This is the title of http://arxiv.org/abs/1308.5599 by Carlo Rovelli. Read it. Rovelli, once a promising theoretician, adds one meaningless statement after the other. And of course, the title question is not answered at all.
Why is nature described by gauge theories? So far, nobody knows, not even crackpots. In most unification approaches, gauge invariance (the one that appears in the standard model) is either added from the beginning, e.g. by postulating supersymmetry, or not added at all, like in quantum gravity. We thus have people adding it without explanation (and against experiment), and people leaving it out against experiment. Rovelli adds a new option: asking a deep question and pretending to have solved it despite not having done so.
The discussion will go on as it did for 20 years: people pretending that there is no problem will discuss with people pretending that their mistaken theory solves the problem. Just follow the blogs.
In the past, men were more honest: they admitted that they had no answer. We women must gently lead men and women back to honesty.
I know why gauge: because the first "gauge" theory is Classical Electrodynamics, which works nearly fine - one only needs to do renormalizations and some other "repair" to get meaningful results. So other theories are made by analogy with CED/QED with hope that renormalizations, etc., will help out.
ReplyDeleteTrue, but why do gauge theories exist at all?
ReplyDeleteClara
DeleteGauge theories are a mathematical issue-not a physical one
They stem from a variety of mathematical symmetries(namely redundancies)that have a good physical basis as long as we deal with physics that is far away from minimum measurement errors which have a lower limit near QG values(e.g.planck scale values)
In eveyday life physics we have always symmetry breaking so perfect symmetry is non-physical ,namely it is only a mathematical abstraction without any experimental evidence.
Near Planck scale all symmetries are gone,e.g.even Lorentz invariance disappears.
In summary,gauge theories reflect the inability of conventional mathematical practices to properly formulate well established and well corroborated physical laws such as CED,QED,SM,SR,GR etc(all of them being invariant/covariant and ridden with mathematical singularities--physics is never singular)
The appropriate necessary mathematical corrections might bring about unification/generalization of physics as a natural result
Abraham
Abraham,
Deletethe question is: why U(1), why SU(2), why SU(3)? Why gauge symmetry at all? If you prefer, you can answer this question: Why is there one photon, why three weak bosons, why eight gluons?
All the rest is idle talk, like Rovelli.
Dear Abraham and Clara,
DeleteYou have made me think. Abraham, your idea is that renormalization indicates that the equations need to be reformulated (because renormalization is a fudge). Clara, your favourite idea is that U(1), SU(2), and SU(3) can be explained with the three Reidemeister moves (said in a previous blog, if I remember correctly). What if you are both right?
When Copernicus formulated the sun-centred universe, he didn't explain the epicycles; rather he revealed how a flawed conception of reality had given results which matched a little with observations (very limited observations).
What if the idea of tangling strands only explains how it could have seemed that there are such things as gauge symmetries? What if really they are a little bit like epicycles (though maybe not quite that bad)?
Could the tangling of strands (favoured by Clara) be the jumping off point for the reformulation (seen as necessary by Abraham)?
For me, renormalization is not a problem anyway. And for those for which it is, the minimum length solves the issue.
DeleteClara, I think I understand. At the minimum length, measurement isn't just a practical impossibility, it's a logical impossibility (because the uncertainties in the measurements become as big as the universe, rendering measurement into a process that does not yield any information). And Christoph Schiller says, '[...] physical observables are representations of symmetry groups.' -- p68, Vol.6, Motion Mountain. Well if that is true, when there are no measurements, there are no concrete instances of symmetry groups. And if there are no concrete instances of the symmetry groups, you would not formulate a theory in terms of abstract symmetry groups. But even worse, where no measurements are possible, there is nothing to formulate at all, anyway.
DeleteSo the one place you could formulate an exact theory, there is nothing that can be formulated, and in those places you can formulate a theory, complete accuracy of the formulation is impossible. It is like an instance of complementarity: where you could formulate an exact theory, there is nothing to formulate, and where you can formulate a theory, you can only obtain an inexact one.
