Incoming links: Path integral formulation
Amazingly confirms the wave particle duality of quantum mechanics.
The effect is even more remarkable when done with individual particles such individual photons or electrons.
Richard Feynman liked to stress how this experiment can illustrate the core ideas of quantum mechanics. Notably, he night have created the infinitely many slits thought experiment which illustrates the path integral formulation.
Thought experiment that illustrates the path integral formulation of quantum field theory.
Mentioned for example in quantum field theory in a nutshell by Anthony Zee (2010) page 8.
TODO holy crap, even this is hard to understand/find a clear definition of.
The Dirac equation, OK, is a partial differential equation, so we can easily understand its definition with basic calculus. We may not be able to solve it efficiently, but at least we understand it.
But what the heck is the mathematical model for a quantum field theory? TODO someone was saying it is equivalent to an infinite set of PDEs somehow. Investigate. Related:
The path integral formulation might actually be the most understandable formulation, as shown at Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979).
The formulation of QFT also appears to be a form of infinite-dimentional calculus.
Quantum electrodynamics by Lifshitz et al. 2nd edition (1982) chapter 1. "The uncertainty principle in the relativistic case" contains an interesting idea:
The foregoing discussion suggests that the theory will not consider the time dependence of particle interaction processes. It will show that in these processes there are no characteristics precisely definable (even within the usual limitations of quantum mechanics); the description of such a process as occurring in the course of time is therefore just as unreal as the classical paths are in non-relativistic quantum mechanics. The only observable quantities are the properties (momenta,
polarizations) of free particles: the initial particles which come into interaction, and the final particles which result from the process.
Theoretical framework on which quantum field theories are based, theories based on framework include:so basically the entire Standard Model
The basic idea is that there is a field for each particle particle type.
E.g. in QED, one for the electron and one for the photon: physics.stackexchange.com/questions/166709/are-electron-fields-and-photon-fields-part-of-the-same-field-in-qed.
And then those fields interact with some Lagrangian.
One way to look at QFT is to split it into two parts:Then interwined with those two is the part "OK, how to solve the equations, if they are solvable at all", which is an open problem: Yang-Mills existence and mass gap.
- deriving the Lagrangians of the Standard Model: why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics?s. This is the easier part, since the lagrangians themselves can be understood with not very advanced mathematics, and derived beautifully from symmetry constraints
- the qantization of fields. This is the hard part Ciro Santilli is unable to understand, TODO mathematical formulation of quantum field theory.
There appear to be two main equivalent formulations of quantum field theory:
Quantum Field Theory visualized by ScienceClic English (2020)
Source. Gives one piece of possibly OK intuition: quantum theories kind of model all possible evolutions of the system at the same time, but with different probabilities. QFT is no different in that aspect.- youtu.be/MmG2ah5Df4g?t=209 describes how the spin number of a field is directly related to how much you have to rotate an element to reach the original position
- youtu.be/MmG2ah5Df4g?t=480 explains which particles are modelled by which spin number
Quantum Fields: The Real Building Blocks of the Universe by David Tong (2017)
Source. Boring, does not give anything except the usual blabla everyone knows from Googling:Quantum Field Theory: What is a particle? by Physics Explained (2021)
Source. Gives some high level analogies between high level principles of non-relativistic quantum mechanics and special relativity in to suggest that there is a minimum quanta of a relativistic quantum field.- the advantage of using Lagrangian mechanics instead of directly trying to work out the equations of motion is that it is easier to guess the Lagrangian correctly, while still imposing some fundamental constraints
- youtu.be/bTcFOE5vpOA?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3375
- Lagrangian mechanics is better for path integral formulation. But the mathematics of that is fuzzy, so not going in that path.
- Hamiltonian mechanics is better for non-path integral formulation
- youtu.be/bTcFOE5vpOA?list=PLDfPUNusx1EpRs-wku83aqYSKfR5fFmfS&t=3449 Hamiltonian formalism requires finding conjugate pairs, and doing a
Author: David Tong.
Number of pages circa 2021: 155.
It should also be noted that those notes are still being updated circa 2020 much after original publication. But without Git to track the LaTeX, it is hard to be sure how much. We'll get there one day, one day.
Some quotes self describing the work:
- Perhaps for this reason Ciro Santilli was not able to get as much as he'd out of those notes either. This is not to say that the notes are bad, just not what Ciro needed, much like P&S:This is a very clear and comprehensive book, covering everything in this course at the right level. To a large extent, our course will follow the first section of this book.
In this course we will not discuss path integral methods, and focus instead on canonical quantization.
A follow up course in the University of Cambridge seems to be the "Advanced QFT course" (AQFT, Quantum field theory II) by David Skinner: www.damtp.cam.ac.uk/user/dbs26/AQFT.html
Some of Feynman's key characteristics are:
- obsession with understanding the experiments well, see also Section "How to teach and learn physics"
- when doing more mathematical stuff, analogous obsession about starting with a concrete example and then generalizing that into the theory
- liked to teach others. At Surely You're Joking, Mr. Feynman for example he mentions that one key problem of the Institute for Advanced Study is that they didn't have to teach, and besides that making you feel useless when were not having new ideas, it is also the case that student's questions often inspire you to look again in some direction which sometimes happens to be profitableHe hated however mentoring others one to one, because almost everyone was too stupid for him
- interest in other natural sciences, and also random art and culture (and especially if it involves pretty women)
Some non-Physics related ones, mostly highlighted at Genius: Richard Feynman and Modern Physics by James Gleick (1994):
- Feynman was a huge womanizer during a certain period of his life
- he hated pomp, going as far as seeming uneducated to some people in the way he spoke, or going out of his way to look like that. This is in stark contrast to "rivals" Murray Gell-Mann and Julian Schwinger, who were posh/snobby.
