A new kind of symmetry shakes up physics
quantamagazine.org
quantamagazine.org
Conservation of angular momentum.
Conservation of momentum corresponds to spatial translation symmetry, not rotational.
As long as dimension n = 3 and so [dimension of R^n] n = n(n-1)/2 [dimension of so(n)]. Not to disregard these low-dimensional isomorphisms; there’s quite a few of them (they run out at about n = 10 IIRC), each one different from the next, and most are important in one way or another. But expressing momenta and angular momenta in those terms gives the impression that their existence is due to the (numerous and sometimes very complex) particulars of three-dimensional space, which it isn’t.
Well, in 2D it's about the same. In 3D it can be the same, as long as the rotation happens on a 2D plane.
This is the root of the whole "axial" and "pseudo" vectors that plague physics -- there's a (Hodge) duality being hidden, and we're stuck with Gibbs & Heaviside's vector calculus.
But a plane (bivector) will always be the natural way to define a rotation.
Isn't it generally said that the earth is rotating around the sun, or is that scientifically inaccurate?
Don't they technically orbit the center of mass, assuming a simplified two-body system?
In the case of Sol and a planet, given the massive (pun intended) disparities, the center of mass is very, very close to the center of Sol - but not coincident.
Not all isometries with a fixed point will be “rotations” in that sense, though—some will be products of them, as in
/ cos u sin u 0 0 \
| -sin u cos u 0 0 |
| 0 0 cos v sin v |
\ 0 0 -sin v cos v /
"Translations are rotations around infinity" is what you get if you compactify the real plane with projective geometry, 1/∞ = 0 is what you get when you close the complex field with an holomorphic-friendly point at infinity.
For a translational "rotation" in 3D, the axis of rotation is the line that is tangent to the infinite "celestial" sphere and perpendicular to the line of translational motion.
The "dualities" mentioned in the article are about two seemingly different quantum field theories actually being equivalent. See here, for example:
https://en.wikipedia.org/wiki/S-duality https://en.wikipedia.org/wiki/Seiberg_duality
Imagine a pair of denim pants, one could say it has the property of being made of denim, and when you bend the pants or move them around the room, they keep being made of denim. Anything you do to the pants that you can undo, like moving them around or bending them, those are invertible symmetries. Now imagine I rip the pants in half: they're still made of denim, but this action is not so easy to invert. So there are actions I can perform on these pants that are hard or impossible to undo, but still maintain the property of them being made of denim, these are non-invertible symmetries.
The example given in the article is a system being split into a superposition in a way that's hard or impossible to undo, sort of like the pants being torn in half, but just because the system is now in a superposition doesn't mean there weren't properties preserved along the way.
Is this something like the physical operation to invert it doesn't exist, even though it's logically possible? The "pants" example, and maybe the superposition example, makes it sound like they're uninvertible for entropy reasons, which seems interesting if it's not an illusion.
In seems like physicists are finding more general conserved quantities associated with more general spaces of physical operations such that not every action is reversible, but there are still conserved quantities associated to the underlying systems, AKA symmetries.
I don't have any solid physical intuition as to what makes an operation irreversible in this context, though, whether it's related to entropy or not.
I can understand that popularizations have to gloss over the math, but they usually at least identify the important points even if they don't get into the weeds of explaining the details. This seems like more of a sleight of hand.
https://physics.stackexchange.com/questions/561118/why-shoul...
Does this relate the String Theory?
> “I have not yet seen shocking results that we didn’t know before, but I have no doubt it’s quite likely this will happen, because this is clearly a much better way of thinking about the problem,” Seiberg said.
This bothers me. What about the empirical evidence from experimentation? Shouldn't that be more important?
The research in the article is about as innocuous as it gets — uncovering another possible way to get a handle on the math of quantum field theories. It’s not like millions of dollars went into the research (just the modest salaries of the four theorists). No major applications as yet — the Quanta title “…shaking up physics” is certainly not true. But it’s another stone in the edifice of science.
