Suppose Ploni eats some meat. He then gets in a spaceship and accelerates to some significant percentage of the speed of light for a short trip into outer space, and then returns home. At the time when he returns home, exactly six hours have passed from the Earth's reference frame; however, because of time dilation, less than 6 hours have passed for him.
This is not an issue of who is right. On Earth, six hours have actually passed, whereas for Ploni, the amount of time has actually been less than six hours. Now that he has returned home, may he eat something with milk?
Answer
The short answer is no. Waiting between consuming meat and consuming dairy has nothing to do with how much time we perceive to have elapsed but with the experience of the person who consumed it. Spaceman Ploni, who decided to eat meat immediately prior to takeoff (a revolting thought), can still taste it when he returns to earth, despite the fact that his more sensible brother, who ate meat with him but who didn't board the space-ship, is now enjoying a milkshake.
Source:
Rambam, Hilkhot Ma'akhalot Asurot 9:28, which gives the reason for waiting six hours as being because of food that is still between the teeth (although see the Kesef Mishna there);
Tur, YD 89:1, which gives the reason as being because of the flavour of the meat that remains in the mouth.
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