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# How can one frame of reference view space as being infinite and another view it as finite?

I read that space can be infinite in one frame of reference and finite in another. Can anyone explain this? Can you give me a book or website to learn more about this?

Physicist Anthony Aguirre briefly stated that finiteness of space is observer dependent on a TV show. He wrote a book and several scientific publications, but I'm not sure which one explains this claim.

(Thanks for your help Neb, and others)

### 3 Answers

- nebLv 72 months agoFavorite Answer
Don’t think it is true. We define spatial extent by measuring along a ‘slice’ of constant time. Since different reference frames have different definitions of a constant time slice, different frames will not necessarily agree on spatial extent. In a ‘normal’ spacetime, different frames cannot have different enough time slices to result in infinite spatial extent for one but not the other. Essentially, a lorentz rotation of time and space cannot equal or exceed the speed of light which certainly limits the amount of relative rotation.

There are some issues with highly curved spacetimes within black holes where it could be argued that the volume could be infinite in one frame but not another, but we can play lots of games with black holes that don’t reasonably reflect reality.

Update - do you have a link where you read that? There may be some context where I need to think about this more ....

- ElizabethLv 72 months ago
Let's suppose I have an infinite universe. I move through it at the speed of light. Length contraction means I see that infinite universe compressed to a single point ... at light speed in my frame of reference, I'm at all locations simultaneously. The universe I see is finite.

- Anonymous2 months ago
Bullsh..s : it cant be either !!!