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- Summary
- If the Bell theorem is interpreted as nonlocality of nature, then what does it tell us about the meaning of Einstein theory of relativity?

Physicists often discuss interpretations of quantum mechanics (QM), but they rarely discuss interpretations of relativity. Which is strange, because the interpretations of quantum non-locality are closely related to interpretations of relativity.

The field of interpretations of relativity is not so rich as the field of quantum interpretations. As far as I am aware, basically there are 4 major interpretations of relativity.

1. Operational interpretation. According to this interpretation, relativity is basically about how the appearance of space, time and some related physical quantities depends on motion (and current position) of the observer. Essentially this is how Einstein originally interpreted relativity in 1905.

2. Spacetime interpretation. According to this interpretation, relativity is not so much about the appearance of space and time to observers, as it is about the 4-dimensional spacetime that does not depend on the observer. This interpretation was first proposed by Minkowski. Einstein didn't like it in the beginning, but later he embraced it in his formulation of general theory of relativity. The spacetime interpretation naturally leads to the block-universe interpretation of the world, according to which time does not flow, meaning that the past, the presence and the future exist on an equal footing.

3. Ether interpretation. This is not really one interpretation but a wide class of different physical theories. One simple version of the ether theory was developed by Lorentz, before Einstein developed his theory of relativity in 1905. According to ether theories, there are absolute space and absolute time, but under certain approximations some physical phenomena obey effective laws of motion that look as if absolute space and time did not exist. The original Lorentz version of ether theory was ruled out by the Michelson-Morley experiment, but some more sophisticated versions of ether theory are still alive.

4. Spacetime+foliation interpretation. This interpretation posits that in addition to spacetime, there is some timelike vector field ##n^{\mu}(x)## that defines a preferred foliation of spacetime, such that ##n^{\mu}(x)## is orthogonal to the spacelike hypersurfaces of the foliation. This preferred foliation defines a preferred notion of simultaneity.

What different interpretations of QM can tell us about those interpretations of relativity? Which interpretations of relativity seem natural from the perspective of which interpretations of QM?

The field of interpretations of relativity is not so rich as the field of quantum interpretations. As far as I am aware, basically there are 4 major interpretations of relativity.

1. Operational interpretation. According to this interpretation, relativity is basically about how the appearance of space, time and some related physical quantities depends on motion (and current position) of the observer. Essentially this is how Einstein originally interpreted relativity in 1905.

2. Spacetime interpretation. According to this interpretation, relativity is not so much about the appearance of space and time to observers, as it is about the 4-dimensional spacetime that does not depend on the observer. This interpretation was first proposed by Minkowski. Einstein didn't like it in the beginning, but later he embraced it in his formulation of general theory of relativity. The spacetime interpretation naturally leads to the block-universe interpretation of the world, according to which time does not flow, meaning that the past, the presence and the future exist on an equal footing.

3. Ether interpretation. This is not really one interpretation but a wide class of different physical theories. One simple version of the ether theory was developed by Lorentz, before Einstein developed his theory of relativity in 1905. According to ether theories, there are absolute space and absolute time, but under certain approximations some physical phenomena obey effective laws of motion that look as if absolute space and time did not exist. The original Lorentz version of ether theory was ruled out by the Michelson-Morley experiment, but some more sophisticated versions of ether theory are still alive.

4. Spacetime+foliation interpretation. This interpretation posits that in addition to spacetime, there is some timelike vector field ##n^{\mu}(x)## that defines a preferred foliation of spacetime, such that ##n^{\mu}(x)## is orthogonal to the spacelike hypersurfaces of the foliation. This preferred foliation defines a preferred notion of simultaneity.

What different interpretations of QM can tell us about those interpretations of relativity? Which interpretations of relativity seem natural from the perspective of which interpretations of QM?