[General] Maxwell's

[John Williamson]

Dear Grahame,

You ask, of course, a very fundamental question and one that may or may not have an answer, depending on your starting standpoint. If one starts with Maxwell, of course, one has already put space and time in there as they are equations with respect to d/dx, d/dy, d/dz and d/dt, with some very particular definitions of the underlying nature of space, time, division and differentiation. One has also put in the “fields” as a basis, and, if one takes the inhomogeneous equations as a starting point one has assumed (quantised) charge as well. Quite a basket of starting assumptions!

For Maxwell, the underlying system of space was left-handed though quantised charge was, of course, not in there yet. Note that Maxwell has also assumed that space exists! The effective metric was (+ + +) for space with time considered separately and the proper signs were taken from experiment. His space was Euclidean! Nowadays one usually uses a right handed system with the (+ - - -) metric. Further one assumes (R R R R) for the four 3D systems of space, electric field, magnetic field and spin. This is the set I used in the 2015 SPIE papers. It is somewhat problematic in that one needs to use a different sign for either the electric or magnetic field in one or the other pair of equations, as is well known. (See Jackson). You see you have already got a lot of starting stuff in there, space, time, charge, fields, a metric, a definition of an algebra assigning meanings to addition subtraction, multiplication, division and (vector) differentiation. One needs to have all this to write down the theory. It is not often realised, but is so, that te underlting maths is different for increasing levels of sophistication as one moves from 3-vector products to 4-vector products. Even then the underlying mathematics of multiplication and division (and hence differentiation) is different for the tensor form (as in the more advanced chapters of Jackson) for the algebra of forms, or for the Clifford algebras Cl(1,3) (and Cl(3,1)).

The underlying question about the nature of space and time is, of course, very interesting and one which has been on my mind almost every waking moment for me for the last four decades since I was a fresh and eager graduate student. One can derive them from more complex systems, of course, but if one looks for the  ultimate simplicity of underlying nature, Occam’s razor, I have not found a smaller set than taking space and time to be fundamental and for everything else (with root energy) to flow from them. I have not yet seen a smaller set from anyone else either.


The initial inspiration for looking at the underlying nature of physical reality, after finishing my first degree and moving on to start a PhD at CERN was from reading David Bohm. The initial inspiration, and work, flowed from a basis idea that, perhaps, everything might be “made from” light. From this standpoint, it is possible to conjecture a possible nature of space and time, indeed one can view them as arising from a variety of different scenarios. More on this later.

During the last four decades I’ve made up possibly of the order of a thousand different “theories” with various starting points and various levels of complexity. Most fell over quite quickly, some have been more long-lived. At the same time many others have been floating ideas, as is evidenced by the activity in this group, with models and constructs which number orders of magnitude more than this. All of these models have set of basis principles, the postulates or underlying axioms on which the theory is based. For me all of them, excepting the one I’m currently working on, fall over somewhere. I will keep doing this until either I become incapable of refining them (by death or otherwise), or it works in every respect, just and no more.

The process of the scientific method applied to this is one looks at the results in the light of experiment, refining those that do not fit in some respect or otherwise rejecting some aspect of the basis and starting again. The theory outlined in the SPIE papers in 2015 falls over in some of the higher order signs, so I have changed the underlying signature to fix this and properly reflect the fact that the electric and fields are fundamentally opposite-handed. On this basis, my present view is that light itself in general, and quantised light in particular, may itself be derived from a deeper paradigm of space, time, root mass and a (slight) modification of the rules of “multiplication” and “division”, which then properly reflects the undelying nature of space and time and thus simplifies the overall picture.

There is an idea which I think is valid, first proposed by Wittgenstein in his “tractatus logico-philosophicus” that one cannot say anything about the basis postulates of any logical system by arguing merely within that system, though mathematicians and physicicts often ascribe this kind of idea to Godel. Any theory, then, may be said to be “good” in so far as it it properly describes all those elements of reality within its remit. At present there are, to my knowledge, only two currently accepted theories which are not known to fail in some limit in this respect: general relativity and quantum electrodynamics (QED). Maxwell, for example, fails in that it says nothing about quantisation, predicting many phenomena that are not observed to occur. Quantum mechanics is pretty good, but non relativistic. Relativistic quantum mechanics gets some aspects of quantised spin, but not quantised charge and does not give a realistic description of what happens in materials, where non-relativistic quantum mechanics proves better. General relativity and QED themselves contain concepts which one may question, such as the postulate of equivalence or general covariance in relativity or the point nature of charge and the underlying infinities in QED. None of these are quite perfect then, and certainly none are complete. A side aim of the new theory is that it should be wholly consistent with the starting points of these two theories, which it is.

