Jacob Barandes, a New Formulation of Quantum Theory [video]

Really, really interesting way to approach QM!

If you've ever been deeply frustrated by the way QM is taught traditionally, (the good old "shut up and calculate, don't expect your intuition to be any kind of useful here") this is very much worth investigating further.

It's personally the very first time I am exposed to an approach to QM that has axioms that make actual intuitive sense and don't seem completely arbitrary like the Dirac+Von-Neuman axioms [1] are.

This theory is also way simpler (less axioms), uses very basic math: basic probability theory, basic linear algebra.

It's also the first time I (I'm not a trained quantum physicist so YMMV) hear a description of QM that does not rely on the mysterious and hand-wavy notions of "observer" and "collapse".

Instead this theory simply models the observer as just another QM system that comes to interact with the system under study when an observation is performed, and if the observer is a large and complex enough QM system, it naturally leads to a "collapse".

Bonuses of the new approach:

    - only uses "traditional" probabilities, the kind you can understand intuitively. No negative probabilities, and as far as I can tell, no particular need to pull in complex numbers to get the theory to work. As far as I can tell, he only uses complex numbers when he proves that "old style" QM can be re-derived from his formulation.

    - the theory does not seem to need "wave" functions and seems to be able to model the dual-slit thingie without having to use interference at all!

    - it properly models the notion of "independent" QM systems and QM systems that actually interact with one another, something that I've never seen satisfactorily defined in the QM textbooks I've tried to study.

     - it uses "general" stochastic systems as a core concept underlying the theory, and it made me realize I never understood how general that framework actually is, because as he explains, most exposure to stochastic systems you receive in academia almost immediately assumes the Markov property.

I unfortunately confess to not mastering enough the traditional way QM is taught/presented (density matrices, operators, wave functions, Hilbert spaces, etc...) to properly follow the part of the video where he seems to completely re-build traditional QM from his own axioms.

However, the rest of the video where he focuses on modeling an arbitrary system evolution using the general theory (not just Markovian) of stochastic systems is crystal clear and makes a ton of sense.

I also really like the way he presents his theory using a system with a finite configuration space of size N (however large N may be), and lets the infinite / analog case just be the exact same theory with N going to countable or even uncountable infinity.

For that latter point, most QM textbook actually introduce QM with a bloody particle on a one dimensional line, thereby creating a giant confusion between configuration space and the actual geometrical space the particle evolves in.

He instead goes straight to arbitrary-size configuration space and manages to do that without ever murkying the whole thing.

As a last remark, while it is a very interesting epistemological thing, in a first watch, you can skip the whole Ptolemaic / Keplerian thing at the start of the video it's only a complicated way to explain that his approach is simpler than the one everyone is used to (and it's a tad boastful ).

[1] https://en.wikipedia.org/wiki/Dirac–von_Neumann_axioms