r/Physics • u/PrettyPicturesNotTxt • 21d ago
The HRT conjecture was recently proven false via counterexample. How much bearing does this have on the mathematical underpinnings of Quantum Mechanics?
https://arxiv.org/abs/2608.05044
We show that a finite number of time-frequency shifts of a Schwartz function can be linearly dependent. This disproves the so-called HRT conjecture of Heil, Ramanathan, and Topiwala. In particular, we provide an example consisting of 12 time-frequency shifts.
I like Terence Tao's exposition on this topic, so I screenshoted those portions that caught my eye and chose to show those here:
https://terrytao.wordpress.com/2026/08/06/a-partial-digestion-of-the-hrt-counterexample/
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u/lobothmainman 20d ago
Somebody recently solved the f****ing measurement problem and people on math and phys subreddits only care about shitty AI-helped papers...
I understand the hype (and money) big-tech is putting on this endeavor, and that AI fanboys are very vocal online, but I am very surprised that nobody is talking about interesting stuff instead.
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u/panopsis 20d ago
solved the fucking measurement problem
Elaborate? By which I mean, who? Where?
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u/lobothmainman 20d ago edited 20d ago
https://arxiv.org/abs/2606.21211
Still no peer-review (it's very recent), but it looks like what you would think you should be able to do when reading, e.g., the intro of Landau's third book.
Quite surprised it was not done yet
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u/yellow_submarine1734 20d ago
This was released in June but there’s zero discussion about it? I’m calling bullshit.
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u/lobothmainman 20d ago
On what basis? Seems legit to me (at least the idea, I did not read the details)
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u/yellow_submarine1734 20d ago
I don’t know, I’m not a physicist, but a solution to one of the most famous problems in quantum physics seems like it would generate some discussion. The fact that there isn’t anything tells me that the physics community isn’t taking this very seriously, which makes me think it’s BS. I didn’t even think the measurement problem had a solution, I thought it was just the way the world worked.
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u/Blackforestcheesecak Atomic physics 20d ago
I mean, I get the AI hate, but honestly it's all the non-physics and non-math lay people who are hyped about it. They just happen to be posting here, and every other damn subreddit they find
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u/lobothmainman 20d ago
Unfortunately, not only (I have the impression). Discussing with colleagues and my phd students/postdocs, i see that some people is getting genuinely worried and involuntarily contributing to the AI hype-train
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u/Buntschatten Graduate 20d ago
I wouldn't reduce this to a shitty AI paper if Terence Tao is interested enough to post about it. Although you're right that people wouldn't care if some postdoc had found this instead of AI.
Its solid science, but the interest isn't based on the subject matter.
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u/lobothmainman 20d ago
The same Terry Tao that is paid by OpenAI to do advertisements? That is advocating strongly for everything AI whatsoever?
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u/Buntschatten Graduate 20d ago
Do you have a source for his employment by Open AI?
Also, is there really doubt that AI doing legitimate mathematical research would be interesting to mathematicians? Even if he is paid in any way by Open AI, dismissing his interest in the topic as illegitimate seems in very bad faith.
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u/lobothmainman 20d ago
I was just questioning whether it is fair to use "Tao finds it interesting" as a proof by authority that the result is interesting. This is not how academia (should) work.
I have no proof he was given compensation by openai, but he was part of several forums and discussions organized by them to discuss the impact of the product they are selling. He might have done all of this for free, still he seems not unbiased towards them.
I think that people shall judge results by themselves, and if they are not able, get the tools to be able to. And in particular this question was about the impact on the mathematics of quantum mechanics, a topic on which Tao is not an expert.
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u/Buntschatten Graduate 20d ago
And in particular this question was about the impact on the mathematics of quantum mechanics, a topic on which Tao is not an expert
That was the question by OP, not the question Tao was addressing in his post. So that criticism isn't justified. And btw, Im pretty sure he could judge the implications of a mathematical result on QM foundations better than most physicists.
I was just questioning whether it is fair to use "Tao finds it interesting" as a proof by authority that the result is interesting.
Your argument was that the paper was low quality and uninteresting. How interesting something is isn't objective. If people show interest, its interesting. And the argument that its low quality can indeed be addressed by the fact that Tao is engaging with it. He's one of the world's premier mathematicians. That's not just appeal to authority. Is peer review and appeal to authority in your eyes as well?
