"take it as a grain of salt" I see what you did there 😁

Develop a lingering, justified suspicion this world is not what it seems? Develop a life long addiction to physics? Sounds good to me.

Part 3 when?

This is BY FAR, the BEST introductory Quantum Field Theory lesson on the internet! Superb work, Sir. Awesome derivations and explanations for us amateur Physicists out here who obsess over finding all of the meaning behind the connection of deep mathematical concepts underlying our physical reality! I'm right here in the fight with you; Researching, wondering and searching for the reasons and answers behind this amazing physical reality and our consciousness that brings it all to life for each one of us to observe daily!

1:02:08 negative h bar c partial mu theta psi bar gamma mu psi: my mans raps faster than eminem

Honestly, if i spend the whole day solving all those equations, i'd have less questions "what the heck is this variable doing?" So, now i have more questions than answers

May you share the code for your beautifully animations

I don’t understand the visuals.

Physically, what is a Klein-Gordon plane wave?

This is an EXCELLENT video, the only thing missing is that the Diraq coefficients are quaternionic, so quaternion coefficient quaternions- which I believe gets us thru Cayley-Dickson math as sedenions. Everyone in academic Physics is just using the wrong algebras- they should be embracing the Cayley-Dickson algebras and all this would practically explain itself. 2Pi operates like an instantaneous mobius strip, which is why the spinora “change flags”.

As a physicist, I recommend to call spin-statistics theorem as a principle. People used to think we have prove that, but no, we just proved it on flat space-time based on causality and special relativity, but spin-statistics property appears on curved space-time and Euclidean space-time too, and no one have published a satisfied proof for those general cases.

would it be wrong to think of spinors as the "square root" of vectors?

From what i watched, it was an amazing video. Unfortunately, I'm still in high school, so I'll save it for later.

1:08:17 Omg. Legendary.

Label: "Intro: Why is EM a thing?" Reality: "Prerequisite courses & material"

Dear Richard, you are an excellent teacher and populariser of mathematical physics, and your animations are amazing. Your puzzlement/disorientation/fascination about spinors and the mathematics that gravitates around them is a common feeling among physicists. Imho it can be attributed essentially to the fact that “geometric algebra” is almost never part of our basic math education. In your speech you mention the reformulation of the Dirac equation in terms of real entities, done with geometric algebra, but not much more. For sure you know this, but let me stress it: In the framework of geometric algebra a spinor is a simple geometrical entity: an un-normalized rotor, in other words, is the combination (the “sum” if you like) of a scalar and a bivector (essentially a plane). To me a rotor is as real as the sum of a number, a vector, a plane, a volume, ... Once you have an algebra all entities can play together with its two operations: sum and product. And you get all the sub-spaces one intuitively would like to have objects for. In standard math we are stuck with vector spaces, which miss more than half of the magic: the multiplication. You wonder why a rotor goes back to its original "orientation" only after rotating by two turns (rotating the objects it acts upon!). Well, in any embedding space, and for any entity (vector, bivector, trivector, ...), rotations are always done by multiplying on the left and on the right, hence twice, by a rotor. The same happens with quaternions. In fact, any rotation is the composition of two reflections. Therefore, each rotor must contain half of the rotation angle. No mysteries, no quantum, just elementary geometry, but covered by a pile of pointlessly unintuitive math in the classical spinor approach. This way of thinking about spinors is not mystical at all, therefore probably less fascinating (like with women, lol). Let me be very cheeky and suggest you the following two sources (I cannot add links to this comment, otherwise it would be cancelled automatically by KZbin): - David Hestenes, “The Genesis of Geometric Algebra”, from 2016 - Antony Lasenby, GAME2020 3. Professor Anthony Lasenby. A new language for physics. (new audio!). Let me also briefly comment on the need for spinors (i.e. rotations with scaling) in QM. The spinor in the Pauli and Dirac equations describes two things at the same time: the orientation of the spin plane and the probability density (for Dirac’s spinors there is an additional parameter, the angle beta, the meaning of which is still debated). The spinor rotates a reference plane, precisely the "mystical i" that appears explicitly in the equations, to the orientation of the spin plane at each point. Since the spinor is an unnormalized rotor, its norm can encode the probability density. Actually, it encodes its square root, since the rotor has to be used twice on its operand. In geometric algebra the squaring is done with the geometric product (what else?), but for the "complex world" one must use the complex multiplication by the conjugate (always pointless complications without geometric algebra). When you are amazed by the consequences of the spin statistic theorem, I can understand your feelings. I have my own way to look at it, but it’s just my opinion. Best of luck with your nice channel!!