Even Apple thinks so according to their Think different campaign: www.feynman.com/fun/think-different/
quantum electrodynamics lectures:
Feynman was apparently seriously interested/amused by computer:
- Video "Los Alamos From Below by Richard Feynman (1975)" see description for the human emulator
- quantum computers as experiments that are hard to predict outcomes was first attributed to Feynman
- www.youtube.com/watch?v=EKWGGDXe5MA Richard Feynman Computer Heuristics Lecture (1986)
Murray Gell-Mann talks about Richard Feynman's intentional anecdote creation
. Source. TODO original interviewer, date and source. Very amusing, he tells how Feynman wouldn't brush his teeth, or purposefully forget to wear jacket and tie when going to the faculty canteen where it was required and so he would use ugly emergency jacket the canteen offered to anyone who had forgotten theirs.Murray Gell-Mann talks about Feynman's partons by Web of Stories (1997)
Source. Listener is likely this Geoffrey West. Key quote:Feynman of course, as usual, put it in a form so that the common people could use it, and experimentalists all over the world now thought they understood things because Feynman had put it in such simple language for them.
Two official websites?
- www.richardfeynman.com/ this one has clearly superior scientific information.
- www.feynman.com/
High level timeline of his life:
In 1948 he published his reworking of classical quantum mechanics in terms of the path integral formulation: journals.aps.org/rmp/abstract/10.1103/RevModPhys.20.367 Space Time Approach to nonrelativistic quantum mechanics (paywalled 2021)
Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) Updated 2024-12-15 +Created 1970-01-01
Talk title shown on intro: "Today's Answers to Newton's Queries about Light".
6 hour lecture, where he tries to explain it to an audience that does not know any modern physics. This is a noble effort.
Part of The Douglas Robb Memorial Lectures lecture series.
Feynman apparently also made a book adaptation: QED: The Strange Theory of Light and Matter. That book is basically word by word the same as the presentation, including the diagrams.
According to www.feynman.com/science/qed-lectures-in-new-zealand/ the official upload is at www.vega.org.uk/video/subseries/8 and Vega does show up as a watermark on the video (though it is too pixilated to guess without knowing it), a project that has been discontinued and has has a non-permissive license. Newbs.
4 parts:This talk has the merit of being very experiment oriented on part 2, big kudos: how to teach and learn physics
- Part 1: is saying "photons exist"
- Part 2: is amazing, and describes how photons move as a sum of all possible paths, not sure if it is relativistic at all though, and suggests that something is minimized in that calculation (the action)
- Part 3: is where he hopelessly tries to explain the crucial part of how electrons join the picture in a similar manner to how photons do.He does make the link to light, saying that there is a function which gives the amplitude for a photon going from A to B, where A and B are spacetime events.And then he mentions that there is a similar function for an electron to go from A to B, but says that that function is too complicated, and gives no intuition unlike the photon one.He does not mention it, but P and E are the so called propagators.This is likely the path integral formulation of QED.On Quantum Mechanical View of Reality by Richard Feynman (1983) he mentions that is a Bessel function, without giving further detail.And also mentions that:where
mis basically a scale factor.
such that both are very similar. And that something similar holds for many other particles.And then, when you draw a Feynman diagram, e.g. electron emits photon and both are detected at given positions, you sum over all the possibilities, each amplitude is given by:summed over all possible Spacetime points.This is basically well said at: youtu.be/rZvgGekvHes?t=3349 from Quantum Mechanical View of Reality by Richard Feynman (1983).TODO: how do electron velocities affect where they are likely to end up? suggests the probability only depends on the spacetime points.Also, this clarifies why computations in QED are so insane: you have to sum over every possible point in space!!! TODO but then how do we calculate anything at all in practice? - Part 4: known problems with QED and thoughts on QCD. Boring.
Richard Feynman Quantum Electrodynamics Lecture at University of Auckland (1979) uploaded by Trev M (2015)
Source. Single upload version. Let's use this one for the timestamps I guess.- youtu.be/Alj6q4Y0TNE?t=2217: photomultiplier tube
- youtu.be/Alj6q4Y0TNE?t=2410: local hidden-variable theory
- youtu.be/Alj6q4Y0TNE?t=6444: mirror experiment shown at en.wikipedia.org/w/index.php?title=Quantum_electrodynamics&oldid=991301352#Probability_amplitudes
- youtu.be/Alj6q4Y0TNE?t=7309: mirror experiment with a diffraction grating pattern painted black leads to reflection at a weird angle
- youtu.be/Alj6q4Y0TNE?t=7627: detector under water to explain refraction
- youtu.be/Alj6q4Y0TNE?t=8050: explains biconvex spherical lens in terms of minimal times
- youtu.be/Alj6q4Y0TNE?t=8402: mentions that for events in a series, you multiply the complex number of each step
- youtu.be/Alj6q4Y0TNE?t=9270: mentions that the up to this point, ignored:but it should not be too hard to add those
- amplitude shrinks down with distance
- photon polarization
- youtu.be/Alj6q4Y0TNE?t=11697: finally starts electron interaction. First point is to add time of event detection.
- youtu.be/Alj6q4Y0TNE?t=13704: electron between plates, and mentions the word action, without giving a clear enough idea of what it is unfortunately
- youtu.be/Alj6q4Y0TNE?t=14467: mentions positrons going back in time, but does not clarify it well enough
- youtu.be/Alj6q4Y0TNE?t=16614: on the fourth part, half is about frontiers in quantum electrodynamics, and half full blown theory of everything. The QED part goes into renormalization and the large number of parameters of the Standard Model