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Physics is unreasonably good at creating new math

https://nautil.us/why-physics-is-unreasonably-good-at-creating-new-math-797056/
A physicist, walking home at night, spots a mathematician colleague under a street lamp staring at the ground, "something wrong?" he asks; "I've dropped my keys" he replies, "whereabouts?" asks the physicist, keen to help. "Over there" says the mathematician pointing; "So why don't you look over there?" retorts the physicist, "the light is better here" says the mathematician.

Disclosure, I'm a mathematician.

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Software developer: It is more important to find out how the keys were dropped in the first place. And after I do that it will be more efficient to just generate new keys.

Disclosure, I'm a software developer

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One of my physics lecturers at university made the offhand observation that the distinction between physics and mathematics is a twentieth-century idea: it wasn't made during the nineteenth century or before, and it seems to be disappearing in the twenty-first.
> it wasn't made during the nineteenth century

That's because people were totally focused on physics, and math was just a useful tool sometimes. Doing physics was the true goal and observation the final arbiter of truth.

Nowadays, that distinction is blurred but for the opposite reason; people think that anything conceived by sound math must be true, and observation has taken a back seat.

To some extent, observation has taken a back seat because we're at the point in our physics journey where we pontificate about things that are too small or too dark and far away to see. We simply can't observe this stuff anymore.
I don’t agree with this. I think there are definitely people like Michio Kaku who have books to sell who spend their time pontificating. People just think that physics looks like pontificating because that’s what it looks like on TV.

But there are also active researchers doing real research. Physics postdocs aren’t just sitting around in a circle making up stories about what the universe is like.

please forgive my ignorance, has there been notable progress in the field of physics in the last decade? noteworthy breakthroughs i mean

i ask out of layman curiosity

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Absolutely, they're still handing out nobels after all.

Personally I think the ER=EPR conjecture and the complexity/action duality hypothesis are incredibly interesting. Technically ER=EPR was formulated in 2000s (maybe 90s?) and CA-duality is approaching if not just past 10 years old, but the thing about asking for breakthroughs is that they take a while to percolate. Ex Hawking radiation wasn't formulated until, like, 50-70 years after the "basis" (schwarzshild, Schrodinger) was formed.

There's also been a ton of productive research integrsting computer science and physics lately ( on hn last week: https://arxiv.org/abs/2403.16850 and 2022 novel prize; https://www.scientificamerican.com/article/the-universe-is-n...)

Also JWST just keeps on giving, and gravitational waves were only confirmed in 2017. If you extend a bit further higgs was in the 2010s

So, in summary, in the late 10 years - we've shown a break in our intuition of physics (nonloca-realness, that 2022 paper) - proposed some novel yet elegant theories (CA-duality, and I'd hope you'd begrudge me er=EPR) - confirmed some insane provings to the underlying reality (gravitational waves)

If those aren't noteworthy, I'd ask what you consider noteworthy any why you consider it noteworthy

The Higgs boson was predicted in 1964. Gravitational waves were predicted in 1916. Bell's theorem was published in 1964. Basically every recent discovery in physics has been observations confirming old predictions and refuting the endless zoo of poorly motivated, imaginary particles that seems to be standard practice these days.

There have been almost no truly significant, novel predictions that have a hope in hell of panning out in like, 40 years or more. The only mildly interesting, novel idea in physics has been quantum computing, and even that was first published in 1980.

> So, in summary, in the late 10 years - we've shown a break in our intuition of physics (nonloca-realness, that 2022 paper)

This paper showed no such thing, it has the same superdeterminism loophole as every other paper attempting to refute local realism.

Physics is stuck in a local QM-GR minimum, and some truly novel ideas are needed to kickstart things again. Oppenheim's postquantum gravity is the first truly novel idea I've seen in awhile.

I also agree that JWST is giving us great data, some of which has placed LCDM on the ropes, but astrophysicists are hard at work adding epicycles to keep it alive.

Experimental validation of a major theory is major physics.

You can't rhetorically gloss over something as important as experimentally validating a 1964 prediction as though it doesn't matter or didn't happen.

If your contention is that a validation of something we already suspected to be true doesn't shatter/shift our paradigm, then how often would you expect that to happen? I would expect it a lot in small ways (so almost every person working in some niche area has probably had some "niche breakthrough" happen in their area that has really changed things) but not a lot in really fundamental overarching ways which for physics I think you could reasonably say has happened about 4 or 5 times in the last 400 years maybe idk: Newton, GR/SR/ quantum mechanics and then whichever ones you want to count out of Maxwell's equations and whatnot.

