special relativity - What is the Andromeda Paradox?

I have been studying causality (specifically why there is no such thing as a simultaneous instant of time across all observers) recently and I keep hearing references to the Andromeda paradox. Can anyone tell me what it is and how it is resolved?

I've tried reading what Wikipedia says about it, but I could really use someone's explanation.

Edit
Ok, after reading the related question, now I'd like to know does this imply there is some sort of privileged reference frame, in which there exists absolute velocity and absolute time? I ask because the answer for the other question seemed to indicate that the actions seem to be at different points of simultaneity but that in fact the person not moving is getting it right. But this seems strange to me because if we accelerated our galaxy to a different speed, we would still perceive our stationary observer as being right even though they'd see something different than before the acceleration.

So who is right? In what frame can we be sure that our present is Andromeda's present?

Answer

There can be at least two different flavors of paradoxes. In one, a result such as 2+2=5 is proved, and the problem must be either incorrect reasoning or a set of assumptions that was invalid. In the other type, exemplified by the EPR paradox, the correct result of an argument is so surprising that it seems like it must be a mistake.

Based on the description in the quote by Penrose, the Andromeda paradox is of the latter type. It is simply a dramatized example of the relativity of simultaneity, which is contrary to our intuition based on everyday life. In Penrose's presentation, the dramatization includes a summary of an imaginary dialog between the two observers, who seem to be confused because they don't understand relativity and expect simultaneity to be absolute. Penrose also comments that logical consistency is retained because events in Andromeda can only be learned about on Earth much later.

The paradox is both trivial and nontrivial. It's trivial because it's simply a description of how the relativity of simultaneity works, and therefore it doesn't require any complicated arguments to resolve. It's nontrivial because the relativity of simultaneity is a surprising and difficult concept when you encounter it for the first time.

It may help if we note that this would be the 2+2=5 type of paradox if it were possible to transmit signals instantaneously in relativity. Then the two observers would be disagreeing about something that they could easily check by faster-than-light communication. One of them would find out that he was wrong, and his frame of reference would have been found to be invalid -- which contradicts the basic assumptions of relativity.