Ciro Santilli @cirosantilli 34

The term and idea was first introduced initialized by Hermann Weyl when he was working on combining electromagnetism and general relativity to formulate Maxwell's equations in curved spacetime in 1918 and published as Gravity and electricity by Hermann Weyl (1918). Based on perception that $U(1)$ symmetry implies charge conservation. The same idea was later adapted for quantum electrodynamics, a context in which is has even more impact.

In 2020 physics, best explained by general relativity.

TODO: does old Newtonian gravity give different force results than general relativity?

Subtle is the Lord by Abraham Pais (1982) chapter III "Relativity, the special theory" mentions that this fact and its importance (we want the laws of physics to look the same on all inertial frames, AKA Lorentz covariance) was first fully relized by poincaré in 1905.

And at that same time poincaré also immediately started to think about the other fundamental force then known: gravity, and off the bat realized that gravitational waves must exist. general relativities is probably just "the simplest way to make gravity Lorentz covariant".

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Combination of electromagnetism and general relativity. Unlike combining quantum mechanics and general relativity, this combination was easier.

TODO any experiments of interest at all?

Physics (like all well done science) is the art of predicting the future by modelling the world with mathematics.

And predicting the future is the first step towards controlling it, i.e.: engineering.

Ciro Santilli doesn't know physics. He writes about it partly to start playing with some scientific content for: OurBigBook.com, partly because this stuff is just amazingly beautiful.

Ciro's main intellectual physics fetishes are to learn quantum electrodynamics (understanding the point of Lie groups being a subpart of that) and condensed matter physics.

Every science is Physics in disguise, but the number of objects in the real world is so large that we can't solve the real equations in practice.

Luckily, due to emergence, we can use uglier higher level approximations of the world to solve many problems, with the complex limits of applicability of those approximations.

Therefore, such higher level approximations are highly specialized, and given different names such as:

As of 2019, all known physics can be described by two theories:

Unifying those two into the theory of everything one of the major goals of modern physics.

Explains how it is possible that everyone observes the same speed of light, even if they are moving towards or opposite to the light!!!

This was first best observed by the Michelson-Morley experiment, which uses the movement of the Earth at different times of the year to try and detect differences in the speed of light.

This leads leads to the following conclusions:

All of this goes of course completely against our daily Physics intuition.

The "special" in the name refers to the fact that it is a superset of general relativity, which also explains gravity in a single framework.

Since time and space get all messed up together, you have to be very careful to understand what it means to say "I observed this to happen over there at that time", otherwise you will go crazy. A good way to think about is this:

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

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: 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.

TODO find/create decent answer.

I think the best answer is something along:

A basic non-precise intuition is that a good model of reality is that electrons do not "interact with one another directly via the electromagnetic field".

A better model happens to be the quantum field theory view that the electromagnetic field interacts with the photon field but not directly with itself, and then the photon field interacts with parts of the electromagnetic field further away.

The more precise statement is that the photon field is a gauge field of the electromagnetic force under local U(1) symmetry, which is described by a Lie group. TODO understand.

This idea was first applied in general relativity, where Einstein understood that the "force of gravity" can be understood just in terms of symmetry and curvature of space. This was later applied o quantum electrodynamics and the entire Standard Model.

From Video "Lorenzo Sadun on the "Yang-Mills and Mass Gap" Millennium problem":

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