The Mathematical Structure of Quantum Mechanics - Try This, Once and for All!
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- čas přidán 12. 04. 2024
- In this video, I challenged myself AND my professor to bring ALL of, or nearly all of, the Mathematical Structure of Quantum Mechanics in one single CZcams video. I hope you like it :)
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#physics #فيزياء #quantum #science #quantumphysics #education #maths #theory #theoreticalphysics #modernphysics #heisenberg #uncertainty
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Best video ever for quantum maths. I will call- Quantum maths in nutshell.
this is good but kinda hard if u are beginner. i recommend watching quantum sense playlist before this, and revise from this.
This is the best and shortest by far, but accurate and direct summary of the mathematical concepts found in quantum mechanics... Congratulations!!
Thanks! Glad you liked it 😊
@@ankidokolo Continuous (classical) is dual to discrete (quantum).
Waves are dual to particles -- quantum duality.
Sine is dual to cosine or dual sine -- the word co means mutual and implies duality.
Real is dual to imaginary -- complex numbers are dual.
Injective is dual to surjective synthesizes bijective or isomorphism -- group theory.
Syntax is dual to semantics -- languages or communication.
If mathematics is a language then it is dual.
Lie groups are dual to Lie algebras.
Vectors (contravariant) are dual to co-vectors (covariant) -- dual bases.
Riemann geometry or curvature is dual -- upper indices are dual to lower indices.
Positive curvature (convergence, syntropy) is dual to negative curvature (divergence, entropy) -- Gauss, Riemann geometry.
Subgroups are dual to subfields -- the Galois correspondence.
Elliptic curves are dual to modular forms.
Categories (form, syntax, objects) are dual to sets (substance, semantics, subjects) -- Category theory.
"Always two there are" -- Yoda.
Poles (eigenvalues) are dual to zeros -- optimized control theory.
All numbers fall within the complex plane hence all numbers are dual.
The integers are self dual as they are their own conjugates.
Duality creates reality!
@@hyperduality2838 Indeed!
@@ankidokolo Watch the following videos about duality, watch at 11 minutes:-
czcams.com/video/DoCYY9sa2kU/video.html
And this at 1 hour 4 minutes:-
czcams.com/video/UjDxk9ZnYJQ/video.html
The Schrodinger representation is dual to the Heisenberg representation -- quantum mechanics.
AdS is dual to CFT.
Duality means that there is a 4th law of thermodynamics:-
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Positive is dual to negative -- numbers or electric charge.
Your mind is syntropic as you are making predictions to track targets and goals or objectives (targets).
"The brain is a prediction machine" -- Karl Friston, neuroscientist.
Energy is dual to matter -- Einstein.
010 - The Eternal Now - T.E.N. d. Realistic Illusions. 010
It came to my attention that at 15:45 the psi's of the row-vector that represents the bra
Impressive man, keep up!!🎉
Fascinating! ^.^
Wow...
Worth watching ten times
For me to fully understand it , I would have to watch it 10,000 times .
thank you
You're welcome
A great video again. This should be everywhere!!
Thanks. And I hope that :)
Though I wasn't able to comprehend all of it, I feel that the effort of being a good reference should be appreciated. Maybe you could make a video series with 3 or 4 minutes each, explaining the math and the operators you demonstrated in a more detailed perspective.
That's a great idea. I'll work on it in the coming weeks 👍😊
The Lie group, the symmetry transformations, Wigner's theorem
Those and more are in my plan. I’ll come to them in this series (playlist). But they are not a direct subject for the mathematical structure for quantum mechanics. Like in all standard textbooks.
Continuous (classical) is dual to discrete (quantum).
Waves are dual to particles -- quantum duality.
Sine is dual to cosine or dual sine -- the word co means mutual and implies duality.
Real is dual to imaginary -- complex numbers are dual.
Injective is dual to surjective synthesizes bijective or isomorphism -- group theory.
Syntax is dual to semantics -- languages or communication.
If mathematics is a language then it is dual.
Lie groups are dual to Lie algebras.
Vectors (contravariant) are dual to co-vectors (covariant) -- dual bases.
Riemann geometry or curvature is dual -- upper indices are dual to lower indices.
Positive curvature (convergence, syntropy) is dual to negative curvature (divergence, entropy) -- Gauss, Riemann geometry.
Subgroups are dual to subfields -- the Galois correspondence.
Elliptic curves are dual to modular forms.
Categories (form, syntax, objects) are dual to sets (substance, semantics, subjects) -- Category theory.
"Always two there are" -- Yoda.
Poles (eigenvalues) are dual to zeros -- optimized control theory.
All numbers fall within the complex plane hence all numbers are dual.
The integers are self dual as they are their own conjugates.
Duality creates reality!
@@hyperduality2838 Can't disagree
@@hyperduality2838There is some merit to this. But Lie groups and Lie algebras are not really dual, instead several Lie groups correspond to the same Lie algebra. Syntax is not necessarily dual to semantics, because on the one hand one semantic can have several syntaxes and one syntax can have several semantics, on the other hand semantics may be considered more like the terrain of reality itself, while syntax may be considered more like a map of reality, thus semantics is richer than syntax. Only Galois subfields correspond to subgroups iirc (or was that normal subgroups?), and also this is more like an adjunction (Galois connection) than an equivalence (duality).
