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In discussing relativity with a (somewhat mathematical) friend the other day, I ran into a problem showing why special and/or general relativity could be considered as exact descriptions of reality rather than just approximations that are working okay so far. Here's his argument:

Special relativity applies to a situation where there is no curvature of spacetime. Since both matter and energy cause curvature, the only situation where special relativity would apply would be one which has no matter and energy, and therefore one which is not achievable in any experiment. And even as a thought experiment, a clock has to have mass and energy and so there can be no exact predictions in such a theory.

He went on to say that therefore the general theory of relativity rests on a very shaky foundation. This is as compared, for example, to thermodynamics which rests comfortably on statistical mechanics and quantum mechanics.

A related question: Special Relativistic approximation to GR

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Carl Brannen
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4 Answers4

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From an experimentalist's point of view, data trumps theory and mathematics too :) .

Special relativity is a measured fact, within the accuracy of our measuring systems, and has not been falsified. It rests on data, as all physical theories.

Edit: Your friends

"the general theory of relativity rests on a very shaky foundation

reflects the necessity of special relativity in any theory of gravity. His argument that

the only situation where special relativity would apply would be one which has no matter and energy, and therefore one which is not achievable in any experiment

is at fault, because he is not including experimental limits and data. Any mathematical curvature is orders of magnitude smaller than our measuring instruments can measure and validate, and physical theories are judged on that.

Physical theories go mathematically as far as the data can take them. Before the observation of particles special relativity was an interesting observation of Lorenz in the Maxwell electromagnetic theory. Before the photoelectric effect classical mechanics sufficed. If ever experiments can go down to the curvatures of gravity for elementary particles, maybe special relativity will be modified to fit the data. It is theories that change to fit the data, not vice versa.

anna v
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The general theory of relativity does not rest on special relativity, so it does not make sense to say the foundation of GR is shaky because SR is shaky. One merely requires consistency, i.e., we want general relativity to reduce to special relativity in the limit.

timur
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Newton's laws of motion are idealized laws as well. You can't have $0$ force acting on a particle in reality since gravity is a long range force and is present everywhere. So these laws are limiting cases as well.

SR is a good description of reality in the above sense. In the limiting case when gravity may be ignored it is a valid theory of reality.

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Special relativity accurately applies to experiments in a lab or reference frame that is small enough that the tidal force (exactly the same thing as spacetime curvature) in it doesn't alter the outcome of the experiment at the given precision. Search the web for: "For sufficiently small regions, the special theory of relativity is correct!!"

finbot
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