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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,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?
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}##.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.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....How do we get backward in time from this ?
The "tachyonic antitelephone" mentioned above, for example.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 travelling 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.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.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.
Who is the explanation targeted at?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.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.
I think one thing that is confusing is a good notion of "past" and "future" in relativity. There is a phenomenon known as "the relativity of simultaneity", which makes this concept a bit difficult to pin down. There's a lot of discussion of the relativity of simultaneity, see for instance any of the numerous threads on "Einstein's train" here or elsewhere, but it's difficult topic. I'll restrict myself to pointing out it's existence here, rather than trying to explain it in any more detail than giving it's name.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?
Even working through the tachyonic anti-telephone concept, this is the part that I'm struggling to get my head around. There is only one ship, so if it's on the launch pad, it is not also orbiting Proxima Centauri b. So someone can't slip in before it launches and blow it up...or if they do, it doesn't then end up orbiting Proxima Centauri b. 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 traveland 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.
If the ship's path through spacetime has a "loop" in it, so it returns to the same spacetime region, then in that region, there could be more than one of it--an earlier version and a later version. This is one of many counterintuitive things that makes it very difficult to think about such scenarios.There is only one ship
This is not just "non-intuitive", it's not possible, at least not if there is one spacetime reality. If there is one spacetime reality, it has to be self-consistent; FTL travel would not change that. This idea has even been formalized as the Novikov self-consistency principle: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
Aha, that's good to know. And it highlights the subtly inherent in time travel, I guess. Nugatory possibly assumed mutiverse type conditions, but irrespective, the whole situation with FTL = time travel is too complex for me to write up, so I'll stick to the basicsThis 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.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.the whole situation with FTL = time travel is too complex for me to write up, so I'll stick to the basics