Are there more than 3 generations of particles in the Standard Model? Updated 2025-01-01 +Created 1970-01-01
No, see: superconductor I-V curve.
Bibliography:
- physics.stackexchange.com/questions/62664/how-can-ohms-law-be-correct-if-superconductors-have-0-resistivity on Physics Stack Exchange
- physics.stackexchange.com/questions/69222/how-can-i-put-a-permanent-current-into-a-superconducting-loop
- www.quora.com/Do-superconductors-produce-infinite-current-I-V-R-R-0-How-do-they-fit-into-quantum-theory
- www.reddit.com/r/askscience/comments/dcgdf/does_superconductivity_imply_infinite_current/
- www.reddit.com/r/askscience/comments/7xhb46/what_would_happen_if_a_voltage_was_applied_to_a/
The discovery of the photon was one of the major initiators of quantum mechanics.
Light was very well known to be a wave through diffraction experiments. So how could it also be a particle???
This was a key development for people to eventually notice that the electron is also a wave.
This process "started" in 1900 with Planck's law which was based on discrete energy packets being exchanged as exposed at On the Theory of the Energy Distribution Law of the Normal Spectrum by Max Planck (1900).
This ideas was reinforced by Einstein's explanation of the photoelectric effect in 1905 in terms of photon.
In the next big development was the Bohr model in 1913, which supposed non-classical physics new quantization rules for the electron which explained the hydrogen emission spectrum. The quantization rule used made use of the Planck constant, and so served an initial link between the emerging quantized nature of light, and that of the electron.
The final phase started in 1923, when Louis de Broglie proposed that in analogy to photons, electrons might also be waves, a statement made more precise through the de Broglie relations.
This event opened the floodgates, and soon matrix mechanics was published in quantum mechanical re-interpretation of kinematic and mechanical relations by Heisenberg (1925), as the first coherent formulation of quantum mechanics.
It was followed by the Schrödinger equation in 1926, which proposed an equivalent partial differential equation formulation to matrix mechanics, a mathematical formulation that was more familiar to physicists than the matrix ideas of Heisenberg.
Inward Bound by Abraham Pais (1988) summarizes his views of the main developments of the subjectit:
- Planck's on the discovery of the quantum theory (1900);
- Einstein's on the light-quantum (1905);
- Bohr's on the hydrogen atom (1913);
- Bose's on what came to be called quantum statistics (1924);
- Heisenberg's on what came to be known as matrix mechanics (1925);
- and Schroedinger's on wave mechanics (1926).
Bibliography:
- physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics on Physics Stack Exchange
- www.youtube.com/watch?v=5hVmeOCJjOU A Brief History of Quantum Mechanics by Sean Carroll (2020) Given at the Royal Institution.
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:
- compound Atwood machine. Here, we can use the coordinates as the heights of masses relative to the axles rather than absolute heights relative to the ground
- double pendulum, using two angles. The Lagrangian approach is simpler than using Newton's laws
- pendulum, use angle instead of x/y
- two-body problem, use the distance between the bodieslagrangian mechanics lectures by Michel van Biezen (2017) is a good starting point.
When doing lagrangian mechanics, we just lump together all generalized coordinates into a single vector 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.
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:
- equations
- unknown functions
- at most second order derivatives of . Those appear because of the chain rule on the second term.
The mixture of so many derivatives is a bit mind mending, so we can clarify them a bit further. At:the 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:
- the part is just like the previous term, just identifies the argument with index ( because we have the non derivative arguments)
- after the partial derivative is taken and returns a new function , then the multivariable chain rule comes in and expands everything into terms
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.
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:
- physics.stackexchange.com/questions/254266/advantages-of-lagrangian-mechanics-over-newtonian-mechanics on Physics Stack Exchange, fucking closed question...
- www.quora.com/Why-was-Lagrangian-formalism-needed-in-the-presence-of-Newtonian-formalism
- www.researchgate.net/post/What_is_the_advantage_of_Lagrangian_formalism_over_Hamiltonian_formalism_in_QFT
Bibliography:
- www.physics.usu.edu/torre/6010_Fall_2010/Lectures.html Physics 6010 Classical Mechanics lecture notes by Charles Torre from Utah State University published on 2010,
- Classical physics only. The last lecture: www.physics.usu.edu/torre/6010_Fall_2010/Lectures/12.pdf mentions Lie algebra more or less briefly.
