of the Galactic Empire. Asimov's Empire comprised 25 million planets, knit together by sleek spaceships hurtling through the galaxy. And how did these spaceships cross the vast gulf between the stars?

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question 2
how fast dose FTL go?
evidence: (1.0003 for air, 1.4 for water)

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Updated 1998 by PEG.
Original by Philip Gibbs 1997.

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.

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 . This wave equation does not allow any causal effect to propagate faster than s. Relativity therefore imposes a limit on elasticity: . 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.

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.

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.

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Updated 1998 by PEG. Original by Philip Gibbs 1997. 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.

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question 1
what does FTL stand for?
evidence: faster than light (FTL)

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Updated 1998 by PEG.
Original by Philip Gibbs 1997.

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.

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 . This wave equation does not allow any causal effect to propagate faster than s. Relativity therefore imposes a limit on elasticity: . 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.

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.

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.

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Updated 1998 by PEG. Original by Philip Gibbs 1997. 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.

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i am working on the topic of FTL
because i want to find out can we make it?
so i can help others understand we can go to other planets