Guessing in physics

Question

“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 we guess is right, to see what it would imply, and then we compare the computation results to nature or we say compare to experiment 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 any difference how beautiful your guess is, it doesn’t matter 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.” (Richard Feynman. Messenger Lectures, Cornell University.)

My question is how to guess?

And my followup question is Broad motivation : I think of the theoretical physics graduate course curriculum as being divided into two halves : first, an ‘un-compromisable’ core minimum of five subjects in which a student should have a thorough critical and analytic skills. These are

1. Classical mechanics (at the level of the standard textbook by Goldstein or Landau-Lifshitz Vol. 1).
2. Quantum mechanics (at the level of the standard textbook “Modern Quantum Mechanics” by Sakurai).
3. Statistical mechanics (at the level of the standard textbook by M. Kardar or R. K. Pathria)
4. Mathematical Physics (at the level of the standard textbook by Arfken or K. F. Riley-M. P. Hobson-S. J. Bence).
5. Classical electrodynamics (at the level of the standard textbooks by Jackson Zangwill). I feel that it is very difficult to go very far in theoretical physics without a deep and thorough understanding of these subjects. To work on a research problem, this needs to be supplemented by three to four courses in the appropriate research area. My reason for this opinion is as follows: each of these core subjects introduce a particular worldview which has been very successful in our understanding of physical reality. These viewpoints recur again and again in theoretical physics (in fact, I would define a theoretical physics problem as one where this happens). Do you agree?

Answer 1

It depends on the circumstances and the person. No one answer fits all.

One example comes from looking how fast stars orbit in galaxies. People estimated how much matter is there, and calculated how fast that Newtonian gravity says they should orbit. The two answers disagree. The stars are orbiting much faster than they should in the outer regions. Something is wrong, so we must guess what is right.

Two ways immediately come to mind (if you are an astrophysicist). Maybe there is more matter than we see. And maybe the law of gravity is wrong.

If there is more matter than we see, we have to guess what kind of matter could be there that we wouldn't see or detect in other ways.

Perhaps it is black holes? We would not see them, but given the amount of dust in the galaxy, we would expect some to be sucked in to black holes. On the way in, it would heat up and glow brightly. We don't see that, so it isn't black holes.

Perhaps there is a lot more dust than we have detected? We would expect that much dust to block the view of stars behind it. We don't see that much blockage, so it isn't dust.

In this way, people have eliminated pretty much every kind of ordinary matter.

Perhaps the law of gravity is wrong? Then people must guess a modified version of the law that looks just the same at the size of the earth, the size of the solar system, the size of a globular cluster, but somewhat different on the size of the whole galaxy. And extremely strong gravity around neutron stars and black holes must not change in ways that would make what we see of them be different. People have proposed changes, but very little survives checks against what we see in the sky.

People are still guessing. The only kind of matter that could fit must not interact with light, electric charges, the strong or weak nuclear forces. The only force that affects it can be gravity. The particles cannot bind together. That doesn't fit any theories.

We have seen enough evidence of speed of stars orbiting in galaxies and gravitational lensing to make us think such a thing is the most likely explanation. But some people are guessing that modified gravity could be the answer, and are making more guesses in that direction.

And everybody is trying to think up more experiments that could eliminate existing guesses, or show more evidence for them.

Answer 2

My question is how to guess?

My answer is: In as educated a way as possible.