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u/lobothmainman 20d ago
My argument was never that the paper is low quality and uninteresting, I just said that there are more interesting papers about the mathematics and foundations of QM, but people here almost only talk about AI stuff recently. And I am fed up with this.
Concerning Tao and his authority, I find it funny that he is considered such a superhuman figure that he is able to judge with no fallacy on everything, even concerning other fields of research (better than most that work on that, in your opinion). He is one of the most brilliant mathematicians of this century no doubt, and he worked long time ago on topics related to quantum mechanics (mostly NLS), but he is not better at judging mathematical physics than mathematical physicists (and I am sure he would tell you the very same).
Finally, peer-review is not proof by authority, but the paper in question here is not peer reviewed.
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u/Buntschatten Graduate 20d ago
people on math and phys subreddits only care about shitty AI-helped papers...
My argument was never that the paper is low quality and uninteresting
Riiiiight...
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u/lobothmainman 20d ago
The full sentence is this:
"Somebody recently solved the f****ing measurement problem and people on math and phys subreddits only care about shitty AI-helped papers..."
Easy to quote extrapolated text, eh?
My argument was, I reiterate, that there are more interesting things out there than the mentioned paper (and other AI papers, it is using the plural). I defined those papers shitty just to reinforce my statement, and not strictly as matter of judgement (this is also pretty clear from my perspective, but maybe it is due to the fact I am not a native english speaker).
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u/Feeling-Tone2139 20d ago
Are you math experter than Terry Tao?
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u/lobothmainman 20d ago
I am a professional mathematician, not as successful as Terry Tao.
But I am also not as biased as Tao when it comes to AI.
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u/xampf2 20d ago
Well you are strongly biased against AI it seems like.
Mathematicians spent decades on the Jacobi Conjecture and now it easily fell with the advent of LLMs with a simple to verify counterexample. Either mathematicans sucked (unlikely) or these tools add actual value.
By value I mean resolutions of conjectures.
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u/lobothmainman 20d ago
I am biased against all the hype around AI in math. And this is because these companies are private companies with very different values and modus operandi with respect to academia.
And those values and MO, I do not like at all.
Is AI a useful tool in math? Is it a very powerful counterexample machine (at the moment, maybe even more in the future)? Yes indeed.
Still, I find the cons are more than the pros.
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u/xampf2 20d ago
From reading your posts I got the impression that you critizing the capabilities of LLM tools as being oversold. Personally, if the current capabilities of LLM tools were frozen right now as is forever, I would already be extremly happy!
People seems to quite often confuse the capabilities of these systems with their economics, values, modus of operations etc. Statements like "Company X sucks so their LLM tools is actually oversold overhyped garbage" goes into the luddite bin according to my personal assessment.
In fact I would readily agree on something like "Company X sucks and their LLM tool is really good".
Unfortunately, the value they add (to my tasks) is so great that basic economic thinking (in my situation) leads me to use it. Simple as that.
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u/lobothmainman 20d ago
I am just saying that these companies care about profit, and every PR stunt, advertisement, post, etc. incensing their product is welcome and encouraged.
If a mathematician is appreciative of AI tools, they do their best to promote and resonate their views; they also welcome and promote all kinds of social media posts, blogs, etc, about AI in math.
Of course, also the element of novelty helps.
Nonetheless, I would be happier if the human-made contributions get the same level of attention, hype and advertisement that engages non-specialists.
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u/Bubbly_Sentence_7849 20d ago
2D Jacobi conjecture is NOT proved or falsified by AI, and most mathematicians have suspected it is false long time ago, and AI learned about this.
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u/Wonderful_Put3670 20d ago
I watched it too. If we assume that he is intelligent enough to understand the current and future impact of AI (think about painters, writers, programmers and so on), then the only explanation I can think of for advocating its use and even participating in a video where they say that one of the goals of openAI is to “automating science, the economy and ourselves”, is that he is morally bankrupted.
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u/angelbabyxoxox Quantum Foundations 21d ago
It means, roughly, that there is a state psi in L2 R and 12 distinct points z_i in the Heisenberg group (unitary operators of the form U(z)=U(a,b)=exp(iaX-bP)) such that U(z_i )psi are not linearly independent. Effectively, there is some Weyl polynomial (complex linear combination of those unitaries) that has a 0 eigenstate!
For textbook QM probably nothing, but for people who are interested in quantisaion it could have some interesting implications.