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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)

#51

Post by eigenket »

prof-dr-ir wrote: post #50
eigenket wrote: post #49

Earlier quoted context omitted.

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 b…

> One typically uses the Schrodinger equation to do so

In my opinion knowing how to use the Schrodinger equation to get the "spectrum of the hydrogen atom" is essentially a matter of historical interest but really not relevant to understanding things. Its quite cool you can do these tricks to derive a nice analytical form for the spectrum, but this approach emphatically does not generalise to more complicated systems (any non-trivial molecule) and even for the hydrogen atom the spectrum you get will be wrong anyway because of relativistic corrections and QFT-corrections.

> 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.

I'm not sure what you're arguing is missing here? Once you've derived Robertson-Schrödinger you've just got a commutator there, for whatever observables you want to apply it to you just plug in the value.

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

I'm not talking about teaching here but thinking. You are probably right that most physics undergrads would not cope well with learning about POVMs. On the other hand I am tempted to argue for not teaching about the position operator and position in Schrödinger-style QM at all, or at least leaving it until quite late on. The way people teach QM has this weird thing where its pretty obviously wrong, because every physics undergrad knows we have special relativity, so there should be some nice symmetry between space and time which is completely missing in the Schrödinger equation. Time in the Schrödinger equation is a coordinate, and space (position) is a self-adjoint operator, which is just manifestly weird. Once you get to quantum field theory this gets fixed and position isn't an operator/observable anymore, it gets demoted back to a coordinate exactly the same as time.

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

#52

Post by lisper »

eigenket wrote: post #51
prof-dr-ir wrote: post #50

Earlier quoted context omitted.

> 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 b…

> One typically uses the Schrodinger equation to do so In my opinion knowing how to use the Schrodinger equation to get the "spectrum of the hydrogen atom" is essentially a matter of historical interest but really not relevant to understanding things. Its quite cool you can do these tricks to derive a nice analytical form for the spectrum, but this approach emphatically does not generalise to more complicated systems…

I just wanted to chime back in here and say that I am finding this discussion absolutely fascinating and enlightening. This is HN at its best. Thank you.

FWIW, as someone who is interested in science pedagogy, and specifically as someone who actively engages with anti-science propaganda like young-earth creationism, I want to contribute this:

> In my opinion knowing how to use the Schrodinger equation to get the "spectrum of the hydrogen atom" is essentially a matter of historical interest but really not relevant to understanding things.

IMHO this is more than historical interest. It's a dramatic illustration of how science actually works, and specifically, that it does not rely on any appeal to authority, despite the superficial appearance of occasionally hearing people say things like, "Einstein teaches us that X" with the implication that X is therefore unquestionable gospel because Einstein said it. Here is an example of a calculation that anyone can do (with enough effort) and compare to the results of experiments that they can likewise do themselves (with enough effort). Of course, most people won't bother to put in this effort, but just knowing that they could if they wanted to is very powerful because it provides an actual reason why other people's results are generally trustworthy: even if you don't do the experiment, someone else might, and if the result turns out to be wrong then it will eventually be called out.

Also...

> this approach emphatically does not generalise to more complicated systems

This is spot on. Speaking from first-hand experience of my own intellectual journey into QM, focusing on single-particle systems and slogans like "any attempt to measure the position of the particle destroys the interference in the two-slit experiment" is extremely misleading. It leads to conceptual dead-ends that make it much harder to wrap your brain around entanglement than it should be. IMHO, QM pedagogy should start with entanglement and decoherence. In this respect, I think Aaronson gets it right.

But mainly I just wanted to thank you both for the privilege of being a fly on the wall while you discuss these things. It has generated a long reading list for me.

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

#53

Post by [deleted] »

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…

[deleted]

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

#54

Post by abdullahkhalids »

eigenket wrote: post #51
prof-dr-ir wrote: post #50

Earlier quoted context omitted.

> 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 b…

> One typically uses the Schrodinger equation to do so In my opinion knowing how to use the Schrodinger equation to get the "spectrum of the hydrogen atom" is essentially a matter of historical interest but really not relevant to understanding things. Its quite cool you can do these tricks to derive a nice analytical form for the spectrum, but this approach emphatically does not generalise to more complicated systems…

I will chime in to say that I have several times taught a course on Quantum Computing using an Scott Aaronson type approach and a course on Quantum Mechanics in the traditional way. With some overlap of students.

The gap in understanding between the students in the two courses is humongous. Both sets of students would need to essentially sit through half a semester of the classes of the other course to understand what they are saying.

The QC students don't know Schrodinger's equation at all, let alone how to solve it for the quantum harmonic oscillator or for the hydrogen atom (without which I agree you don't know QM). And the QM students know what Hamiltonian dynamics look like, but little about unitary dynamics.

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

#55

Post by abdullahkhalids »

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.

That's only kind of true. Standard continuous-variable quantum mechanics has all sorts of consistency problems, and the only way to get reasonable predictions out is to paper over infinities and pretend they don't exist.

I know there are what are called C*-algebras, which help solve some of these issues, but I don't know anything about them. I do know that the Hilbert Space approach is not sufficient.

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

#56

Post by vingt_regards »

danbruc wrote: post #28

I 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 distribu…

> 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.

A Gaussian distribution, I think. But they're certaintly not the same function, and it should be immediately obvious to a math grad with experience in physics. The sinc function, for one, has secondary maxima (its plot in the article is very convenienty cropped to allow pretending those don't exist). Just put a hair in the path of a laser beam and you will see the local maxima in light intensity! Their "single-slit" string procedure, on the other hand, can only generate a single central peak. This really makes no sense at all.

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

#57

Post by Ste_Tokyo »

emblaegh wrote: post #10
Ste_Tokyo wrote: post #3

[flagged]

I can imagine you snubbing Hamilton by going all "can the least action principle explain a single phenomenon not already explained by the forces + newton's laws? Thought not. Crank". I have no idea what worfram's model is about, and I agree that the language he uses to publicise it is kinda twatty. However your insane criterion for what constitutes a theory/formalism worth exploring is clearly guided by your bias aga…

Does the "Wolfram Model" allow easier analysis of certain physical situations like the Hamiltonian does? Thought not. So what's your point?

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

#58

Post by Ste_Tokyo »

evanb wrote: post #6
Ste_Tokyo wrote: post #3

[flagged]

That's not the kind of model it is. The standard model is one example of a quantum field theory. You should think of Wolfram's idea as a different formalism (ie. not QFT), not a different example. It so happens that Wolfram's multiway model (allegedly, I can't evaluate it fairly for myself) also contains GR as a low-energy limit. It's like inventing a new operating system (we currently have 3ish, Newtonian, Quantum,…

Of course it contains GR as a low-energy limit. Where it can be physically checked, it is equivalent to the existing successful theory; where it makes new predictions, it can't be checked and so is almost certainly wrong. To make progress in physics you need to apply yourself to a real open problem (like "Dark Matter") or get new data (from quantum computers or primordial gravitational waves, maybe). The only good thing that can be said about Wolfram is that he is not paid with my taxes, because plenty of cranks in physics are.
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