FTL and Violating Causality

[georgie_leech]

That post contains no mathematical proof or demonstration on any level. It uses mathematical concepts as illustrative device. They are different things. Again, those concepts are not nonsense, just the lack of demonstration of the conclusion.

I'm confused, are you looking for mathematical proof of a scientific theory (which is impossible), or a complete course on special relativity? Because the latter require you be familiar with Lorentz Transformations. They look like this:

Unpacking the math of that can be a college lecture all on its own. Why that math applies is another lecture. Are you asking for that?

[Grey_Wolf_c]

That post contains no mathematical proof or demonstration on any level. It uses mathematical concepts as illustrative device. They are different things. Again, those concepts are not nonsense, just the lack of demonstration of the conclusion.

The post contains a link to a very extensive series of webpages crammed with the mathematical proof and demonstrations you are asking for.

GW

[FireJustice]

I see all head bashing isnt as much of FTL traveling, but the problem that is "instantantaneous communication".

You really want instant communication, something that experimental evidence shows not even particle and energy carriers sense each other can do, they still bound to c.

no surprise that breaks your universe.

[Grey_Wolf_c]

I see all head bashing isnt as much of FTL traveling, but the problem that is "instantantaneous communication".

You really want instant communication, something that experimental evidence shows not even particle and energy carriers sense each other can do, they still bound to c.

no surprise that breaks your universe.

Not quite. Instantaneous communication is the simplest way to show how causality violations arise. But any form of FTL communication (or transportation) would still cause causality violations, regardless of actual supra-luminal speed.

GW

[Bohandas]

How would instantaneous communication cause causality violations? I understand how a conventional speed above c could cause them due to the facy that the arrow of time would flip of one could somehow accelerate past c; but hypotentical instantaneous communication by definition would not do this, displacement into the past or future is not "instantaneous"

[Grey_Wolf_c]

How would instantaneous communication cause causality violations? I understand how a conventional speed above c could cause them due to the facy that the arrow of time would flip of one could somehow accelerate past c; but hypotentical instantaneous communication by definition would not do this, displacement into the past or future is not "instantaneous"

The core principle of (special) relativity is that, no matter how fast you're traveling and in what direction, if you measure the speed of a light beam (in a vacuum) relative to yourself you will always get the same result. If this requires the physics of the universe to contort in weird ways in order to produce that result, then guess what? The universe does, in fact, contort in exactly those weird ways.

Now, take that as given and start imagining scenarios. Let's start with two spaceships a light year away from Earth, one stationary and the other traveling towards Earth at 50% the speed of light. They are at the same location, and they each notice a light beam at their location that is traveling towards Earth. The stationary one will, of course, calculate that this light beam will reach Earth one year from now. From the moving one's perspective, however, the Earth is moving towards him at 50% c (remember, all motion is relative). In his view, part of the distance will be covered by the Earth's movement, so the light beam will have less distance to travel, but the light is still traveling at the same speed as per relativity's core principle so it will take less than a year for the light beam to reach Earth.

So, these two aliens disagree about how much time will pass before the light beam reaches Earth, and this disagreement happens because one of them is moving differently from the other. And, importantly, this disagreement is a fundamental aspect of how the universe really works, not just a perceptual artifact.

Now, the aliens will obviously agree that the light beam passed each of them at the same moment because they were both there together (however briefly) when it happened. If they start calculating time as measured on Earth, they will also agree that the moment of the light beam reaching Earth happens at the same Earth time for each of them. Now consider what result each alien will get for the question "what time is it on Earth right now". The stationary alien will calculate that "now" on Earth is "one year before the light beam hits". The moving alien will calculate that "now" on Earth is "significantly less than one year before the light beam hits". Again, this result is a fundamental part of how the universe works, not merely a perceptual artifact.

Now imagine that both aliens and the Earth have infinite-speed communication devices. The stationary alien sends a message to Earth, which arrives immediately - as per the previous paragraph, it arrives one year before the light beam does. Earth forwards this message to the moving alien, and the message arrives immediately. The message was sent from Earth one year before the light beam hits, so it arrives one year before the light beam hits. But in the moving alien's frame, the light beam hitting Earth is less than a year away, which means "one year before the light beam hits Earth" is in the past! Earth's forwarded message arrives back at the observer location before it was sent!

Tada, the FTL communication device has now violated causality by sending a message into the past.

