- Dark matter is a problem.
- Dark energy is a problem
- Neutrino masses are a problem.
- The observed abundance of matter over antimatter is a problem.
- Quantum gravity is a problem.
In contrast:
- The hierarchy “problem” is a puzzle.
- The strong CP “problem” is a puzzle.
- The spectrum of fermion masses and mixing angles in the Standard Model is a puzzle.
- The cosmological flatness “problem” is a puzzle.
- The quantization of electric charge is a puzzle.
- The interpretation of Quantum Mechanics is a puzzle.
- The question of why there are exactly three spatial dimensions is a puzzle.
- The question of why there are exactly three fermion families is a puzzle.
- The question of why the standard model gauge symmetry is $SU(3) \times SU(2) \times U(1)$ is a puzzle.
- The strengths of the fundamental forces is a puzzle.
A problem is an inconsistency in a given theory (observation vs. theory or within a theory). A puzzle is something that seems to require an explanation.
Problems need solutions, puzzles don’t. Nature doesn’t care about what we find strange. We can ignore puzzles and nothing goes wrong.
So it seems obvious that we should focus on real problems. They are “the most promising route to progress“.
But there are rather simple solutions for most problems.
- We can explain dark matter using one or multiple new particles which we add to the particle zoo.
- We can explain neutrino masses using right-handed neutrinos.
- We can explain dark energy using the cosmological constant.
- We can explain the baryon asymmetry using leptogenesis.
Of course, it is possible to come up with alternative solutions. But these are usually baroque and seem as if you take a sledgehammer to crack a nut. Thus, as long as the simplest solutions aren’t experimentally excluded, it makes sense to stick with them. (C.f. Occam’s razor)
But unfortunately, experimental confirmation of these simple solutions wouldn’t be a huge step forward. The discovery of a dark matter particle or right-handed neutrinos wouldn’t lead to a paradigm shift. In some sense, they would simply be new facts which we add to the list of what we know about nature.
Formulated differently, working on problems is a safe bet with a rather small expected return on investment. Progress is more or less guaranteed because there has to be a solution, but will probably be quite small in the grand scheme of things.
And that’s why puzzles are interesting.
They have the potential to lead to paradigm shifts. But they are a lot riskier because it isn’t even clear that a solution exists or is needed at all.
- An explanation why there are exactly three spatial dimensions possibly requires an understanding of how spacetime itself emerges.
- A complete explanation of the fermion spectrum possibly requires a completely new perspective what elementary particles are.
- An explanation of the standard model gauge symmetry probably requires a new understanding of how symmetries emerge in nature.
- A resolution of the hierarchy puzzle probably requires a new way to understand why fundamental parameters have the values they have.
And that’s why I wouldn’t dismiss puzzles as bad problems. They are in a different category. It’s important to keep them separate. But it makes sense to think about them analogous to how it makes sense for some people to invest in startups and not only in established big companies.