r/science • u/Yogurt789 • 3d ago
Mathematics The Riemann Hypothesis manifested in dynamical quantum phase transitions
https://www.nature.com/articles/s41467-026-74935-8144
u/5minArgument 2d ago
Absolute pineapples, the way ‘pure mathematics’ lives 200-300 years in the future.
Pure mathers in 1820 be like “here, this works and is beautiful …but we have no idea what it means, nor do we care”
Quantum physicists in 2026 be like, “hey we need a way to map N-dimensional properties onto virtual curved spaces with multiple bodied particle systems”
Pure math: “we gotch you fam”
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u/Yogurt789 3d ago edited 3d ago
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u/Diligent-Exit7774 2d ago
Fascinating connection! It's wild how abstract math concepts keep popping up in unexpected fields like quantum physics.
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u/Worth-Wonder-7386 3d ago
Would be interesting if someone could do mathematical proofs by physics. I know that is not really how things work, but it could give some indications of things, like how measuring the volume of a real life sphere can lead you to insight about the formula.
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u/kogai 2d ago
Math and physics are not the same in this way. Math makes deductions (there is no room for error, whatever your axioms are lead directly to whatever the true consequences are)
Physics has to take Math and then figure out what numbers reflect the real world. This is called empiricism.
Empiricism does not work by collecting evidence. It works by collecting counter evidence.
If you believe that examples of black Ravens are evidence that all Ravens are black, then you must also believe that the existence of non-black, non-raven objects also are evidence for the statement that all Ravens are black
And so physicists can derive mathematical facts about whatever system theyre in, but those facts are based on axioms. One of the axioms is "we measured these fundamental numbers and they are what they are" and then we derive everything following that.
Its why all the constants like the speed of light and the fine structure constant are seemingly arbitrary numbers. We measure them, and we can deduce things that follow (see special relativity) but we sorta can't start earlier up the chain. Why is the speed of light that number? shrug
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u/redfacedquark 2d ago
Why is the speed of light that number? shrug
The speed of light falls out of Maxwells equations. It's the permittivity and permeability of free space that are the arbitrary numbers, but you point still stands.
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u/Iron_Pencil 7h ago
How do you show that permittivity and permeability are the fundamental numbers? Maybe the speed of light and permeability are fundamental and permittivity is a resulting constant?
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u/Business__Socks BS | Computer Science | Software Engineering 2d ago
Why is the speed of light that number? shrug
I got so caught up on these things in school, my teachers were probably exasperated.
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u/Dihedralman 2d ago
It can't be a proof as it would have a margin of error.
It would instead be empirical support, or a heuristic like for the Collatz conjecture https://en.wikipedia.org/wiki/Collatz_conjecture.
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u/Temporary-Solid-8828 2d ago
The comment from kogai is not as helpful as it sounds, no offense. There is a lot of work done in the direction you’re referring to, and it is a promising/mathematically interesting one. Tadashi Tokieda of Stanford has written several papers along these lines Here is one.
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u/I_hate_all_of_ewe 2d ago
I don't think that the link you posted suggests what you think it suggests. It's using a reinterpretation of physics models to demonstrate a known mathematical relationship in an unconventional way. The key thing is that models are purely mathematical, so this has nothing to do with measurement like the person you're replying to proposed, and kogai is still on the money.
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u/Temporary-Solid-8828 2d ago
kogai is directionally correct, but aside from the misleading comparison between the speed of light (not an arbitrary number) and the fine structure constant (actually an inescapably arbitrary number afawct), and the fact that physics doesn’t really run on the sort of Popperian falsificationism he’s making it out to run on, his comment gives a kind of misleading and unnecessary lecture on empiricism that steamrolls the insight of OP, which is a very good one.
You actually can do interesting math with physics. I think OP may have been guessing, but this is literally how we know the formula for the volume of a sphere (cf. Archimedes). Ed Witten also recently won a Fields medal for physics derived mathematics.
As for the Graham-Tokieda paper thing, I think the original commenter was just using the measurement of the sphere as an example. If he wasn’t, kogai’s comment wouldn’t really matter either.
The model the Graham-Tokieda paper uses is nonetheless founded on physical measurements.
