As of 2019, the more formal name for particle physics, which is notably missing general relativity to achieve the theory of everything.

https://cds.cern.ch/record/799984/files/0401010.pdf The Making of the Standard Model by Steven Weinberg mentions three crucial elements that made up the standard model post earlier less generalized quantum electrodynamics understandings

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.

There are also however also unsolved problems in electroweak interaction + strong interaction, which if achieved is referred to as a Grand Unified Theory. Reaching a GUT is considered a sensible intermediate step before TOE.

The current state of Physics has been the result of several previous unifications as shown at: https://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?

TODO arguments, proofs

A suggested at Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles", it appears that in the Standard Model, the behaviour of each particle can be uniquely defined by the following five numbers:

- due to spacetime symmetries:
- due to internal symmetries:

E.g. for the electron we have:

- mass: $9.1×10_{−31}$
- spin: 1/2
- electric charge: $1.6×10_{−29}$
- weak charge: -1/2
- color charge: 0

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.

So people started theorizing some hack that would fix up the equations, and they came up with the higgs mechanism.

Can be contrasted with baryons as mentioned at baryon vs meson vs lepton.

Behaviour fully described by quantum electrodynamics.

Experiments to measure it:

The 2019 redefinition of the SI base units defines it precisely and uses it as a measure of charge: https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units#Ampere

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.

As mentioned e.g. at QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) chapter 1.6 "Hole theory", Dirac initially wanted to think of the holes in his hole theory as the protons, as a way to not have to postulate a new particle, the positron, and as a way to "explain" the proton in similar terms. Others however soon proposed arguments why the positron would need to have the same mass, and this idea had to be discarded.

Clear experiment diagram which explains that the droplet mass determined with Stoke's law:

American Scientific, LLC sells a ready made educational kit for this: https://www.youtube.com/watch?v=EV3BtoMGA9c

Here's some actual footage of a droplet on a well described more one-off setup:

This American video likely from the 60's shows it with amazing contrast: https://www.youtube.com/watch?v=_UDT2FcyeA4

Hypothesized as the explanation for continuous electron energy spectrum in beta decay in 1930 by .

First observed directly by the Cowan-Reines neutrino experiment.

composite particle made up of an odd number of elementary particles.

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".

composite particle made up of an even number of elementary particles, most commonly one particle and one anti-particle.

This can be contrasted with mesons, which have an odd number of elementary particles, as mentioned at baryon vs meson vs lepton.

Conceptually the simplest mesons. All of them have neutral color charge:

- charged: down + anti-up or up + anti-down, therefore with net electrical charge $±1$ electron charge
- neutral: down + anti-down or up + anti-up, therefore with net electrical charge 0

One strange quark bound with one up quark or a down quark. 6 combinations exist, 4 if we consider antiparticles the same as particles.

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).

Combination of other sub-Lagrangians for each of the forces, e.g.:

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.:

- derivation of the quantum electrodynamics Lagrangian
- Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 7 "Interaction Theory" derives all three of quantum electrodynamics, weak interaction and quantum chromodynamics Lagrangian from each of the symmetries!

One bit underlying reason is: Noether's theorem.

Notably, https://axelmaas.blogspot.com/2010/08/global-and-local-symmetries.html gives a good overview:

so it seems that that's why they are so key: local symmetries map to the forces themselves!!!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.

https://axelmaas.blogspot.com/2010/09/symmetries-of-standard-model.html then goes over all symmetries of the Standard Model uber quickly, including the global ones.

- Advanced quantum field theory lecture by Tobias Osborne (2017)
- An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011)
- Defining properties of elementary particles
- General relativity
- Grand Unified Theory
- Local symmetry
- Particle physics
- Photon
- Physics
- Quantum field theory
- Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979)
- Theory of everything
- Weak interaction
- What does it mean that photons are force carriers for electromagnetism?
- Why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics?
- Why do the electron and the proton have the same charge except for the opposite signs?