A Simple Experiment to Prove that “God Doesn’t Throw Dice”

Picture by Dmitry Buterin

In his famous “cat” paper Erwin Schrödinger wrote that the wave function “embodies the totality of theoretical future expectations (of measurement outcomes), as laid down in a catalogue.” [1] He continued this comparison throughout the paper using expectations, predictions, statements and knowledge interchangeably to describe the contents of this catalogue.

A precise prediction of all values which can be measured is a part of the knowledge embodied in the wave function that Schrödinger considered the most important and enabling the entire calculational scheme of quantum mechanics to work properly. “First of all, there is no reference to previous measurements; these are not necessary. Secondly, the statement certainly does not lag in precision, on the contrary, it is far more accurate than any real measurement could ever be.” He wrote. “And one can well imagine how important this precise statement is: much more important than the knowledge of which of these values actually occurs, or with what probability each value occurs in particular cases.” [1]

Schrödinger’s ideas from 1935 could be considered outdated unless Anton Zeilinger who shared a Nobel prize in physics for the experimental validation of quantum entanglement in 2022 wouldn’t write in 2017, “A most modern position which leads directly to today’s applications of entanglement is Schrödinger’s analysis of entanglement in terms of ‘expectation catalogues’ [2].

The idea of using catalogues of expectations to perform quantum computations is supported by the fact that such foundational principles of quantum mechanics as Heisenberg’s indeterminacy, Dirac’s superposition of states and Schrödinger’s entanglement “were discovered only indirectly, as consequences of a previously established mathematical scheme, instead of being built up directly from experimental facts” as Paul Dirac who in 1933 shared with Schrödinger a Nobel prize for the creation of quantum mechanics put it. [3]

A simple experiment can be set up to validate if the application of catalogues of expectations can, for instance, predict the exact result of a single observation that is now considered as absolutely unpredictable.

For such an experiment we need a wave function that embodies a very simple catalogue of expectations of only two observable values of only one parameter, for example the wave function of a spin of an electron.

We will follow Schrödinger’s simple logic, “When the ψ-function is known, and a measurement is made, yielding a certain outcome, then the new ψ-function is again known; that is all.” [1] Then, as we already have all possible certain outcomes in the catalogue, we can expand the number of new wave functions to all possible measurement outcomes in line with the “many worlds” idea of Hugh Everett. [4]

Please, note that we are using catalogues of expectations without performing any ‘actual’ measurements. Therefore, many wave functions represent many not ‘actual’ but hypothetical worlds. For each of such a hypothetical world, however, its own probability distribution can be obtained by raising its wave function to the absolute square.

Individual probability distributions of all worlds can be then ranked by the level of variational free energy proposed as the measure of surprise by the most influential neuroscientist in the world Karl Friston. [5]

The most surprising, hence interesting, world should be the one that will be ‘chosen’ in the actual observation following the hypothesis of Freeman Dyson, the creator of the mathematical formalism of quantum electrodynamics. “Somehow the universe has a tendency to be as interesting as possible. As time goes on it becomes more and more diverse, more and more interesting”, he said. [6]

After making a prediction using the wave function of an actual electron as a catalogue of expectations we will perform an actual measure of spin on the electron to check if the prediction holds.

This is a basic scheme to test also the very bold, speculative and provocative hypothesis of the universal consciousness (the ultimate observer) as according to Dyson, “To be as interesting as possible the universe must be conscious of itself” [6]

Einstein’s claim that “God doesn’t throw dice” can be also proven this way.

References:

1. Schrödinger, Erwin. The Present Status of Quantum Mechanics. Die Naturwissenschaften 1935. Volume 23, Issue 48.
2. Zeilinger, Anton, Light for the quantum. Entangled photons and their applications: a very personal perspective. Published 15 June 2017 • © 2017 The Royal Swedish Academy of Sciences
3. Dirac, P. A. M. “Bakerian Lecture. The Physical Interpretation of Quantum Mechanics.” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, vol. 180, no. 980, 1942, pp. 1–40.
4. Everett, Hugh, The Theory Of The Universal Wave Function, The Many-Worlds Interpretation of Quantum Mechanics, Princeton University Press Princeton, New Jersey, 1973
5. Parr, Thomas, Pezzulo, Giovanni, Friston, Karl J. Active Inference: The Free Energy Principle in Mind, Brain, and Behavior. https://doi.org/10.7551/mitpress/12441.001.0001. ISBN (electronic): 9780262369978. The MIT Press. 2022
6. Dyson, Freeman. Interview with Rigas Laiks. Spring 2016