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A new kind of symmetry shakes up physics
- drdeca 3y ago> Rotational symmetries lead to the law of conservation of momentum. Conservation of angular momentum. Conservation of momentum corresponds to spatial translation symmetry, not rotational.
- antognini 3y agoAt least in some formulations (e.g. using bivectors and geometric algebra) you can treat a spatial translation as being a rotation about a point at infinity.
- ThrowawayTestr 3y agoIs that like saying sin(x)=x?
- joe__f 3y agoYou mean, for small x, sin(x) ~= x? I've been thinking for a while and I can't see a way that it's like that
- ThrowawayTestr 3y agoLike if you zoom in on a circle close enough it looks like a straight line.
- topaz0 3y agoThis is basically it, yes, along with cos(x) = 1. If the axis of rotation is much further than the distance that you move through upon rotation, the angle of rotation is very close to zero, so the approximations are very good. In the limit that the axis of rotation is infinitely far away, it is exact.
- hoseja 3y agoCoincidentally, a recent relevant XKCD: https://xkcd.com/2761/ https://xkcd.com/2761/
- afiori 3y agoIt is more like saying 1/∞ = 0. "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.
- gowld 3y agosort of... A line is a circle (more precisely, a cline ("circle-or-line") with infinite radius and center on the "horizon" (In 1D, the horizon is the 2 points at +/infinity. In 2-D, the horizon an infinite circular boundary around the plane. In 3-D, it's an infinite circular sphere). The center's position determines the slope/angle of the line. 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.
- mananaysiempre 3y ago(A line at infinity, of course, as rotations are about axes, not points, and in three dimensions an axis is a line.) 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.
- rcme 3y agoYou can rotate around a line, it doesn't necessarily need to be an axis.
- mananaysiempre 3y agoI don’t really see your point, sorry? In arbitrary dimension, you rotate in an oriented plane (aka a bivector up to a positive constant) around a fixed point, if anything; I meant to call that an “axis” by abusing the terminology a bit (it’s an oriented line in three dimensions and a point plus an orientation, i.e. either “clockwise” or “counterclockwise”, in two). 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 / with non-boring values of u and v.
- deleted 3y ago[deleted]
- danbruc 3y agoRotations of a point happen in a plane around some point in the plane, not around a line or axis. In two dimensions there is no line perpendicular to the plane to rotate around, in four and higher dimensions there is no unique plane perpendicular to any given line. It is only in three dimensions that rotating in a plane and around a line coincide.
- not2b 3y agoThey've corrected the story (angular momentum, not momentum) and added a note at the end.
- ww520 3y ago> the symmetries apply to higher-dimensional objects such as lines, rather than lower-dimensional objects such as particles at single points in space. Does this relate the String Theory?
- nhatcher 3y agoYes, the charged objects here are strings and membranes.
- hoseja 3y agoI am more and more convinced the Theory of Everything will turn out to be purely topological, with spacetime swirling, knotting and swelling in ways that look like the fundamental forces from up here.
- montjoy 3y agoFTA: > 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).
- goatlover 3y agoCue incoming Sabine Hossenfelder YT video takedown. > “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?
- nhatcher 3y agoFacepalm. That's exactly the first thing I thought. I don't know if I am more tired of those blatant statements without any basis or of Sabine's expected reaction. 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.
- asplake 3y ago> But last May, three physicists proved that the 1969 verdict was only half the story. It wasn’t just that the presupposed symmetry wasn’t there — it was that higher symmetries were. And when those symmetries were incorporated into the theoretical picture, the predicted and observed decay rates matched exactly. … > [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.
- rini17 3y agoThey do mention condensed matter physics. If it really makes maths easier there, that means instant practical relevance.
- garbagecoder 3y agoGood for her. Before her there were people like Lee Smolin. They eventually get cancelled by the physics community, like short sellers in investment, no one wants to hear the sad trumpet but the "market" doesn't function without skeptics. 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.
- matthewfelgate 3y agoSuper Asymmetry?
- iorrus 3y agoLooks to be related to projective geometry in some way in which every point symmetry has a matching “dual” or line symmetry. https://en.m.wikipedia.org/wiki/Projective_geometry#Duality https://en.m.wikipedia.org/wiki/Projective_geometry#Duality
- prof-dr-ir 3y agoIt is not. Sorry to disappoint. :) 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/S-duality https://en.wikipedia.org/wiki/Seiberg_duality https://en.wikipedia.org/wiki/Seiberg_duality
- eastWestMath 3y agoIs this some flavour of groupoids symmetry?
- andrewflnr 3y agoI'm sorry, "non-invertible symmetry"? In what way is that still a symmetry?
- mathgenius 3y agoYeah, it's a reference to how "category theory" generalizes "group theory". So if transformations in a group are called "symmetries" then you might call the transformations in a category "generalized symmetries" or "non-invertible symmetries" as in this article.
- throwaway81523 3y agoErm the whole idea of a symmetry is that it is a group invariant. If they're using the term in some more general way, it would help if they said what the new way was. The article is otherwise almost completely uninformative. What on earth is a "generalized symmetry", especially one that still has something like a conservation law? Does it have applications in math as well as physics? E.g. topologists are always looking for new invariants. 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.
- Robotbeat 3y agoRead the original paper: https://arxiv.org/abs/1412.5148 https://arxiv.org/abs/1412.5148
- gowld 3y agoApparently the QM and condensed matter people use the term "defect" for a (possibly non-invertible) transformation (semigroup or similar), and a "symmetry" is an "invertible" "defect". https://physics.stackexchange.com/questions/561118/why-should-symmetries-be-described-by-invertible-transformations https://physics.stackexchange.com/questions/561118/why-shoul...
- IanKerr 3y ago
- totally 3y agoIs symmetry between left and right brain what allows consciousness to exist?
- SketchySeaBeast 3y agoGiven that the left and right brain aren't exactly symmetrical and will receive and process different inputs that seems like a no.
- eimrine 3y agoIf some experimentator will destroy a half of his brain in such a way to not harm anything else - does he have a chance to keep being consciouness? That experiment kind of answers the question.
- SketchySeaBeast 3y agohttps://www.uclahealth.org/medical-services/pediatric-neurosurgery/conditions-treatment/pediatric-epilepsy-surgery/epilepsy-treatment/hemispherectomy https://www.uclahealth.org/medical-services/pediatric-neuros... 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. [1] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7281896/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7281896/
- eimrine 3y agoIn my opinion, one is between "this needs to be remembered, I will need this later" and "I have already remembered this, immediately recover!".
- jfengel 3y agoClearly not, since you can have consciousness with only half a brain. Even a full hemispherectomy doesn't make you not conscious. In fact, there may be little change to the personality or cognition at all. 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.
- UberFly 3y agoI have nothing smart to say about the topic, but it is awesome as always to read about these kind of efforts to crack open murky but promising concepts that are posed. Also, the writer did a great job presenting it all.
- coldtea 3y agoPhysics "breaks up" 4-5 times every year judging from such articles. Reality being that there have been no major new developments for decades...