[riotnrrd]

The effects of relativity cause that thought experiment to fall apart quickly. I build two clocks, and send one to alpha centauri and back in a spaceship. When the travelling clock gets back to Earth it will be showing a different time (because of time dilation during acceleration). What does "the same clock reading" mean then?

[foobarian]

Yes of course they won't show the same time if you bring them back. But the point is to argue that it is possible for there to be a "right now," as defined by what the traveling clock shows, outside of our light cone.