And my god when you see the esoterica in some (most?) other academic fields, the unrelenting complaints about the solipsism of physics seem totally misdirected. When an upper bound on some complicated measure on the distribution of prime numbers is lowered, no chorus of jackals assembles on the internet to mock the proof for its lack of real world relevance. The other day I spoke with a classics professor whose primary research was on a possible alternative interpretation of one line in a Latin poem. I found it interesting and worthwhile, but wow another level of remove from the so-called real world of engineering application and commerce.
Also, to be clear, whether or not mathematical physics work winds up elucidating experiments, it is still correct and “useful” math. It’s not for nothing that the math community gave Edward Witten a Fields medal.
I'm not very generous though. I personally think the majority of people are more interested in being right or sounding clever than arriving at truth or understanding.
there's a term-of-hate for this "poser" like in parent's username. regardless of whether HN or the internet at large has a poser problem, drawing attention to it is off topic at best and hateful at worst - otoh we could be happy that the zeitgeist holds theoretical physics in high enough regard as to draw posers (iow we could have worse problems!)
> What is it about theoretical physics that makes people on the internet (with zero understanding of the context) feel entitled to snarkily attack results such as this?
This is about you.
> And within these theories it’s often necessary to go beyond points and particles to think about one-dimensional lines, or strings (which are conceptually distinct from the strings in string theory).
And for that matter, they literally discuss observations in TFA, what are you on about.
Anyway, if you don't know the role symmetries have played in physics for well over a century at this point, you aren't qualified to discuss the subject.
…
> [The] fractional quantum Hall effect, involves the spontaneous reorganization of electrons, but without any apparent symmetry being broken. This made it an uncomfortable outlier within the theory of phase transitions. That is, until a paper in 2018 by Xiao-Gang Wen of the Massachusetts Institute of Technology helped establish that the quantum Hall effect does in fact break a symmetry — just not a traditional one.
Sometimes experimental results aren’t even the important part. Lorentz Ether Theory and Special Relativity make the exactly same predictions. Yet only one of them is considered revolutionary. And it isn’t the one that was invented first.
How so?
> Sometimes experimental results aren’t even the important part.
When are experiments ever not important? What is a theory without experimental results?
I know you've mentioned Special Relativity but let me illustrate my point using General Relativity:
When Einstein came up with General Relativity, few people believed him – until experiments proved him right[0]. But the hype was over soon after because there were not many things one could predict (beyond rather simple things in cosmology). While hype came back briefly during the Golden Age of Relativity between 1960 and 1975[1], afterwards everyone lost interest in GR once more because there were still barely any experiments you could do. That is, until recently, when people found gravitational waves and started taking "photos" of black holes.
So do you think that Special Relativity would be as well-known and popular today if people hadn't proven it right in countless experiments and found applications in many other areas? Personally, I think SR would probably be known only among physicists today, as a correct but somewhat arcane theory some patent clerk from the early 20th century came up with.
Don't get me wrong. Some theories are impressive. But they're much more impressive if they turn out to be correct. :)
[0]: https://en.wikipedia.org/wiki/General_relativity#cite_ref-14
[1]: https://link.springer.com/article/10.1007/s10714-017-2203-1
A theory created after an experiment is just fudging. A new theory allows you to come up with new experiments to test it. Or to come up with new theoretical extensions. Or to build a research agenda.
> So do you think that Special Relativity would be as well-known and popular today if people hadn't proven it right in countless experiments and found applications in many other areas?
There is no empirical evidence that supports SR over LET. There can’t be any, mathematically.
So you're saying people came up with Maxwell's equations, quantum mechanics, the standard model of cosmology, et cetera, by… fudging?
How do you even devise a new theory without indications from experiments? There is a reason why there's a "crisis" in theoretical high-energy physics these days. Everyone is waiting for "new physics" to show up in experiments.
Partly, yes, though I am not really familiar with the exact context behind them. People fudge theories so those theories would fit known data. That alone doesn't guarantee that those theories would fit future data.
> How do you even devise a new theory without indications from experiments?
