General relativity (and other theories) when proven wrong

Words like "proven" and "wrong" have to be used carefully in this context. It is more meaningful to talk about "accuracy" and "limits". If an experiment was conducted tomorrow that contradicted general relativity it would by no means make general relativity a useless theory, nor would we get rid of it.

The purpose of theories in physics isn't to "prove" anything about the real world. This isn't even something they are capable of doing. Their purpose is to as accurately as possible predict the outcome of experiments.

Of course if there comes a time when a prediction of general relativity is not found in nature the likely reaction will be to attempt to reconcile the theory with the experiment, rather than throwing it out and starting from square 1.

Every currently accepted physical theory will likely be eventually found "wrong" at some scale. But all their predictions have already been experimentally verified a zillion-and-one times at the scales currently accessible to apparatus we know how to construct. So all these theories will forever be valid approximations to "the truth" at these scales, i.e., any more foundationally correct theory will necessarily reduce to our currently accepted approximate theories at these scales.

Take Newtonian mechanics, for example. Go too fast and it fails, requiring the use of special relativity. But $sqrt{1-v^2/c^2}$ reduces to $1$ when $vll c$, so special relativity reduces to newtonian. Or study very small masses and it again fails, requiring quantum mechanics. Or study very large masses and it fails yet again, requiring general relativity.

And since you bring it up, maybe even general relativity will eventually fail. For example, maybe $G$ varies over cosmological times, which would require some kind of modification to general relativity. Oh, and maybe it might be this kind of modification -- https://pubs.giss.nasa.gov/abs/ca00010g.html But even if Canuto, et al, are right, general relativity will remain a valid approximation at the time scales accessible to our currently available apparatus.

You cannot prove a theory wrong, because a theory is like a world-view. Claiming that a theory can be proven wrong is like claiming that the concept of "color" or "speed" is wrong. Theories can of course be inconsistent, but they would then be rejected instantly.

Now, physics theories are still connected to "real life" with what is called a model. To understand the difference between a theory and a model, a good analogy is to think of a theory as the rules of a game, and of a model as a very game (as in, a concrete game that is happening with all of its specificities, choices, etc). The very game is constrained by the rules of the game, and it is what is tangible or "measurable". You're never "measuring" the rules of a game, as you never "measure" a theory. At best, you can "measure" a model of a theory.

Obviously, some properties of a theory are universally true, in the sense that they are true in every model, but it is never easy to conclude that what you measured is what you think you did.

Why is it so? Quite simply, because there is a big difference between the abstract model you write on your piece of paper in a given theoretical framework (say, a model of black hole in general relativity), and a "real life" phenomenon.

First, to identify the "real life phenomenon" as a very model you wrote explicitely on your piece of paper is not choice-free. A choice is involved, and by choice I mean that someone used of his subjectivity to actually claim that what he measures "in real life" is actually identified to this abstract model written on a piece of paper.

Already here, you understand that people can easily object that this identification is legitimate. Maybe the predictions made by your model are not wrong, but the measured "real life" phenomenon is actually not represented faithfully by your abstract model. I call this the downward modelization problem.

Secondly, it is always possible to complexify an abstract model so that it predicts what you measure with good enough accuracy. Well, that's kind of trivial, as you can always add as many free parameters as you want, and do a fit of the curve of your "real life" phenomenon. The question of finding a simple, canonical enough abstract model that predicts your real life phenomenon is at least as hard as the problem above. I call this one the upward modelization problem.

So, what would happen now if the prediction of an abstract model are not fitting the measures of a "real life" phenomenon? If the measures are contradicting a universal claim, then assuming there is no mistake in your measurement apparatus, that would kind of "prove" the theory wrong. Smart physicists are never going to assume that though (stupid ones are going to publish thousands of articles about why it is so tho, think of neutrino going faster than c years ago). If anything, when such a universal claim is "rejected" by a measure, the first thing that comes to mind to smart physicists, is that the experiment was poorly done. The same comes to mind to experimentalists by the way. They need a way to be convinced that their apparatus is good, and they precisely conclude that it is so when their measure of a universal claim (or say, or physics constant) fits what is accepted in the theory.

What if the rejected claim is non-universal? Well, most people will now assume that you did a mistake in the downward modelization, as in, you "forgot to add some effects to your model". They will then try to add these "missing effects" into the abstract model to find a "cheated" solution to the upward modelization problem. The solution is "cheated" because it is rare that it is going to be canonical or legitimate, and somehow, the newly created cheated abstract model of your theory is able to predict with a good enough accuracy your real life phenomenon.

So, what do you do to actually reject a theory, or even to realize that a phenomenon you measured is actually rejecting a theory rather than a model (like, say, dark matter)? There is no choice-free, algorithmic way to do it. You're forced to use your brain, which is apparently hard for most physicists in 2020.

In 2011, the OPERA experiment claimed to have detected neutrinos that traveled faster than the speed of light. Einstein's theory of relativity doesn't allow particles with mass to travel faster than the speed of light, so this experiment violated his theory of relativity.

What happened subsequently, is described in this truly excellent summary, which gives a timeline of all the discussion and further experiments that were done afterwards.

I'm not going to repeat that article here, but here's the gist of it:

• First: How much attention the result gets will depend on the credibility of the experiment (was it done by "armchair" physicists that have no credentials in physics, such as these medical doctors who published a paper two weeks ago in the Macedonian Journal of Medical Sciences saying that there's a black hole at the centre of Earth?). The anomalous OPERA experiment was a collaboration between CERN and LNGS that was conducted by very reputable physicists, so the "violation" of Einstein's theory of relativity got widespread media attention.
• But next, the experiment has to be reproducible in order to be taken seriously enough to discount such a successful theory like relativity. Because the theory being violated in this case (the theory of relativity) is such a major cornerstone of modern physics, and the experiment was extremely expensive, before the whole world starts trying to replicate the results experimentally, the OPERA research group did an "internal replication" attempt. In this case, the neutrinos seemed to travel even faster than in the first experiment, meaning that the speed of light was surpassed by even more than they originally thought!
• Still, the result was too expensive to entirely reproduce elsewhere, so the OPERA group more carefully evaluated the possible sources of error. After two additional sources of error were accounted for (a loose link between the master clock and the GPS receiver, and a clock on an electronic board ticking faster than the expected 10 MHz), it was found that the experiment did not actually detect anything traveling faster than the speed of light.
• What would happen if the error analysis still resulted in the final speed being faster than the speed of light? Many possibilities:
  • Scientists would try to reproduce the experiment externally (e.g. a different group of scientists from a different institution, maybe even a different country, might try to reproduce the experiment).
  • In the case of the OPERA experiment, it would likely be too expensive for another country to create a detector to re-do this experiment, so scientists would instead try to think of ways to reproduce the result in other ways. For example, if they can reproduce the "essential" aspects of the experiment, without the exact same setup, which is likely more elaborate since the original experiment was actually done for a different end goal (the purpose of the original experiment was not to detect neutrinos traveling faster than the speed of light, which was discovered only by "accident").
  • In the meantime, theorists around the world would be coming up with possible explanations for why the speed was detected to be faster than the speed of light.
  • If all experiments confirm that the result is reproducible, and no theorists are able to offer an explanation for this that is consistent with the theory in question (in this case the presently accepted theory of relativity), then modifications of the original theory, and entirely new theories that are consistent with all other experimental results, will be explored.

Some steps in the above sequence may vary, depending on the type of experiment, its scale, and the theory being violated.