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windy miller
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As I understand if it were possible to send a single faster than light then one can send a signal back into the past. What is the simplest way to explain how this would happen?
Google for "tachyonic antitelephone" - the Wikipedia article is pretty good,windy miller said:As I understand if it were possible to send a single faster than light then one can send a signal back into the past. What is the simplest way to explain how this would happen?
.Scott said:The issue is how things look from different inertial reference frames.
Something that is traveling at the speed of light will appear to be traveling at that speed in all inertial reference frames.
Something traveling slower than the speed of light will appear to be traveling at some speed less than the speed of light in all inertial reference frames - but not necessarily the same speed.
But something traveling faster than light will appear to be traveling either faster than light or backwards through time depending on which inertial reference frame it is viewed from.
I'm not sure if you can get it from the Lorentz transform, but if a clock is approaching you at greater than the speed of light, the first you see of it will be as it passes you. Then you will see it at earlier and earlier times as the light reaches you from those more distant locations. So you would see the hands on the clock move backwards.jk22 said:Do you have any calculation for this ? As I viewed, Lorentz transform for faster than light induces an imaginary spacetime, from ##\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}##. If ##v\gt c## then ##\gamma\in i\mathbb{R}##.
How do we get backward in time from this ?
You don't. You get nonsense, because the Lorentz transformations are derived from assumptions that are equivalent to assuming that the speed is less than ##c## so using a larger value is internally inconsistent. However...jk22 said:How do we get backward in time from this ?
The "tachyonic antitelephone" mentioned above, for example..Scott said:If you can send messages faster than the speed of light, there is a procedure for relaying the message among three reference frames that allows the message to be drilled back through time.
No. The problem with FTL is the relationship between the start of the journey and the arrival at the destination, no matter how the journey happens. If something leaves point A and arrives at point B before a flash of light traveling in the ordinary manner could, then someone in the universe will find that the arrival happens before the departure - and will be able to stop the departure (perhaps by blowing up the FTL ship on the launchpad) after the ship has already arrived at the destination.Tghu Verd said:For the purposed of a novel I'm writing, does the 'FTL = time travel' situation change if the FTL is via a wormhole
It depends on how it works. The problem with FTL travel in relativity is that there's no global definition of what "at the same time" means for things that aren't in the same place. The tachyonic anti-telephone exploits the fact that "ship arrives at the same time as it leaves" can mean different things in order to build a (potentially paradoxical) time loop.Tghu Verd said:For the purposed of a novel I'm writing, does the 'FTL = time travel' situation change if the FTL is via a wormhole to effect instantaneous travel and the end-points are a significant distance apart? Such as light days or even light years.
windy miller said:As I understand if it were possible to send a single faster than light then one can send a signal back into the past. What is the simplest way to explain how this would happen?
This is general relativity rather than special relativity so things are a little bit more complicated. For a bit of background, if an object/particle/signal travels slower than light locally it is said to have a timelike curve or worldline. If it is like a tachyon that goes faster than light locally it is said to have a spacelike curve. Massive objects must travel on timelike curves.Tghu Verd said:does the 'FTL = time travel' situation change if the FTL is via a wormhole to effect instantaneous travel and the end-points are a significant distance apart? Such as light days or even light years.
In this case, the ship is not actually moving faster than c the conventional sense. It does not accelerate to faster than c, or even anywhere near c.
windy miller said:As I understand if it were possible to send a single faster than light then one can send a signal back into the past. What is the simplest way to explain how this would happen?
Nugatory said:and will be able to stop the departure (perhaps by blowing up the FTL ship on the launchpad) after the ship has already arrived at the destination.
Tghu Verd said:There is only one ship
Tghu Verd said:It is clearly non-intuitive to have a situation where the ship launches, goes into orbit elsewhere, then is blown up before it launches, all because of FTL travel
PeterDonis said:This is not just "non-intuitive", it's not possible, at least not if there is one spacetime reality.
No - the point is that if you allow faster than light travel in relativity, without restrictions of the type I proposed, you do get paradoxes. That's one of the reasons we believe it's impossible, because we have no evidence of anything that would stop paradoxes if FTL were possible. And we'd like to think the universe makes some kind of sense.Tghu Verd said:Aha, that's good to know. And it highlights the subtly inherent in time travel, I guess. Nugatory possibly assumed mutiverse type conditions
If you want to acknowledge it, simply put in a line about physicists' worries about FTL leading to paradoxes turning out to be unfounded as a result of (imaginary) future theories. And otherwise ignore it as you suggest.Tghu Verd said:the whole situation with FTL = time travel is too complex for me to write up, so I'll stick to the basics
FTL (Faster-than-light) signal refers to a hypothetical form of communication that travels faster than the speed of light. In special relativity (SR), the theory of how objects move in space and time, the speed of light is considered to be the maximum speed at which any form of matter or information can travel.
If FTL signals were possible, they would violate the fundamental principles of SR, such as the laws of causality and the relativity of simultaneity. This could potentially lead to paradoxes and break the laws of physics as we know them.
So far, there is no scientific evidence for the existence of FTL signals. The theory of relativity has been extensively tested and has consistently shown that the speed of light is indeed the maximum speed at which anything can travel. While there have been some experiments that claim to have observed FTL particles, these have not been widely accepted by the scientific community.
FTL signals are often associated with the concept of time travel because if information could travel faster than the speed of light, it could potentially reach its destination before it was sent. This could lead to causality paradoxes and the possibility of altering the past. However, the existence of FTL signals does not necessarily imply the possibility of time travel.
There are some theories, such as the Alcubierre drive and the traversable wormhole, that suggest ways in which FTL signals could be achieved within the framework of SR. However, these theories are still highly speculative and have not been proven to be feasible. They also require exotic forms of matter and energy that have not been observed in nature.