# Are there any resources of lists of attempts at non-probabilistic models of quantum mechanics, with debunking?

For example, some introductory resource I was reading years ago (forget which one) brought up such an attempt: imagine if a qbit wasn't a complex state vector which collapses probabilistically on measurement, but rather functioned as a tiny "coin" as follows (forgive the crude drawing): As far as I can recall, whenever the qbit goes through a quantum gate the coin is rotated some amount, then when "measuring" the qbit you basically just look from the perspective of the basis you're measuring (say the |0>/|1> basis) and the result you see is whichever side of the coin is facing that basis (in the diagram, heads). Honestly I think I got half the details wrong on this, but it was something like that.

This was entertaining to learn about, so does anyone know of a good collection of such half-baked (or full-baked) attempts at de-probability-izing quantum mechanics? Bonus if it actually includes this coin example.

• How does your coin example capture qubit states? Unitary operators on a qubit form the group $SU(2)$, which can be mapped to $SO(3)$ (or 3D rotations; module the double cover) but not $SO(2)$ (2D rotations). So your coin interpretation just wouldn't work since it's only restricted to a circle (unless you restrict yourself to only use rotations along a fixed axis). Maybe you can clarify the example a bit more explicitly? – keisuke.akira Jul 8 '20 at 20:22
• The example is half-remembered, I will try to find it. Anyway the question is about resources documenting attempts similar to this – ahelwer Jul 8 '20 at 21:06

## 2 Answers

Einstein, Podolsky and Rosen's (local) Hidden Variable theory is the most famous deterministic attempt to explain Quantum Mechanics. You can take a look at the wiki on the explanation: https://en.wikipedia.org/wiki/Hidden-variable_theory. As proved later on by Bell, this theory was not "possible" given the theory could not account for experimental behavior when observing correlations between entangled states.

Within the wiki there's a second hidden-variable theory which is supposed to mathematically describe Quantum Phenomena in a deterministic way (Bohm-Debroglie Theory), but it is not considered a possible theory given the necessary assumptions to be made for it to work (multidimensional physical space, among others)

You could start from there :)

The coin example is incorrect (that is, different from QM) if you consider correlations of measurements of entangled qubits in different bases.

If you want a more advanced attempt of building a deterministic theory underlying QM, have a look at Gerard 't Hooft book The Cellular Automaton Interpretation of Quantum Mechanics which is free now.