Steven,
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Originally Posted by sjastro
We live on a (near) spherical surface.
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We only know that because we can rise above it (in both theory and practice), but by doing that, we are introducing an external system of reference.
Quote:
Originally Posted by sjastro
We can travel around along a great arc on the Earth's surface and end up in the same spot we departed. Clearly this is not possible if the surface is infinite.
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But we could keep going indefinitely, couldn't we? We'd only
Quote:
Originally Posted by sjastro
end up in the same spot we departed.
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because we, not physical constraints, have decided to "end" our journey there.
By nominating a departure point, and by further stating that we could only be there once, we, not "the Universe" have defined the limits.
Quote:
Originally Posted by sjastro
Cosmologists have used a similar principle to test if the Universe in finite and spherical. A photon emitted could traverse a spherical Universe and end up near the same spot of emission.
Since the anisotropic regions of the cosmic radiation background can now be well resolved, double images in the background would indicate this phenomena.
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Just because this hasn't been observed doesn't mean it' not happening, since "well resolved" is clearly less than 100% resolved.
Edit: I might add that the further a photon travels, the less likely it is to maintain its original direction due to gravitational and other factors along the way. It would not seem unreasonable to think that given enough spacetime, a photon would eventually be turned back onto its origin, if not somehow rendered non existant in the process. As a result, perhaps the question of infinity is irrelevant because all possible trajectories of our photon are interlinked loops between which it can change. That way, it could avoid returning to the keen observer for a very long time but still be in a loop at any given time.