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Our present understanding of nature is far from complete.
Real problems are things related to unexplained observed phenomena, like dark matter or dark energy.
In addition, there are things that we can describe but do not understand. These are not really problems but rather puzzles. Examples are the still not understood masses and mixing angles of the elementary particles or also the hierarchy puzzle and the question why strong interactions do not violate CP symmetry.
The 5 Great Problems
For more information, see the chapter "The Five Great Problems in Theoretical Physics" in the book "Time Reborn" by Lee Smolin.
The laws of physics seem to be composed out of five fundamental ingredients:
- 1 Identical particles.
- 2 Gauge interactions.
- 3 Fermi statistics.
- 4 Chiral fermions.
- 5 Gravity.
The question is whether one can find a “deeper structure” that gives rise to all five of these phenomena. In addition to being consistent with our current understanding of the universe, such a structure would be quite appealing from a theoretical point of view: it would unify and explain the origin of these seemingly mysterious and disconnected phenomena. The U(/1)xSU(2)xSU(3) Standard Model fails to provide such a complete story for even the first four phenomena. Although it describes identical particles, gauge interactions, Fermi statistics, and chiral fermions in a single theory, each of these components are introduced independently and by hand. For example, field theory is introduced to explain identical particles, vector gauge fields are introduced to describe gauge interactions Yang and Mills, 1954, and anticommuting fields are introduced to explain Fermi statistics. One wonders—where do these mysterious gauge symmetries and anticommuting fields come from? Why does nature choose such peculiar things as fermions and gauge bosons to describe itself?
Colloquium: Photons and electrons as emergent phenomena Michael Levin and Xiao-Gang Wen https://journals.aps.org/rmp/pdf/10.1103/RevModPhys.77.871