Can a Theory be Proven Right?

This is based on one of the lectures of Richard Feynman (1918–1988), a theoretical physicist and Nobel Prize winner, describing the process by which theory and practical studies are used together to make scientific discoveries.

In general, we look for a new law by the following process:

First, we guess it. Then we compute the consequences of the guess to see what, if this is right, if this law that we guess is right, we see what it would imply. And then we compare those computation results to nature, or we say compare it to experiments or experience. Compare it directly with observations to see if it works. If it disagrees with experiment, it's wrong.

In that simple statement is the key to science. It doesn't make a difference how beautiful your guess is. It doesn't make any difference how smart you are, who made the guess, or what his name is. If it disagrees with experiment, it's wrong. That's all there is to it. It's true, however, that one has to check a little bit to make sure that it's wrong, because someone who did the experiment may have reported it incorrectly. Or there may have been some feature in the experiment that wasn't noticed, like some kind of dirt and so on. That's an obvious check. Furthermore, the person who computed the consequences even may have been the same one who made the guesses, may have made some mistake in the analysis.

Those are obvious remarks. So when I say, if it disagrees with experiment, it's wrong, I mean after the experiment has been checked, the calculations have been checked, the thing has been moved back and forth a few times to make sure that the consequences are logical consequences from the guess, and that it, in fact, it disagrees with a very carefully checked experiment. This will give you somewhat a wrong impression of science. It means that we keep on guessing possibilities and compare it to experiments. And this is to put an experiment on a really, a little bit weak position.

It turns out that the experimenters have a certain individual character. They like to do experiments, even if nobody's guessed yet. So it's very often true that experiments in a region in which people know this theorist doesn't know anything, nobody's guessed yet. For instance, we may have guessed all these laws, but we don't know whether they really work at very high energy, because it's just a good guess that they work at high energy. So experimenter says, let's try higher energy. And therefore, experiment produces errors every once in a while, that is, it produces a discovery that one of the things that we thought of is wrong. So what I would say, if the experiment can produce unexpected results, and that starts to make us guess again. For instance, an unexpected result is a mu-meson and its neutrino, which was not guessed at by anybody, whatever, before it was discovered. And still, nobody has any method of guessing by which this is a natural thing.

Now you see, of course, that with this method, we can disprove any definite theory. You have a definite theory and a real guess from which you can really compute consequences, which could be compared to experiment, then in principle, we can get rid of any theory. We can always prove any definite theory wrong.

Notice, however, we never prove it right. Suppose that you invent a good guess, calculate the consequences, discover that every type of consequence that you calculate agrees with experiment. Is the theory then right? No. It is simply not proved wrong. Because in the future, there could be a wider range of experiments that compute a wider range of consequences, and you may discover that the thing is wrong. That's why laws like Newton's laws for the motion of planets last such a long time. He guessed the law of gravitation, calculated all the kinds of consequences for the solar system, and so on, compared them to experiments, and it took several hundred years before the slight error of the motion of Mercury was developed.

During all that time, the theory had been failed to be proved wrong and could be taken to be temporarily right. But it can never be proved right, because tomorrow's experiment may succeed in proving what you thought was right, wrong. So we never are right. We can only be sure we're wrong. However, it's rather remarkable that we can last so long. I mean, Have some idea which will last so long.

References:
https://en.wikiquote.org/wiki/Richard_Feynman
http://www.feynmanlectures.info/
http://www.zyvex.com/nanotech/feynman.html