PHYS771 Lecture 9: Quantum(scottaaronson.com)
scottaaronson.com
PHYS771 Lecture 9: Quantum
https://scottaaronson.com/democritus/lec9.html
32 comments
read it, cool idea to present starting with negative probability, didn’t love it as an intro, liked ivan_ah’s treatment better. also didn’t like that Scott pushed complex numbers to the end given their intimate connection to waves and phase and interference which was not discussed and is core to my personal intuition so far.
To be honest, the quantum groups are my fav formalism in that general field http://sporadic.stanford.edu/quantum/
I met quantum by the first way, it is natural. However I agree the latter approach, quantum is more math than physics to me. With the age of quantum is about to come, I will read this lecture.
Love this, I agree that for someone new to QM the historical approach is probably not the best idea (though I can imagine many physicists would be upset by the qbistic vibes of the article).
But, if you have the prerequisites already (classical mechanics, electrodynamics and thermodynamics), it does make for a fascinating story. Malcolm Longair's couple of books titled "Concepts in Physics" are a great place where you can learn the history in detail.
But, if you have the prerequisites already (classical mechanics, electrodynamics and thermodynamics), it does make for a fascinating story. Malcolm Longair's couple of books titled "Concepts in Physics" are a great place where you can learn the history in detail.
If anyone is interested to learn more about quantum mechanics and the Dirac ket notation, check this out: https://minireference.com/static/excerpts/noBSLA_quantum_cha... (79pp; includes exercises and problems with solutions)
It's the last chapter from my linear algebra book. The book is not free, but I'm happy to make this chapter free because QM is cool stuff.
It's the last chapter from my linear algebra book. The book is not free, but I'm happy to make this chapter free because QM is cool stuff.
This is very well written. I checked for a couple of common issues that arise in introductory presentations of quantum mechanics, and found that you navigated most of them correctly.
For example, in the entanglement section, you did discuss that entanglement is a basis independent property, which is a critical point to make - basis dependent "entanglement" exists in classical systems; it is just correlation.
However, I disagree with the inclusion of the paragraph starting "There is something strange about the EPR state." The emphasis on 'immediately' in conjunction with the large distance between Alice and Bob is particularly problematic. The setting of EPR experiments is necessarily in a relativistic world, and in that world time is only a local property. Saying things happen simultaneously (= immediately) implies the presence of a privileged frame of reference, which is exactly what we don't want to do. There are ways of saying these things correctly, but that requires a lot more setup.
I also have a minor nitpick in the sentence below" "We have complete certainty about the state of the composite system |\psi_-\rangle^{AB} , and complete uncertainty about the states of the individual subsystems controlled by Alice and Bob" Since, entanglement exists on a scale, it is better to delete the second "complete" in the sentence, as we can have only partial uncertainty (in the sense of some entanglement measure) about Alice and Bob's systems.
For example, in the entanglement section, you did discuss that entanglement is a basis independent property, which is a critical point to make - basis dependent "entanglement" exists in classical systems; it is just correlation.
However, I disagree with the inclusion of the paragraph starting "There is something strange about the EPR state." The emphasis on 'immediately' in conjunction with the large distance between Alice and Bob is particularly problematic. The setting of EPR experiments is necessarily in a relativistic world, and in that world time is only a local property. Saying things happen simultaneously (= immediately) implies the presence of a privileged frame of reference, which is exactly what we don't want to do. There are ways of saying these things correctly, but that requires a lot more setup.
I also have a minor nitpick in the sentence below" "We have complete certainty about the state of the composite system |\psi_-\rangle^{AB} , and complete uncertainty about the states of the individual subsystems controlled by Alice and Bob" Since, entanglement exists on a scale, it is better to delete the second "complete" in the sentence, as we can have only partial uncertainty (in the sense of some entanglement measure) about Alice and Bob's systems.
Thanks for taking a look and reporting the issues. I'll add clarifications around the "immediately" and remove the second "complete" as per your suggestions.
Your books are indeed excellent!
I was wondering... what's your opinion on Geometric Algebra? (If you have one)
I was wondering... what's your opinion on Geometric Algebra? (If you have one)
I've watched a few talks and seen cool computational demos about it (see for example https://news.ycombinator.com/item?id=22282452 ), but I still don't really understand it... or should I say I can't "wedge" it into my head ;)
The uniformity of operations and the fact it works in all dimensions is very appealing, but I remember there were some very counter-intuitive aspects too, so I'm not fully on board. Still very cool though!
