GAME2020 3. Professor Anthony Lasenby. A new language for physics. (new audio!)
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- Опубліковано 22 сер 2021
- Cambridge's professor of cosmology and astrophysics Anthony Lasenby takes you through the Geometric Algebra view of all fundamental forces.
More information at bivector.net
This version has updated audio.
I feel like standing and clapping every few seconds while watching this. Definitely will revisit and/or explore in detail.
i wish there was more new content on GA for physics on youtube it really isn’t talked about enough
True ;-;
It seems, GA is mostly taught as a simpler replacement for the common approaches.
So you still have to know/understand the classical solutions and then get equivalent formulations, that are probably easier to implement and maybe to adjust, if you get the fundamentals of GA.
Yet, as GA is the simpler approach anyways, why start with the classical ways and only prove that GA can yield the same results, instead focus on describing everything in GA only, because there it is said to have more geometrical meaning, is consistent etc. and also provide more examples.
@@realedna i completely agree with you
@@realedna I think that in academic circles it will be talked about more among researchers and slowly trickle down into undergraduate curricula with time. In the meantime the best we can do is access resources for self study I suppose
@@realedna The way techniques gain stature in tradition, is when people solve problems or make new discoveries using them.
Thanks for the excellent lecture, now working through the excellent book "Geometric Algebra for Physicists". £68.
Wonderful talk thanks a lot !
Fantastic. He ansver many questions for me.
Fantastic!
Thanks!
Yeah, this mathematical tool is just like a computer compared to a slide ruler. I'm gonna make the steps to leave the slide ruler home and bring geometric algebra with me for the remainder of my physics.
Excellent physics video
2:05:00 Do you have any paper showing the research that have been done about the role of that beta in this equation?
I was expecting/hoping for an introduction to simpler physics concepts (classical mechanics) using GA instead of trying to derive a formula of everything in STA.
This lecture only provides a glimpse of how GA can simplify and unify common concepts in modern physics like quantum theory, particle physics and the theory of relativity.
Yet, it doesn't help much getting a grasp of space time, quantum state, wave functions, operators, particles, spinors, ...
It has given some very interesting hints and clues though, that complex topics previously taking decades to derive, understand, work with and master may now be studied in just a few years.
While I did come into this presentation already understanding the concept of spacetime, I thought the STA here made it extremely clear with exquisite clarity. What sort of questions did it leave you with? I'm not calling you a dummy, I'm just curious about where the conceptual gap is.
As for the rest of those concepts, you're clearly correct that this is not intended as a primer on their meaning in QM. Honestly, the presentation would have been much shorter and more educational if he didn't bother with the traditional concepts at all, instead doing everything in STA from the get go. I really wish I learned it all this way first. However, the goal here seems to be demonstrating the equivalence of the STA to the traditional mathematics first and the STA conceptualization second; he couldn't do the former without running through the needlessly complicated traditional concepts. If I ever find a UA-cam series that teaches physics with STA from scratch, I'll try to remember to give it to you, but at present it doesn't seem to exist. You will have to put your phone down and read the book :)
@@davidhand9721 have you tried Mathoma channel or Peter Joot's videos?
I just finished reading Alan Macdonald's books on GA/GC and was wondering if you had any recommendations for other books to read?
What about Geometric Algebra for Physicists by Doran and Lasenby?
Also the book Space-Time Algebra by David Hestenes. It is short (100 pages) . "Geometric Algebra for physicist is more general as it touches more fields. It is about 500-600 pages.
Once we get into the calculus, it appears that the traditional del operators, del• (divergence) and del× (curl), are mixed in. However, we've redefined the del operator for the STA; what, then, do the new del• and del× operators mean, and how are they computed? Am I reading it wrong?
I'm also sort of confused by the use of the × product later on. I see that it's defined as the half commutator, but isn't that also the definition of either the dot product or wedge product as well?
I think I saw a del^ in there, too. What does that mean?
