As of 2019, the Standard Model and general relativity are incompatible. Once those are unified, we will have one equation to describe the entirety of physics.
The current state of Physics has been the result of several previous unifications as shown at: en.wikipedia.org/wiki/Theory_of_everything#Conventional_sequence_of_theories so it is expected that this last missing unification is likely to happen one day, potentially conditional on humanity having enough energy to observe new phenomena.
Appears to be an unsolved physics problem. TODO why? Don't they all fit into the Standard Model already? So why is strong force less unified with electroweak, than electromagnetic + weak is unified in electroweak?
Once you specify these properties, you could in theory just pluck them into the Standard Model Lagrangian and you could simulate what happens.
Setting new random values for those properties would also allow us to create new particles. It appears unknown why we only see the particles that we do, and why they have the values of properties they have.
Initially there were mathematical reasons why people suspected that all boson needed to have 0 mass as is the case for photons a gluons, see Goldstone's theorem.
However, experiments showed that the W boson and the Z boson both has large non-zero masses.
So people started theorizing some hack that would fix up the equations, and they came up with the higgs mechanism.
Given the view of the Standard Model where the electron and quarks are just completely separate matter fields, there is at first sight no clear theoretical requirement for that.
Because they interact weakly with matter and mostly just escape out of nuclear reactors, you can likely locate all nuclear reactors on Earth by measuring neutrino flows:
"Barys" means "heavy" in Greek, because protons and neutrons was what made most of the mass of known ordinary matter, as opposed notably to electrons.
Baryons can be contrasted with:
mesons, which have an even number of elementary particles. The name meson comes from "medium" since their most common examples have two quarks rather than three as the most common baryons such as protons. So they have less mass than a proton, but more than an electron, this medium mass.
leptons, which are much lighter particles such as the electron. "Leptos" means "fine, small, thin".
Source. Basically shows Richard Feynman 15 minutes on a blackboard explaining the experimental basis of the eightfold way really well, while at the same time hyperactively moving all over. The word symmetry gets tossed a few times.
The growing number of parameters of the Standard Model is one big source of worry for early 21st century physics, much like the growing number of particles was a worry in the beginning of the 20th (but that one was solved by 2020).
Physicists love to talk about that stuff, but no one ever has the guts to explain it into enough detail to show its beauty!!!
Perhaps the wisest thing is to just focus entirely on the U(1) part to start with, which is the quantum electrodynamics one, which is the simplest and most useful and historically first one to come around.
Perhaps the best explanation is that if you assume those internal symmetries, then you can systematically make "obvious" educated guesses at the interacting part of the Standard Model Lagrangian, which is the fundamental part of the Standard Model. See e.g.:
A local symmetry transformation is much more complicated to visualize. Take a rectangular grid of the billiard balls from the last post, say ten times ten. Each ball is spherical symmetric, and thus invariant under a rotation. The system now has a global and a local symmetry. A global symmetry transformation would rotate each ball by the same amount in the same direction, leaving the system unchanged. A local symmetry transformation would rotate each ball about a different amount and around a different axis, still leaving the system to the eye unchanged. The system has also an additional global symmetry. Moving the whole grid to the left or to the right leaves the grid unchanged. However, no such local symmetry exists: Moving only one ball will destroy the grid's structure.
Such global and local symmetries play an important role in physics. The global symmetries are found to be associated with properties of particles, e. g., whether they are matter or antimatter, whether they carry electric charge, and so on. Local symmetries are found to be associated with forces. In fact, all the fundamental forces of nature are associated with very special local symmetries. For example, the weak force is actually associated in a very intricate way with local rotations of a four-dimensional sphere. The reason is that, invisible to the eye, everything charged under the weak force can be characterized by a arrow pointing from the center to the surface of such a four-dimensional sphere. This arrow can be rotated in a certain way and at every individual point, without changing anything which can be measured. It is thus a local symmetry. This will become more clearer over time, as at the moment of first encounter this appears to be very strange indeed.
so it seems that that's why they are so key: local symmetries map to the forces themselves!!!
Ciro Santilli
OurBigBook.com