[raganwald]

I am constantly reading that information cannot travel faster than light, and I accept each of the explanations as to why the various methods for attempting to send information faster than light do not work.

What I do not understand is whether sending information faster than light would cause a paradox of any sort. It may be that it happens to be impossible. But is it necessarily impossible?

[martincmartin]

But is it necessarily impossible?

Yes, because of time dilation. In particular, suppose that, in some reference frame, you can send a message from location A to location B faster than light. In that reference frame, it arrives at B after it leaves A. Then, in some other reference frame (moving at less than the speed of light relative to the first), it arrives at B before it leaves A.

So, we can reverse that: Let's say I (in Boston) want to send you (in Toronto) a message that you'll receive before I send it. Then I simply figure out a reference frame where the message would travel forward in time but faster than light. Then I use the faster-than-light communication in that reference frame to send it to you.

If you now do the same -- choose a 3rd reference frame, where the message from Toronto to Boston travels forward in time but faster than light, but where on the Earth's surface it travels backward in time -- you can now send your reply before I send my message.

Then I can arrange a simple grandmother paradox. e.g. I plan to send a message to you at 2pm, but if I get your reply before 2pm, I don't actually send it.

EDIT:

In particular, if one observer measures an event as happening at position-time (x, y, z, t), and another observer is moving at speed u along the x axis, that observer will see:

x' = (x - ut) / sqrt(1 - u^2/c^2)

y' = y

z' = z

t' = (t - ux/c^2) / sqrt(1 - u^2/c^2)

(This is the Lorentz transformation.)

Suppose the first observer can send info faster than light. Suppose she sends it along the x axis at a speed of 2c. You can repeat the derivation with any kc where k > 1. If the sending event is at position-time (0, 0, 0, 0), and it takes one time unit to get there, then the receiving event in her frame is (2c, 0, 0, 1).

What does the other observer see? Let's suppose they're moving more than half the speed of light, say 3/4 the speed of light. The sending event is the origin, and the origin maps to the origin, so that's easy. For the receiving event:

x' = (x - ut) / sqrt(1 - u^2/c^2) = (2c - (3/4 c) * 1) / sqrt(1 - (3/4 c)^2/c^2)

y' = y = 0

z' = z = 0

t' = (t - ux/c^2) / sqrt(1 - u^2/c^2) = (1 - (3/4 c) * 2 * c/c^2) / sqrt(1 - (3/4 c)^2 / c^2) = (1 - 3/4 * 2) / sqrt(1 - (3/4)^2).

In the formula for t', note that the first term, 1 - 3/4 * 2, is negative.

So, if I can send messages at a speed of k * c, then an observer moving with a speed greater than c/k in the same direction sees the message arrive before it leaves. That description is very easy to reverse.

[Groxx]

I've seen that explanation over and over, but I don't see why there's a problem with something arriving at B before B sees it leave A. We have the same situation with faster-than-sound travel, but it doesn't appear to be impossible.

Granted, it's not impossible by that proof because we have faster means of communication (you can detect something before its sound reaches you) (or maybe because it's slower than light), but that's not a problem with faster-than-light communication either. By hypothetically accepting that there's a FTL communication method, didn't you just accept that there's something faster than light?

Wouldn't that imply there's something we don't know about time dilation (if FTL comm is achieved), given that it defines such a thing as impossible? It's a circular argument, it's impossible by this proof because this proof relies on it being impossible. So arguing a hypothesis which rejects that requirement with this proof is ignoring the hypothetical universe that was constructed, and it's not a proof at all.

[bermanoid]

...I don't see why there's a problem with something arriving at B before B sees it leave A.

The problem is that if something arrives at B before B sees it leave A, then there is a way to arrange for a message to be sent from B to A, and a response back from A to B, such that the response arrives before the message was sent.

This is a consequence of special relativity, which allows any spacelike vector to be transformed into any spacelike vector (and any timelike into any other timelike) by a subluminal (less than light speed) change in observer velocity. If you can do any spacelike (FTL) transmission of data, then you can do every spacelike transmission of data if you care to go through the trouble (which is not to say it would be easy, just that physics doesn't prohibit it). Combining spacelike vectors lets you move back in time, so causality is screwed beyond belief.

