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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)

#41

Post by rfonseca »

ImHereToVote wrote: post #20
eigenket wrote: post #15

Earlier 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?

This paper [1] models some simple (r) NN as ODEs, and uses ODE tools to train and for inference. It’s a start.

[1] https://arxiv.org/abs/1806.07366

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

#42

Post by jereees »

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.

Before this I didn’t know Stephen hosted “Live CEOing” sessions and now I wish this was the norm!

0: https://www.twitch.tv/videos/2083073452 (timestamp around 50:00)

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

#43

Post by ImHereToVote »

api wrote: post #40
mikk14 wrote: post #30

Earlier quoted context omitted.

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...

Is it really true that we don't really understand why transformers work so well? I mean we obviously understand how they work at a pure mechanical level, and we have this analogy with lookup (keys, queries, values) and "attention," but do we really get it ? Can someone explain to me why that design works so much better than lots of other things like RNNs? Or did we just tinker a lot (a method known as "graduate stude…

We really don't have a mathematical theory for large complexity. We are kinda in alchemy stage for this "science".

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

#44

Post by monktastic1 »

weinzierl wrote: post #11

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. 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…

In case it's not obvious from what others have said, doing QM on observables with discrete spectra looks very different from that on continuous spectra. Different mathematical tools are helpful in each case.

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

#45

Post by ernesto95 »

nabla9 wrote: post #31
prof-dr-ir wrote: post #27

Earlier quoted context omitted.

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

To counter your unenthusiasm, think about it from a mathematician's perspective. Mathematics of QM does not live in some separate corner created to do physics. The need for QM created short-lived confusion, now it's all embedded into a much larger coherent mathematical structure. For a pure mathematician, quantum mechanics is a lovely introduction to Hilbert Spaces.

True, but from a mathematician's point of view, the theory quickly becomes complicated (and in some sense limited) if you really want to do things rigorously when working with continuous systems, something that does not happen with finite dimensional systems as the parent comment probably alludes to.

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

#46

Post by prof-dr-ir »

eigenket wrote: post #32
prof-dr-ir wrote: post #27

Earlier quoted context omitted.

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

I think this is a very common view, and a somewhat mistaken one. Quantum mechanics is used in very different ways by people in quantum information, condensed matter, many body physics, quantum field theory, nuclear physics and may other (sub)fields. Of course it will be difficult for a quantum information theorist if they try to apply what they know directly to a hydrogen atom, but (speaking from experience) it will…

With conceptually straightforward I meant that the concepts are easy to pick up.

For example, the paper you cite is entirely understandable for anyone with some training in hermitian QM. In contrast, good luck trying to understand elementary concepts like the spectrum of the hydrogen atom or interference of matter waves from unitary QM.

Of course the field of quantum info has progressed enormously and has its own interesting challenges, for which hermitian QM is all but useless.

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

#47

Post by eigenket »

prof-dr-ir wrote: post #46
eigenket wrote: post #32

Earlier quoted context omitted.

I think this is a very common view, and a somewhat mistaken one. Quantum mechanics is used in very different ways by people in quantum information, condensed matter, many body physics, quantum field theory, nuclear physics and may other (sub)fields. Of course it will be difficult for a quantum information theorist if they try to apply what they know directly to a hydrogen atom, but (speaking from experience) it will…

With conceptually straightforward I meant that the concepts are easy to pick up. For example, the paper you cite is entirely understandable for anyone with some training in hermitian QM. In contrast, good luck trying to understand elementary concepts like the spectrum of the hydrogen atom or interference of matter waves from unitary QM. Of course the field of quantum info has progressed enormously and has its own int…

I think maybe we have some difference in how we're talking about things.

Concepts like the spectrum of the hydrogen atom or interference phenomena aren't particularly difficult to understand conceptually: the Hamiltonian has some eigenvectors and eigenvalues, you use the Dirac equation and work them out. The "matter waves" interfere essentially in the same way that waves on the surface of a pond do.

The things that you're calling conceptual understanding I guess must be different to this: maybe something like detailed calculations of the structure of the spectrum?

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

#48

Post by prof-dr-ir »

eigenket wrote: post #47
prof-dr-ir wrote: post #46

Earlier quoted context omitted.

With conceptually straightforward I meant that the concepts are easy to pick up. For example, the paper you cite is entirely understandable for anyone with some training in hermitian QM. In contrast, good luck trying to understand elementary concepts like the spectrum of the hydrogen atom or interference of matter waves from unitary QM. Of course the field of quantum info has progressed enormously and has its own int…

I think maybe we have some difference in how we're talking about things. Concepts like the spectrum of the hydrogen atom or interference phenomena aren't particularly difficult to understand conceptually: the Hamiltonian has some eigenvectors and eigenvalues, you use the Dirac equation and work them out. The "matter waves" interfere essentially in the same way that waves on the surface of a pond do. The things that y…

In my definition, someone cannot claim to know QM if they do not know (a) Heisenberg's uncertainty principle, (b) how to compute interference patterns or (c) how to compute the spectrum of hydrogen.

