Origin and Nature of Gauge Principle

[friend]

Philosophy of Science 101:
Topics: Realism vs Phenominalism, Empiricism vs Rationalism, and the problem of Induction.
Major figures: Carl Popper and Sam Kuhn.

A proposition "proved" by logic alone is just an extension of whatever model was used for axioms... it just says that the proposition is consistent with these models. It does not tell you that the proposition is true of Nature.

The models themselves must include synthetic propositions if they are to be scientific - and the truth of synthetic statements cannot be known a-priori. There are some things you cannot know just by thinking about them. i.e. you have to go look. It is not just physics that is like this - it's any empirical science.

We should consider that whatever synthetic proposition we would start with can be comprised of a conjunction of other propositions used to describe it in finer detail. And even these can be decomposed into a conjunction of even finer propositions. And this process can go on until we are considering propositions that carry the minimum of physical information, exists or does not exist, on or off, true or false, propositions in the most basic general form, pure informational. And if this is done, then at that level we are describing physics in terms of abstract logic alone.

Which means that Deep Thought cannot deduce the existence of rice pudding and income tax starting from, "I think, therefore I am". Which is why it's a joke.

It would be a serious paradigm shift to go from the normal trial-and-error method of science, to including physics as a part of math or logic. I don't think any attempt would even be considered in refereed publications, even if it were easily understandable with high-school math. And so there will be no attempt to publish here. But if you really want to see the math, then send me a Private Message, and I'll give you a link. That might prove to be a very interesting conversation.

 

[Simon Bridge]

...until we are considering propositions that carry the minimum of physical information, exists or does not exist, on or off, true or false, propositions in the most basic general form, pure informational. And if this is done, then at that level we are describing physics in terms of abstract logic alone.

The logic applies only to the description - not to the truth of the propositions, which cannot be determined by logic alone, being synthetic.

It would be a serious paradigm shift to go from the normal trial-and-error method of science, to including physics as a part of math or logic.

You mean, showing that empiricism is wrong?
The kind of description you are talking about first requires that there are synthetic propositions whose truth can be known a-priori. Is this what you are saying?
Because that would be a major breakthrough that has eluded some of the best minds for centuries.

 

[friend]

The logic applies only to the description - not to the truth of the propositions, which cannot be determined by logic alone, being synthetic.

All physical laws do not specify any actual observation. They all only apply to hypothetical situations, given these hypothetical inputs (not saying that it actually exists or not) we should expect this result as a consequence. So no theory (proposed or accepted) specifies the truthvalue of any actual physical event described by a proposition. We are ignoring the truthvalue of our propositions.

But that does not allow us to ignore that we must use propositions to describe physical situations (observed or proposed). If we accept that we must use propositions to describe things (without actually knowing the truthvalue), then the question is how far can we break it down into constituent propositions? Can we go as far as to specify a continuous set of propositions specifying the hypothetical points of some spacetime manifold? I believe this is what we do in SR and GR, where we call each point in the continuum an "event". And proposition may be another word for event.

You mean, showing that empiricism is wrong?

No. Empiricism is just curve-fitting, finding the most accurate math equations to predict other events. And we have become quite cleaver in finding the hidden mathematical patterns behind the date, this symmetry or that, etc. In my opinion, this really does not explain anything. You only end up pushing the question a little further and beg the question, then why that math.

Some may prefer to think that we cannot derive physics from logic for fear of the possibility that if we did and observation proved that theory wrong, then reality would be illogical, and that is too much of a dilemma for some people to consider. I prefer to have more faith than that.

The kind of description you are talking about first requires that there are synthetic propositions whose truth can be known a-priori. Is this what you are saying?

No. See above. All theory addresses only hypothetical situations and does not even address the truthvalue of any particular proposition.

 

[Simon Bridge]

Well I guess I invited this sort of response...
I think we agree that the logical description of physics would be just that, a description, with no way of assigning a truth value to anything :) However, physics is not just a particular collection of statements about the World is it?
At least, not as practiced by the physicists I know.

... sorry, I don't really do philosophical hair-splitting.

Can you relate all that more directly and concretely to the topic of the thread?

 

[friend]

Well I guess I invited this sort of response...
I think we agree that the logical description of physics would be just that, a description, with no way of assigning a truth value to anything :) However, physics is not just a particular collection of statements about the World is it?
At least, not as practiced by the physicists I know.

... sorry, I don't really do philosophical hair-splitting.

Can you relate all that more directly and concretely to the topic of the thread?

Not without referring to my unpublish(able) works. PM me if you want details.

 

[friend]

Not without referring to my unpublish(able) works. PM me if you want details.

Yes, if I were to just blurt out my summary or conclusions, it would seem speculative, and I'd get an infraction for my efforts. But maybe if I were to work backwards and quote my sources, then it might seem to fit.