The only thing I understood was the pew pew noises

Uzumaki moment

Amazingly brainfucking.

You make a student feel smart whilst they are learning, which is a truly uncommon and empowering feeling. With this topic you've changed my world view in 3 hours, I shall never be the same! Thank you!

Brent Spinor is the man.

It's time to post again

I love how math, which is an entirely made up way of defining the laws of physics, is treated as a be all end all "if this didnt exist neither would we" as if we didnt invent math. It exists as the primary way we have agreed to describe and define observed laws of physics, if it didnt exist we would simply use some other made up method of defining these laws. Just bc it works doesnt necessarily mean its correct and the fact that there are "unsolvable equations" and things that cannot be defined with math should tip you all pff that it is not infact the perfect undenyable truth of our universe like all mathematicians like to treat it as

Following :)

Wow! I've been trying to get a feel for fiber bundles for ages, but now it's clear. And it's clear why it wasn't clear before! :) I love your piece about mathematical stars! Amazing animations too! Love to know how you made them.😍

Very good . Thanks

I dont think it is incorrect. We can use only real numbers. Any physical phenomenon can ultimately be described using only real numbers, as the observable outcomes (e.g., displacement, velocity, or energy) are real-valued. However, avoiding complex numbers entirely often results in less elegant, more cumbersome, and computationally intensive formulations. So it is only simlification .

It really amazes me that there are people who actually spent time developing whole theories about... how you can rotate something (???!!!). God bless them.

Very nice presentation...👌💗👍❣️👏🌹🤛❤️💐💐💐

Thanks for such a clear graphic and explanatory presentation. This inspired one to review a publication by Elizabeth Rauscher & Richard Amoroso: "Orbiting the Moons of Pluto: Complex Solutions to the Einstein, Maxwell, Schrodinger and Dirac Equations" published by World Scientific that goes "beyond"!

I watch this to sleep but I've watched so many times that I think I've already got to the middle of the video and that I understand what is going on

Man after class 12th, the Indian teachers ain't doing it, it's just they aren't able to explain these well so I have to resort to other sources of medium to get enough knowledge so that I could at least pass my exam tomorrow. Now, I think I ain't passing my exam. I am just in 1st semester and I think I do not even need this many in-depth details, also this section of quantum mechanics is in the chemistry syllabus which is not even my main course subject. I am confused by the syllabus and the university people who made the syllabus. They just put all those random words in the syllabus expecting us to study everything that a physics major student studies in their 2nd year of college particularly when their studies in their major subject starts.

1:28:00 Magnetic monopoles haven't been observed in nature, but they are theoretically possible (and quasi monopoles have been observed in places like Bose Einstein condensates) and they are derived from the same gauge theory. Instead of having one single 4 current and one single 4 potential, you have two of them. The one of the 4 currents is (electric charge, electric current) and the other is (magnetic charge, magnetic current). Basically, you just need to symmetrize Maxwell's laws as the magnetic charge affects the divergence of B, and the magnetic current affects the rotational of E. The thing about gauge theory is that you can fit so many things in this bad boi.

1:03:30 Theoretical physicist redefining infinite to zero and calling it "renormalization": What do you mean we cannot do whatever solves the problem "just because"?

Is it possible to multiply two complex numbers with real and imaginary parts not zero and the result being equal to zero?

Weird how when I sleep, autoplay tries to make me smarter.

I knew that a 'wiggle' is homotopic to a octo- puss without knowing any math. Turns out all I needed to experience were 'wiggles/ jiggles' and pus. Math is fundamentally rooted in our experience - then we construct the rest God gave us integers, the rest are details - kronecker. Maybe he experienced wiggles/ jiggles and pus too. Naughty but devishly clever.