Aaronson claims that QM "can be derived" (quote from the original comment) are followed by an introduction to some aspects of QM that leads to strictly none of these things. That is why I am unhappy with it, and I still do not see why I am "somewhat mistaken" (quote from you).

In fact, I can go even further and say that (from a quick glance at least) in his whole book positions and momenta make no appearance, let alone the correspondence principle. (I do not even see hermitian operators!) Without them I just do not see any reasonable "derivation" of (or, more properly, argumentation for) what I call QM.

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

#49

Post by eigenket »

prof-dr-ir wrote: post #48
eigenket wrote: post #47

Earlier quoted context omitted.

I think maybe we have some difference in how we're talking about things. Concepts like the spectrum of the hydrogen atom or interference phenomena aren't particularly difficult to understand conceptually: the Hamiltonian has some eigenvectors and eigenvalues, you use the Dirac equation and work them out. The "matter waves" interfere essentially in the same way that waves on the surface of a pond do. The things that y…

In my definition, someone cannot claim to know QM if they do not know (a) Heisenberg's uncertainty principle, (b) how to compute interference patterns or (c) how to compute the spectrum of hydrogen. Aaronson claims that QM "can be derived" (quote from the original comment) are followed by an introduction to some aspects of QM that leads to strictly none of these things. That is why I am unhappy with it, and I still d…

Ah, I see. You've changed from talking about concepts and conceptual understanding to talking about computations.

I completely agree with you that from the perspective of a quantum information theorist computing the spectrum of the hydrogen atom is a rather complicated thing. I disagree wholeheartedly that this is part of the essence of quantum mechanics.

The hydrogen atom is one system, understanding conceptually that its behavior is governed by a self-adjoint operator and its spectrum is very relevant to the whole of quantum physics. Understanding exactly the details of the calculation I think are not. Especially because if you do the calculation within quantum mechanics without quantum field theory you will obtain a somewhat incorrect result anyway (you will miss interesting phenomena like Lamb shift).

Similarly interference is an interesting phenomenon that one needs to understand to understand quantum mechanics, but understanding the specific calculation of how interference makes nice patterns in some example setup isn't particularly enlightening.

I agree that the Heisenberg uncertainty principle is important, but it certainly be derived from Aaronson's point of view (e.g. the standard Robertson-Schrödinger inequality is easily obtained).

As an aside, I also think that self-adjoint operators and the correspondence principle are a fairly terrible way to think about observables in quantum mechanics. An obvious fact is that every measurement of (for example) the position of a particle has some unavoidable experimental error (our apparatus only has finite resolution) so the thing we actually measure in reality is some fuzzy observable which can not be represented as a self-adjoint operator. A POVM is a much more natural candidate (as a physicist it is natural to assume that the thing you get by adding some classical noise to your measurement is still a measurement).

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

#50

Post by prof-dr-ir »

eigenket wrote: post #49
prof-dr-ir wrote: post #48

Earlier quoted context omitted.

In my definition, someone cannot claim to know QM if they do not know (a) Heisenberg's uncertainty principle, (b) how to compute interference patterns or (c) how to compute the spectrum of hydrogen. Aaronson claims that QM "can be derived" (quote from the original comment) are followed by an introduction to some aspects of QM that leads to strictly none of these things. That is why I am unhappy with it, and I still d…

Ah, I see. You've changed from talking about concepts and conceptual understanding to talking about computations. I completely agree with you that from the perspective of a quantum information theorist computing the spectrum of the hydrogen atom is a rather complicated thing. I disagree wholeheartedly that this is part of the essence of quantum mechanics. The hydrogen atom is one system, understanding conceptually th…

> Ah, I see. You've changed from talking about concepts and conceptual understanding to talking about computations.

No, or at least I did not mean to: I said "know how to compute", not "compute". One typically uses the Schrodinger equation to do so (although Pauli did not need it), but this starting point is nowhere to be found here.

> I agree that the Heisenberg uncertainty principle is important, but it certainly be derived from Aaronson's point of view (e.g. the standard Robertson-Schrödinger inequality is easily obtained).

Robertson-Schrödinger is fairly trivial, at least in Aaronson's finite-dimensional world. But you conveniently forgot how to "derive" the part of QM that actually gives you the value of the commutator sitting on the right-hand side. So will you just postulate it? That sounds pretty terrible pedagogically, and it might be better to provide at least some general discussion. And that discussion is exactly what I am advocating as a necessary ingredient in any self-respecting introduction to (let alone derivation of) QM.

> I also think that self-adjoint operators and the correspondence principle are a fairly terrible way to think about observables in quantum mechanics.

No teacher of QM should introduce POVMs before talking about positions and momenta.

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