Ciro Santilli @cirosantilli 34

The key initial quantum electrodynamics experiments:

Too many fun skit videos for Ciro Santilli's taste, but does have some serious derivations in quantum electrodynamics.

Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) mentions it several times.

This was one of the first two great successes of quantum electrodynamics, the other one being the Lamb shift.

In youtu.be/UKbp85zpdcY?t=52 from freeman Dyson Web of Stories interview (1998) Dyson mentions that the original key experiment was from Kusch and Foley from Columbia University, and that in 1948, Julian Schwinger reached the correct value from his calculations.

Apparently first published at The Magnetic Moment of the Electron by Kusch and Foley (1948).

Bibliography:

Can be thought as being produced from gluon-gluon lines of the Feynman diagrams of quantum chromodynamics. This is in contrast to quantum electrodynamics, in which there are no photon-photon vertices, because the photon does not have charge unlike gluons.

This phenomena makes the strong force be very very different from electromagnetism.

URL: www.youtube.com/channel/UCd02pSRrecAVFOPjB-bfv-Q

Covers some specific hardcore subjects, notably quantum electrodynamics, in full mathematical detail, e.g.: "Quantum Field Theory Lecture Series" playlist: www.youtube.com/playlist?list=PLSpklniGdSfSsk7BSZjONcfhRGKNa2uou

As of 2020 Dietterich was a condensed matter PhD candidate or post-doc at the University of Minnesota Twin Cities, and he lives in Minnesota, sources:

Unfortunately the channel is too obsessed with mathematical detail (which it does amazingly), and does not give enough examples/application/intuition, which is what would be useful to most people, thus falling too much on the hardcore side of the missing link between basic and advanced.

This channel does have on merit however: compared to other university courses, it is much more direct, which might mean that you get to something interesting before you got bored to death, Section "You can learn more from older students than from faculty" comes to mind.

Videos generally involves short talks + a detailed read-through of a pre-prepared PDF. Dietterich has refused however giving the PDF or LaTeX source as of 2020 on comments unfortunately... what a wasted opportunity for society. TODO find the comment. Sam, if you ever Google yourself to this page, let's make a collab on OurBigBook.com and fucking change education forever man.

Full name as shown in channel content: Samuel Dietterich. Other accounts:

Adds special relativity to the Schrödinger equation, and the following conclusions come basically as a direct consequence of this!

Experiments explained:

Experiments not explained: those that quantum electrodynamics explains like:See also: Dirac equation vs quantum electrodynamics.

The Dirac equation is a set of 4 partial differential equations on 4 complex valued wave functions. The full explicit form in Planck units is shown e.g. in Video 1. "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=1010:Then as done at physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600 from why are complex numbers used in the Schrodinger equation?, we could further split those equations up into a system of 8 equations on 8 real-valued functions.

If you are a pussy and work a soul crushing job, this is one way to lie to yourself that your life is still worth living: do one cool thing every day.

Find a time in which your mind hasn't yet been destroyed by useless work, usually in the morning before work, and do one thing you actually like in life.

Work a little less well for you boss, and a little better for yourself. Ross Ulbricht:Selling drugs online is not advisable however.

Even better, try to reach an official agreement with your employer to work 20% less than the standard work week. For example, you could work one day less every week, and do whatever you want on that day. It is not possible to push your passion to weekends, because your brain is too tired. "You keep all non-company-related IP you develop on that time" is a key clause obviously.

On a related note, good employers must allow employees to do whichever the fuck "crazy projects", "needed refactorings or other efficiency gains" and "learn things deeply" at least 20% of their time if employees want that: en.wikipedia.org/wiki/20%25_Project. Employees must choose if they want to do it one day a week or two hours per day. One day per month initiatives are bullshit. Another related name: genius hour.

Highly relevant on this topic: Video "What Predicts Academic Ability? by Jordan B Peterson (2017)".

Maybe you will be fired, but long term, having tried, or even succeeded your dream, or a one of its side effects, will be infinitely more satisfying.

The same goes for school, and maybe even more so because your parents can still support you there. Some Gods who actually followed this advice and didn't end up living under a bridge:

Gandhi TODO source:

Behavior fully described by quantum electrodynamics.