So to expect something like that every decade is not realistic.

> You can't rhetorically gloss over something as important as experimentally validating a 1964 prediction as though it doesn't matter or didn't happen.

I'm not, I'm pointing out that theoretical progress has stagnated. Experimentalists are doing great.

> So to expect something like that every decade is not realistic.

I'm not expecting it every decade, but we've had 4 decades of recycling the same ideas using the same failed approaches to try to patch gaps in existing theory using bogus arguments, which ends up funding poorly motivated experiments that then find nothing. I think Sabine Hossenfelder elaborated the problems here in excellent detail (see "Lost in Math").

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You don't consider ER=EPR as novel? Or CA-duality? Agreed that Post-quantum gravity is really cool and "fresh"

Higgs/Bell/GW were experimental results, I was indeed trying to show that there's a huge lag between prediction and observation.

Imo the paradigm shift that we're slowly undergoing is thinking about physics from a information theoretic perspective instead of a kinematics one. I'd argue that's even more fundamental of a change than Newtonian physics to early GR & QM.

They might be novel mathematical constructs but seemingly have no bearing on our universe. ER=EPR doesn't really solve anything because GR remains fundamentally incompatible with QM's linearity. That's the problem that needs to be solved. The core idea of ER=EPR wasn't even particularly novel, as Hadley effectively did something very similar back in 1997 [1].

CA-duality is again mathematically interesting, but physically dubious because it's based on anti-de Sitter space, which does not describe our universe.

Information theoretical formulations of QM are mildly interesting, but I don't think they will be revolutionary, and I don't think they are tackling the core problem, which is QM's linearity where we classically observe a non-linear universe.

[1] https://arxiv.org/abs/quant-ph/9706018

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Math probably split off a bit because of the attempts at formalization. That was a useful tangent though, arguably giving us computer science via the lambda calculus, Turing machines, etc.
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I understand that one huge reason for Ed Witten's optimism about strong theory is this very fact. That, in his terms, the process of building out string theory has led to the uncovering of so much "buried treasure" in the form of novel developments of maths.

Of course it's not anything like a proof but something that bolsters an intuition.

And that amounted to 60 years (and counting) of absolutely nothing in terms of how the physical world works.

Even Witten's achievements objectively reduce to an alternate proof of the positivity energy theorem in GR.

This is an abject failure by all metrics.

Witten has revolutionized mathematical physics, and his development of topological quantum field theory was nothing short of monumental.

Much of Witten's own point above is that advancements in string theory have cashed out in revolutionary new mathematical approaches that would be of lasting value even string theory itself never receives any experimental confirmation.

I think article highlights something very beautiful about how physics, including string theory, have lead to the creation of new math, and how that is suggestive of an unmet promise. To ignore that just to come in and repeat for the 1000th time the world's most repeated thing about string theory, and take a completely unnecessary cheap shot at Ed Witten is the perfect embodiment of why comment sections can too often be a depressing waste of time.

The only cheap thing here is the amount of actual physics that came out of all of this ptolemaic endeavor.

And writing ptolemaic is probably too charitable because the Almagest at least predicted movements quite well at the time (apparently it now deviates too much).

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Is your preferred remedy that quantum gravity be entirely defunded, or instead that more funding be redirected to any of the other programs to study quantum gravity? If the latter, which ones in your opinion are more likely to be productive than string theory?
Your suggestion implicitly asserts that string theory was productive, which is exactly the claim that seems to be in contention.

I don't think it's too wild to suggest that, without the constraints of string theory imposed by advisors, lots of novel approaches would have been tried. We have no idea what could have been produced.

As for quantum gravity specifically, arguably not much progress will be made without more data, and we now have some proposed experiments that can be conducted here on Earth to test them.

There are in fact exceptionally strong incentives to discover alternatives to quantum gravity which could be tested in experiments. These are the same incentives that always drive the scientific process, and new theories cost next to zero to produce. The reason string theory is popular is not because string theorists somehow prevent funding of other directions. It is because string theory has given us tools like AdS/CFT that are useful in other contexts to understand real physics—-and the alternatives have not (yet). There are many physicists who spend their lives studying alternatives to string theory with 100% of their time. I hope for their sake that there is a similar pot of gold at the end of their rainbows. It has not yet materialized.
Oh Ads, you mean that space that emphatically does NOT describe our universe? Ads/CFT is overblown. It's just an interesting mathematical result that hasn't borne much meaningful fruit for actual physics.

