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Is there a way, in Einstein's relativity (special and general) to view spacetime from a point of view that sits "outside" of it, to intuitively understand it?

We humans can only see 3 dimensions. But, if we were able to see 4 dimensions (or more) would the subject of relativity be simpler and more intuitive to us?

If for example, our Universe only had 1 dimension for space and 1 dimension for time, how would spacetime "look" in the special and general theory relativity of that Universe, if it had one?

Would we be able to picture such a 2D spacetime and intuitively understand it from some kind of "bird's eye view"?

I have heard that spacetime is called a "minkowski spacetime". But what if that spacetime only had 2 dimensions (1 for space and 1 for time as we saw earlier) how would that spacetime look like from the outside or from a-far?

Nuke
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In some cases, it may help to view the spacetime "extrinsically" because the "geometry" might be more familiar to you.....

  • For example, if you were studying a flat (1+1)-dimensional spacetime with the "Asteroids or Pac-Man (video game) topology", you might find it useful to represent it with a torus (the 2D-surface of a donut with a hole) embedded in three dimensions.

However, (as we understand things today) such a higher-dimensional extrinsic viewpoint won't help you with "the physics" (as observers in that spacetime would deal with).... The physics (as we understand things today) is "intrinsic" to the spacetime.

So, in general, I don't think "thinking about spacetimes extrinsically" is useful for physics.

(P.S. Since I don't think that there is a unique extrinsic viewpoint, it seems to me that any "attempt to do physics extrinsically" depends on the choice of extrinsic viewpoint. It's akin to a choice of coordinates... )

robphy
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