- www.damtp.cam.ac.uk/user/tong/dynamics/two.pdf by David Tong
physicist with lots of focus on politically incorrect/Right wing stuff:
- motls.blogspot.com/ his blog
- physics.stackexchange.com/users/1236/lubo%c5%a1-motl he has lots of contributions to Physics Stack Exchange
- settheory.net/crackpot-physics: some comments about him from settheory.net
A major difficulty of getting such this to work is that may university teachers want to retain closed copyright of their work because they:
- want to publish a book later and get paid. Yes, the root problem is that teachers get paid way too little and have way too little job security for the incredibly important and difficult extremely difficult job they are doing, and we have to vote to change that
- are afraid that if amazing material is made freely available, then they would not be needed and lose their jobs. Once again, job security issue.
- believe that if anyone were allowed to touch their precious content, those people would just "screw it up" and make it worse
- don't even want to publish their notes online because "someone will copy it and take their credit". What a mentality! In order to prevent a theft, you are basically guaranteeing that your work will be completely forgotten!
- don't want students to read the notes and skip class, because spoken word has magic properties and imparts knowledge that cannot otherwise conveyed by a book
- are afraid that mistakes will be found in their material. Reputation is of course everything in academia, since there is no money.So it's less risky to have closed, more buggy notes, than open, more correct ones.This can be seen clearly for example on Physics Stack Exchange, and most notably in particle physics (well, which is basically the only subject that really gets asked, since anything more experimental is going to be blocked off by patents/interlab competition), where a large proportion incredibly amazing users have anonymous profiles.They prefer to get no reputation gains from their amazing contributions, due to the fear that a single mistake will ruin their career.This is in stark contrast for example to Stack Overflow, where almost all top users are not anonymous:List of top users: physics.stackexchange.com/users?tab=Reputation&filter=all and some notable anonymous ones:
- physics.stackexchange.com/users/2451/qmechanic
- physics.stackexchange.com/users/50583/acuriousmind
- physics.stackexchange.com/users/43351/profrob
- physics.stackexchange.com/users/84967/accidentalfouriertransform
- physics.stackexchange.com/users/56997/curiousone
- physics.stackexchange.com/users/139781/probably-someone
- physics.stackexchange.com/users/206691/chiral-anomaly
Therefore the only way is to find teachers who are:The forced option therefore seems like a more bulk efficient starting point for searches.
- enlightened to use such licenses
- forced by their organizations to use such licenses
No matter how much effort a single person puts into writing perfect tutorials, they will never beat 1000x people + an algorithm.
It is not simply a matter of how much time you have. The fundamental reason is that each person has a different background and different skills. Notably the young students have radically different understanding than that of the experienced teacher.
Therefore, those that refuse to contribute to such platforms, or at least license their content with open licenses, will inevitably have their work forgotten in favor of those that have contributed to the more open platform, which will eventually dominate everything.
Perhaps OurBigBook.com is not he killer platform that will make this happen. Perhaps the world is not yet ready for it. But Ciro believes that this will happen, sooner or later, inevitable, and he wants to give it a shot.
Also worth checking:
- jornal.usp.br/universidade/usp-de-sao-carlos-oferece-aulas-de-graduacao-em-matematica-e-estatistica-abertas-ao-publico/ "Open Classroom" program from the University of São Paulo. We should Google for "Open Classroom" a bit more actually.
- open.ed.ac.uk/about/: talk only
TODO can anything interesting and deep be said about "why phase transition happens?" physics.stackexchange.com/questions/29128/what-causes-a-phase-transition on Physics Stack Exchange
This is the true key question: what are the most important algorithms that would be accelerated by quantum computing?
Some candidates:
- Shor's algorithm: this one will actually make humanity worse off, as we will be forced into post-quantum cryptography that will likely be less efficient than existing classical cryptography to implement
- quantum algorithm for linear systems of equations, and related application of systems of linear equations
- Grover's algorithm: speedup not exponential. Still useful for anything?
- Quantum Fourier transform: TODO is the speedup exponential or not?
- Deutsch: solves an useless problem
- NISQ algorithms
Do you have proper optimization or quantum chemistry algorithms that will make trillions?
Maybe there is some room for doubt because some applications might be way better in some implementations, but we should at least have a good general idea.