I'm sorry, but string theorists absolutely do prevent funding other research because funding is finite, grad students have to research something their advisors think is worthy, and their advisors have their heads full of "beautiful math" so that's what they tell their students to work on if they want their PhDs, and that's what they hire their post grads to work on if they want a job.

Only now as the strong theory haze has started dissipating are we starting to see novel approaches, like Oppenheim's post quantum gravity theory.

No, this is a shallow understanding of AdS/CFT. If you want to study quantum gravity when it is weakly coupled to matter, you can use AdS/CFT regardless of whether the background space is asymptotically AdS by embedding a brane near the boundary and working in a perturbative expansion. If you want to study the physics of quantum de Sitter space with a field theory dual, you can study any of the recent work on TTbar deformations. And anyway, surely you aren’t arguing that conformal field theories are irrelevant for physics? Because that would obviously be an untenable position, and the whole point is that quantum gravity AdS (basically) is CFT (it’s an equality! It goes both ways), just in different variables. You can actually study non-gravitational physics with it, using a gravitational language. That’s awesome stuff! Please don’t dismiss this fascinating field too quickly.

By the way, I know Oppenheim personally. He gets funding from string grants. Nobody is angry about that. Anybody can do this. I don’t think his theory is going to pass any experimental validation (it requires a really severe violation of a physical principle we have tested over and over) but the entire community has always supported and listened. He gives talks at major universities. He’s not an outcast or renegade or something.

> Because that would obviously be an untenable position, and the whole point is that quantum gravity AdS (basically) is CFT (it’s an equality! It goes both ways), just in different variables. You can actually study non-gravitational physics with it, using a gravitational language. That’s awesome stuff!

Which makes it an interesting mathematical construct, but in what way does that actually help physics? I included a link to one critique of Ads/CFT in another post, and others have critiqued its applications to QCD and other alleged "successes" because the important properties to do meaningful work in those domains just aren't there.

The versions of this correspondence that are easy to work with also depend on supersymmetry, for which every experiment has failed to find any evidence in the expected regimes. In the old days we'd call this "refuted", but these days it just means reworking it (adding a new epicycle?) to get "new bounds".

Ads/CFT is a mildly interesting mathematical derivation, but its actual utility for physics is questionable.

> He gets funding from string grants. Nobody is angry about that. Anybody can do this.

Maybe anybody can do this now, and I think that's because, as I said, string theory's stranglehold has weakened because of well-motivated criticisms over the past 15 years or so. The evidence of string theory's former dominance is right in what you said: string theory grants.

> but the entire community has always supported and listened.

I think some physicists are open minded, and some are not. You need only look at how physicists who work MOND are treated to see how not open minded some physicists are. MOND is not a final theory, but it and the people who work on it are scorned despite it's unreasonably good predictive success over the last 40 years.

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>Ads/CFT is overblown

This is a preposterously uncharitable characterization of something that again, was I think a triumph of string theory, the likes of which cannot be claimed by any competing theory. It is a framework for understanding black hole information loss, and it even has specific applications in condensed matter physics for modeling high temperature superconductors.

Sorry, but I'll have to side with Nobel laureate Anderson who disagrees about the utility of Ads/CFT for condensed matter physics:

https://pubs.aip.org/physicstoday/article/66/4/9/414412/Stra...

Like I said, Ads/CFT's alleged "successes" are overblown.

As for it being a framework for understanding black hole information loss, it's merely one idea that has questionable application to our universe. We'll see if anything actually useful comes from it.

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I've long thought physics is a subsection of maths and reality is a mathematical object that exists the same way that prime numbers or the Mandelbrot set do. Hence the unreasonable effectiveness of one in the other.
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This is the well known litany from string theorists to try and justify the inordinate amount of money threw at them to get back nothing of physical value: no falsifiable prediction.

Instead of reasoning on the worth of the effort spent in this direction to investigate nature (a very tangible companion) they try to steer the discourse toward this nonsense. We spent >50 years listening to these tales and the time has long passed since we are required to stop playing with these smoke and mirrors.

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They have probably produced some new maths, maybe as much as if you threw similar amounts of money at the maths department?
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