Special Relativity + some basic mechanics leads to an apparent contradiction in the expected measurements, which is only resolved by introducing a curved space(time). So this would be a failure of self-consistency: the same theory leads to two different results for the same experiment.
However, the two measurements of ostensibly the same thing are done by different observers, so there is no requirement that they should agree. Introducing curved space for the rotating disk shows how to calculate distances consistently.
The problem is that it’s inconsistent with solid-body physics?
Solid-body physics is an approximation. This isn’t hard to show. Just bend something.
Consider the model of masses connected by springs. This is consistent with special relativity, and can be used to model solid-body physics. In fact, it’s a more accurate model of reality than solid-body physics.
Special Relativity + some basic mechanics leads to an apparent contradiction in the expected measurements, which is only resolved by introducing a curved space(time). So this would be a failure of self-consistency: the same theory leads to two different results for the same experiment.
However, the two measurements of ostensibly the same thing are done by different observers, so there is no requirement that they should agree. Introducing curved space for the rotating disk shows how to calculate distances consistently.
The problem is that it’s inconsistent with solid-body physics?
Solid-body physics is an approximation. This isn’t hard to show. Just bend something.
Consider the model of masses connected by springs. This is consistent with special relativity, and can be used to model solid-body physics. In fact, it’s a more accurate model of reality than solid-body physics.
No, that’s not the issue. The problem is that no flat-space configuration works.
The spacetime itself is flat (if the mass of the pie is negligible), but the spacelike slices are curved because you’re slicing it in a weird way.