Very good video. There is one trick, however. Dirac equation arise from a generalization of wave equation to be compatible with relativity. Special relativity is derived from two principles: All inertial observers are equivalent and the speed of light in vacuum is constant. The fact that the speed of light in vacuum is constant arise from the fact that in Maxwell's equations, the speed of light in vacuum is the inverse of the square root of two constants, thus it is also a constant. All of this is to say that Electromagnetism just is. There is no explanation for it other than Nature wills it. While I really enjoy this video, as it is always nice to see known things from a new point of view, ultimately it is "obvious" that one can derive electromagnetism from the Dirac equation, as electromagnetism is, in some sense, fundamentally engraved in the very core of that equation. While this is not an explanation of the existence of electromagnetism, it is satisfying to recover the ingredients from the final product. It is also a good reminder that great theories do not appear out of the void, but as a consequence of previous great theories. For all the greatness and prestige of Relativity, it is "simply" stating that Maxwell equations are correct, and following their consequences beyond our intuition, beyond our primal need of a universal time and space. If one think about that, it is very paradoxical that nowadays, the biggest conflict is between Quantum Chromodynamic and General Relativity, when the first is the nth generalization of the concepts of electromagnetism, which again is the origin of relativity. At some point along the way, EM and Relativity went from best friends to bitter enemies.

Quantum mechanics : trying to measure a drop of water using another drop of water.

No strings theory, no spinors. Fractals space my friends. α = 1꞉ ᴾᴵ√ ̅̅ ̅̅ ̅̅(2⁴+5⁴)ᵠ · e⁵ ̅̅ ̅̅ ̅̅ α ≈ 1/137 fine structure constant - fractal ratio α = 1/(641^φ*e^5)^(1/π) = 0,00729735256776... φ = 1,61803398... golden ratio, e = 2,71828182... (Napier's constant, Euler's number) This formula explains why our Universe is filled with structures containing the golden ratio and Euler's number (e) on both the cosmic and subatomic scale. boson H = 125,97585 GeV = (2W+Z)/2 mᵉ·(2⁴+5⁴)²·(3/5) = 125975,8558 MeV boson Z⁰ = 91,18761 GeV = 2H-2W boson W = 80,38205 GeV = (2H-Z)/2 boson H = 125,97585 GeV = (2W+Z)/2 mᵉ·(2⁴+5⁴)²·(3/5) = 125975,8558 MeV boson Z⁰ = 91,18761 GeV = 2H-2W boson W = 80,38205 GeV = (2H-Z)/2 electron (mᵉ) = [H/(2⁴+5⁴)²]·(5/3) = 0,51099895 MeV muon (mᵐ) = 105,658373568 MeV = mᵉ · ᵉ√ ̅̅ ̅̅(2⁴+5⁴)·(5⁵-2·3³)̅̅ ̅̅ e = 2,7182818284... (Napier's constant, Euler's number); mᵐ = muon mass ; mᵉ = electron mass mᵐ = mᵉ * [(2⁴+5⁴)*(5⁵-2·3³)]^(1/e) tau (mᵗ) = 1 776,938 MeV = mᵉ · [(2⁴+5⁴)ᵠ꞉(2·5)-e] φ = 1,6180339887... golden ratio ; mᵗ = mᵉ * [(2⁴+5⁴)^ᵠ /(2*5)-e] mᵗ = mᵐ · ⁴√ ̅̅ ̅̅ 2⁷·5⁴-3 ̅̅ ̅̅ Proton-to-electron mass ratio: 2(2·3·5)²+[2(u+u+d)-mᵉ]/mᵉ = 1 836,15267 Binding energy of gluons in the baryon: mᵉ·2(2·3·5)² Binding energy of gluons in the meson: mᵉ·2(2·5)² quark d = 4,75416145 MeV quark u = 2,36916387 MeV quark s = 95,5 MeV electron= mᵉ = 0,51099895 MeV proton = mᵉ·2(2·3·5)²+2(u+u+d)-mᵉ = 938,27208943 MeV neutron = mᵉ·2(2·3·5)²+2(u+d+d+mᵉ)-d-(1/2)mᵉ = 939,56542052 MeV kaon = mᵉ·2(2·5)²+4(u+s) = 493,677 MeV

Good question but answer it's not zero because of it must have been analysis before

2.718281828459^3.1415926535898*-1 +1=? culculat whit calculator

Time and space are the same thing at the microcosm, as time gets more dense it moves faster and it gets more distant locally both physically and theoretically from the viewer, as the point and chance of intersection becomes smaller

this is wokeness

That video about the Belt trick and a few others have helped me understand somewhat about what spin represents, but this video is able to initiate people with little math ability to the mathematical beauty and rigor of this mapping of real to complex rotations! Your graphics were a near perfect aid for this purpose! The physical quality of fermions I can intuit now is that they are _tenacious_ little critters. Thank you very much indeed.