It's a two-way process. You need experiments to improve theory, and you need theory to create experiments.
Sure, but that's sort of a triviality. It's true for any theory.
> It's a two-way process. You need experiments to improve theory, and you need theory to create experiments.
I agree that it's a two-way process but I wouldn't say you need theory to create experiments and I think I've given sufficiently many counter examples to illustrate this.
What we (as humans) do need theory for is to make sense of our experiments (or of the world, really) and discover new experimental setups that might uncover something interesting (not explained by the current theory). On the other hand, without theory there's no concept of "unexplained by theory" in the first place. Our experiments would probably resemble random walks (in the sense that they're not driven by theory) but that doesn't mean we couldn't uncover interesting phenomena, let alone run experiments at all.
Getting back to the "making sense of the world" point: Take an AI for instance. It could probably be trained on experimental data alone and make suggestions for future experiments and give predictions, without a simple, coherent and human-understandable theory behind them[0]. This, too, illustrates that experiments would be possible (and worthwhile) even without theory.
Note that I'm not at all trying to play down the role of theory. To the contrary, I'm saying all this as a former theoretical physicist myself. I just see experiment and theory as equals.
[0]: Isn't this more or less what a human baby does as it learns?
It is not a triviality. OP and many other people insist that nothing is important unless there is empirical evidence. Was there any empirical evidence that the Higgs boson is real and all competing theories are wrong before physicists spent billions of dollars to find it? Yet it was one of the most convincing theories, even if most of the evidence was theoretical, intuitive and aesthetic rather than empirical. I think you, as a former theoretical physicist, can come up with a dozen theories that are uglier but could fit old data just as well. The most trivial way to do it is just to say that in those experiment we should’ve expected those results and so on without any generalization. But of course numerous more sophisticated wrong theories would be possible. There is no theory that is so bad that it can’t be “fixed” with a few epicycles. By the way, Ptolemaic vs Copernician model is another good example of two different theories with similar or exactly the same fit w.r.t. to old experiments and observations.
> This, too, illustrates that experiments would be possible (and worthwhile) even without theory
That just illustrates that you can build a theoretical model with lots of free parameters and low interpretability.
> Note that I'm not at all trying to play down the role of theory.
Right. And I was just responding to OP who completely downplayed it.
Theoretical particle physics is in a tough spot. I really hope in my lifetime I will get the change to learn new theories.
I am hopeful, still. But we either invent or we fail.
Theoretical discoveries are good, but some ego, some hype for funding, and some clickbaiting have made reporting on science even from the better sources like Quanta too focused on finding aliens and the grand unification or commercial fusion or whatever at least just by what gets written and posted, it seems like that.
He runs a prestigious institute (Perimeter) and has published several books and papers since his 2006 polemic "The Trouble with Physics"
http://leesmolin.com/wp-content/uploads/2019/04/cv_Lee-Smoli...
Could you tell me more about this or lead me where to read about it? All I know of him is that I came across some of his talks/interviews on youtube and found them incredibly refreshing. I am a physics graduate that left entirely dissatisfied and feel he's the lecturer that I wish I could have had. Is he viewed as a crackpot?
Sabine is getting too famous to not ultimately get resentment.
Apparently, something in my comment there really made a lot of people mad (or one person with several accounts), and I'm unsure why. I would love someone to explain to me how they think science should function without skeptics.
Especially in the clickbait era.
No one thinks this. People dislike Hossenfelder and Smolin because they're peddling their own hot takes as established fact to a lay audience utterly unequipped to tell the difference.
YOU don't think this, but there are clearly people out there who don't want to hear their wild speculation isn't real. It's human nature.
Reality being that there have been no major new developments for decades...
The symmetry between right and left brain doesn't really correspond to the types of symmetries they're talking about in the article. They're usually expressed as "The laws of physics are independent of X; you can substitute X with Y and the laws work the same." There isn't any kind of substitution here, so no place to apply the symmetry.
It's literally a medical procedure that children (or adults[1]) with extreme seizures or epilepsy undergo so that they can live more normal lives.