So I'd like to start by noticing the relationship between the symmetries of the standard model and the Cayley-Dickson construction of the hypercomplex numbers. The Caley-Dickson construction seems to be an iterative process, and I'd like to show where this same iterative process comes from in the path integral of QM. So give me a few days to look up some references before I get too far.

 

[friend]

So I'd like to start by noticing the relationship between the symmetries of the standard model and the Cayley-Dickson construction of the hypercomplex numbers. The Caley-Dickson construction seems to be an iterative process, and I'd like to show where this same iterative process comes from in the path integral of QM. So give me a few days to look up some references before I get too far.

It is generally accepted that the symmetry of the SM is U(1)XSU(2)XSU(3), and the question is why these and no others?

Some have shown that these symmetries are related to the hypercomplex division algebras of the complex numbers, the quaternions, and the octonions. See here and here, which seem pretty well referenced. They equate the algebra of the quaternions to the algebra of the Pauli spin matices, and equate the algebra of the octonions to the algebra of the Gell-Mann λ matrices of the SU(3) symmetry. And also Sir Michael Atiyah Ph.D has discussed the relevance of these normed division algebras in the Youtube video here, starting at minute 29:00. The question remains, however, why these division algebras?

The Cayley-Dickson construction of the hypercomplex numbers is an iterative process such that the quaternions can be constructed from the complex numbers, and in the same way the octonions can be constructed from the quaternions. John Baez has an explanation of this iterative process here.

The Feynman path integral of a real, classical field, introduces a complex number to produce a quantum field, and this gives us the U(1) symmetry. This suggests to me that we could iterate the process by using a quaternion in the path integral of a complex field to get the SU(2) symmetry, and use an octionion in the path integral of a quaternion field to get the SU(3) symmetry. This is not present practice. But it does seem to suggest itself. Further study is required in order to say anything definitive. If applicable, this would explain the origin of the symmetries of the Standard Model.

 

[Ilja]

It is generally accepted that the symmetry of the SM is U(1)XSU(2)XSU(3), and the question is why these and no others?

Yes. But there is more to be explained: This group acts on the fermions in a very special way, which is described by the charges of the fermions. The number of the fermions and all the charges of all these fermions have to be explained too.

arXiv:0908.0591 proposes a solution, is published in Foundations of Physics, vol. 39, nr. 1, p. 73 (2009), but I have not received much reaction, except for an invitation to publish arXiv:0912.3892 in Reimer, A. (ed.), Horizons in World Physics, Volume 278, Nova Science Publishers (2012).

 

[kye]

It is generally accepted that the symmetry of the SM is U(1)XSU(2)XSU(3), and the question is why these and no others?

Some have shown that these symmetries are related to the hypercomplex division algebras of the complex numbers, the quaternions, and the octonions. See here and here, which seem pretty well referenced. They equate the algebra of the quaternions to the algebra of the Pauli spin matices, and equate the algebra of the octonions to the algebra of the Gell-Mann λ matrices of the SU(3) symmetry. And also Sir Michael Atiyah Ph.D has discussed the relevance of these normed division algebras in the Youtube video here, starting at minute 29:00. The question remains, however, why these division algebras?

The Cayley-Dickson construction of the hypercomplex numbers is an iterative process such that the quaternions can be constructed from the complex numbers, and in the same way the octonions can be constructed from the quaternions. John Baez has an explanation of this iterative process here.

The Feynman path integral of a real, classical field, introduces a complex number to produce a quantum field, and this gives us the U(1) symmetry. This suggests to me that we could iterate the process by using a quaternion in the path integral of a complex field to get the SU(2) symmetry, and use an octionion in the path integral of a quaternion field to get the SU(3) symmetry. This is not present practice. But it does seem to suggest itself. Further study is required in order to say anything definitive. If applicable, this would explain the origin of the symmetries of the Standard Model.

Do you or anyone knows of any papers at arxiv or peer reviewed paper in which free quarks can occurred from a certain gauge symmetry (from different vacuum condition) that is different from the basic symmetry where they are bound (or can't be isolated)?

 

[Berlin]

There are many examples where people try to relate the specific groups of the standard model to another 'higher' principle. But in many cases you do not get something new in explaining physics. So, those solutions more or less translate the assumption into another assumption without solving or predicting anything. I few years ago Christoph Schiller related the groups of the standard model to the three Reidemeister moves. When I saw this first, i thought, holy s*** this must be it, but in the end it did not explain much and merely created a new set of questions of the same size. However, the history of physics proves that reformulating a problem can be very strong, and indeed the basis for progress, which was more difficult in the other formulation. Let's hope we find one!

Berlin