I guess old school vectors, dot-, and cross- products have the benefit of history behind them, so they feel more intuitive, whereas geometric algebra operations feel somehow foreign to us (to me at least). It would be interesting to see what happens if a student learns geometric algebra first, maybe it will feel more natural then.
The uniformity of operations and the fact it works in all dimensions is very appealing, but I remember there were some very counter-intuitive aspects too, so I'm not fully on board. Still very cool though!
I guess old school vectors, dot-, and cross- products have the benefit of history behind them, so they feel more intuitive, whereas geometric algebra operations feel somehow foreign to us (to me at least). It would be interesting to see what happens if a student learns geometric algebra first, maybe it will feel more natural then.
Thanks for your take on it!
> It would be interesting to see what happens if a student learns geometric algebra first, maybe it will feel more natural then.
Yeah, I've noticed some people [0] advocating for using it for all physics as soon as possible too.
[0]: https://www.cambridge.org/core/books/geometric-algebra-for-p...
> It would be interesting to see what happens if a student learns geometric algebra first, maybe it will feel more natural then.
Yeah, I've noticed some people [0] advocating for using it for all physics as soon as possible too.
[0]: https://www.cambridge.org/core/books/geometric-algebra-for-p...
i read your book cover to cover it was amazing
edit: https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0...
edit: https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0...
I was checking out the kindle version preview on amazon. You know, when you click "Read Sample".
The mathematical formulas seem to be badly formatted and hard to read. I reckon this is just a problem with the html conversion for the preview.
Can somebody confirm that it looks fine on the kindle?
The mathematical formulas seem to be badly formatted and hard to read. I reckon this is just a problem with the html conversion for the preview.
Can somebody confirm that it looks fine on the kindle?
Please do not buy the Kindle version form amazon; it's not mine ... someone pirated it! I'm reporting it now, but it keeps on happening.
I would recommend you get a print copy since it's much better for learning, but if you prefer digital-only copy you can get it through gumraod: https://gum.co/noBSLA It comes in PDF, ePub, and mobi formats. Here is an ePub preview (of another book) so you can see the math rendering: https://minireference.com/static/excerpts/noBSmath_v5_previe... I worked for 2+ years to get this to look decent, see https://minireference.com/blog/generating-epub-from-latex/
I would recommend you get a print copy since it's much better for learning, but if you prefer digital-only copy you can get it through gumraod: https://gum.co/noBSLA It comes in PDF, ePub, and mobi formats. Here is an ePub preview (of another book) so you can see the math rendering: https://minireference.com/static/excerpts/noBSmath_v5_previe... I worked for 2+ years to get this to look decent, see https://minireference.com/blog/generating-epub-from-latex/
I had no idea that can be possible! For the record, it was on amazon UK.
I will definitely follow your advice and get the paper version.
I will definitely follow your advice and get the paper version.
> I will get the paper version.
Nice! I have a free-eBook-when-you-buy-a-print-copy policy. Please send me a picture of the book when you receive it or some other proof-of-purchase, and I'll hook you up with a PDF with matching page numbers. This way you'll be able to easily switch between print copy and digital as you need.
Nice! I have a free-eBook-when-you-buy-a-print-copy policy. Please send me a picture of the book when you receive it or some other proof-of-purchase, and I'll hook you up with a PDF with matching page numbers. This way you'll be able to easily switch between print copy and digital as you need.
amazon report page is not broken for me, firefox mobile ios
I managed to get on a report page via the KDP portal. Very weird, since it's the same URL, but the form showed up because I was coming from a different referred. Oh well, reported successuflly now (I think).
Thx for confirming it wasn't just me. I was starting to doubt so I edited my comment.
update: I figured out what is going on... It's the classic curse of the extra slash!
- BROKEN = https://www.amazon.com/report/infringement/
- WORKS = https://www.amazon.com/report/infringement
Thx for confirming it wasn't just me. I was starting to doubt so I edited my comment.
update: I figured out what is going on... It's the classic curse of the extra slash!
- BROKEN = https://www.amazon.com/report/infringement/
- WORKS = https://www.amazon.com/report/infringement
sorry, i read this printed. It is textbook length, studying requires lots of flipping around. everything else kindle tho
Hey thx man! Always good to hear from readers.
> For example, I've had experts in quantum field theory -- people who've spent years calculating path integrals of mind-boggling complexity -- ask me to explain the Bell inequality to them.
My favourite quantum mechanics textbook is Griffiths: Introduction to Quantum Mechanics. It is popular as a textbook for the first quantum mechanics course, which is typically in the second or third year of a physics curriculum. It has sections on EPR paradox and Bell's Theorem. First edition was published in 1994.