However, clear information on this really hard to come by, not sure why.
Whenever asked e.g. at: physics.stackexchange.com/questions/3390/can-anybody-provide-a-simple-example-of-a-quantum-computer-algorithm/3407 on Physics Stack Exchange people say the infinite mantra:
Lists:
- Quantum Algorithm Zoo: the leading list as of 2020
- quantum computing computational chemistry algorithms is the area that Ciro and many people are te most excited about is
- cstheory.stackexchange.com/questions/3888/np-intermediate-problems-with-efficient-quantum-solutions
- mathoverflow.net/questions/33597/are-there-any-known-quantum-algorithms-that-clearly-fall-outside-a-few-narrow-cla
Ron Maimon is a male human theoretical physicist with an all but dissertation started in 1995 at Cornell University[ref][ref].
Ron is mostly known for simultaneously:
- the amazing free online content he has published in online forums such as Stack Overflow and Quora, notably about particle physics, until around 2014 when Ron disappeared from the Internet entirely. Ciro Santilli figures he's hanging out with Ettore Majorana somewhere in the metaverse.
- having either been blocked from or quit every single website he participates in, partly due to his highly combative nature, e.g.:He explicitly defends this combative approach at youtu.be/ObXbKbpkSjQ?t=944 from Video 1. "Ron Maimon interview with Jeff Meverson (2014)":
- Physics Stack Exchange: physics.meta.stackexchange.com/users/4864/ron-maimon
physics.meta.stackexchange.com/questions/976/physics-ses-inability-to-deal-with-users-who-are-highly-persistent-have-kook-b user Marty Green makes one of the best characterizations of Ron's approach to science/collaboration:The thing about Ron Maimon is he definitely comes here to talk about physics. I personally can't get into discussions with him for two reasons: first, he's so single-minded in his own point of view that you can't really communicate with him back and forth; secondly, the structure of this forum is simply not conducive to extended discussions. But he sometimes posts things that are so coherently argued and with such intricate detail that even if I can't understand them myself, I just can't believe he's simply pulling this stuff out of his ass.
- physics.meta.stackexchange.com/questions/1376/what-violation-caused-this-suspension user Jerry Schirmer makes another good comment:
The thing that makes me pretty angry about Ron's behaviour is that he does not distinguish between common consensus belief and his own private research - this makes evaluating his claims hard for a third party not familiar with physics.
- Quora: www.quora.com/profile/Ron-Maimon. Ron was very active on Quora, until he was blocked for his views on the Boston Marathon bombing as mentioned at Video 1. "Ron Maimon interview with Jeff Meverson (2014)"
And notably, relevant to cirosantilli.com/china-dictatorship/stack-overflow-mods-refuse-to-clarify-if-anti-ccp-imagery-is-allowed-or-not-2021In order to have this process work [finding of truth] it is extremely important that the tone is hostile, that it is like a court of law, where you have an adversarial relationship with your opponent. Because if you have a friendly relationship with your opponent, then political consensus is preserved.
and he then also mentions that Wolfgang Pauli was a major proponent of this in physics, and so was Galileo.Unfortunately, when you're in a minority, the only way to correct the consensus view is to just shout it, and repeat it, until people go and look and check for themselves. The reason is that it creates an adversarial atmosphere where the people have to pick sides, and they don't like to pick sides, they would rather have everyone be happy. So when you have to pick sides, what do you do? You either butt out, you just leave it alone, you run away. Or you sit and review the evidence until you know which side to pick.
- Physics Stack Exchange: physics.meta.stackexchange.com/users/4864/ron-maimon
Ron seems to share a few philosophies which Ciro greatly agrees with as part of Cirism, which together with his knowledge of physics, make Ciro greatly respect Ron. Such philosophies include:
- he gives great importance to the history of physics and learning from original papers. He appears to know this insanely well, notably emphasizing that there is value in tutorials written by early pioneers of the field, see also Section "How to teach and learn physics". TODO find quote. Ciro Santilli distinctly remembers one specifically taking about this, but can't find it anymore.
