Alcubierre warp drive and the second law of thermodynamics

It seems to me that if one had a functional Alcubierre drive and used it there would be some subluminal frame of reference in which time was going backwards for the spaceship which probably for it and for macroscopic objects in it which constitute a reasonably closed system would be a violation of the second law of thermodynamics and thus the Alcubierre drive is impossible unless one were to assume there is a privileged rest frame in which the second law of thermodynamics must apply but it can be violated for others.

Or am I missing something?

What do you mean time was going backwards? Did you get this from a Lorentz transformation?

Consider the following case. I will use the Earth's frame of reference to describe the scenario. Spaceship 1 is heading away from Earth using the Alcubierre drive and is at rest inertially with respect to it but is moving around 2c due to the spacial distortion effects of the drive. Spaceship 2 is farther away from Earth moving towards it directly at but not on a collision course with the first spacecraft. When the second spacecraft passes the first it will see the first moving backwards in time since photons from it from earlier in time will arrive at it later than those later in time. It this merely an illusion or is the first spacecraft moving backwards in time with respect to the second spacecraft's frame of reference?

PeterDonis
Mentor
2020 Award
I will use the Earth's frame of reference to describe the scenario.

Unfortunately, you can't, at least not if by "frame of reference" you mean "a frame of reference the way it works in special relativity", which is what you appear to be assuming. If there is an Alcubierre drive present, spacetime is not flat, and you can't construct a global inertial frame the way you can in SR. That means you can't use intuitions about the way things would appear in a global inertial frame in SR.

When the second spacecraft passes the first it will see the first moving backwards in time since photons from it from earlier in time will arrive at it later than those later in time.

You are assuming that photons travel in the presence of an Alcubierre drive the same way they travel in flat spacetime. This is not the case.

Consider, for example, a photon emitted directly forward by the spaceship inside the Alcubierre drive's warp bubble. If we take your statement that the ship is traveling at 2c with respect to the "Earth frame" at face value, then the ship should pass that photon and leave it behind. But it won't; the photon will arrive at the ship's destination before the ship does.

I'm not sure if anyone has done a detailed analysis of how observers moving at various speeds well outside an Alcubierre drive's warp bubble would see the warp bubble and the ship inside it moving. But I do know that the simple analysis you are trying to make using SR intuitions is not correct.

plasmon_shmasmon