My favourite quantum mechanics textbook is Griffiths: Introduction to Quantum Mechanics. It is popular as a textbook for the first quantum mechanics course, which is typically in the second or third year of a physics curriculum. It has sections on EPR paradox and Bell's Theorem. First edition was published in 1994.
The cat book again! It seems everyone recommends Griffiths. I finally gave in and my copy should be arriving in a couple weeks.
I've looked through the Feynman lectures a bit, and although it's very nice for a free resource, it doesn't seem to be used very much at all in curriculums.
I've looked through the Feynman lectures a bit, and although it's very nice for a free resource, it doesn't seem to be used very much at all in curriculums.
Feynman is not sufficient as a physics textbook.
Afaik the main games in town are Griffiths, Townsend, and Sakurai if you are a tryhard
iirc I prefer Sakurai & Townsends treatment over Griffiths but I might be misremembering
e: oh yes, i think griffiths intentionally avoids dirac notation which imo screws you later on down the line
Afaik the main games in town are Griffiths, Townsend, and Sakurai if you are a tryhard
iirc I prefer Sakurai & Townsends treatment over Griffiths but I might be misremembering
e: oh yes, i think griffiths intentionally avoids dirac notation which imo screws you later on down the line
Griffiths absolutely uses dirac notation.
Weinberg’s excellent (but not widely used!) quantum mechanics textbook does not, and being proficient in Weinberg’s text would not hinder anyone.
Weinberg’s excellent (but not widely used!) quantum mechanics textbook does not, and being proficient in Weinberg’s text would not hinder anyone.
I think it just focuses heavily on wave mechanics and gets to dirac rather late
i like townsend because it’s like baby sakurai
i like townsend because it’s like baby sakurai
Chapter 3 is Dirac formalism and its used for the remaining 9 chapters.
edit: I also like Sakurai, but I actually kind of like Weinberg’s non-dirac textbook better (I’ve only read the first edition)
edit: I also like Sakurai, but I actually kind of like Weinberg’s non-dirac textbook better (I’ve only read the first edition)
So in terms of accessibility, Weinberg < Griffiths < Sakurai?
what are the challengers? there are a few twitter scientists who have written QM textbooks that haven’t made their way into university curriculum yet
sakurai & townsend are the traditional challengers, when i was taking it i didn’t really think the modern challengers were up to snuff but that might have changed
"The second way to teach quantum mechanics leaves a blow-by-blow account of its discovery to the historians, and instead starts directly from the conceptual core -- namely, a certain generalization of probability theory to allow minus signs"
In my opinion, this is not the most natural and easiest way to get into quantum mechanics.
And there are also (undergraduate) physics books that tackle the quantum mechanical concepts directly, e.g:
https://www.feynmanlectures.caltech.edu/III_toc.html
especially:
https://www.feynmanlectures.caltech.edu/III_03.html (Probability Amplitudes)
Negative probabilities (Wigner Functions) are more advanced:
https://en.wikipedia.org/wiki/Wigner_quasiprobability_distri...
Lucien Hardy "Reconstructing quantum theory" is really conceptional, but I think it is not the best way to start.
https://arxiv.org/abs/1303.1538
In my opinion, this is not the most natural and easiest way to get into quantum mechanics.
And there are also (undergraduate) physics books that tackle the quantum mechanical concepts directly, e.g:
https://www.feynmanlectures.caltech.edu/III_toc.html
especially:
https://www.feynmanlectures.caltech.edu/III_03.html (Probability Amplitudes)
Negative probabilities (Wigner Functions) are more advanced:
https://en.wikipedia.org/wiki/Wigner_quasiprobability_distri...
Lucien Hardy "Reconstructing quantum theory" is really conceptional, but I think it is not the best way to start.
https://arxiv.org/abs/1303.1538
Wigner Functions are great and all, but they work quite badly for finite dimensional systems. Specifically they are a bit complicated for odd dimensional systems and don't work at all for even dimensional systems (see e.g. [1]). Given their limited applicability I don't see why we should treat them as particuarly fundamental when introducing quantum mechanics to students.
[1] https://arxiv.org/pdf/quant-ph/0507094.pdf
[1] https://arxiv.org/pdf/quant-ph/0507094.pdf
I am not sure if this is how it is a correct representation. I believe a common approach is to do a short history of quantum in the first year, and then do a from the ground up approach in the second and third year. Depending on who teaches it, this is either starting from a particle in a box or the approach stated here. The historical story is useful, because it tells a little bit of the why.