- education views, notably emphasising autodidacticism
- www.quora.com/Why-should-high-school-students-learn-physics/answer/Ron-Maimon, highlighted at gmachine1729.livejournal.com/161418.html: "Why should high school students learn physics?" Answer:Yes, please, give it to me baby:
But they should learn it, preferably on their own, because the school doesn't know how to teach physics. Physics is extremely interesting, even the elementary kind. It takes the mathematics you learn in high school and uses it to describe certain natural phenomenon completely, beyond what was imagined possible in the wildest dreams of people like Pythagoras or Archimedes. If you have a computer, Newton's laws plus a tiny code can produce the motion of the planets around the sun, the motion of a free-twirling baton, the motion of colliding billiards, it's very simple.
- www.quora.com/Why-should-high-school-students-learn-physics/answer/Ron-Maimon, highlighted at gmachine1729.livejournal.com/161418.html: "Why should high school students learn physics?" Answer:
- enthusiasm for molecular biology technologies, seen e.g. at: www.quora.com/Why-are-an-abundance-of-physicists-moving-to-theoretical-biology/answer/Ron-Maimon on Quora:Ciro is actually specifically curious about whole cell simulation which he makes reference to.
[biology] is also clearly going to be the major technology of the 21st century, you should have a sugar outlet next to the electrical outlet, and plug in artificial biological technology made out of artificial cells. To plan these requires a complete method of describing biological cells, a precise model of all the processes, so that you can make artificial ones, and it produces a type of precise control on single-molecule chemistry that makes chemists drool.
- effortless effort and the to explain everything he knows online. These can be seen at www.quora.com/How-do-you-control-your-urge-to-access-the-internet-so-you-can-complete-your-assignments "How do you control your urge to access the Internet so you can complete your assignments?":
I don't. I consider the internet the first priority, as it will be viewed by thousands of people, and will have a real impact, while other assignments are lower priority, as they will only have an impact locally.
- his cheapness as in Ciro Santilli's cheapness as mentioned at youtu.be/ObXbKbpkSjQ?t=2454 from Video 1. "Ron Maimon interview with Jeff Meverson (2014)":Interviewer: there's a question on Quora where you say that you took a vow of poverty when you were very young.Ron: I was ten, I mean, most people would give it up, but I mean I figured I didn't have any need to give it up, so I just kept with it, I mean, I was never was really offered that much more. When we started the startup, I think I was offered 50k, but I said "no, I'll keep it 40k, I took a vow", and then they gave me 40k. And that of sort of set an example, the CEO also took 40k. It was a very good thing because we had very little money, we were a startup, and we were going by seed money.
However he also subscribes to some theories which Ciro Santilli considers conspiracy theories, e.g. his ideas about the Boston Marathon bombing that got him banned from Quora (a ban which Ciro strongly opposes due to freedom of speech concerns!), but the physics might be sound, Ciro Santilli does not know enough physics to judge, but it often feels that what he says makes sense.
chat.stackexchange.com/transcript/message/7104585#7104585 mentions that he was at Cornell University and did all but dissertation, but he mentions that he was still self-taught:This is corroborated e.g. at: web.archive.org/web/20201226171231/http://pages.physics.cornell.edu/~gtoombes/Student_Index.html (original pages.physics.cornell.edu/~gtoombes/Student_Index.html down as of 2023).
Eugene Seidel: On your personal info page you write that you are not a physics Ph.D. but does that mean you were a physics undergrad in college then went to grad school and finished ABD... or are you entirely self taught?Ron Maimon: ABD. I am self- taught though, I only went to school for accreditation. I had a thesis worth of work at the time I left grad-school,Eugene Seidel: ok thanksRon Maimon: I was just kind of sickened by academic stuff that was going on--- large extra dimensions were popular then.Eric Walker: Anyway, thanks Ron -- I'll get back to you with more questions soon, I'm sure.Ron Maimon: Also I was at Cornell, my advisor left for Cincinnatti, and I was not in very good standing there (I was kind of a jerk, as I still am). Some friends wanted to start a biotech company called "Gene Network Sciences", and I joined them.
At youtu.be/ObXbKbpkSjQ?t=2454 from Video 1. "Ron Maimon interview with Jeff Meverson (2014)" he mentions his brother is a professor. At physics.stackexchange.com/questions/32382/could-we-build-a-supercomputer-out-of-wires-and-switches-instead-of-a-microchip confirms that his brother's name is "Gaby Maimon", so this neuroscience professor at the Rockerfeller University is likely him: www.rockefeller.edu/our-scientists/heads-of-laboratories/985-gaby-maimon/. Looks, age, location and research interest match.
