Lab Notes for a Scientific Revolution (Physics)

July 27, 2007

Follow Up Discussion of Lab Note 1 — a 2007 Update

Filed under: Physics,Science — Jay R. Yablon @ 8:57 am

My colleague and co-moderator Peter Enders over at SPF asked for some clarifications on the 1984 paper.  You can read his queries, and my reply, over at:

http://groups.google.com/group/sci.physics.foundations/browse_frm/thread/d6676287ecd56235/73757d374d47b064#73757d374d47b064.

I have tried to summarize what I now see the main points of this paper to be, 23 years later.  You may view this 2007 summary, which is only three pages long, at the link below:

A 2007 Update of the 1984 Paper

Jay.

July 24, 2007

Lab Note 1: My 1984 Unpublished Paper on Geometrodynamics with Sources

Filed under: Physics,Science — Jay R. Yablon @ 4:51 am

The following is a PDF version of my 1984 unpublished paper:

An Extension of Reinich’s Already Unified Theory to Electromagnetic Sources, In a Simply-Connected Spacetime Topology

This is a good starting point for my blog, first, for historical reasons, and secondly, because this paper is still of interest to me today, and still influences my work heavily in at least two ways:

First: writing this paper was the first time that I because attuned to the importance of duality and duality symmetry.  Reinich showed that gravitation and electromagnetism are, classically, “already unified” if one considers “source-free” electrodynamics, which, implicitly, also thereby introduces a duality symmetry between electric and magnetic fields.  This led me to consider whether and under what circumstances Wheeler / Reinich’s approach might be extended to include sources.  The fly in the ointment, of course, is the absence of an observed symmetry between electric and magnetic sources.  We definitely observe electric charges.  We definitely do not observe magnetic charges, or, if we do, we don’t know that they are magnetic charges and we do not experience them in the same way as we experience electric charges.  Therefore, to extend Reinich, which is the cornerstone of Wheeler’s “Geometrodynamics,” to include sources, one must of necessity grapple with the absence of observed duality between electric and magnetic sources.  I have therefore come to regard the question of WHY we do not observe a duality symmetry between electric and magnetic courses, and, in modern parlance, the question of HOW one might start with such a symmetry and then “break” or “hide” this symmetry, to be the oldest unresolved question in theoretical physics, dating all the way back to Maxwell’s time.  Of course, with the quantum revolution which started right in 1900, this question got lost in the shuffle, but it still subsists as a fundamentally-important, unresolved physics question.

Secondly, in this 1984 paper, I first became aware of that there exist — at least formally speaking — third rank antisymmetric sources, in addition to the first rank sources that we regard classically as electric currents.  You will see these in the 1984 paper.  MTW’s Gravitation also talks about first/third rank duality, but only in a formal way, and without connecting the third rank antisymmetric tensors to anything physical beyond their first-rank duals.  For twenty years, I was aware of these third rank antisymmetric sources, but thought of them as some unexplained, unphysical oddity with merely formal utility.  Then, in early 2005, it occurred to me that these third rank antisymmetric sources, in non-abelian gauge theory, may, as a formal matter, come to be regarded as baryons.  Those have followed my work are aware that since that time, I have become absolutely convinced that it will one day be recognized that baryon sources are, in fact, to be regarded in spacetime as third-rank antisymmetric tensor sources.  If the establishment ever catches on to this, you know where you first heard it.