Perhaps it's because we are defining operators, e.g. A = del • B => A psi = (del psi) • B? Is that it? I bet that's it, but I'd still appreciate an expert opinion.
The commutator works for bivectors also, geometric product definition of inner and outer products works only when one factor is a 1 vector
Exactly what leo said. The wedge product isn't anticommutative in general, but it is e.g. For vectors. In general it's just the highest-grade of the geometric product
Can you explain spin 1/2 entanglement classically?
It's the consequence of angular momentum conservation in Hilbert space. Not sure how that is supposed to become classical. Hilbert space is still a quantum mechanical construct to describe an infinite ensemble. Such an ensemble is simply not necessary for classical systems. The deceptive part about the quantum mechanics of angular momentum is that it is a finite dimensional Hilbert space, which simplifies a lot of things and makes them look almost classical. If you do an actual experiment, however, then you will see that it's not classical at all. A series of Stern-Gerlach magnets turned by 90 degrees should prove to you very quickly that the number of physical degrees of freedom to explain the separation of one beam into two, then four, then eight etc.. can not be finite if we use classical theory. And it isn't. What people aren't explaining to you in beginner's classes for quantum mechanics is where those "infinite degrees of freedom" originate. They are the loss of knowledge about the state of the vacuum on the forward light cone, which is always in our future, i.e. it is fundamentally unknowable.
@@schmetterling4477 I am talking of the stern gerlach, where he shows it can be explained by a classical population of particles that align either parallel or antiparallel to B. But I am sure there is no way to do the same (I hope I were wrong) with a pair of entangled particles, that he did not discuss at all.
@@wolphramjonny7751 A classical population does not explain Stern Gerlach. That's the entire point of these experiments. In a classical population the state would be located in entirety in the individual corpuscle, which would require an infinite phase space per corpuscle. That model is unphysical even in classical mechanics because it neglects the back-reaction of the individual corpuscle on the magnetic field. The localization in angular momentum space is, instead, a collective phenomenon of the magnetic field and the electron (or silver atom if you go with the proper experimental details) field. Whatever quantum of angular momentum "the particle" gains, the field loses and vice versa. Since the em field extends to infinity and propagates at the speed of light, we can only tell that the balance of angular momenta is conserved but not where the missing or gained angular momentum of "the particle" went. This is rarely explained properly at the undergrad and layman level. QM is a good example of a near perfect theory that is being taught extremely poorly (I believe only thermodynamics takes the second rank in that category).
@@wolphramjonny7751 Entanglement is simply a really silly way to think about conservation and symmetry.
59:00
15:25 Why do you need four vectors? Why don't just use 3 special vectors and for the time use the scalar (1)?
I think you could do that for special relativity, but the additional vector completes the algebra (such as having 3D space as the even subalgebra)
time is a vector not a scalar
That actually does work; using it generates the "algebra of physical Space" (the Geometric algebra of ℝ³), and the sum of a vector and a scalar is known as a paravector. However, Spacetime algebra generally works out more nicely, and provides clearer geometric meaning to several quantities.
In addition, the assignment of time to being a scalar is somewhat arbitrary, and it is often nicer to treat it as a vector quantity (i.e. on equal footing with space)
I don't see how it could work; if time is the scalar part, then the rest frame spatial vectors (sigma 1-3) would just be the spatial gamma vectors, not bivectors. You could only go so far with it before the scheme becomes a mess of rank conflicts and arbitrary special rules. Besides, we need the scalar part when we get to QM, right?
I actually prefer the opposite metric where the space vectors square to 1 and time squares to -1, and I don't know if it would change anything. It all works out in traditional SR/GR, but I can imagine that screwing things up getting into QM. It's just more consistent with 3D VGA, it's not worth messing with the success of STA as it's outlined here.
They are in the full algebra of STA, γ⁰⋅γ⁰ = τ is the time scalar (proper time) and σ¹ = γ¹γ⁰, σ² = γ²γ⁰ and σ³ = γ³γ⁰ are the spatial vectors (proper lengths).