Some notable technical posts:
Some notable history posts:
- physics.stackexchange.com/questions/18632/good-book-on-the-history-of-quantum-mechanics/18643#18643 about the history of quantum mechanics give the quadratic explanation
- and closely related for the factor 2: physics.stackexchange.com/questions/27847/why-is-there-a-frac-1-2-in-frac-1-2-mv2/27916#27916
Bibliography:
- gmachine1729.livejournal.com/161418.html Ron Maimon answers about physics and math on Quora (part 1) by Sheng Li (2020) contains a selection of some amazing Ron Maimon posts
- www.reddit.com/r/RonMaimon/ someone made a Reddit for him. Less than 100 users as of 2022, but has potential.
- some Quora threads about him, oh the irony:
- www.quora.com/Is-Ron-Maimon-actually-a-pioneer-or-a-jest
- www.quora.com/Are-Ron-Maimons-answers-on-mathematics-physics-and-computer-science-factually-correct
- www.quora.com/What-do-people-think-of-Ron-Maimons-paper-Computational-Theory-of-Biological-Function-I
- www.quora.com/Who-is-Ron-Maimon/answer/Ron-MaimonAlso in a comment he explains something to a now deleted comment, presumably asking why he dropped out of grad school, and gives a lot more insight:
I'm a physics grad school drop-out working in theoretical biology but I still do physics when I get a chance, but not right now because I am in a middle of a project to understand the properties of a certain virus as completely as possible.
It's a complicated boring story.I dropped out mainly to do biology with friends at a startup, because I figured out how you're supposed to do theory in biology, but also I truly believe it was next to impossible for me to get a degree without selling out, and I would rather be shot than write a paper with an idea I don't believe.My grad school phase was a disaster. I first worked for Eric Siggia, but I got away because he had me do something boring and safe, I figured I have only a limited number of years before I turn 30 and my brain rots, and I wasn't going to sell out and do second-rate stuff. I found a young guy at the department doing interesting things (Siggia was also doing interesting things, like RNA interactions, he just wouldn't assign any of them to ME), this was Philip Argyres, and got him to take me. Argyres wanted me to work on large-extra dimensions (this was 1998), but I made it clear to him that I would rather be boiled in oil. I worked a little bit on a crappy experimental setup that didn't work at all, because I didn't know enough about electromagnetic screening nor about how to set up experiment. But EVERYONE LOVED IT! This is also how I knew it was shit. Good work is when everyone hates it. But I learned Lifschitz's ideas for quantum electrodynamics in media from this project.Me and every competent young person in high-energy physics knew large extra dimensions was a fraud on the day it came out, and I had no intention of doing anything except killing the theory. Once Wikipedia appeared, I did my best to kill it by exposing it's charlatanry on the page for large extra dimension. That was in 2005 (after getting fired from the company), and from this point onward large-extra-dimensions lost steam. But I can't tell how much of this was my doing.Argyres liked N=2 theory, and we did something minor in N=2 SUSY models around 2000, but I was bogged down here, because I was trying to do Nicolai map for these, and it ALMOST worked for years, but it never quite worked. But I knew from the moduli interpretation and Seiberg-Witten solution that it must work. If I live long enough, I'll figure it out, I am still sure it isn't hard. But this was the link to statistical stochastic models, the work I was doing with Jennifer Schwarz, and I wanted to link up the two bodies of work (they naturally do through Nicolai map).But I had my own discovery, the first real discovery I made, in 1999, this thing that I called the mass-charge inequality, what Vafa and Motl called "the weakest-force principle" when they discovered it in 2006. It was swampland, and Vafa hadn't yet begun swampland. My advisor didn't believe my result was correct, because he saw me say many stupid things before this. So he wouldn't write it or develop it with me (but I had read about Veltman telling 'tHooft he couldn't publish the beta-function, I knew Argyres was wrong about this)Anyway, Argyres left for Cincinnatti in 2000, and I joined the company then. I was in the company until january 2005. Then they fired me, which was ok, by then it was a miserable hell-hole full of business types.I discovered Wikipedia, and started killing large extra dimensions. I wanted to finish my thesis, and some people agreed to help me do this, but I had told myself "no thesis until you get the Nicolai map sorted out" and I never did. I worked with Chris Henley a little bit, who wanted me to do some stuff for him, and I discovered an interesting model for high-Tc, but Henley said it was out of fasion, and nobody would care, even though I knew it was the key to the phenomenon (still unpublished, but soon).This was 2008-2009, and I became obsessed with cold fusion, so Henley dropped me, as I had clearly gone crazy. I developed the theory of cold fusion during the last weeks of working for Henley. Then I dropped out for good.Honestly, by the time I was gone, I realized that the internet would make a degree counterproductive, because I knew I had better internet writing skills than any of the old people, I was a Usenet person. Online, the degrees and accreditation were actually a hinderance. So by this point, I secretly preferred not to have a PhD, because I knew I was good at physics, and I could attack from the outside and win. It's not too hard if you know the technical material.The only problem is that I was unemployed and isolated in Ithaca for about 7 years after having gone through my first productive phase. But I developed the cold-fusion ideas in this period, I learned a lot of mathematics, and I developed a ton of biology ideas that are mostly unpublished, but will be published soon. It astonished people that I could have no degree and be unemployed and have such a sky-high ego. The reason is that I could evaluate my own stuff, and I liked it!
