# Origin and Nature of Gauge Principle

1. Nov 2, 2013

### kye

Gauge Principle is successful in strong electroweak force modeling in the the form U(1), SU(2), SU(3) and in GR but it fails in SU(5) or attempted gauge symmetry between leptons and quarks, it fails in Supersymmetry, fails in Supergravity, and even fails in String Theory.

Don't we even know why there is Gauge Principle and it's domain of applicability? What are good best papers written about this in the past and at present? What is your thought of it?

2. Nov 2, 2013

3. Nov 2, 2013

### kye

The former, do you see it more as some kind of Noether Theorem or Conservation Law or Spontaneous Symmetry Breaking where it is more of a feature?

4. Nov 2, 2013

### Simon Bridge

No - I just think that what the Universe does is a subset of all possible things that can be described by maths.
The guage principle breaks in those situations where the assumptions no longer apply ... something else happens.
It's like when you can and cannot use freshman ballistics equations.

5. Nov 2, 2013

### kye

Can you give an everyday example of the gauge principle? For the spontaneous symmetry breaking, Smolin said when babies are born, they are all infants and the symmetry is there.. and when they grow up, they go to different schools, make different choices and the symmetry is broken. He doesn't use any everyday example of the gauge principle. Thanks.

6. Nov 2, 2013

### marcus

http://arxiv.org/abs/1308.5599
Why Gauge?
Carlo Rovelli
(Submitted on 26 Aug 2013)
The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge variables describe handles though which systems couple. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. This observation leads to a physical interpretation for the ubiquity of gauge: it is a consequence of a relational structure of the physical quantities.
7 pages

7. Nov 2, 2013

### Simon Bridge

When we are talking about these things, it is tricky to separate the map from the territory.
Rovelli's observation about the sense in which gauge variables can be measured is important for this.

8. Nov 2, 2013

### marcus

I agree.
OP opened up a multifaceted bunch of questions. We had an earlier thread called Why do gauge theories win out? It did not stay focused but was wide-ranging, which isn't necessarily bad. Garrett Lisi joined in at one point. Here are posts #11 and 14 of that thread:
I wouldn't urge anyone, e.g. Kye (the OP), to go rummage thru that earlier discussion for ANSWERS, it is so wide ranging. But Kye I did want you to know about the earlier thread on related topic.

9. Nov 4, 2013

### kye

U(1) has one gauge generator in terms of electromagnetic field
Su(2) has 3 generators in terms of +W, -W and neutral Z
Su(3) has 8 generators in terms of the 8 gluon fields
Gauge theories are renormalizable and Higgs is already a consequence of gauge theory.

In beyond the standard model papers in arxiv.. they propose higher symmetries like Su(5) or even Su(10).. but this would have dozens of generator fields or even hundreds. Maybe there isn't any. I mean. Can't it be said that those U(1) + Su(2) and Su(3) of the standard model is the last of them.. and higher theories no longer use gauge principle? Remember in string theory and supergravity, they all use gauge principle and most papers in arxiv is based on this. Maybe gauge principle has limited domain of applicability. What are the other principles besides gauge principles that others are working on?

10. Nov 4, 2013

### marcus

If you are interested in WHY there is a gauge principle, then how about you have a look at the paper that Simon Bridge and I were talking about? It is comparatively short, simple, non-technical.

The paper gives a broad overview of the different kinds of successful gauge theory. To understand gauge theory success one probably has to understand how really general the principal is. It is not just about U(1) and SU(2) and SU(3) and groups like that. The principle is much more general. You know the diffeomorphism group. This is the group that defines "general covariance". GR is a gauge theory with the diffeo group as its gauge group.

The fact that our basic theory of space-time, geometry, gravity, is ALSO a gauge theory makes the principle much more impressive than it would be if it merely appeared in particle physics field theory defined on flat Euclidean or flat Minkowski (special relativity = flat relativity) geometry.

11. Nov 4, 2013

### kye

I read the paper. I don't think 100% of physicists agree with it. Is there more papers like it from the perpective of others (more QFT related like strings versus the geometry approach of LQG)? Thanks.

12. Nov 4, 2013

### Simon Bridge

Where you have two physicists you'll find at least three opinions.

The paper provides an overview of the main ideas on the subject.
It includes citatons that you can follow up on. You can also loo for papers citing that one - soe of those will be from detractors.

It is very difficult to now how to pitch the responses here.
Do you now what it means to have a covariant Lagrangian?
What is your experience of Lagrangian mechanics like?