Infinite speed is an extreme case, used to make the illustration clearer, but any communication speed faster than light can be used to set up a similar scenario. As message travel speed decreases towards the speed of light, the required combination of observer speed and message distance to produce a causality violation increases, but it's always possible if the message travels at all faster than light.

Yours,

Grey Wolf

[jayem]

I'm confused, are you looking for mathematical proof of a scientific theory (which is impossible)

That said once you've got the 2 axioms and accept that the co-ordinates differ in frames and define g such that x'=g(x+vt) you only have to convince yourself that g is nice for the formula to 'just' fall out.

Spoiler

Show

If g depended independently on x,x',t,t' then would screwy things happen as you change the origins?
If g depended on temperature or charge then what would happen?

So to some extent that's just a definition, it would I think be possible to instead say, we're keeping a universal co-ordinate system and maxwells equations and lose the benefits of inertial frames. Actually working in it would be hellish* (at high speeds, as in relativity at low speeds the consequences can be ignored).
Similarly it would be possible to have a uniform co-ordinate system and inertial frames but change maxwells equations. Again working with it would be hellish (and high speeds will come up)
Or some really strange hybrid to get all of the weaknesses without any benefit.

*The easiest way would be to do the maths in a relativistic model in the sensible frame and then report everything back in 'earth frame'**.
**Except of course Earth isn't in an inertial frame, so that would be a lousy choice.

What you can't have is all three properties kept, and getting rid of one of them works much much better than the other.


ETA There are a number of derivations of the transforms on wiki, we could all copy/rederive our favorite one out. but it would be a bit pointless.

[Bohandas]

Yours,

Grey Wolf

I think I get it now; it causes problems because what's instantaneous varies as much as length and duration do

[Douglas]

Ok, here goes my attempt at getting the math right without looking anything up. This will start off the same as my last writeup, but go further to reconcile the inconsistencies.

Assumptions:
1) Light travels at the same speed in all reference frames. This is a foundational principle of Relativity.
2) If you specify both location and time, then that is a consistent reference point that all reference frames can use. They might label it with different numbers, but as long as you know what reference frame the numbers are in you can convert them to yours and work with it.
3) An event, such as "X beam of light is emitted from Y source", inherently specifies both location and time.
4) Communication through wormholes occurs instantaneously in the rest frame of the wormhole in question.

There are two planets, L on the left and R on the right, at rest relative to each other. They are 1 light year apart in their rest frame. There is a stationary permanent wormhole connecting them, wormhole X. A traveling wormhole Y moving at half the speed of light to the right happens to come by, momentarily providing a second connection between L and R. The ends of wormhole Y reach L and R simultaneously in wormhole Y's rest frame. At the moment when wormhole Y reaches planet R in X's rest frame, planet L sends a message through wormhole X and planet R forwards it back through wormhole Y and at the same time fires a laser at planet L through normal space.

Reference event A: The message goes through R, and the laser beam leaves R.
Reference event B: The laser beam arrive at L.
Derived event C: The message is sent from L.
Derived event D: The message arrives back at L.

Now, we've got a full specification of location and time for events A and B, but only location for C and D. Let's calculate their times relative to reference event B.

Event C: This goes through wormhole X, which is at rest relative to both planets. In that frame, it will take light 1 year to travel from event A to event B. Event C is simultaneous with A in this frame, so event C happens 1 year before B.

Event D: This goes through wormhole Y, which is moving right at .5 c. In the frame where Y is at rest, planets L and R are moving the opposite direction - left - at .5 c. The laser beam is chasing L at 1 c while L is running away from it at .5 c. It will take the laser's light 2 years to reach planet L. Event D is simultaneous with A in this frame, so event D happens 2 years before B.

The message arrived at time B - 2 years, and was sent at time B - 1 year. The message arrived 1 year before it was sent.

But wait, if the message arrived at time B - 2 but was sent at time B - 1, then in X's rest frame (where B-1 is when the R ends of the wormhole meet) the LY wormhole end has already passed LX when the R ends meet. This means that in X's rest frame, Y must be shorter than 1 light year. But how much shorter? Well, it pretty much has to be a ratio because nothing else would scale the right way, and it has to apply in both frame conversions equally because physics doesn't care about your choice of reference frame. I'll call this ratio D for Distance (because R is already taken).

More precisely, D is the ratio of Y's length in X's rest frame to Y's length in its own rest frame. By symmetry, it is also the ratio of X's length in Y's rest frame to X's length in X's rest frame. And now I have to redo my math.

