Exactly how is causality violated by superluminal travel?

JesseM

No way to explain it without using the concept of frames. Of course you don't have to understand frames in detail, basically what you need to know is the following:

1) A frame is just a coordinate system for assigning position and time coordinates to different events in spacetime.

2) According to relativity, the laws of physics (including those pertaining to FTL transmissions) must work the same way in all inertial frames (not really to important to understand in detail the way 'inertial frames' are defined, the important thing is just that they are the rest frames for slower-than-light observers that aren't accelerating and thus experience no G-forces).

3) In relativity different inertial frames define "simultaneity" differently due to the relativity of simultaneity, meaning that if you have two events A and B at different spatial locations which occured at the same time-coordinate in one inertial frame, then there are other inertial frames where A happened at an earlier time coordinate than B, and still others where B happened at an earlier time coordinate than A.

4) If A is the event of a signal being transmitted and B is the event of the signal being received, then as long as the signal was traveling at the speed of light or slower, all inertial frames agree A happened at an earlier time coordinate than B. But if the separation between A and B is such that the signal would need to travel FTL (for example, if in the coordinates of some inertial frame A happened on Earth in 2010 while B happened 4 light-years away in 2012, so the signal moved 4 light years in 2 years in this frame), then it would always be possible to find one inertial frame where A and B happened at the same time-coordinate (so the signal traveled infinitely fast in this frame), and some other frames where the signal was actually received at an earlier time than it was transmitted (B happened at an earlier time coordinate than A).

5) Combining #4 with #2, if it is possible in at least one frame for a signal to travel backwards in time (so it was received before it was sent), this must be possible in all frames. Thus if FTL transmitters are possible, and Alice and Bob are two slower-than-light observers moving apart and carrying FTL transmitters with them, it should be possible for Alice to send a message to Bob which moves FTL in her frame but backwards in time in his frame, and for Bob to send a reply which moves FTL in his frame but backwards in time in Alice's frame, such that Alice actually receives Bob's reply before she sent the original message, a clear causality violation in every frame.

Fredrik

See also this post (and the comment about the typo in #138).

BeefyDog

I know this is an old post, but isn't the reason why there would be causality violations simply a function of the speed of light a constant - thereby making relativity mathematics useless in ANY case involving formulas involving v>c?

Fredrik

No, that's not the reason. The causality violations are derived from special relativity. See the post I linked to above. Note that there's no need to ask about the experiences or the point of view of the tachyons (the particles moving faster than c). The only coordinate systems that we need to consider are the ones in which a tachyon emitter/detector is stationary. These are ordinary inertial frames.

LaserMind

The speed of light and E/M? But gravity has the same speed too. Its actually the fastest speed of information travel that is a limited to c.

I agree with you that if we assume nothing can go faster than light then strong causality would fail if anything did somehow manage to go faster than light. That follows from simple logic not any physics laws.

So it leaves the more interesting question of why that speed is as it is rather than lets assume its the fastest speed.

Takers anyone? (without obfuscation of course)....

nitsuj

Im a simpleton, it should be mentioned this is observed causality being discussed, in which case...big deal.

Getting information faster then expected hardly means a "break/failure" in causality right?

It would mean observations of cause/effect are not invariant.

DrGreg

No, there is more to it than that. If we assume someone can send some information faster than light (FTL) relative to themselves, and if special relativity is correct, then anyone else must also be able to send information at that same FTL speed relative to themselves. It can be shown that if you have two such observers moving apart at high speed, a FTL signal can be sent from one to the other and back again, so that the first observer receives the signal before she sent it.

See Tachyonic antitelephone for details.

LaserMind

I having been looking for that piece of mathematics for a long time. Can you write the proof out or refer me to it? Or explain in words.

Secondly
There is breaking 'weak causality' and breaking 'strong causality'. Breaking weak causality is just fine - and probably happening in quantum step changes.

So, if the speed of 'information travel' was faster than the maximum speed (achieved by some unspecified means) it could break weak causality - sure. There is nothing wrong with that (mathematically or conceptually).