13. Nov 5, 2013

### marcus

So far no particle physicist has disagreed, nor has any physicist of any sort. It's early days. Rovelli is the first person AFAIK to ask the question why gauge theories are so so successful (GR, Electrodynamics, QCD etc etc) and to come up with this answer (to a question YOU also were asking).

Here is the response to his idea from an unrelated couple of particle physicists, not quantum gravity people. Not in any sense colleagues or allies of Rovelli--they just happened to like his idea about "why gauge?" as it applies in high energy physics.

Page 37 of
It is often considered that gauge symmetry is simply a mathematical redundancy of the theory. Gauge non-invariant quantities are therefore not considered as physical. However, as nicely stressed by Rovelli in Ref. [142], by coupling gauge non-invariant quantities from different systems, one can form new gauge-invariant quantities. One can therefore in some sense “measure” gauge non-invariant quantities of a system as long as it is relative to another system. The QCD factorization theorems allow one to separate the leading contribution of a scattering amplitude into hard and soft parts. The Wilson lines entering the definition of the parton distributions ￼represent in some sense the relative phase between these hard and soft parts.
http://inspirehep.net/record/1254431
http://arxiv.org/abs/arXiv:1309.4235
The angular momentum controversy: What's it all about and does it matter?
E. Leader (Imperial Coll., London), C. Lorce (Orsay, IPN and Liege, IFPA)
(Submitted on 17 Sep 2013)
The general question, crucial to an understanding of the internal structure of the nucleon, of how to split the total angular momentum of a photon or gluon into spin and orbital contributions is one of the most important and interesting challenges faced by gauge theories like Quantum Electrodynamics and Quantum Chromodynamics. This is particularly challenging since all QED textbooks...
96 pages, 11 figures. (review article, invited contribute to *Physics Reports*)
Elliot Leader is a prominent particle physics phenomenologist whose recent papers tend to be about QCD.
His over 100 published papers have gained around 3300 citations by other researchers, an average of over 30 per paper. No connection with Loop, or quantum gravity, or Rovelli. He just happens to like how Rovelli's idea applies to QCD QED, and Standard Model stuff, quarks etc.
http://inspirehep.net/author/profile/E.Leader.1 (a few "very well known", or "famous" papers. his profile enumerates, no less)

Nice reception

Cedric Lorce is a younger guy, started publishing only 6 years ago or so, fewer papers. fewer citations (around 22 per published paper). Less prominent but looking good for someone at his stage of career. He is also a HEP phenomenologist
http://inspirehep.net/author/profile/C.Lorce.1

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Last edited: Nov 5, 2013
14. Nov 5, 2013

### kye

The reason for this thread is because I was wondering why Grand Unified Theories (GUT) or Su(5) fails. I read the following in Lee Smolin "The Trouble With Physics" (for perspective and to get a feel of the gravity of the situation):

"He and I found ourselves trying to pinpoint when particle physics had ceased to be the fast-moving field that had excited us in graduate school. We both concluded that the turning point was the discovery that protons don't decay within the time predicted by the SU(5) grand unified theory. "I would have bet my life - well, maybe not my life, but you know what I mean - that protons would decay," was how he put it. "SU(5) was such a beautiful theory, everything fit into it perfectly - then it turned out not to be true."

Indeed, it would be hard to underestimate the implications of this negative result. SU(5) is the most elegant way imaginable of unifying quarks with leptons, and it leads to a codification of the properties of the standard model in simple terms. Even after twenty-five years, I still find it stunning that SU(5) doesn't work. "

(((())))

Lee Smolin said that after 1973, all theories made failed (remember the Higgs theory was discovered earlier)..so from GUT to Supergravity to Supersymmetry to String Theory (no supersymmetric and extra dimensions detected at LHC)... Why? Why doesn't the Gauge Principle made SU(5) right?? (To Simon Bridge, I'm still studying the paper and will do the rest of the week analyzing every detail of it.. to figure out why GUT fails.. do you know why?)

15. Nov 5, 2013

### marcus

It's staring you in the face. You are ignoring the diffeomorphism gauge group. (the no fixed prior geometry idea). All the theories you are talking about are defined on fixed mostly FLAT geometry. The 4D geometry of special relativity is flat (minkowski space).
That is unrealistic. Nature doesn't work like that. Matter affects geometry. Geometry determines CAUSAL relations among events. Realistic physics has to be built on dynamically curving geometry or it is a dead end. Physics departments around the country seem to be getting the idea (hire people in cosmology and astrophysics who are familar with GR, not merely flat space people).