Event C's calculations are unaffected. It takes light 1 year to travel from event A to event B, event C is simultaneous with A in the frame, so event C happens 1 year before B.

Event D: This goes through wormhole Y, which is moving right at .5 c. In the frame where Y is at rest, planets L and R are moving the opposite direction - left - at .5 c. The laser beam is chasing L at 1 c while L is running away from it at .5 c. And now things get tricky.

Wormhole Y's ends are some distance d apart in their own frame. As per the problem setup, this is the same as the distance between L and R in Y's frame. By the definition of the ratio D and the fact that L and R are 1 light year apart in their own rest frame, this means d = D * 1 ly. The length of wormhole Y in X's rest frame is thus D^2 * 1 ly.

Anyway, the laser beam is gaining on L at .5 c and will take d / (.5 c) years to catch up. Hmm, if D = .5 then it takes 1 year and the times sync up - the laser would reach L in 1 year in both frames. Both frames would agree that the forwarded message was received back at the same time as it was sent. Except they would disagree about where the forwarded message arrived. In Y's frame the two wormholes are the same length and the round trip happens with no trouble, but in X's frame Y is only .25 light years long so the return trip dumps the forwarded message only a quarter of the way back. So, D can't be .5 without something else going on too.

All right, I need another variable. t is the time it takes the laser beam to reach L in Y's rest frame. t = d / .5c

The forwarded message arrives back at planet L at time B - t years. At that time, the LX and LY wormhole ends are located at the same place. The message is sent at time B - 1 year. At that time, the RX and RY wormhole ends are located at the same place. And one more relationship, the distance in X's rest frame between the two planets (1 light year) is covered by the combination of Y's length in that frame plus the .5c travel time for the remaining distance.

1 (total distance) = D^2 (Y's length) + .5 (speed) * ((B - 1) (end time) - (B - t) (start time))
1 = D^2 + .5 * ((B - 1) - (B - t))
1 = D^2 + .5 * (B - 1 - B + t)
1 = D^2 + .5 * (t - 1)
1 = D^2 + .5 * (D/.5 - 1)
1 = D^2 + .5 * (2D - 1)
1 = D^2 + D - .5
1.75 = D^2 + D - .25
1.75 = (D+.5)^2
D+.5 = 1.75^.5
D = 1.75^.5 - .5 = .822876 approximately

t = 1.6457 approx.

Ok then. *Ahem*. Event D: This goes through wormhole Y, which is moving right at .5 c. In the frame where Y is at rest, planets L and R are moving the opposite direction - left - at .5 c and are about .8229 light years apart. The laser beam is chasing L and 1 c while L is running away from it at .5 c. It will take the laser's light about 1.6457 years to reach planet L. Event D is simultaneous with A in this frame, so event D happens about 1.6457 years before B.

The message arrived at time B - 1.6457 years, and was sent at time B - 1 year. The message arrived .6457 years before it was sent.

In X's frame, the message pops out of wormhole end LY when it passes LX. 0.6457 years later, wormhole end RY (which started D^2 = 0.6771 light years away) reaches wormhole end RX, and planet L sends the message, planet R forwards it, and planet R sends the laser beam. 1 year later, the laser beam arrives.

In Y's frame, Y (which is .8229 light years long) is the same length as X, and the two ends of each wormhole meet at the same time. At that time, the message pops out of wormhole end RX, and planet R forwards it and sends the laser beam. 0.6457 years later, planet L sends the message. 1 year after that, the laser beam arrives.

Turns out I didn't need to bring in time dilation to make the numbers work out, at least to this point. The end result is not the ultimately correct formula because of that, however. I think to add time dilation and fully fix the formula I'd have to add a mirror off to the side and have another laser beam bounce off of the mirror on its way from R to L.

[jayem]

I'm definitely a little confused as to being sure what's what in which frame.
I think you may have had the same object moving at 0.5c in both reference frames? In which case that would account for the missing time dilation.
Either that or it's come out implicitly because you do know the speeds of everything in the same frame as you know the distance (and hence can just divide x/v).

But will have to follow later.

[Lvl 2 Expert]

Yours,

Grey Wolf

So you could set up a temporal forward observation post. A fast spinning space station sufficiently far out with am instacom antenna on the outer rim. Communications are timed in such a way that the antenna receives messages from earth on the inbound leg of the rotation while sending the same messages back on the outbound leg. The person sitting by the radio on Earth can now send messages to his past self.