[Groxx]

>The problem is that if something arrives at B before B sees it leave A, then there is a way to arrange for a message to be sent from B to A, and a response back from A to B, such that the response arrives before the message was sent.

No, you're changing your terms in that sentence. If something arrives at B before B sees it leave A, it doesn't imply it hasn't left A. B could send a response that similarly goes faster than B sees, and the whole system could end up with A receiving a response from B before A sees B receive the original message. B still sent the message after A sent theirs.

That's not a paradox, that's just faster communication than sight. Similar to how two people can jog towards each other, and receive a response before they reach the other person, much less reach each other's starting points.

---

As I have in another reply in this main thread, I understand that this is what special relativity says. But I also thought special relativity says it's impossible to travel faster than light, so is anything outside what it claims is possible even within its rule-set? How does special relativity apply to the apparently-contradictory world of quantum behavior? Even Einstein didn't think quantum mechanics was correct and didn't fit with relativity, but we deal with quantum behavior on a daily basis, so it's very definitely real.

edit: perhaps more clearly:

Special relativity claims that anything faster than c goes back in time. (I think/thought) it also claims anything faster than c is impossible. But it's an easy thought-exercise to cause instantaneous transmission without causing a paradox, an easy solution being things happening faster than sound not causing paradoxes. Just because you haven't heard it doesn't imply it hasn't happened yet.

[hugh3]

I've seen that explanation over and over, but I don't see why there's a problem with something arriving at B before B sees it leave A. We have the same situation with faster-than-sound travel, but it doesn't appear to be impossible.

It's a subtle point, and it's very difficult to explain in layman's terms. On the other hand, it's very easy to explain once you know how to draw and interpret a Minkowski diagram.

But basically, special relativity means that if you can travel faster than the speed of light then you can travel back in time. An explanation of why that's shorter than a full explanation of special relativity will seem unsatisfying.

So instead of reading handwavey explanations on the internet recommend going out and properly learning special relativity from a textbook. (D'Inverno is pretty good, though it's only one among many.)

A philosophy lecturer of mine said that nobody should be allowed to graduate university unless they understand (a) relativity, (b) quantum mechanics and (c) Gödel's theorem, and I'm inclined to agree. You just can't consider yourself educated in the 21st century without a basic grounding in the important advances of the 20th.

[Groxx]

I thought special relativity also means that it is impossible to travel faster than light. So anything outside its range of what's possible can be calculated as utter nonsense without invalidating the theory within its range. Similar to how quantum effects seem to work by entirely different and contradictory rules, while still very clearly working.

[hugh3]

Yes and no. It predicts the impossibility of travelling faster than the speed of light and predicts which kinds of impossible you'd get if you did.

The first level of impossible is that you can't accelerate a body past c no matter how hard you try since continued acceleration will just get it arbitrarily close to c (in every reference frame). The second level of impossibility is that if you did find a magical way to do that then you'd wind up with time travel.

[ignifero]

Think of the same object A arriving in B before it even leaves B.

[raganwald]

Time dilation:

http://en.wikipedia.org/wiki/Time_dilation

Ok, so let's take two twins, Raj and Ragan. Raj is orbiting a massive cosmological object, Ragan is on the surface. Ragan's time appears to travel slower than Raj's time.

Does FTL communication between Ragan and Raj ever create a situation where messages can travel backwards in time? Does bringing an observer into it help?

[martincmartin]

As you were posting this, I edited my post to fill in more details. You've got me re-reading my special relativity texts, which I haven't touched in 20 years, and for which I thank you. :)

[jerf]

It's difficult to explain some of the other things mentioned in this thread without going to math, like why FTL = time travel. It should also be mentioned that the reason why time travel is a problem is not merely that you can send a signal backwards in time, but that the signal may be used to then prevent the sending of the signal. Moreover, it isn't necessarily the case that this requires a human; you can get something like an asteroid going around the loop and knocking itself off the path that led it around the CTC in the first place, so having this sort of paradox in the universe is genuinely bad and does not require human involvement.