Look at the HEP-theory job market. Look at what specialties the physics departments in the USA and Canada want applicants for faculty jobs to have.
These are the posted first-time faculty job openings for 2014, in HEP-theory. Roughly half the postings specify cosmology and astrophysics. Ten years ago half the HEP-theory hires were in string! there has been a big shift in what physcs departments are looking for, in young HEP-theorists.

16. Nov 12, 2013

### kye

Marcus or anyone, I've thought deeply of this and read all suggested papers. But I can't understand why the fundamental forces has symmetry related to 1,2,3 gauge generators. Why can't two fundamental forces be described by say the same Su(2)? In other words, the invariance of phase in U(1) and invariance of weak isopin in S(2) and invariance of colors in S(3) are not related... or is there a vital relationship between phase, weak isopin, colors that they need internal symmetry related to 1, 2, 3? In 3D object, we know the length and width and depth is related to 1 dimension, 2 dimension, 3 dimension.. but the 1,2,3 in the fundamental forces... how are they related.. why the internal symmetry generators need to be 1,2,3.. anything I missed? any papers that discussed this?

17. Nov 12, 2013

### Blackforest

Thanks so much for this fantastic document (pedagogy +++). May I ask two byside and technical questions concerning § II A, at the very beginning? For example : "Does the relations (13) (14) and (15) allow cyclic phy functions?" "What kind of product is connecting p and a in the exponent?"

Otherwise for kye
"Why gauge theories? And why they are so successful and useful?" Certainly because they are helping us to do a classification in the set of all what is existing. Two seemingly different objects or phenomenologies appear to be in fact the same as soon as we are able to discover a gauge connecting them (example: electricity and magnetism). Conversely an object and a valid gauge being given, we are a priori able to predict the deformations of the initial object. Funny; but this is a general and intuitive concept. It certainly also participates to the quest of unity in physics.... a dream.

The number of generators is related to the dimension of the set which is generated; e.g.: SU(2) has dimension (2 x 2) - 1 = 3. It is mathematic,more exactly: algebra. The concept of dimension can be confusing because it has a mathematical or a physical meaning depending on the context where you are working. It is (perhaps) a hasard if the dimension of SU(2) is also the dimension of our real space.

Last edited: Nov 12, 2013
18. Nov 12, 2013

### kye

I know the difference between dimensions in physical space and the internal symmetry space of gauge theory. What I'm asking is what is the relationship of phase, weakisopin, colors of the em and strong force why they have 1,2,3 in U(1)+SU(2)+SU(3), why not U(2)+SU(4)+SU(7), or why can't the strong force be mediated by say 3 gluons (and only two special quarks) instead of 8 gluons (or 3 normal quarks), what is the intimate relationship of phase, weakisopin, and colors and why the fundamental forces are not made by duplicate gauge.. is it a coincident that they are 1, 2, 3? Maybe the wave functions would be redundant if two fundamental forces were described by the same SU(2)? For example. The EM force can be SU(2) by symmetry of electric charge and magnetic charge (magnetic monopoles) at high temperature (of the big bang) and the symmetry broken to make it just U(1) and the monopoles disappear. So I'm asking if there is a rule or not that the gauge forces need to be U(1)+SU(2)+SU(3). Can it be SU(2)+SU(2)+SU(3) for example (just for sake of discussion) or is the sequential 1,2,3 violated? Hope people get what I mean.

19. Nov 23, 2013

### Ilja

There is no such explanation in the Standard Model, and there cannot be anything similar in Quantum Field Theory, because every gauge group and every representation of this gauge group on some number of fermions would be possible. With a minor exception (anomaly freedom).

So you need some more fundamental theory, one which makes a hypothesis about the nature of these fundamental fields. Grand Unification is clearly the wrong way - at best, it gives a larger group, but the gauge group as well as the fermions remain as arbitrary and unexplained as in the SM. SU(5) may be more beautiful in some abstract mathematical sense of beauty and simplicity, but it remains unexplained.

You have to do something completely different to explain such groups and particles. You have to build more fundamental models. The example how to do this is kinetic theory: One starts with the atomic hypothesis and tries to explain the observable fields of thermodynamics and hydrodynamics in terms of these hypothetical fundamental atoms.

In Foundations of Physics, vol. 39, nr. 1, p. 73 (2009) http://arxiv.org/abs/0908.0591 you can find my proposal for such a more fundamental model. Quite successful, it would give an answer to your question.

