Incoming links: Standard Model
Advanced quantum field theory lecture by Tobias Osborne (2017) Updated 2024-12-15 +Created 1970-01-01
When the word "advanced" precedes QFT, you know that the brainrape is imminent!!!
Big goal: explain the Standard Model.
An Introduction to Tensors and Group Theory for Physicists by Nadir Jeevanjee (2011) Updated 2024-12-15 +Created 1970-01-01
This does not seem to go deep into the Standard Model as Physics from Symmetry by Jakob Schwichtenberg (2015), appears to focus more on more basic applications.
But because it is more basic, it does explain some things quite well.
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:
E.g. for the electron we have:
- mass:
- spin: 1/2
- electric charge:
- 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.
Unifies both special relativity and gravity.
Not compatible with the Standard Model, and the 2020 unification attempts are called theory of everything.
One of the main motivations for it was likely having forces not be instantaneous, but rather mediated by field to maintain the principle of locality, just like electromagnetism did earlier.
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?
Local symmetries appear to be a synonym to internal symmetry, see description at: Section "Internal and spacetime symmetries".
As mentioned at Quote , local symmetries map to forces in the Standard Model.
Appears to be a synonym for: gauge symmetry.
A local symmetry is a transformation that you apply a different transformation for each point, instead of a single transformation for every point.
TODO what's the point of a local symmetry?
Bibliography:
- lecture 3
- physics.stackexchange.com/questions/48188/local-and-global-symmetries
- www.physics.rutgers.edu/grad/618/lects/localsym.pdf by Joel Shapiro gives one nice high level intuitive idea:
In relativistic physics, global objects are awkward because the finite velocity with which effects can propagate is expressed naturally in terms of local objects. For this reason high energy physics is expressed in terms of a field theory.
- Quora:
Currently an informal name for the Standard Model
Chronological outline of the key theories:
- Maxwell's equations
- Schrödinger equation
- Date: 1926
- Numerical predictions:
- hydrogen spectral line, excluding finer structure such as 2p up and down split: en.wikipedia.org/wiki/Fine-structure_constant
- Dirac equation
- Date: 1928
- Numerical predictions:
- hydrogen spectral line including 2p split, but excluding even finer structure such as Lamb shift
- Qualitative predictions:
- Antimatter
- Spin as part of the equation
- quantum electrodynamics
- Date: 1947 onwards
- Numerical predictions:
- Qualitative predictions:
- Antimatter
- spin as part of the equation
Initially light was though of as a wave because it experienced interference as shown by experiments such as:
But then, some key experiments also start suggesting that light is made up of discrete packets:and in the understanding of the 2020 Standard Model the photon is one of the elementary particles.
- Compton scattering, also suggests that photons carry momentum
- photoelectric effect
- single photon production and detection experiments
This duality is fully described mathematically by quantum electrodynamics, where the photon is modelled as a quantized excitation of the photon field.
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.
xkcd 435: Fields arranged by purity
. Source. Reductionism comes to mind.
Physically accurate genie by Psychomic
. Source. This sane square composition from: www.reddit.com/r/funny/comments/u08dw3/nice_guy_genie/.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. 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
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.
Explains beta decay. TODO why/how.
Maybe a good view of why this force was needed given beta decay experiments is: in beta decay, a neutron is getting split up into an electron and a proton. Therefore, those charges must be contained inside the neutron somehow to start with. But then what could possibly make a positive and a negative particle separate?
- the electromagnetic force should hold them together
- the strong force seems to hold positive charges together. Could it then be pushing opposite-charges apart? Why not?
- gravity is too weak
www.thestargarden.co.uk/Weak-nuclear-force.html gives a quick and dirty:Also interesting:
Beta decay could not be explained by the strong nuclear force, the force that's responsible for holding the atomic nucleus together, because this force doesn't affect electrons. It couldn't be explained by the electromagnetic force, because this does not affect neutrons, and the force of gravity is far too weak to be responsible. Since this new atomic force was not as strong as the strong nuclear force, it was dubbed the weak nuclear force.
While the photon 'carries' charge, and therefore mediates the electromagnetic force, the Z and W bosons are said to carry a property known as 'weak isospin'. W bosons mediate the weak force when particles with charge are involved, and Z bosons mediate the weak force when neutral particles are involved.
Weak Nuclear Force and Standard Model of particle physics by Physics Videos by Eugene Khutoryansky (2018)
Source. Some decent visualizations of the field lines. What does it mean that photons are force carriers for electromagnetism? Updated 2024-12-15 +Created 1970-01-01
TODO find/create decent answer.
I think the best answer is something along:
- local symmetries of the Lagrangian imply conserved currents. gives conserved charges.
- OK now. We want a local symmetry. And we also want:Given all of that, the most obvious and direct thing we reach a guess at the quantum electrodynamics Lagrangian is Video "Deriving the qED Lagrangian by Dietterich Labs (2018)"
- Dirac equation: quantum relativistic Newton's laws that specify what forces do to the fields
- electromagnetism: specifies what causes forces based on currents. But not what it does to masses.
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":
- www.youtube.com/watch?v=pCQ9GIqpGBI&t=1663s mentions this idea first came about from Hermann Weyl.
- youtu.be/pCQ9GIqpGBI?t=2827 mentions that in that case the curvature is given by the electromagnetic tensor.
Bibliography:
- www.youtube.com/watch?v=qtf6U3FfDNQ Symmetry and Quantum Electrodynamics (The Standard Model Part 1) by ZAP Physics (2021)
- www.youtube.com/watch?v=OQF7kkWjVWM The Symmetry and Simplicity of the Laws of Nature and the Higgs Boson by Juan Maldacena (2012). Meh, also too basic.
Why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics? Updated 2024-12-15 +Created 1970-01-01
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 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, 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.
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.
Why do the electron and the proton have the same charge except for the opposite signs? Updated 2024-12-15 +Created 1970-01-01
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.