But as to FTL, let me horrifically simplify. Imagine space as a 2D grid of points. Vertical is time (up is the future), left-right is 1D of space. Take every point, and connect it to the one directly above it, the one above and right, and the one above and left, with a directed link. You are allowed to move through spacetime along those lines. You can see your past and future lightcones on this graph, if you look. Light always travels diagonally on this graph.

Normal travel in this horrifically degenerate spacetime is travel that can be expressed on those links. FTL is somehow figuring out how to bypass the graph structure of space, which the shape of that space doesn't permit. Space is literally shaped so that FTL isn't really possible.

Reality is of course substantially more complicated than this, and this model is useless for any purpose beyond trying to show what I mean by space being shaped such that FTL isn't possible.

This also sort of demonstrates another thing, which is that ultimately, any point that you can't reach is, from the point of view of where you are, really the same. They are all equally simply "unreachable". So you if you create an "unreachable" drive that lets you get there, you can basically just use it twice to jump far away from where you are now, then from there just jump directly into your past. Also, there is no compelling reason to think you would have a drive that would only let you go "one light year"; it would open the entire universe to you. In General Relativity, this still basically holds true, though it requires more explanations about how there isn't one true reference frame, etc, etc, but FTL really is time travel and it really does just shoot physics and causality full of holes.

[bermanoid]

It should also be mentioned that the reason why time travel is a problem is not merely that you can send a signal backwards in time, but that the signal may be used to then prevent the sending of the signal.

This is not necessarily a problem - in a quantum mechanical formulation, it's simple enough to resolve (for instance) a grandfather paradox by looking at quantum interference around causal loops (almost 100% analogous to the way interference on a violin string will restrict stable modes to certain frequencies, interference around a causal loop will only allow stable self-sustaining situations to survive, so any grandfather paradox would self-interfere and not be allowed). The main difference is that with closed timelike curves the quantum effects can get a lot stronger than without them, even affecting very large objects.

[jerf]

I was sticking to GR for simplicity.

[bermanoid]

Right on, and I'm with you there - causality violation is a nasty nasty thing in physics, and causes all sorts of problems.

Even in GR, you can sort of allow causality violations if you're talking about field theory, but it's not pleasant; the problem is that the usual existence/uniqueness proofs (things like "If a solution to the field equations exists on some spacelike slice of spacetime satisfying a bunch of conditions, then there exists a (maybe unique) solution if that spacelike slice is carried forward in time", roughly speaking) usually rely on strong causality assumptions, and for instance it's pretty easy, depending on the situation, to come up with initial field configurations that have no solutions as they're swept forward because of closed timelike curves further along the manifold.

[llimllib]

This page looks to answer your question with a fairly comprehensive "we're not sure": http://www.desy.de/user/projects/Physics/Relativity/SpeedOfL...

(I can't vouch for its accuracy. It seems that the grandfather paradox is the biggest problem with FTL communication)

[raganwald]

The suggestion seems to be that FTL communication is equivalent to sending information back in time. But the explanation on this page asks me to make massive leaps. I can only imagine it is not meant to explain, but rather as a reminder for people who already understand the explanation.

[chulan]

Quantum entanglement seems to allow instantaneous info transfer over any distance. Any Quantum Physicists on here?

[hugh3]

Any Quantum Physicists on here?

j0.

Indeed it does seem to allow that, and this is right at the heart of the quantum measurement problem. The three popular ways out of this are:

1. To ignore it entirely, stating that we don't really care about the implications of quantum mechanics and are just happy that it's useful for calculating things. LA LA LA!

2. To declare that yes, well, maybe it sort-of does, but it doesn't matter because there's no actual information being transmitted. I can't use quantum entanglement to send a message to Alpha Centauri, since I have no control over the sequence of bits which get transmitted; the most I can do is ensure that both they and I wind up with the same string of completely random bits.

