I've been saying for years that special relativity can be defined as "the claim that space and time can be represented mathematically by Minkowski space", but this isn't really true. Minkowski space is just a mathematical structure, and as such it doesn't make any predictions about the real world that we can test in experiments. In order to turn the model into a theory of physics, we have to make some identifications between things in the model and things in the real world. For example:(adsbygoogle = window.adsbygoogle || []).push({});

A time-like geodesic = the motion of a massive particle unaffected by forces

A time-like curve = the motion of a massive particle

A null geodesic= the motion of a massless particle

The integral of [itex]\sqrt{-g_{\mu\nu}dx^\mu dx^\nu}[/itex] along a time-like curve = what a clock measures when its motion is described by that curve

Do you know if someone has already made a complete list of the identifications that are necessary? I think it would be interesting to see one. One thing I'm interested in is if there's a set of identifications that defines a theory of physics that'sonlycapable of describing inertial motion. (Does it make any sense at all to say that SR can't handle acceleration even though Minkowski space clearly can?)

If there is no such complete list, maybe we can make one right here. Post what you think should be on it.

Do we need to mention meter sticks, accelerometers and other kinds of measuring devices, or can we (in principle) measure everything with clocks, light, mirrors and photon detectors?

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# Identifications between the model and the real world

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