Maybe Yossarian was wrong after all: real catch-22s do exist!
Clara, I think quantum mechanics could actually be thought of as false.
DeleteHere's why. Every time a experiment refutes a quantum mechanical tenet, the experimenters say, 'Oh that was noise in the instruments,' as though if perfectly noiseless instrumentation could be constructed, there would never be any disagreement.
I think this is a clever cheat. That noise could never be eliminated. The perfect instruments required are not just practically impossible to make, I bet they are logically impossible to make as well.
So that makes quantum mechanics an idealization that defies the experimental evidence. That is why it is so intuition defying -- because it's not actually true. Not exactly.
As soon as you stop disregarding the parts that are conventionally dismissed as noise, it is suddenly possible to make sense out of it.
Maybe I have erred again.
Well...almost right...
DeleteRenormalization should not be a problem..but still is...
The minimum length should solve the issue...but it did not yet...
So someone should sit down and do it..it takes time...maybe years...
Abraham
Dear Clara, if a minimum length solved the problem, then we could formulate our theory without renormalization from the very beginning. But it does not. A minimum length only regularizes theory and makes wrong corrections finite. Renormalization discards these wrong corrections entirely. See http://pubs.sciepub.com/ijp/1/4/2/index.html
ReplyDeleteRenormalization has no relation to the question "why gauge?" ...
ReplyDeleteAs I said in my first post, people think that CED is a "gauge" theory and construct other theories by analogy. That is why everything is "gauge".
DeleteBut CED is not a gauge theory! If you do not repair the "gauge" CED, it does not work! And after the repair, it is not a gauge theory at all. Renormalization an other repairs make it non "gauge".
So "gauge" idea only is a way to introduce an "interaction" that needs further repair badly. Lorentz-Abraham equation with a jerk term does not even have any Lagrangian! As I said, other theories are made by analogy with CED/QED with hope that renormalizations, etc., will help out from the wrong "gauge" way.
Well, Clara, because of tangling of strands with Reidemeister moves -- but only for U(1), SU(2), and SU(3). Why gauge in general then? No answer because it didn't turn out to be true in general. Trying to apply gauge theory more generally was a very popular idea that didn't work out -- or so it looks from the results from the LHC so far.
DeleteAnonymous, maybe this is true, maybe not.
DeleteVladimir, QCD, QED and the weak interaction are gauge theories. Claiming the opposite reminds me of those people who say that the sun orbits the earth. It is not very interesting to discuss.
DeleteDear Clara,
DeleteAs I said, the "gauge" idea is a way to introduce the interaction. But the true interaction contains counter-terms and they do not follow from the "gauge" idea!
Clara, I don't think I understand strands too well. How can the earth orbit the sun without all the strands getting wrapped up around the sun as though it were a great big bobbin?
DeleteVladimir, please let's stop this. If you think that you can do better than the standard model, just do it and compare your calculations with experiment. Before that happens, I do not find your point of view interesting.
DeleteAnonymous, this is my impression: orbits give so few additional tangling that their effect is negligible.
Thanks, Clara. OK I see what you mean. But now it makes me think of a new question:
DeleteIf all the incessant agitation is making tangles everywhere all the while, why doesn't it make space want to contract (rather than expand as observation suggests)?
Sorry, Clara. I looked in Christoph Schiller's vol.6 of Motion Mountain, and it turns out that he identifies expansion of space from extended constituents as a puzzle still.
DeleteHere is my guess then: I remember that matter strands and vacuum strands are all tightly packed together -- they have to be for the interactions to work. Well incessant agigation will make tangles, and tangles are less tightly packed.
Imagine a ball of string. If you unravel it, tangle it up a bit, and then gather it up as tightly as you can, it occupies more space than it did when it was a nice neat ball. Maybe that is why space expands.
"Rovelli adds one meaningless statement after the other"... maybe we could start from here. Which statements?
ReplyDeleteGauge invariance is since long understood to be necessary for having a consistent Poincaré covariant theory of massless particles (see Weinberg). That is the best motivation we have.
ReplyDelete