Mind blown. Good thing spin-spin coupling has so far avoided being useful for communication. Although it would be kind of cool to one time see someone do this, like a general fighting a war with near-perfect foreknowledge or an inventor cribbing his own future notes to develop some great innovation in about as much time as it takes to build it.

[NichG]

I found another way to construct the argument which might be easier.

Lets say I have a sequence of events at spacetime coordinates x(t) from the point of view of some arbitrary frame A. When I say 'from the point of view' I'm already removing the time it takes for a signal to arrive, so these are the actual spacetime coordinates of the events. Each event is a signal which counts upwards. Lets assume everything is 1d for simplicitly.

If the spatial distance between two of the points |dx| is always <= c*|dt|, then all subluminal frames of reference agree that the signal counts upwards with respect to time coordinate, regardless of the actual pattern of time of arrival of signals in that frame of reference.

On the other hand, if the spatial distance between two of the points |dx| > c*|dt|, then it is possible to find some frame of reference in which the signal counts downwards with respect to time coordinate (again, regardless of the actual pattern of time of arrival of signals in that frame).

Mathematically this is probably the simplest, since it just needs one application of the Lorenz transform. For simplicity, going with c=1 here. If I take points x1,t1 and x2,t2 and apply a Lorenz boost for a change in velocity dv, the new time coordinates are:

t1' = gamma*(t1 - dv*x1)
t2' = gamma*(t2 - dv*x2)

When can t2'-t1' have a different sign than t2-t1?
We have: t2'-t1' = gamma * ( (t2-t1) - dv*(x2-x1) )

Now, lets do a substitution that x2-x1 = v0*(t2-t1). This doesn't actually suffer any loss of generality since for any nonzero x2-x1 we can just find the constant v0 = (t2-t1)/(x2-x1), but it makes the math easy. So now:

t2'-t1' = (t2-t1) * gamma * ( 1 - dv*v0 )

This reverses sign when dv*v0 = 1. If |dv|<1 (e.g. we're only considering frames of reference which are themselves subluminal), this only happens for |v0|>1. Similarly, if |v0|<1, the only frames which can reverse the order of events are themselves superluminal frames.

[Beleriphon]

Keep in mind though, that while General and Special Relativity are "just" theories, they have been tested and tested and tested countless times, and, to my knowledge, have never been disproven.

Both are theories in so far as they are currently impossible to actually test using empirical tests. I mean we can't accelerate something to C just based on the fact that it would take more energy than we can produce currently. However, from a pure math standpoint nothing has demonstrated that either aren't true.

In terms of saving Bob's dog stuck on the lets say Mars (largely due to the distances involved, the moon is only about 1 light second away) with an instant teleporter think of it this way.

You and Bob observe his dog stuck on Mars with a really amazing telescope. You hope into the teleporter, show up on Mars, grab the dog and hop back. Yay, Bob's dog isn't a pupsicle. However, youi and Bob look back through the telescope, Bob's dog is still on Mars, because there's roughly a 20 minute delay from your perspective, even though Bob's dog is happyily wagging his tail beside Bob. You wait 20 minutes, and you see your self rescue Bob's dog and teleport back. So in effect, from your perspective everything happened instantly, but from the relative perspective of anything else it didn't happen instantly. Thus time travel.

Does it make sense for a practical understanding standpoint without involving some very strange physics phenomenon? Not really, but from a theoretical physics standpoint, time travel is involved. And when we start using math to examine what is happening, then things start to get extra weird where time values start to go negative, or result in zeroes, or even increase at exponential rates.

I think the only thing that doesn't violate causality is quark pairing, because they are paired and quantum physics is weird. Really, really weird.

[Douglas]

Both are theories in so far as they are currently impossible to actually test using empirical tests. I mean we can't accelerate something to C just based on the fact that it would take more energy than we can produce currently. However, from a pure math standpoint nothing has demonstrated that either aren't true

We have accelerated (very tiny) things to very near c, and the results match Relativity. Whether through direct experimentation or just observation of natural phenomena, both theories have also been tested in many other ways. Relativity went from "pure math" to "empirically tested" loooooooooong ago.

