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I've been pondering the measurement of distance and how it is affected by relativity and was wondering if there is some general consensus on whether spacetime is infinitely divisible?

I spent a few hours Googling but didn't come across any definitive statements either way.

I came up with the following experiment which could conceivably answer the question but find my limited knowlege isn't getting me any closer.

If you have a photon source and a photon detector and systematically fire individual photons at the detector from all points on a geodesic sphere with extremely fine tesselation (on the order of an atom between points) could there conceivably be some radius where light took longer to travel along a given vector than other vectors?

If there is a limit to how finely space can be divided then at some point, there should be a time difference because light would have to hop from node to node of the underlying structure of space and some vectors would have more nodes to hop.

If space is infinitely divisible then no matter how far the photon source is from the detector, the time would always be the same for a given radius.

Anyone care to hazard a guess?

I spent a few hours Googling but didn't come across any definitive statements either way.

I came up with the following experiment which could conceivably answer the question but find my limited knowlege isn't getting me any closer.

If you have a photon source and a photon detector and systematically fire individual photons at the detector from all points on a geodesic sphere with extremely fine tesselation (on the order of an atom between points) could there conceivably be some radius where light took longer to travel along a given vector than other vectors?

If there is a limit to how finely space can be divided then at some point, there should be a time difference because light would have to hop from node to node of the underlying structure of space and some vectors would have more nodes to hop.

If space is infinitely divisible then no matter how far the photon source is from the detector, the time would always be the same for a given radius.

Anyone care to hazard a guess?

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