Superluminal and temporal effect

[Edward Wij]

In special relativity, anything superluminal can make things go backward in time in some frame.. is there some kind of exception or would there be away to make it not happen? for instance.. if the signal travels via wormhole which appears instantaneous in different points in spacetime, would there still be this effect of backward in time in some frames?

Is there any papers or references regarding this aspect?

 

[PeterDonis]

The short answer is, no, there are no exceptions. However, the whole subject of whether superluminal objects (usually called "tachyons") are possible, and if so, how they behave, is more complicated than it appears. For example, rather than interpreting a tachyon as "going backward in time" in some frame, we can just reverse our interpretation of which event is the "emission" of the tachyon and which is the "absorption" of it.

This Usenet Physics FAQ article is relevant:

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

 

[Nugatory]

Consider a light signal and a traveller who both leave point A at the same time and eventually arrive at point B. For the traveller's journey to be superluminal (of course it cannot be) he would have to arrive at B before the light. However, there are frames in which all events at B before the arrival of the light signal happen before the light signal and the traveller have left A; and in these frames our hypothetical superluminal traveller would have arrived before he left. How the traveller gets from A to B (whether by wormhole, or StarTrek warp drive, or hitching a ride with a flock of superluminal flying pigs, or by Alcubierre drive, or by magic) is irrelevant.

Google for "tachyonic antitelephone" for more on the relationship between superluminal travel and going backwards in time.

 

[Edward Wij]

Consider a light signal and a traveller who both leave point A at the same time and eventually arrive at point B. For the traveller's journey to be superluminal (of course it cannot be) he would have to arrive at B before the light. However, there are frames in which all events at B before the arrival of the light signal happen before the light signal and the traveller have left A; and in these frames our hypothetical superluminal traveller would have arrived before he left. How the traveller gets from A to B (whether by wormhole, or StarTrek warp drive, or hitching a ride with a flock of superluminal flying pigs, or by Alcubierre drive, or by magic) is irrelevant.

Google for "tachyonic antitelephone" for more on the relationship between superluminal travel and going backwards in time.

So wormholes would violate special relativity.. but there were wormholes theorized.. how did they go over the fact wormholes would mean backward in time causality?

 

[Nugatory]

So wormholes would violate special relativity.. but there were wormholes theorized.. how did they go over the fact wormholes would mean backward in time causality?

Strictly speaking, special relativity does not prohibit faster than light travel (although it does prohibit acceleration to from subluminal to superluminal speeds). It merely tells us that we cannot have faster than light travel unless we are willing to swallow backwards causality with it. This becomes an absolute prohibition because swallowing backwards causality is pretty much impossible.

There are solutions of the equations of general relativity like the wormhole and alcubierre solutions, that allow backwards causality problems and closed timelike curves (that's another good google search term). The general consensus is that these are unphysical even though the math works. It's rather like answering the question "a square plot of land has an area of 100 square meters; how long are its sides?" with "negative ten meters"; the math works, and there's no doubt that negative ten squared equals one hundred, but you won't find any such plots of land anywhere.

 

[Edward Wij]

Strictly speaking, special relativity does not prohibit faster than light travel (although it does prohibit acceleration to from subluminal to superluminal speeds). It merely tells us that we cannot have faster than light travel unless we are willing to swallow backwards causality with it. This becomes an absolute prohibition because swallowing backwards causality is pretty much impossible.

There are solutions of the equations of general relativity like the wormhole and alcubierre solutions, that allow backwards causality problems and closed timelike curves (that's another good google search term). The general consensus is that these are unphysical even though the math works. It's rather like answering the question "a square plot of land has an area of 100 square meters; how long are its sides?" with "negative ten meters"; the math works, and there's no doubt that negative ten squared equals one hundred, but you won't find any such plots of land anywhere.

But if the foliations of spacetime can be adjusted, then it can serve as reference for simultaneity. For example. If you can control the foliations such that the relativity of simultaneity is right between the entangled pair, and you can *somehow* control the entanglement to send signal, then it won't violate causality. The key is foliations of spacetime, would you agree?

 

[Nugatory]

But if the foliations of spacetime can be adjusted, then it can serve as reference for simultaneity. For example. If you can control the foliations such that the relativity of simultaneity is right between the entangled pair, and you can *somehow* control the entanglement to send signal, then it won't violate causality. The key is foliations of spacetime, would you agree?

No. The foliation is just a mathematical trick for describing the space-time, more complicated but with no more physical significance than choosing which inertial frame you'll use to describe a problem in special relativity. The causal relationships between events are the same no matter how we assign coordinates to them, and there's no getting around the fact that if you get from A to B ahead of a light signal, someone somewhere will have you arriving before you left.

 

[Edward Wij]

No. The foliation is just a mathematical trick for describing the space-time, more complicated but with no more physical significance than choosing which inertial frame you'll use to describe a problem in special relativity. The causal relationships between events are the same no matter how we assign coordinates to them, and there's no getting around the fact that if you get from A to B ahead of a light signal, someone somewhere will have you arriving before you left.

I was referring to foliations as having preferred frame.. so if the preferred frame is movable and you can set it anywhere (meaning you can *actually* adjust spacetime for the foliations, then you can bypass causality violations? I'm talking not just choosing which inertial frame but actually setting it up for real. Of course this was just hypothetical for sake of discussion of manipulating the variables of spacetime (say call it metric engineering). If this could be done. Then causality can be readjusted and no violations of causality even for superluminal or instantaneous signal?

 

[PeterDonis]

if you get from A to B ahead of a light signal

It's worth noting that, for curved spacetimes like wormholes and the Alcubierre metric, an observer traveling "faster than light" to a distant location will not actually get there before a light signal that travels the same route. That is, if you shine a light ahead of you through the wormhole or through the Alcubierre warp bubble, that light will get to your destination before you do. But there may be other light signals emitted from your starting point (ones that don't go through the wormhole or the warp bubble) that reach your destination later than you do.

Also, while wormhole and Alcubierre spacetimes can have timelike worldlines that go "faster than light" in the restricted sense described above, that's not the same as an object traveling on a spacelike worldline, which is what "faster than light" means in SR, where spacetime is flat. In the wormhole and Alcubierre spacetimes, the existence of "faster than light" travel in the restricted sense does not necessarily imply closed causal loops. The main reason wormholes and Alcubierre warp drives are considered unphysical is that they require exotic matter.