Einstein's special relativity was a great and very bold insight, and was based on a sceptical philosophy of Ernst Mach's. This philosophy is that abstract concepts like time and space modify so that whatever it is you see of a process, in your reference frame, that is 'real', which means the normal laws of physics have to apply to it. That includes, presumably, the second law of thermodyamics that entropy/disorder must increase.
Now imagine, just for the sake of argument, that you're zooming away from a supernova at more than the speed of light. As you go, you're overtaking the light coming from the supernova, so you'll see the supernova going backwards in time (rather like the introduction to the film Contact, where a spaceship traveling away from the Earth at speeds greater than light relives radio history backwards). A layman might explain this as just being how you see it, but if we accept special relativity (and it has been well tested in this way, by Hafele and Keating, 1974) we have to go further and say that this backwards supernova is 'real' so the laws of physics must apply to it. This is alright for most of the laws of physics since most are easily reversible. For example, you can reverse the velocity of every particle in the supernova and they still obey Newton's laws, but if you see the supernova converging on itself then there is a reduction of entropy in time, since it is approaching a special state. This violates the second law of thermodynamics. So special relativity's insistence on what you see being 'real' forbids faster than light travel if we accept this second law. A related problem is that causality is violated too.
A more famous reason that relativity forbids faster than light travel is that when an object approaches light speed its inertial mass approaches infinity and you can't push it any faster so it has constant speed. However, MiHsC challenges this because at a constant velocity the Unruh waves that MiHsC assumes cause inertia would become larger than the Hubble scale and vanish, so the inertial mass would dissipate in a new way. This means, if you do the maths, that MiHsC predicts that a tiny minimum acceleration remains, even at the speed of light, meaning that this barrier can be broken.
The problem I have now is that, if this is true, how can I reconcile MiHsC and its tentative faster than light possibility, with the supernova problem and the violation of causality I mentioned above?
Quote by Werner Heisenberg: "How fortunate we have found a paradox. Now we have some hope of making progress!"
3 comments:
Maybe our understanding of causality is wrong? Or too limited?
I'm working on a paper to argue that time is 'erased' in simpler systems. Might solve some causality problem but I don't know yet.
Mike - since I've shown that 2LoT is not an absolute law but instead a description of what generally happens, and that there is a rather large loophole in it when we're considering photons rather than only massy particles, breaking 2LoT in the FTL universe can't be considered a problem. We can currently produce a system where entropy will naturally reduce rather than increase, and where a system at thermal equilibrium will by itself separate into warmer and cooler sections. A more severe problem is causality, though, since seeing a broken teacup reassemble itself and jump from the floor back to the table would be a little strange. Whereas gravity would still hold the planets in orbit, it would seem to be reversed at ground level based on what we see happen.
However, there may not be a real problem, since we know that the relative speed is FTL, and thus we know that what we are seeing and measuring is distorted by that velocity. As I see it, Relativity (both SR and GR) tell you what you will measure to happen and you need to apply corrections in order to work out what is actually happening (and Quantum theory and Horizon Mechanics tell you what will actually happen). Providing that the supernova, in its own frame of reference, continues to obey the normal laws of physics, and we know our relative velocities so we can work out how that is distorted in what we measure to be happening, then insisting that the same rules apply to what we see to be happening seems a logical step too far.
Paradoxes are useful. It's however interesting that QI implies that FTL is possible. If we keep a force acting on the body, then that energy is being stored in the inertial/gravitational mass. This also implies that you can continue to accelerate forever and still not reach the speed of light, irrespective of whether the inertial mass disappears if you actually did so.
Since all bodies above absolute zero will emit EM radiation according to the Stefan-Boltzmann law, there's another paradox when we look at a body moving at a constant velocity. If you are in a different reference-frame then you'll see that it is emitting higher-energy photons in its direction of travel than it will behind it, yet the numbers of photons each way will be the same. Since photons carry momentum, then the body must appear to be slowing down relative to your frame. That's again following the idea of "all laws of physics must be the same". Another observer will see a different acceleration, so there's as many different accelerations on that object as there are observers. There is maybe thus a "universal" frame of reference that a warm body will decelerate with reference to, and the observers need to correct their observations based on their own velocities relative to that universal frame.
I thus think that the assertion of all frames being equivalent, and that the laws in our frame will be seen to apply in another, may not be an absolute truth but only a guide for when the relative velocities are not too large.
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