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On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
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Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#22Earlier quoted context omitted.
It was formulated at least twice in different versions. First by Heisenberg with his matrix mechanics and shortly afterwards by Schrödinger in terms of wave-functions. 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 equivale…
I wonder if there is a wave formulation for LLM's and transformers in general?
You can probably write down a differential equation which models them but I doubt such a thing would be particularly interesting.
Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#23Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#24I 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. 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 Mu…
Scott Aaronson has an insightful essay on this in chapter 9 of his excellent book, "Quantum Computing Since Democritus". The TL;DR is that quantum mechanics can be derived as a generalization of probability theory using the 2-norm instead of the 1-norm. In Aaronson's words: "Quantum mechanics is what you would inevitably come up with if you started with probability theory, and then said, let's try to generalize it so…
I was thinking about Aaronson when I added the CHSH game to the comment, because one of his essays (which I unfortunately could not find anymore) made that click for me.
Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#25I 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. 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 Mu…
Scott Aaronson has an insightful essay on this in chapter 9 of his excellent book, "Quantum Computing Since Democritus". The TL;DR is that quantum mechanics can be derived as a generalization of probability theory using the 2-norm instead of the 1-norm. In Aaronson's words: "Quantum mechanics is what you would inevitably come up with if you started with probability theory, and then said, let's try to generalize it so…
This page has lecture notes by Aaronson on exactly that topic
Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#26Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#27I 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. 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 Mu…
Scott Aaronson has an insightful essay on this in chapter 9 of his excellent book, "Quantum Computing Since Democritus". The TL;DR is that quantum mechanics can be derived as a generalization of probability theory using the 2-norm instead of the 1-norm. In Aaronson's words: "Quantum mechanics is what you would inevitably come up with if you started with probability theory, and then said, let's try to generalize it so…
To counter your enthusiasm I must say that I rather disliked his reasoning. My problem is essentially that what Aaronson's calls "the theory" is a somewhat bastardized version of quantum mechanics that might suffice for quantum computing but, in my opinion, not for physics.
I discussed the difference earlier: https://news.ycombinator.com/item?id=38255476
Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#28I just skimmed the article for sanity checking and it looks more like crackpottery than science to me.
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.
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.
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.
Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#29I 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. 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 Mu…
I would like to stress what is also mentioned in a sibling comment: quantum mechanics' original formulation was not in terms of a wave function and differential equations.
Heisenberg's matrix mechanics was the first, and formulated entirely in terms of linear algebra. See for example the introduction of basic linear algebra techniques in the famous Bohr-Jordan paper from 1925:
Re: On the Double-Slit Experiment and Quantum Interference in the Wolfram Model (2020)
#30Earlier quoted context omitted.
It was formulated at least twice in different versions. First by Heisenberg with his matrix mechanics and shortly afterwards by Schrödinger in terms of wave-functions. 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 equivale…
I wonder if there is a wave formulation for LLM's and transformers in general?
I don't know if this is exactly what you are thinking about, but there are some physicists working to understand what happens in transformers: https://proceedings.neurips.cc/paper_files/paper/2023/file/b...