On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)

For example, Werner Heisenberg's doctoral thesis[1] arose from a contract of his doctor father Arnold Sommerfeld from a company that dealt with the channelling of the Isar river through the city of Munich. Very practical problems involving differential equations - kind of the bread and butter of physicists and engineers at the time.

What if quantum mechanics was found today in a world where the bread and butter has shifted to computer science, linear algebra and discrete math? Would we still end up with waves and differential equations, or would another formulation arise more naturally?

EDIT: I think a beautiful (but imperfect) example to illustrate this dichotomy in the ways of thinking is how the Bell inequality can be approached with photons and polarization or as a game. Thinking about Alice and Bob or polarized light, which would you prefer?

[1] https://ntrs.nasa.gov/citations/19930093939

There was considerable disagreement between the factions of physicists who favoured the different versions which essentially ended when after some considerable theoretical effort (mostly by Dirac) it was shown that the two pictures are exactly equivalent.

Physicists still use whichever formulation is most suitable for whatever problem they're trying to solve, for example if you're analysing the something where you care about a bunch of bound states like the simple harmonic oscillator or the hydrogen atom then the matrix picture tends to be easier to work with.

You are right that wave mechanics was more popular than matrix mechanics because physicists were already very familiar with wave methods.

> Regarding the similarity to a double slit interference pattern, what I found in my investigation (see my previous comment) is it was solely the result of the sorting algorithm used for the X coordinates of each possible outcome/weight. Ordering by the average X location results in a binomial distribution, but there are still ties to deal with. Applying secondary sorting to those based on the position of the left or rightmost X creates secondary binomial distributions within the main binomial distribution, similar to what Jonathan showed, except without all the spikiness because his example wasn’t consistently sorted in this manner.

> You can see the sorting I’m talking about by looking at the sorting of Xs in the output of weights in Jonathan’s double-slit examples. The bottom half is sorted as I stated, but the top half is somewhat out of order, corresponding to the spikes in the tallest curve in the center of the graphs.

> Maxime C, I had the same question as you – Why choose this sorting method for encoding the photon positions? My conclusion is that it doesn’t work however. Each additional step run with a large string produces an additional secondary binomial distribution. To get a smooth curve, we’d need to run billions of steps on a large string, but then we we’d also see billions of peaks, which no longer compares well with the expected diffraction pattern.