3. Go to a no-collapse ("many-worlds") theory of quantum mechanics, in which there isn't any superluminal communication required (why? It's nonobvious and hard to explain but if you're willing to trust me then you can just go along with it for now...)

My personal preference is for (3) but the implications of many-worlds theories are so horrifying that it remains quite controversial.

[rdtsc]

Not _info_ transfer but it allows instantaneous collapse of the entangled state into known states after the measurement is done on a entangled system.

Here is how I remember it (and I am just a comp sci nerd, not a physicist so please correct me):

* you have 2 qubits Q1 and Q2. You entangle them. Now you have an entangled system Q1Q2.

* You separate Q1 and Q2 in space. Let's say you put Q2 on a spaceship and blast it into space, but leave Q1 in the lab on earth.

* After some time you measure Q1 to get its value. At that point the entanglement of Q1Q2 collapses. You now know the value of Q1 that you just measured and at the same time Q2 is forced to a known value too.

* At _appears_ as if you could send information this way but you cannot. Think about it. You don't know what value you'll measure in the lab for Q1. So you can't force Q2 to be a certain value either.

* Let's think about it another way -- suppose you tell the spaceship operator that if Q2 collapses to |0> then they should turn the spaceship immediately around and head back home and if it collapses to |1> they should arm their weapons and prepare for an alien attack. Now you are on earth in control of Q1, and you want to force Q2 to be measured to |1> because you know the aliens are coming. There is nothing you can do to Q1 to force Q2 to be measured as |1>.

[aquark]

OK, but can you detect in the spaceship when Q2 collapses? (I know no quantum physics beyond a few articles0

If so why can't you simply modulate the signal on top of a series of collapsing entangled pairs. Basically morse code with the timing of the collapses, you don't care what value they collapse too.

[incremental]

Nice try, but no - basically, to use your phrasing, there's nothing to detect when Q2 collapses.

[rdtsc]

No. You can ask the spaceship to measure Q2 after a certain period of time. So "fly away and at a specific time T measure Q2" would be the command. Sorry I should have made that more clear.

[Alex3917]

Some people like to point out that technically the information isn't traveling through space, but to me this seems like a rather academic distinction. This is the relevant wikipedia article:

http://en.wikipedia.org/wiki/Bells_theorem

See also:

http://forum-network.org/lecture/how-hippies-saved-physics

[lisper]

http://www.flownet.com/ron/QM.pdf

[pygy_]

I'm not a physicist, I'm just repeating something I read somewhere (I cant even remember where).

As far as I know, general relativity relies on the existence of a finite speed upper bound. It appears that this bound is equal to the speed of light, but any higher speed would do.

[raganwald]

I understand that, although my own explanation is more along the lines that c represents a fundamental constant describing the geometry of space, and that the reason no physical object can travel faster than light is that the speed of light represents the shortest distance in space-time between any two points.

[Confusion]

Information can kill (indirectly, for instance by driving someone to commit murder or suicide) and as such it is the grandfather paradox from the article all over again.

[phlux]

>I am constantly reading that information cannot travel faster than light

(I am not sure if this analogy works - if it is flawed, please help me fix it until it is correct)

Lets assume that you are on a computer connected to another machine that is at the exact furthest opposite possible on the globe, via fiber.

The remote machine will display a question, which you have never seen before and do not know the answer to, but you can read the question and then the answer to the question will be displayed.

Is it impossible that you could not derive an answer to the question fast than the answer could be displayed?

Thus, information (your derived answer) arriving in your head faster than the information arriving on screen as delivered at the speed of light?

My assumption is that information can be derived/created/transferred/understood faster than linear light travel as the processing of thoughts in our minds is semaphoric/symbolic and parrallel - light transmission is serial.

[ignifero]

Yes because it would break Causality, you would have the broken cup along with the intact one. You may ask "why have causality"? Well, it's your pick, either FTL, or Causality.

btw, a great book about time (and time loops) is Igor Novikov's "River of time"