Backlinks:
- 2022: twitter.com/johncarlosbaez/status/1556085484937310209 by John Baez. This page was one of the top Google hits for "Ron Maimon" at the time.
I like relativistic quantum mechanics.
Best mathematical explanation: Section "Spin comes naturally when adding relativity to quantum mechanics".
Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles" has an amazing summary of the preceding chapters the spin value has a relation to the representations of the Lorentz group, which encodes the spacetime symmetry that each particle observes. These symmetries can be characterized by small integer numbers:
- spin 0: representation
- spin half: representation
- spin 1: representationAs usual, we don't know why there aren't elementary particles with other spins, as we could construct them.
The wave equation contains the entire state of a particle.
From mathematical formulation of quantum mechanics remember that the wave equation is a vector in Hilbert space.
And a single vector can be represented in many different ways in different basis, and two of those ways happen to be the position and the momentum representations.
More importantly, position and momentum are first and foremost operators associated with observables: the position operator and the momentum operator. And both of their eigenvalue sets form a basis of the Hilbert space according to the spectral theorem.
When you represent a wave equation as a function, you have to say what the variable of the function means. And depending on weather you say "it means position" or "it means momentum", the position and momentum operators will be written differently.
This is well shown at: Video "Visualization of Quantum Physics (Quantum Mechanics) by udiprod (2017)".
Furthermore, the position and momentum representations are equivalent: one is the Fourier transform of the other: position and momentum space. Remember that notably we can always take the Fourier transform of a function in due to Carleson's theorem.
Then the uncertainty principle follows immediately from a general property of the Fourier transform: en.wikipedia.org/w/index.php?title=Fourier_transform&oldid=961707157#Uncertainty_principle
In precise terms, the uncertainty principle talks about the standard deviation of two measures.
We can visualize the uncertainty principle more intuitively by thinking of a wave function that is a real flat top bump function with a flat top in 1D. We can then change the width of the support, but when we do that, the top goes higher to keep probability equal to 1. The momentum is 0 everywhere, except in the edges of the support. Then:
- to localize the wave in space at position 0 to reduce the space uncertainty, we have to reduce the support. However, doing so makes the momentum variation on the edges more and more important, as the slope will go up and down faster (higher top, and less x space for descent), leading to a larger variance (note that average momentum is still 0, due to to symmetry of the bump function)
- to localize the momentum as much as possible at 0, we can make the support wider and wider. This makes the bumps at the edges smaller and smaller. However, this also obviously delocalises the wave function more and more, increasing the variance of x
Bibliography:
- www.youtube.com/watch?v=bIIjIZBKgtI&list=PL54DF0652B30D99A4&index=59 "K2. Heisenberg Uncertainty Relation" by doctorphys (2011)
- physics.stackexchange.com/questions/132111/uncertainty-principle-intuition Uncertainty Principle Intuition on Physics Stack Exchange
- why the square: physics.stackexchange.com/questions/535/why-does-kinetic-energy-increase-quadratically-not-linearly-with-speed on Physics Stack Exchange. Ron Maimon's answer is great, as it relies only on the following staring points:He also offers a symmetry argument considering the case of potential energy.
- why the half: physics.stackexchange.com/questions/27847/why-is-there-a-frac-1-2-in-frac-1-2-mv2 on Physics Stack Exchange