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The problem is that Born’s rule was not really more than a smart guess — there was no fundamental reason that led Born to propose it. “It was an intuition without a precise justification,” said Adán Cabello, a quantum theorist at the University of Seville in Spain. “But it worked.” And yet for the past 90 years and more, no one has been able to explain why.
Born’s probability postulate is where the puzzle really is. [..] If we could understand where the Born rule comes from, we might finally understand what the vexed concept of measurement really means in quantum theory.
Representation Theory and Quantum Mechanics
Representation theory is important in physics for a billion reasons, but here is one: Hilbert spaces are complex vector spaces, so any group action on a Hilbert space will necessarily be a group representation. Therefore, if we want to understand how groups can act on quantum mechanical state spaces, we must understand representation theory. This shouldn’t be very surprising. Quantum mechanics is really just glorified linear algebra, and representation theory is all about using linear algebra to study groups.
First time I've heard of "moment maps":
The topic with the least explicit foreshadowing is the relationship between Hamiltonian mechanics, the moment map, and quantization, which is the last topic of these notes. The story of the moment map is perhaps my favorite one here, if only because it is poorly explained everywhere else. The moment map gives a much richer connection between symmetries and conserved quantities than Noether’s theorem, and should be better known by physics students.
Michael Nielsen's Future of Matter
This site has a lot of interesting articles on the future of matter. What possible phases of matter that don't exist naturally could we create? How does anyonic quasiparticle matter behave?
Creating new phases of matter via long distant entanglement. Can potentially lead to robust quantum error-correcting computers if the anyon model is physically realizable.
Really enjoyed Mermin's book on Quantum Computer Science. Still need to read Nielsens book as well.
Interesting quote by Feynman:
But the motion to keep the planet going in a straight line has no known reason. The reason why things coast for ever has never been found out. The law of inertia has no known origin.
The Character of Physical Law @ z-library
A modified-newtonian-dynamics-like (MOND) theory (Modified Inertia from a Hubble-scale Casimir effect). Kind of far out but proposes an explanation of inertia via Unruh radiation.
Unlikely to pan out but would be really cool if it does