Most of your other dualities are correct, although the duality between "real" and "imaginary" depends on an Archimedean metric, if we use a p-adic ultrametric instead (for some prime p) we get a more complex situation where "complex" numbers are infinite dimensional (over p-adic numbers, the analog of real numbers) instead of two dimensional. This is even more true if we avoid metrics and create algebraic numbers over the rational numbers as a base field. We may also use a formal metric on functions in one variable over the finite field GF(q) where q = p^n for some prime p and positive integer n, and i think we can create "complex" numbers over this field as well.
We may consider position as belonging to the matter aspect and momentum as belonging to the motion aspect, while the wave function is belonging to the consciousness aspect. These three are the fundamental aspects of all reality: motion, consciousness and matter, nothing can exist without partaking in all of them.
Along all the dualities (orthogonalities) of linear algebra, where an inner product over V makes V naturally isomorphic to V*, there are also a few trialities, namely in 1, 2, 4 and 8 dimensions of V, working over real numbers.
The one in 8 dimensions is most interesting, because here we have three equivalent representations of Spin(V) even working over complex numbers. These are the vector representation and the two half-spinor representations, which may represent consciousness, and the dual matter and motion, all of them dual (or "trial") to each other in this case.
And yes, to me it is fully possible to be both scientific and metaphysical simultaneously.
Wow, this was great! I was a little confused at first by the statement v=x/t instead of v= distance/t or dx/dt. But man, I’ve watched about half of this and it is great! It’s the best connection I’ve ever seen between each step from a plane wave to the Fourier transform with uncertainty. It really helps me see how it all comes together. Thanks. By the way - if the voice was AI, no problem. It was very well done.
Thanks Micheal ! And you're welcome :) For the voice, yes, actually, because my English accent is somewhat heavy on the ear. But the content/the text..etc. is 1000% made by me. I'm happy you liked it.
Such a beautiful presentation with so many typographical errors…
I know 😥 and I’m sad for that
It’s like watching a textbook, though… :)
As far as I understood , Dirac demanded an anti-particle in time.ng backwards
Yes he did. But that’s for the relativistic part of quantum mechanics ☺️
@@ankidokolo That means what ? IT IS Not right ?
No it's right. But only at high energies (small wavelengths) and high speeds. The rules of quantum mechanics does not change in the relativistic part of it. But Schrödinger's Equation just doesn't work in it.
@@ankidokolo Thank you, now got that, relativistic means near light velocity, didn't know that Schrödinger equation doesn't work then. He had big struggle with Heisenberg about his equation I have heard.
Yep, it doesn't work relativistically. It changes its form upon "Lorentz transforming." You're very welcome.
First 43 seconds are incorrect unless velocity is constant.
I agree that the notation there isn’t the best. When I made the video I didn’t actually expect so many viewers. There are some writing errors also. Anyway, the quantum part is alright.
@@ankidokolo Thank You
Wasn't IT Feynman who said, If you think you have understood Quantum mechanics, you haven't understood it ? 😅
Yeah he said a lot of things. But actually you can, and that’s why math exists. It‘s not intuitive that’s all.
@@ankidokolo I adore that , get more and more interested in maths, but couldnt follows that even with degree in medicine. 😅
Yeah, it needs repeating and reading to get insight. Some people got it a little wrong. The video is meant to help by reading textbooks. It doesn't replace textbooks. Actually nothing does.
Iam 829 subscriber
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Just as I was really starting to absorb the contents of your well prepared video POW suddenly and with no warning something on the screen pops up that is totally unrelated to the video content interrupting my train if thought. PLEASE HAVE RESPECT FOR YOUR VIEWERS AND DO NOT LET CZcams INTERRUPT YOUR VIDEOS BY FLASHING TOTALLY UNRELATED CONTENT.
You mean ads? I have no control over that, yet.
Yes! He has no control over Ads.
Here’s an idea buy CZcams red
@@chancegeorge5583 Here's an idea post on CZcams and RUMBLE. Here's another idea BOYCOT products from CZcams ads that obnoxiously interrupt their videos.
Speaking of respect ….. cultivate some, perhaps ?
The ONLY thing you have to know is in atoms you have stationnary waves called électrons. A stationnary wave is a wave that oscillates around the same point, ie for an atom the nucleus, without propagate. This is called a bounded state, the electron is bounded to the atom. At the time it propagates, it becomes nearly a free electron, i.e a ionization, so approximatively a spherical wave and no more a stationnary wave. We dont give a fuck about Hilbert space. Of course knowing basis of eigenfunctions for divers hamiltonian is a good tool. But Hilbert space remains a tool, you can discard it. Hermitian operator, eigenfunction, partial diferential equation, variationnal principle, thats it.
The relativistic case is by far more complicated however.
😂😂😂😂 yes yes Of COOOURSE!
Angry boy can’t read. Open ANY quantum mechanics book and read the MATHEMATICAL STRUCTURE chapter. And ONLY when you’re ready come back and discuss, little boy.
@@ankidokolo yes it is, go read my paper "real space quantum mechanics" O Loiselet. Hilbert space of functions is secondary. It is explained from a very physical point of view.
010 - The Eternal Now - T.E.N. d. Realistic Illusions. 010
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