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.
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.
I was wondering... what's your opinion on Geometric Algebra? (If you have one)
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.
> 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...
edit: https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0...
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?
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/
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/
I will definitely follow your advice and 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.