Jed Brody

Most of science (and physics in particular) books nowadays are crap. Is there any physics explained to people (professional or layman) beyond the 10 (mostly wrong) concepts about quantum mechanics that are focused in every pop science book? I don't think they treat enough science. It's all just "sexy-sounding topics". What do people take away from them, in terms of "learning about science"? Very little or nothing at all. Why not explain more genuine science? I’ve a minor in theoretical physics; I'm also interested in quantum field theory, general relativity, cosmology in general. Just to make clear that I'm not against theoretical perspective for the point that I want to make: I think most science books should be heavier on explaining the applications of physical theories, and how physics has solved certain problems. If you don’t teach people stuff, physics has very practical use. With certain “science” writers start going on in a circle-jerk about how mysterious it all is with its voodoo aspects, it’s time to throw the book against a wall!

Brody’s attempt at explaining one of the most difficult concepts in Quantum Physics almost deserves a Novel prize all by itself and it might become one of the most remarkable clear popular books on entanglement. I cannot imagine a simpler exposition on the topic with lesser distortion - something that necessarily comes with speaking physics non-mathematically. Some pop physics books nowadays makes one wonder whether popular expositions in physics really aid understanding as much as we'd like to believe. On the other hand, for some strange reason, popular exposition on mathematics seems to fair much better than physics. One would have thought it’d be the other way around!

I don't want to claim that entanglement becomes trivial to understand once someone knows the underlying mathematics. In fact, beginning math students are also confused by the fact that not all elements of the tensor product of two spaces (in this case Hilbert spaces) are tensor products of two elements but are linear combinations (entangled states) of these elementary tensors (pure states).

With me so far?

If yes, keep reading. If not, stop.

There are similarities between Quantum and Classical Mechanics. You can have a least action, Lagrangians/Hamiltonians for both (Feynman’s PhD). There’s deep structure for Classical Mechanics which eventually (group-wise) gets to Quantum Mechanics (vide this paper by Hiley and de Gosson, 2010). You could also say in Classical Mechanics that energy conservation for a particle moving in absolute space (non-rel.) directly leads to a least action (once you’ve got dE = -F.dl that implies the least action principle and also the H-J equation). There are various ways to Quantum Mechanics (and you don’t even need Hilbert spaces for that matter). It seems some physicists only go to Quantum Mechanics for calculation and practical purposes....ROTFL! But Quantum Mechanics is much more than shut-up-and-calculate. That’s not physics; it’s not investigating Nature. It’s Kuhnian "puzzle-solving" of quantum problems [just remembered the Hamilton-Jacobi equation ∂S/∂t + H = 0 is another way of describing a classical system. From which you can wiggle your way to the Schrödinger equation - the Hamilton-Jacobi equation is indeed a good motivation to get to the Schrödinger equation (and is already very similar to it). You still need to introduce non-zero commutators between overseables that give you operators. So I don't see how you could "avoid" any of the quantumness and "stay more classical" with that approach. Whether you "go quantum" from that basis or you just introduce a "correspondence principle" where you say "here's a set of rules of how we form operators from classical quantities like position x, momentum -iħ∂/∂x, angular momentum, ...].

Whichever way, if you are motivated by classical mechanics, but you want to avoid the mathematical complexity of quantum mechanics, do read Brody’s book. Classical mechanics is a good approximation in some regimes, but overall it's wrong and there's no "going back to classical" in physics. Quantum Entanglement is just one of the examples that does not have a Classical counterpart. Shy students and readers might wrongly shy away from the ambiguities in the Quantum Mechanics interpretations, but please read Brody’s take on Quantum Entanglement just the same (I reiterate this point), if you feel up to a good intellectual challenge.… (plus d'informations)