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**Slicing the spacetime "loaf"**

I’m having a little trouble understanding an analogy in Greene’s “Fabric of the Cosmos.” I would be grateful for any attempts to explain this or to point me to some examples on the web.

I’m reading about spacetime and the Greene equates spacetime with a loaf of bread that can be sliced at different angles. In Newton’s view, two observers at each side of the “loaf” would experience “now” at the same time which looks like a straight cut through the loaf of spacetime. Relativity says that if the observers are in motion then the cut through spacetime is at an angle and thus the spacetime loaf would be cut at an angle meaning that the observers “now” would be significantly different from each other.

Greene gives an example of you and “Chewie” both sitting on a couch. Chewie is 10 billion light years away. Ignoring rotations of planets and stuff, if both you and Chewie are stationary then you two can say you experience the same now. HOWEVER, if Chewie gets up and walks at about 10 mph away from you – his now will be about 150 years before yours. If Chewie walks towards you – his now will be about 150 after you. (I may have mixed up the moving toward=after your now; moving away = toward your now but regardless….)

I can’t wrap my head around this. I understand (pretty well for a non-physicist) general time dilation effects and the basic ideas of relativity. But I can’t figure out how and why the angle of the “slice through the spacetime loaf” changes forward 150 years or back 150 years by Chewie moving towards or away from you. Is this just an extrapolation of the moving train with two people shooting at each other when a flash occurs on the train and the observers on the train say the shots occur at the same time and the stationary observers (off the train) say one fired before the other?

I appreciate any help you guys can give. I’ve been puzzled by this for days.

Thanks!

John