# Faster than light - time

1. Feb 15, 2015

### Cobalt101

I'm still having trouble working out why faster than light speed equates to time travel. I understand that for the traveller time slows down the faster he/she travels and have familiarised myself with the standard examples of Earth man and space man using the Lorentz equations. At the extreme, I also get that at c the observed traveller's clock slows to zero. So for example a photon travelling at c will "experience" no time as it travels say away to, and then immediately, back from a galaxy 100,000 light years from Earth. On Earth 200,000 years will have passed.
For the photon, no time will have passed at all.

For a scenario of faster than light, say twice the speed of light, 100,000 years will pass on Earth. Presumably the maths show that for the photon (or if you like a neutrino) time went backwards. But what does this mean ?

2. Feb 15, 2015

### DaveC426913

Photons cannot travel faster than c. They must always travel at c. And photons do not experience time at all.

What you might look at is tachyons. Hypothetical particles that must travel faster than c, and cannot slow down to c or below it. And travel backwards through time

3. Feb 16, 2015

### Staff: Mentor

No; it's more complicated than that.

A tachyon--a particle that travels faster than light--travels on a spacelike worldline. But the concept of "elapsed time", or "experienced time"--the correct technical term is "proper time"--only applies to a timelike worldline. It simply doesn't make sense for a spacelike worldline. So the question "how much time elapses on the tachyon's clock as it travels from Earth to the galaxy 100,000 light-years away" has no answer; it's asking about something that isn't well-defined.

When people say that tachyons can "travel backwards in time", they are referring to one of two things. The first is simply that, for two events that are spacelike separated, their time ordering is frame-dependent. So, for example, if we label the event of the tachyon leaving Earth as event E, and the event of it arriving at the galaxy 100,000 light-years away as event G, then in the Earth frame, event E happens, say, 50,000 years after event G (this assumes that the tachyon travels at twice the speed of light in the Earth frame); but there will be other frames in which event E happens at the same time as event G, and still other frames in which event E happens after event G. In those latter frames, the tachyon "appears" to be traveling backwards in time.

But actually, it's even more complicated than that. Consider the viewpoint of someone at rest in a frame in which event E happens after event G. This person would say that the tachyon traveled from the distant galaxy to Earth, rather than from Earth to the galaxy. So actually, the question of which direction the tachyon is "really" traveling is not well-defined either--its direction of travel is frame-dependent, because the time ordering of the endpoints of its journey is frame-dependent. The upshot of all this is that this first sense of a tachyon "traveling backwards in time" is not really a problem with time travel so much as a problem with the general idea of tachyons in itself, or rather with trying to reconcile the idea of tachyons with our normal understanding of causality and the ordering of events.

There is a second sense in which tachyons enable "time travel", however, which is not frame-dependent--but it does require an assumption about how tachyons move relative to their source. The assumption is that any tachyon source generates tachyons that move at some fixed velocity (determined by the internal structure of the source, presumably) relative to the source. This is really just a way of saying that whatever the laws of physics are that govern tachyon sources (assuming such laws exist), they must be Lorentz invariant.

If this assumption is true, then we can easily construct a closed "time loop" of communication using tachyon signals (note that we are also assuming that tachyons don't just travel faster than light, but can be used to send signals faster than light, which has its own problems--see the link below). Suppose we use our tachyon communicator to send a signal from Earth to a spaceship which is traveling away from Earth towards a distant star at half the speed of light. For simplicity, we will assume that tachyon signals from this model of communicator travel instantaneously, relative to the source. We'll suppose the ship is 5 light-years away at the instant (Earth time) that the signal is sent. That means the signal arrives at that same instant (Earth time) on the ship.

Now the ship sends back an acknowledgement using its own tachyon communicator, which is the same model as the one on Earth. Since tachyons travel instantaneously relative to the source, this return signal arrives on Earth at the same instant it was sent, in the frame of the ship. But this means the signal arrives earlier, on Earth, than the outbound signal that it is supposed to be a response to! Specifically, if you work out the math, it arrives 2.5 years earlier. This creates a closed loop of communication, which, if actual information could be sent this way, would create a lot of problems.

The Usenet Physics FAQ article on tachyons discusses other issues involving tachyons, including what happens when you try to model them quantum mechanically:

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html

4. Feb 16, 2015

### Paulibus

[
Yes --- it's accepted that one can't send information via tachyons (faster than light), if indeed such
things 'exist'. But there are humbler physical entities that seem to me to be able to outrun the
waves that carry them. Here's my story:

I live facing west, across an ocean beach. Early in the morning, iff the sea is sufficiently calm,
with incoming unbroken waves only a few decimeters high, waves appear as dark lines
advancing into a background of shoaling sea, brightened by the dawn sky. I’ve often
observed that such waves can generate small reflections when they reach the waterline. These
reflections, receding, then meet incoming waves, often causing them to break. Such breaks spread
rapidly from a point, to a line along a wave, and do so very much faster than the waves themselves

I’ve also observed that the directions of (the wave vectors of) the incoming waves and the
reflected waves are not quite perpendicular to the waterline. (This is a real sandy beach, on a
viscous sea -- not a model, ideal-fluid, smooth-planed beach one!)

The result is that the lines of the incident and reflected waves are seldom quite parallel. So these
oppositely-moving waves first meet at a point; where the break starts and spreads, I suppose,
along the bisector of the waves’ lines. The spreading of the break is a physical happening; a
change in the localised circling motions of water that constitutes such waves, and a change that
propagates very much faster than the waves themselves do. It’s not just a chimera, like the
scissoring together of two non-parallel geometrical moving lines.

It seems to me that this spreading of a break in a water wave can and does carry information (say
about irregularities in the beach) much faster than shallow-water waves themselves move. Why can’t EM
waves do likewise? Or are the fields that constitute EM waves just not as ‘real’ as water is to us?

Last edited: Feb 16, 2015
5. Feb 16, 2015

### Staff: Mentor

Sure; that's because the speed of sound in water (which is the speed at which "information" can be transmitted through water by a disturbance like what you describe) is much faster than the speed of the waves. But both speeds are still much, much slower than the speed of light.

Because EM waves move at the speed of light, and nothing can carry information faster than light.

Actually, the more precise way of saying the above is that EM waves in vacuum move at the speed of light (meaning $c$, the speed of light in vacuum), and nothing can carry information faster than that speed. But in a material medium, EM waves can move slower than that, and it is possible for information to be transmitted through the medium faster than those waves travel. But it will still be transmitted no faster than the speed of light in vacuum.

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