I know very little about SR -- just the transformation equations I learned in high school. I remember reading somewhere that time dilation is a symmetric artifact of the synchronization convention, and that, by itself, it isn't the reason for differential aging. The reason, if I'm remembering accurately, had to do with geometric interpretation and also the idea that 'empty space' isn't really emptly. I'm sure you get naive questions all the time from laypersons (like me) who have difficulty getting wrapped around the idea that aging is a function of velocity (or is it a function of acceleration?) Anyway, I'm thinking, velocity wrt what? Remembering that the transformations had to do with two observers, each with their own clock, moving relative to each other, I wondered if they would record the same time (for, say, a round trip by one of them from the Earth to the Andromeda galaxy and back) if they were both using the *same* clock (say, revolutions of the Earth around the Sun). Of course, the traveller would record fewer revolutions on his way to Andromeda than on his way back, and the rate at which he recorded them would be different than the rate at which the Earthbound observer recorded them. However, on landing back on Earth, wouldn't the traveller have recorded the same total number of revolutions for his trip as the Earthbound observer? If not, why? If so, then what would it mean to say that they aged differently?