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I first learned this in a book by a prominent physicist, so I am inclined to think it is an accurate reading of the physics. Unfortunately I do not remember which so I cannot give you a citation (it was possibly Brian Greene or Frank Wilczek), but maybe there will be a physicist reading this thread who can chime in.

The angular movement thing is this: Imagine you have a frame of reference on the tip of your nose. The X axis points straight away from your face, the Y axis is to your left, Z is up. Now start turning your head to the left. To a tiny observer living on the tip of your nose, the relative speed along the Y axis of a faraway planet has suddenly become very high. The further the planet, the faster the speed (this part is just grade-school geometry).

But let me also just say that you do not have to believe this at all in order to believe my original point; I just brought it up as an extreme crazy case.

So if you don't believe the extreme crazy case, think of the standard example: you get into a space ship or something and zip around really fast. And you are thinking about things closer to you. The math says the same thing: as your light cone changes, the set of spacetime intervals, that have time distance 0 from you, changes as well. So from your relative position the "now" at these faraway points goes back and forth. This is basic, basic relativity.

And actually, yeah, forget about the relative speed, since that is not central to the real issue. The real issue is just that when your light cone changes, the set of points that are simultaneous with you changes (all these points are outside your light cone except for the one you occupy). You cannot observe them directly because they are outside your light cone.

It most certainly is not an accurate reading of physics. What is simultaneous in relation to deep space objects is just a function of their distance from us. Any movement we make is completely negligible, because at those scales the Earth and the far away object are for all purposes point particles.

If you or anyone else can remember where you heard about this idea that would be great, because it is fascinating.

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