This comment by Matt Kelly seems to be the most pertinent<p>> 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.<p>> 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.<p>> 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.
This is from four years ago, and there are some comments on the article by Matt Kelly that show that the "interference pattern" is just an artefact. The author did not respond despite several requests to do so.
I often wonder how much the fact that quantum mechanics' original formulation was in terms of a wave function and differential equations has to do with the ubiquity and importance of these topics at that particular era.<p>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.<p>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?<p>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?<p>[1] <a href="https://ntrs.nasa.gov/citations/19930093939" rel="nofollow">https://ntrs.nasa.gov/citations/19930093939</a>
On yesterday’s live stream[0] on Stephen Wolfram’s Twitch the team went through several improvement proposals to functions in WolframAlpha, including QuantumCircuitOperator which is a variant of a String Diagram.<p>Before this I didn’t know Stephen hosted “Live CEOing” sessions and now I wish this was the norm!<p>0: <a href="https://www.twitch.tv/videos/2083073452" rel="nofollow">https://www.twitch.tv/videos/2083073452</a> (timestamp around 50:00)
Mindscape episode with Stephen Wolfram from 2021 which might also be of interest. I enjoyed it even if most of it was way over my head. It is probably overly-ambitious and probably a dead end but it's an worthy attempt (if you have the money) and he's definitely not a crank. Eccentric maybe though.<p><a href="https://www.preposterousuniverse.com/podcast/2021/07/12/155-stephen-wolfram-on-computation-hypergraphs-and-fundamental-physics/" rel="nofollow">https://www.preposterousuniverse.com/podcast/2021/07/12/155-...</a>
I just skimmed the article for sanity checking and it looks more like crackpottery than science to me.<p>Looking at the numbers on the graphs for single-slit diffraction, they are just binomial coefficient, at least mostly, not sure why there are pieces missing in the last rows. That is also what you expect when you repeatedly make binary decisions to go left or right. The article does not mention the binomial distributions once, it only appears in a comment.<p>And then they claim that it converge to the actual single-slit diffraction distribution, something with a Chebyshev polynomial and the sinc function, according to the article. Seemingly without justification besides looking at graphs and noting that they are both bell shaped. As said, not sure what is going on in the last rows of the graphs, but I would almost bet that the two functions are not the same, even in the limit as it becomes a Poisson distribution plus whatever the last rows do.<p>Why do they not just proof that the two are the same? The entire article seems to be about getting numbers out of their multiway system and then concluding that - if you squint hard enough - they look somewhat like diffraction patterns.