[Grey_Wolf_c]

Both are theories in so far as they are currently impossible to actually test using empirical tests. I mean we can't accelerate something to C just based on the fact that it would take more energy than we can produce currently. However, from a pure math standpoint nothing has demonstrated that either aren't true

Both are theories in so far as that's all they can ever be. There isn't a next step after "theory" in science. In order of usefulness, it goes law -> hypothesis -> theory.

A Law describes an aspect of reality, but gives no mechanism for it.
A Hypothesis suggests a testable mechanism for a law, but lacks testing to validate it.
A Theory is a hypothesis that has been tested and not found to fail (or rather found to fail less than the previous Theory for the same Law)

Special and General Relativity both have been very thoroughly tested in every way which we are capable of. Yes, some areas of the theory remains untested because we lack the ability to do so, but it is incorrect to say that they are "impossible to actually test using empirical tests". Even something as basic as observing stars' light bending around the sun is a test of General Relativity.

Grey Wolf

[Max_Killjoy]

Both are theories in so far as they are currently impossible to actually test using empirical tests. I mean we can't accelerate something to C just based on the fact that it would take more energy than we can produce currently. However, from a pure math standpoint nothing has demonstrated that either aren't true.

In terms of saving Bob's dog stuck on the lets say Mars (largely due to the distances involved, the moon is only about 1 light second away) with an instant teleporter think of it this way.

You and Bob observe his dog stuck on Mars with a really amazing telescope. You hope into the teleporter, show up on Mars, grab the dog and hop back. Yay, Bob's dog isn't a pupsicle. However, youi and Bob look back through the telescope, Bob's dog is still on Mars, because there's roughly a 20 minute delay from your perspective, even though Bob's dog is happyily wagging his tail beside Bob. You wait 20 minutes, and you see your self rescue Bob's dog and teleport back. So in effect, from your perspective everything happened instantly, but from the relative perspective of anything else it didn't happen instantly. Thus time travel.

Does it make sense for a practical understanding standpoint without involving some very strange physics phenomenon? Not really, but from a theoretical physics standpoint, time travel is involved. And when we start using math to examine what is happening, then things start to get extra weird where time values start to go negative, or result in zeroes, or even increase at exponential rates.

That's always the sort of example that has left me completely unimpressed. I see no causality violation and no time travel what so ever in that example.

Who cares if the light from the event takes longer to get back from Mars than you do.

[NichG]

Both are theories in so far as they are currently impossible to actually test using empirical tests. I mean we can't accelerate something to C just based on the fact that it would take more energy than we can produce currently. However, from a pure math standpoint nothing has demonstrated that either aren't true.

In terms of saving Bob's dog stuck on the lets say Mars (largely due to the distances involved, the moon is only about 1 light second away) with an instant teleporter think of it this way.

You and Bob observe his dog stuck on Mars with a really amazing telescope. You hope into the teleporter, show up on Mars, grab the dog and hop back. Yay, Bob's dog isn't a pupsicle. However, youi and Bob look back through the telescope, Bob's dog is still on Mars, because there's roughly a 20 minute delay from your perspective, even though Bob's dog is happyily wagging his tail beside Bob. You wait 20 minutes, and you see your self rescue Bob's dog and teleport back. So in effect, from your perspective everything happened instantly, but from the relative perspective of anything else it didn't happen instantly. Thus time travel.

That's just a signal propagation time effect, which you'd also have classically. That kind of thing is subtracted out already when talking about the spacetime coordinates of events, and doesn't have to do with the actual causality violations. It's an unfortunately misleading example because it'd be easy to conclude that the propagation time effect is the only thing that's going on.

[Lvl 2 Expert]

So you could set up a temporal forward observation post. A fast spinning space station sufficiently far out with am instacom antenna on the outer rim. Communications are timed in such a way that the antenna receives messages from earth on the inbound leg of the rotation while sending the same messages back on the outbound leg. The person sitting by the radio on Earth can now send messages to his past self.

Mind blown. Good thing spin-spin coupling has so far avoided being useful for communication. Although it would be kind of cool to one time see someone do this, like a general fighting a war with near-perfect foreknowledge or an inventor cribbing his own future notes to develop some great innovation in about as much time as it takes to build it.

And of course it's ten hours later before I realize you can just repeat the trick. Ones you have a construction like this were the delay in the wiring and such is less than the time won by it you can keep sending any message back and forward to bring it back all the way to when the machine was first activated.

okay, I might have just convinced myself there's a very slight possibility "the singularity" could be a thing.