But, unfortunately, theories of this type (at least if different from string theory) are anathema in modern physics. They are far too close to good old ether models. If you start research in this direction, you have no chance to find jobs in fundamental physics, there will be no conferences, almost no appropriate journals, it becomes extremely hard to publish a paper. Essentially you have to be an independent researcher, living on your own money.

20. Nov 23, 2013

### friend

I don't know if you can "explain" the SM. All physics can do is notice mathematical patterns in the data. If you found some symmetry that incorporates U(1)SU(2)SU(3), then you'd ask what explains that. The demand for explanations don't stop until you derive physics from the fundamental principles of logic. Then there is nothing left to question except your faculties of reason. Some think that is a lost cause with no agreed upon start. But I have seen some efforts that look promising even if unpublished in peer reviewed sources.

21. Nov 23, 2013

### Ilja

To explain means, of course, to explain in terms of some more fundamental theory. No problem - one has to take a look at the particular theory (in term of its own the simplicity and beauty) and what it explains. To derive a nontrivial physical theory from logic is simply nonsense.

The standard model, of course, explains a lot of our world. But it remains sufficiently complex so that it is reasonable to hope for a simpler, more fundamental theory which is able to explain the standard model.

My proposal, http://arxiv.org/abs/0908.0591, does this job. And it is peer-reviewed,

22. Nov 23, 2013

### friend

This last statement of yours is a contradiction of terms. Of course we think physical reality is logical in some way in the finest of detail. To think otherwise is to suggest that something in reality is not logical. And I don't think you can actually prove that. So I have to think that the symmetries of physics are logical, but in which direction they exactly break may be arbitrary.

So if you are looking for a theory that arbitrarily breaks into the standard model, there may be many theories that break in this way. Otherwise, there is a unique theory/symmetry that results in the SM, and I'd have to think we would have found that by now.

23. Nov 24, 2013

### Ilja

The laws of physics have to be compatible with the rules of logic. So there should be no contradiction between the physical theory and logic. But they cannot be derived from logic. This would be something completely different.

And, indeed, there may be very different more fundamental theories which have the Standard Model as some large distance (or whatever else) limit. One has to make guesses to find one. I do not really doubt that among the landscape of possibilities of string theory there may be also something similar to the SM. So, this is not really the interesting question.

The interesting question is what is explained by the more fundamental theory. Kepler has hoped that the number of planets and their distances may be explained by a more fundamental theory. This has been given up. Keplers laws, except the one which associates the planetes with the Platonian bodies, have been derived, thus, explained, by the more fundamental Newtonian theory. The number of the planets, as well as their distances from the Sun, remain unexplained and are considered to be historical accidents.

So, if string theory would be successful, and identify one of the myriad of possibilities with the SM, the SM would not have been explained. It would remain an accident. A lot of very very different "standard models" would have been compatible with string theory too. So string theory does not predict the standard model, and does not explain its properties. Why three generations, why three colors? This remains unanswered, there could have been five, six, twenty or a million generetations, or two or four or a billion colors.

In my model, the situation is different. The number of fermions is predicted, the gauge group and its action is predicted almost exactly. Replace left with right is the other possible maximal gauge group compatible with the proposed principles. Another gauge group or another number of fermions would require a different model or different principles, or some additional restrictions - in other words, a different theory. So, this theory explains essential properties of the SM.

This does not change the fact that the model itself, as well as the principles used there, are hypotheses. They cannot be derived from pure logic. No notrivial physical theory can be derived from pure logical principles.

24. Nov 24, 2013

### friend

I appreciate your efforts. Perhaps you did find some reasons for the SM. But I really think you need to refrain from statements like the last one. You can't actually prove it. Or can you point us to some paper that does prove physics is definitely not derivable from logical principles? Imagine that, someone showing us the math that proves physics is not derivable. Are you thinking in terms of Gödel's Incompleteness Theorem? Then I would remind you that the completeness of physics in not the same effort as the completeness of math. No one thinks it will take every derivable math equation to describe physical laws. We are only looking for a minimal number of equations that describe everything.

Last edited: Nov 24, 2013
25. Nov 24, 2013

### Ilja

Sorry, but what can be derived from logic is part of logic, and therefore part of mathematics, not of physics. This is a quite trivial subdivision of different domains of knowledge which is part of common sense.

I recommend you to read some introductions into philosophy of science. Or something about the scientific method in general. Popper would be a good idea. But the very idea that physics can be derived from logic is so far outside of common sense that nobody will consider it seriously.

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