I think they are a tool to calculate the probability of different types of particle decays and particle collision outcomes. TODO Minimal example of that.

And they can be derived from a more complete quantum electrodynamics formulation via perturbation theory.

Can be used for all of quantum electrodynamics, weak interaction and quantum chromodynamics.

At Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979), an intuitive explanation of them in termes of sum of products of propagators is given.

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.

Force carrier of quantum chromodynamics, like the photon is the force carrier of quantum electrodynamics.

One big difference is that it carrier itself color charge.

Head of the theoretical division at the Los Alamos Laboratory during the Manhattan Project.

Richard Feynman was working under him there, and was promoted to team lead by him because Richard impressed Hans.

He was also the person under which Freeman Dyson was originally under when he moved from the United Kingdom to the United States.

And Hans also impressed Feynman, both were problem solvers, and liked solving mental arithmetic and numerical analysis.

This relationship is what brought Feynman to Cornell University after World War II, Hans' institution, which is where Feynman did the main part of his Nobel prize winning work on quantum electrodynamics.

Hans must have been the perfect PhD advisor. He's always smiling, and he seemed so approachable. And he was incredibly capable, notably in his calculation skills, which were much more important in those pre-computer days.

Small splits present in all levels due to interaction between the electron spin and the nuclear spin if it is present, i.e. the nucleus has an even number of nucleons.

As the name suggests, this energy split is very small, since the influence of the nucleus spin on the electron spin is relatively small compared to other fine structure.

TODO confirm: does it need quantum electrodynamics or is the Dirac equation enough?

The most important examples:

Richard Feynman's mentor at Princeton University, and notable contributor to his development of quantum electrodynamics.

Worked with Niels Bohr at one point.

Web of Stories interview (1996): www.youtube.com/playlist?list=PLVV0r6CmEsFzVlqiUh95Q881umWUPjQbB. He's a bit slow, you wonder if he's going to continute or not! One wonders if it is because of age, or he's always been like that.

Extremely precocious, borderline child prodigy, he was reading Dirac at 13-14 from the library.

He started working at night and sleeping during the moring/early afternoon while he was at university.

He was the type of guy that was so good that he didn't really have to follow the university rules very much. He would get into trouble for not following some stupid requirement, but he was so good that they would just let him get away with it.

Besides quantum electrodynamics, Julian worked on radar at the Rad Lab during World War II, unlike most other top physicists who went to Los Alamos Laboratory to work on the atomic bomb, and he made important contributions there on calculating the best shape of the parts and so on.

He was known for being very formal mathematically and sometimes hard to understand, in stark contrast to Feynman which was much more lose and understandable, especially after Freeman Dyson translated him to the masses.

However, QED and the men who made it: Dyson, Feynman, Schwinger, and Tomonaga by Silvan Schweber (1994) does emphacise that he was actually also very practical in the sense that he always aimed to obtain definite numbers out of his calculations, and that was not only the case for the Lamb shift.

Originally it was likely created to study constrained mechanical systems where you want to use some "custom convenient" variables to parametrize things instead of global x, y, z. Classical examples that you must have in mind include:

When doing lagrangian mechanics, we just lump together all generalized coordinates into a single vector $\overrightarrow{q}(t):\mathbb{R}\to {\mathbb{R}}^n$ that maps time to the full state:where each component can be anything, either the x/y/z coordinates relative to the ground of different particles, or angles, or nay other crazy thing we want.

The Lagrangian is a function ${\mathbb{R}}^n\times {\mathbb{R}}^n\times \mathbb{R}\to \mathbb{R}$ that maps:to a real number.

Then, the stationary action principle says that the actual path taken obeys the Euler-Lagrange equation:This produces a system of partial differential equations with:

The mixture of so many derivatives is a bit mind mending, so we can clarify them a bit further. At:the $q_i$ is just identifying which argument of the Lagrangian we are differentiating by: the i-th according to the order of our definition of the Lagrangian. It is not the actual function, just a mnemonic.

Then at:

However, people later noticed that the Lagrangian had some nice properties related to Lie group continuous symmetries.