Let me now tiptoe into some of the mathematics which I think is important to keep in mind.   I will start with the known mathematical identity:
eq1.jpg
between any two antisymmetric tensors A and B in spacetime, where * denotes “duality” employing the Levi-Civita tensor in the usual way.  This identity applies even where A and B are non-Abelian, and it is one of the most important, yet least-utilized identities in (classical) physics.    Especially, when we associate A and B with the field strength tensors F of QED and QCD, then the third-rank antisymmetric term B_{\tau\sigma;\mu}+B_{\sigma\mu;\tau}+B_{\mu\tau;\sigma} can be thought of as a third-rank antisymmetric source (and also as a magnetic charge) while *B^{\tau\sigma}\,_{;\tau} is of course related to first-rank sources, namely, current densities J.  Further, equation (1), in terms of its differential order, is in the nature of a dynamical equation between the first and third rank sources, and it is at the same differential order as the Bianchi identity of gravitational theory.  It is as a result of all these connections that the fundamental relationship of the 1984 paper,  R_{\mu\nu}=0 emerges as an alternative statement for Maxwell’s equations with sources, so long as there is a duality symmetry between electric and magnetic sources.  Note, particularly, the discussion in section 6 of this 1984 paper, which is based on one of Einstein’s final papers on the Relativistic Theory of the Non-Symmetric Field, and which contains an explicit calculation showing the strength of the electromagentic and gravitational field equations to be identical.  I believe that in this last paper, Einstein was laying out for future generations, an important guidepost for achieving unfication between (classical) gravitational and electromagentic theories.   So, the identity (1) is important to keep in mind, and one ought to be inquiring into the physical content of this identity, and not just its mathematical existence.

The second piece of mathematics to keep in mind is what happens to third-rank antisymmetric tensors in the above, when Yang-Mills (non-Abelian) gauge theory is considered.  t’Hooft and Polyakov were the first to recognize that magnetic sources become non-vanishing in non-Abelian gauge theories.  For Abelian gauge theory this term is identical to zero, but for Yang-Mills, if one defines a field strength tensor F in the usual way, then, with group indexes suppressed:
eq2.jpg
which in the language of forms is:
eq3.jpg
This object is non-zero, it is a source, and it ought to exist somewhere in the observable universe.  Also, in light of how such sources enter into equation (1), on a par with electric sources, this is, in my view, the start of the trail that leads to understanding baryons.  Again, the seeds of these two lines of inquiry, are already contained in the 1984 paper.   I will have more to say about baryons in a later lab note.

Finally, one should also keep in mind that the electric current, in the language of forms, is specified by:
 eq4.jpg
This too, is a three-form, based on a third-rank, antisymmetric tensor.  We need to understand these third rank antisymmetric tensors on their own terms, and not just as a formalism in relation to their first-rank duals.  If I have not made myself clear, let me do so one more time: these third-rank antisymmetric tensor sources underlie the very existence of baryons, which in turn underlie the vast bulk of our material universe.  One day, everyone will come to recognize this.

In the spirit of the blog, this is my first lab note.

July 22, 2007

Welcome to Jay R. Yablon’s Physics Weblog

Filed under: Physics,Science — Jay R. Yablon @ 9:42 pm

 Dear Friends:

Welcome to my new Weblog “Lab Notes for a Scientific Revolution.”

Those of you who have followed my Usenet discussions know that I am a maverick physicist who is willing to think outside the box in order to gain new insights into the nature of our material universe.  By way of background, I am a co-moderator of the Usenet group sci.physics.foundations.  Vocationally, I am a patent attorney and in the thirteen years I have been in private practice, have secured over 100 US and foreign patents for my clients.  Avocationally, I am a physicist.  As an undergraduate at MIT, I double-majored in electrical engineering/computer science, and political science.  I opted out of what I originally intended to be a major in physics, because I believed that had I done so, I would have lost my ability to see the subject objectively, that is, I would have learned all the trees, but then found it difficult to see the forest.

Instead, after graduation, I formulated my own course of study, which started with special and general relativity (which to me are the “gold standards” of theoretical physics), then moved to elementary particle physics.  Presently, I am studying quantum field theory.  As I study each subject, it is important to me not to merely take the subject at face value or regurgitate subject matter or learn every possible calculation, but to put together my own understanding of the subject on premises which are simple and intuitive and fundamental, not unlike how one can view general relativity, for all of its mathematical complexity, as little more than geometry and the dynamics of geometry.  I believe strongly that Wheeler was on  the right track when he proposed geometrodynamics, and am certain that one day we will uncover a purely geometrodynamic understanding of nature.  I remain a counterrevolutionary regarding the probabilistic interpretations of quantum mechanics, though find great value in the statistical methods used, for example, to understand thermodynamics on the basis of collective molecular motion.