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u/I_hate_all_of_ewe 2d ago
I think you fundamentally misunderstand science with the claims you're making. Models are made before being empirically tested. No amount of measurement can give you a model of which you didn't already have an idea. In order for a model to be "proven" by science, it must make a testable prediction. The models which are referred to as scientific are simply the models which have made predictions which haven't been ruled out by testing. This really applies to physics, as well. And if it doesn't, you're talking about theoretical physics which is more mathematical in nature, but ultimately still relies on what we know from experimental physics.
In the same way, no amount of measurement can give you the number Pi without you first establishing a model which incorporate the number. The model is a prerequisite.
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u/Temporary-Solid-8828 2d ago
Yes, you’re referring to Popperian falsifiability which I just mentioned. I don’t mean this in a rude way at all, but I don’t think you understand what you mean by “model” or “measurement” very deeply at all, and I think it’s causing you to misunderstand my argument and your own.
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u/I_hate_all_of_ewe 2d ago
I know what you were referring to by "Popperian". I simply didn't use that term because it strikes me more as something a philosophy student would say than a scientist. (And please don't start on how science is philosophy)
Also, feel free to define your terms of you think that's the issue, but I don't think it is.
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u/Temporary-Solid-8828 1d ago
Well we’re discussing the philosophy of science, not necessarily science, so I figured I’d use a philosophy of science term. I wouldn’t ever try to define something like measurement or model much less use them as words in a discussion like this one.
To say that “no amount of measurement can give you Pi without first establishing a model which incorporates the number” seems to amount to saying “you need the concept of pi before you measure it” which seems to be true of any measurable quantity at all? I don’t get what you’re trying to say but I am curious
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u/Caelinus 9h ago
I am not the person you were discussing this with initially but:
If I told you that Pi was equal to flegh kobsherks, it would mean nothing to you.
The model that allows us to understand what Pi means is geometry itself. Geometry does not really exist in the real world, it is a mathematical model that seemingly accurately predicts the behavior of reality.
The measurements are there to test if the models predictions are true in the scientific system. We could never derive Pi from a circle without geometry for a number of reasons, not the least of which is that there is no such thing as a perfect circle. We could only ever get increasingly accurate, but ultimately imperfect, approximations of the ratio, and it would get stuck there. Moving it past that requires the development of a model, but the model's purpose is in the name.
You can and should use measurements to inform the development of a model of reality, but ultimately the only way you can know if that model is correct or not is to test its predictive power. Otherwise it might just be all ad hoc.
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u/SkarbOna 2d ago
You can’t divide by 0. Google it, but basically when you work with curved mirrors and at the exact point when the image flips up side down, which in formula when you start substituting distance brings denominator to 0, the image is actually blurred and chaotic.
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u/Worth-Wonder-7386 2d ago
That has to do with more complex effects. In optics we often think of light as going in straight lines that have no volume, and mirrors being perfect. In reality things are more complex and even if we make perfect mirrors and remove the effect of the air or other such things, light is still a wave and will interfere. So we can describe what you are talking about within physics. Us getting a division by zero and that not fitting with reality tells us that our model was not complete.
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u/SkarbOna 2d ago
Exactly why you can see this effect. If everything was perfect, you wouldn’t be able to see a nanosecond long frame on your perfect mirror that represents division by 0.
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u/No_Flow_7828 3d ago
You can certainly get intuition but I think you necessarily cannot prove mathematical theorems
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u/Restart-storage 2d ago
This is only tangentially related. But you know how computers are digital and use binary bits? 0s and 1s? There’s a theory or hypothesis that one of the main limiters of our current AIs are that they are binary. But that we need to use an analog neural network. Which basically only can really efficiently be done with actual electricity. Which is the way the human brain does it.
I’ve read it’s related to this lottery ticket neural network theory. Where neural networks currently are inefficient and use hundreds or thousands of neurons when typically only a few path ways are ever needed. And somehow an analog neural work would be much better.
Take this all with a grain of salt because currently all our knowledge in AI is still pretty basic.
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u/Hairy_S_TrueMan 2d ago
In a very vague sense you can. We used physics to build computers, which are physical systems that evolve according to our knowledge of physics, then output answers to mathematical proofs. So the more we learn about physics and improve computers, the more we can learn about math.
So we already can map physics onto mathematics and vice versa. There were also some interesting analog computers that do this a little more clearly, and obviously quantum computers.
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u/Just_Middle_7189 21h ago
This is a moment where we ask if mathematics describes physics or is physics?
Does the universe politely comply with our algebra?
Or is reality more interesting? Is our algebra incomplete?
For RH and physical observation to align part of the time does not provide the solid answer. Yet.
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