But, it could not alter a history on its journey because that would break strong causality and then an 'event' could happen before the 'cause' which (I believe) is an absurdity.

What do you think?

Fredrik

It's explained in the Wikipedia article he linked to. It's also explained in the post I linked to earlier. So you should start by reading one (or both) of those.

In the post I linked to, I explained how sending an instantaneous* message can prevent that message from being sent. I don't know how you define "weak" and "strong" causality, but nothing can be a stronger causality violation than a genuine contradiction.

*) I used infinite-speed particles in that post only to make it easier to visualize it in a spacetime diagram.

DrGreg

Fredrik has already given two places to look.

Here is a third where I give a specific numerical example:
Speeds greater than the speed of light, post #42 There is also an illustrative space-time diagram (although for different values) in post #32 of that same thread.

LaserMind

Sorry to be a bit bemused by this... but.. doesn't Lorentz assume a priori that nothing travels faster than light therefore his equations are the result.
Then when we say, well, in this situation something IS travelling faster than light. But then Lorentz would be based on a false assumption and the equations are incorrect?

The time turns out negative in the mathematics, but the equations used are not correct because we are assuming something is FTL (that we earlier stated was not possible).

Is there a really easy example that is unambiguous and easy to follow? All the examples quoted seem convoluted and hard to follow. And surely we needn't use a space-time diagram?

Any takers?

Fredrik

No, it's not that simple.

I can't imagine that there's an example that's easier to understand than the one I described. The only thing that could make it easier is if I had drawn the spacetime diagram instead of just described it.

Spacetime diagrams are orders of magnitude easier to understand than almost everything else in physics. They are certainly easier to understand than Lorentz transformations, which require algebra, while spacetime diagrams require no math skills at all.

DrGreg

No, it assumes the observers are inertial and therefore can't travel faster than light, but you can measure any events at all. My post that I linked to begins with three events, without any mention of motion.

LaserMind

OK. Right. I have this simpler scenario. Its very simple- I hope.

Bob (the cause) kills Alice (the effect) with a laser beam that takes 10 minutes to arrive at her location.

Alice's friend (Martha) sees the dead Alice and jumps into an FTL rocket to try to reverse the death. She travels back to Bob at 5 times the speed of light. So at 5c time goes backwards and she arrives at Bob a minute before he fires his laser and implores him not to shoot.

Bob is prevented from shooting. But Alice is already dead.

Now t1 = t2/SQRT(1 - vSQUARED/cSQUARED)
= t2SQRT(1 - 25)
= t2SQRT(-25)













If something cannot be explained simply then you do not understand it. (Einstein)

LaserMind

Assume light travels a planks length in one clock tick - and also assume that this is ontologically how light (or information) travels in space-time.

Then Lorentz corrections can be applied and all is dandy as we know already.

Now, assume that in one click of the clock an entity can travel multiple planks lengths instead of just one - steps. The previous Lorentz correction is no longer applicable.

That 'entity' could be a wave-function that travels in single steps and leaves no trace of its path. Why no trace? Because it jumped in one step. A wave-function is not information per se - it is 'knowledge of quantum states'. So it is allowed to go ftl.

Fredrik

An object emitted at speed 5c at the event of Alice's death, going at 5c in the direction towards Bob, reaches Bob 12 minutes after he fired the laser.

Also, the whole idea of Alice jumping into an FTL rocket is inconsistent with SR. Massive particles (like the ones in her body) can't be accelerated to, or past, the speed of light. The energy required to accelerate her to speed v goes to infinity as v→c.

Only if you take this as a definition of what it means to understand something. I don't think that would make sense though. Physics is no longer about things that can be explained in simple terms. That doesn't mean that physics can't be understood.

SR is however one of those things that can be explained in simple terms. Spacetime diagrams are by far the simplest.

The Planck length has no special significance in special or general relativity. It only becomes relevant in quantum theories of gravity. Do you want to analyze this scenario using relativity or a quantum theory of gravity? What quantum theories of gravity do you know?