Most fundamentally, I am an unabashed practitioner of the “scientific method” of iterative trial and error and correction through feedback.  Some of my critics might say that most of my emphasis is on “error” ;-), but I heed closely the words of Thomas Alva Edison: “I have not failed. I’ve just found 10,000 ways that won’t work.” One must be wiling to make errors, even silly errors, in order to make advances, and anyone who does not have the courage to do so is not suited to advancing the frontiers of human knowledge.

I have, over a number of years, noticed that much of what we already know about the physical universe — if viewed in a different way than usual, or developed down a somewhat different path than what is conventional — can lead to some very interesting new insights.  Sometimes, what we think is an insight turns out to be a dead end. Other times, our insight may be an ember which, if only we fanned in just the right way, can become a roaring fire of new knowledge.  These various “insights” and “embers” — some possible leads, others dead ends, are what I have termed “lab notes.”  Unfortunately, I find that the physics “establishment” — to borrow a pejorative from back in the 1960s — has become all too skilled at stamping out rather than fanning possible embers of new knowledge. 

When one is in a lab, practicing scientific method, one takes systematic notes about what one is observing.  Going back over those notes, and trying to synthesize those notes into something that makes theoretical sense, is the heart of scientific method.  When we carry out a serious gedanken, i.e., thought experiment, and wander into possibly unexplored paths, preparing good lab notes is equally important.  When Lewis and Clark explored the American Northwest, their diaries were filled with notes of their explorations.

In the course of my explorations, I have developed a number of insights, some of which may lead to new directions in physics, and others of which may lead nowhere.  But, if even a single lead goes somewhere, then the effort is worthwhile.  As just one example, in my explorations I have noted that electric and magnetic sources in electrodynamics can be represented as third-rank antisymmetric sources in spacetime.  When non-Abelian (Yang-Mills) gauge groups are employed, these sources are non-vanishing (I believe t’Hooft and Polyakov were among the first to see this).  I believe that these third-rank antisymmetric sources, in fact, lay the theoretical foundation for the observed three-component sources we have come to know, experimentally, as baryons.  My best “lab notes” on this, to date, are at http://home.nycap.rr.com/jry/Papers/Baryon%20Paper.pdf.

So, over the coming weeks and months, I will use this blog to compile my years of “lab notes” under one roof.  To put all the embers in one place.  If you wish, you may think of this as something of a scientific diary.  This may mean nothing, or, perhaps, this may turn out to be a contribution to the advancement of humankind’s knowledge of the material universe.  Either way, I do know for certain that nothing good is ever achieved without taking risk and making concerted effort.

Finally, although a maverick, I am a very conservative physicist.  I do not believe in lightly discarding that which clearly works.  I believe in building on what works, or incorporating what works as a special case of something even larger and more-encompassing.  I believe in building “on the shoulders of giants,” and recognize that the giants of ages past became so with good reason.  We do not tear down that which is established, we try to build it up further, understand it better, and make it simpler.  One of the great tragedies of the 20th century, is that our understanding of physics became so complex and so esoteric, that a genuine understanding of the material universe via the discipline we call “physics” is now thought to be beyond the comprehension of even very intelligent scientists and engineers who are not directly in the field.  This, to me, does not prove that physics can only be comprehended by an elite few; rather, it indicates that those who think they understand physics, do not understand it as simply as they ought to, or as simply as nature sees herself.

I am starting this blog not to simply talk at my readers, but to hear from you.  I am a thoroughgoing believer in collaboration.  I also believe in the adage that great progress can be made, as long as it is not important who gets the credit.  I hope that my readers will work with me to fan some of these embers, and that together, we can move physics forward toward a new scientific revolution.

Jay.

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