Introduction to Mathematics of Spinors (from a self-learner)

Resources for learning spinors:
Video showing all the different types of spinor invariants found in a Lagrangian from QFT:

Books:
"Introduction to 2-Spinors in General Relativity" by Peter J. O'Donnell
"Introduction to Supersymmetry" by Wiedamann
"The Theory of Spinors. The Geometry of Minkowski Spacetime" by Naber, G. L.

[nzuckman]

Bro did you just intuitively demonstrate the rotational property of spinors in less than 2 minutes? Goddamn I wasn't ready 🤯

[Cosmalano]

This is fantastic. Ive also been self teaching myself spinors and I feel like I’m right on the cusp of fully getting it.

[JgM-iejy]

This is by far the most brutal introduction I have ever seen.

But based on your Tensor Calculus series, I am confident you can take me to a yet higher level.

This will be a magnificent journey.

[cezarionescu]

I love it when people go in deep in this concepts and share what they have learned. Knew most of the stuff but gotta say it was iluminating and will enjoy to watch your leactures

[aryankumarprasad]

I have been thinking of self learning it for a week. Thanks

[ili]

I love your videos, .You make complicate things much more simpler. I've been struggling with spinors for a while so this series looks fantastic. Thank you for your work.

[fredrickvanriler]

Great video ❇️❗️ can’t wait to see more lectures from you on Quantum Mechanics!

[canyadigit]

This is an early Christmas gift. I’m currently studying quantum from griffiths, and the explanation of spin and spinors suck. Thanks so much Chris!

[parthabanerjee]

1.20 mins into your video and my 6 years old misconception has been addressed. Keep up the good work, buddy. Autodidacts learn and teach better because no professor or university sets the boundary of their knowledge and understanding.

[SpotterVideo]

Conservation of Spatial Curvature (Both Matter and Energy described as "Quanta" of Spatial Curvature. A string is revealed to be twisted cord when viewed up close.)

Is there an alternative interpretation of "Asymptotic Freedom"? What if Quarks are actually made up of twisted tubes which become physically entangled with two other twisted tubes to produce a proton? Instead of the Strong Force being mediated by the constant exchange of gluons, it would be mediated by the physical entanglement of these twisted tubes. When only two twisted tubules are entangled, a meson is produced which is unstable and rapidly unwinds (decays) into something else. A proton would be analogous to three twisted rubber bands becoming entangled and the "Quarks" would be the places where the tubes are tangled together. The behavior would be the same as rubber balls (representing the Quarks) connected with twisted rubber bands being separated from each other or placed closer together producing the exact same phenomenon as "Asymptotic Freedom" in protons and neutrons. The force would become greater as the balls are separated, but the force would become less if the balls were placed closer together. Therefore, the gluon is a synthetic particle (zero mass, zero charge) invented to explain the Strong Force. An artificial Christmas tree can hold the ornaments in place, but it is not a real tree.

String Theory was not a waste of time, because Geometry is the key to Math and Physics. However, can we describe Standard Model interactions using only one extra spatial dimension? What did some of the old clockmakers use to store the energy to power the clock? Was it a string or was it a spring?

What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles? Fixing the Standard Model with more particles is like trying to mend a torn fishing net with small rubber balls, instead of a piece of twisted twine.

Quantum Entangled Twisted Tubules:
“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct.” Neils Bohr
(lecture on a theory of elementary particles given by Wolfgang Pauli in New York, c. 1957–8, in Scientific American vol. 199, no. 3, 1958)

The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with some aspects of the “Twistor Theory” of Roger Penrose, and the work of Eric Weinstein on “Geometric Unity”, and the work of Dr. Lisa Randall on the possibility of one extra spatial dimension? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?

When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if Quark/Gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks where the tubes are entangled? (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Charge" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.

Modern physicists say the Strong Force is mediated by a constant exchange of Gluons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.

Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. If a twisted tube winds up on one end and unwinds on the other end as it moves through space, this would help explain the “spin” of normal particles, and perhaps also the “Higgs Field”. However, if the end of the twisted tube joins to the other end of the twisted tube forming a twisted torus (neutrino), would this help explain “Parity Symmetry” violation in Beta Decay? Could the conversion of twist cycles to writhe cycles through the process of supercoiling help explain “neutrino oscillations”? Spatial curvature (mass) would be conserved, but the structure could change.

Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?

Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?

Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons

. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The production of the torus may help explain the “Symmetry Violation” in Beta Decay, because one end of the broken tube section is connected to the other end of the tube produced, like a snake eating its tail. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process, which is also found in DNA molecules. Could the production of multiple writhe cycles help explain the three generations of quarks and neutrinos? If the twist cycles increase, the writhe cycles would also have a tendency to increase.

Gamma photons are produced when a tube unwinds producing electromagnetic waves. ( Mass=1/Length )

The “Electric Charge” of electrons or positrons would be the result of one twist cycle being displayed at the 3D-4D surface interface of the particle. The physical entanglement of twisted tubes in quarks within protons and neutrons and mesons displays an overall external surface charge of an integer number. Because the neutrinos do not have open tube ends, (They are a twisted torus.) they have no overall electric charge.

Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms.

In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.

1= Hypertubule diameter at 4D interface

137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.

The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)

How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?

Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?

I started out imagining a subatomic Einstein-Rosen Bridge whose internal surface is twisted with either a Right-Hand twist, or a Left-Hand twist producing a twisted 3D/4D membrane. This topological Soliton model grew out of that simple idea. I was also trying to imagine a way to stuff the curvature of a 3 D sine wave into subatomic particles.
.

[tomkerruish]

I followed the link, and I must tell you, I had absolutely no clue that you're not a native speaker of English. The only possible hint of an accent is your speaking tempo, which reminded me of the comedian Steven Wright, and was beautifully appropriate for your "What Is Momentum?" video, which still leaves me in stitches.

[fixed-point]

This is just exactly what I'm looking for.

[gsgp]

This is interesting.
I hope you start a new project about this topic.

[adityas.thcsudhanshus.th]

Great Intro! For Spinors, I'm Thankfull to you, because, I understand a Major Part of it as of Honestly speaking, hope to see more Videos on Theoretical Topics and TGR & TQFT! BTW, I'm just in 8th grade now(13y/o). Thank you very much for such a great video!.

[geoffreyfaust]

Thank you, Chris!
Quick question: I have been through your tensor calc. and relativity videos; thanks again! But all I know on the spinor subject is from reading Roger Penrose's non-technical writings (Fashion Faith and Fantasy, mostly), as well as watching Dr. Penrose's somewhat difficult to follow assorted YouTube appearances. Would you recommend that I start my study of spinors from your videos that are linked here OR should I go to your 20 video series Spinors for Beginners"?
Thanks again fort al your hard work!
G. Faust

[diegocarrera]

Hey eigenchris, I love your videos. I have to say the are really one of the best math content on YouTube. I was wondering if you could check and explain Geometric Algebra because I think it it links all the content from tensors and spinors. But I don't know how. Thanks for your amazing content

[BloobleBonker]

Wow! Thankyou so much for doing this. I've been looking for just this.

[DrDeuteron]

I think for physicists the biggest problem is the mathematical precision and the overlap of many areas that happens in su(2). What's a group vs. and algebra? Generators vs representations. Matrix vs column vector...who's 'in-the-group'? Vectors are the adjoint rep of su(2) but fundamental rep of so(3), and so(3)'s adjoint rep is also vectors? How do quaternions and Clifford play a role? Is spin(n) the spin group in n-dimensions, and su(2) just happens to look like spin(2)? what is spin(n) vs su(n)?
Physicswise: Bloch sphere is for any 2-state system, but for spin it's special because any point on the surface is spin up for some axis.
How are pauli and Dirac spinors related? Are Pauli spinors 'accidentally relativistic'?
What about photon polarization with it's missing state...does it have a group?aka: poincare' sphere vs bloch sphere.

[ronaldbarrett]

Keep at it! We need to learn moe. Thank you

[anikmandal]

I'm just going to learn about this thing! And I found your new video! :)