Basically it seems that the easiest way to come up with new quantum field theory models is to first find the Lagrangian, and then derive the equations of motion from them.

For every continuous symmetry in the system (modelled by a Lie group), there is a corresponding conservation law: local symmetries of the Lagrangian imply conserved currents.
Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "The Best Path" mentions that Richard Feynman didn't like the Lagrangian mechanics approach when he started university at MIT, because he felt it was too magical. The reason is that the Lagrangian approach basically starts from the principle that "nature minimizes the action across time globally". This implies that things that will happen in the future are also taken into consideration when deciding what has to happen before them! Much like the lifeguard in the lifegard problem making global decisions about the future. However, chapter "Least Action in Quantum Mechanics" comments that Feynman later notice that this was indeed necessary while developping Wheeler-Feynman absorber theory into quantum electrodynamics, because they felt that it would make more sense to consider things that way while playing with ideas such as positrons are electrons travelling back in time. This is in contrast with Hamiltonian mechanics, where the idea of time moving foward is more directly present, e.g. as in the Schrödinger equation.

Furthermore, given the symmetry, we can calculate the derived conservation law, and vice versa.

And partly due to the above observations, it was noticed that the easiest way to describe the fundamental laws of particle physics and make calculations with them is to first formulate their Lagrangian somehow: why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics?s.

TODO advantages:

Bibliography:

Published as "Fine Structure of the Hydrogen Atom by a Microwave Method" by Willis Lamb and Robert Retherford (1947) on Physical Review. This one actually has open accesses as of 2021, miracle! journals.aps.org/pr/pdf/10.1103/PhysRev.72.241

Microwave technology was developed in World War II for radar, notably at the MIT Radiation Laboratory. Before that, people were using much higher frequencies such as the visible spectrum. But to detect small energy differences, you need to look into longer wavelengths.

This experiment was fundamental to the development of quantum electrodynamics. As mentioned at Genius: Richard Feynman and Modern Physics by James Gleick (1994) chapter "Shrinking the infinities", before the experiment, people already knew that trying to add electromagnetism to the Dirac equation led to infinities using previous methods, and something needed to change urgently. However for the first time now the theorists had one precise number to try and hack their formulas to reach, not just a philosophical debate about infinities, and this led to major breakthroughs. The same book also describes the experiment briefly as:

It is two pages and a half long.

They were at Columbia University in the Columbia Radiation Laboratory. Robert was Willis' graduate student.

Previous less experiments had already hinted at this effect, but they were too imprecise to be sure.

2s/2p energy split in the hydrogen emission spectrum, not predicted by the Dirac equation, but explained by quantum electrodynamics, which is one of the first great triumphs of that theory.

Note that for atoms with multiple electrons, 2s/2p shifts are expected: Why does 2s have less energy than 1s if they have the same principal quantum number?. The surprise was observing that on hydrogen which only has one electron.

Initial experiment: Lamb-Retherford experiment.

On the return from the train from the Shelter Island Conference in New York, Hans Bethe managed to do a non-relativistic calculation of the Lamb shift. He then published as The Electromagnetic Shift of Energy Levels by Hans Bethe (1947) which is still paywalled as of 2021, fuck me: journals.aps.org/pr/abstract/10.1103/PhysRev.72.339 by Physical Review.

The Electromagnetic Shift of Energy Levels Freeman Dyson (1948) published on Physical Review is apparently a relativistic analysis of the same: journals.aps.org/pr/abstract/10.1103/PhysRev.73.617 also paywalled as of 2021.

TODO how do the infinities show up, and how did people solve them?

www.mdpi.com/2624-8174/2/2/8/pdf History and Some Aspects of the Lamb Shift by G. Jordan Maclay (2019)

Unified all previous electro-magnetism theories into one equation.

Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.

The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.

The equations are a system of partial differential equation.

The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:and two known input functions:

Due to the conservation of charge however, those input functions have the following restriction:

Also consider the following cases:

The goal of finding $\overrightarrow{\mathbf{E}}$ and $\overrightarrow{\mathbf{B}}$ is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.

Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:

You should also review the intuitive interpretation of divergence and curl.