At the beginning of the 21st century it should be noted that the accepted “standard model” has a basis of roughly a hundred basis starting points which are not derived from a deeper principle.

These include, in the standard approach, the acceptance of a zoo of fundamental particles, three heavy and three light leptons, quarks, gluons the Higgs boson, all the “fundamental” constants, such things as the postulate of equivalence as well as an undelying assumption about the (relativistic) nature of space and time and a mathematics which is taken to be a given. They also contain a set of basis equations of motion and interaction ranging from Newton’s laws, the Maxwell equations, ordinary and relativistic quantum mechanics through Hamiltonian and Lagrangian formulations to perturbative gauge theories such as quantum electrodynamics and non-perturbative ones such as quantum chromodynamics. The latter has, by itself, of the order of fifty free parametrs, some of which are omnipotent in describing any conceivable future experiment. With that many free (and hidden!) parameters it can fit any conceivable elephant or any dog’s breakfast.

What I have been trying to do for these four decades is find a way to simplify this basis down to a minimal set of starting parameters. I’m hoping and trying to find THE minimal set of starting parameters from which everything else follows, and hence solves Hilbert’s sixth problem. The two papers presented at SPIE were a step along that path. They took as a basis ONLY space and time and root-energy as well as a sharpening of the mathematics we use to describe (differential equation) theories, the concept of a “mathematics of reality”. Now that mathematics of reality, if it can be uncovered together with the starting parameters, is the solution of Hilbert’s sixth.  The 2015 papers took as a basis basis a stiff and strong underlying space time characterised by two of the three parameters epsilon mu and the speed of light c. It did not start with field, but derived it. It did not start with charge either, and derived that too. Despite that it was not yet wholly internally consistent to all orders, as became clear as I started developing tools to look at higher order differentials. That is what I have been working on for the last two years.

The mathematics of reality has an underlying implicit order of the way and hierarchy in which things happen (see Bohm “Wholeness and the implicate order for an introduction to the importance of order, for example). This mathematics is much more proscriptive and constrained than we are used to. It has to be perfectly constrained to parallel that basis if it is to describe all of reality, just and no more.

>From the starting axioms I derived in the 2015 work the underlying nature of light, a fully relativistic wave-function with photon-like properties, and a self-confined matter-light vortex corresponding to the physical electron. It was shortly afterwards, however, that I found a flaw in the system, in that the underlying handedness of one of the elements had been forced to be right-handed when it is intrinsically left-handed. Changing the underlying maths changes the theory (of course) and I am still working on checking (with a few friends) whether the new one does, indeed, derive all of physics. That is all those quarks leptons and the fundamental theories on which they are all based. So far so good, but it is a lot of work.


Now one can, of course, take other starting points. Martin and my work in the 1997 paper “is the electron a localised photon” took the properties of light (as a photon) as the starting point and derived from that, and an postulated self-confinement mechanism, the nature of charge, quantum spin, the anomalous magnetic moment, and the uncertainty and exclusion principles. One can get a long way starting with light, or starting with the Maxwell equations. Likewise others, notably Carver Mead, have got a long with with electrodynamics starting with quantised angular momentu,

Of course starting from Maxwell, to derive Maxwell would be a very circular argument indeed. Also, it is (relatively) easy to show that there are no forces in Maxwell alone capable of confining a photon to orbit in such a way as to constitute an electron. One needs to add to it. Martin is trying this at the moment by extending Harry Bateman’s method into a more realistic algebra of the underlying reality. This may well work! Batemans book “The mathematical analysis of electrical and optical wave motion in the basis of Maxwell’s equations” should anyway be on everyone’s reading list. I have now derived strong confinement forces, strong enough to hold the charge together, in the interaction of (root) mass and field, as in the 2015 pair of papers.

Now I quite like Chandra’s extension to look at space and time as a complex tension field. This takes, however, a simpler version of my starting point. For me space is not merely complex, though it contains this as a sub-algebra. Complex is too simple. For me “tension” is only one aspect. Crucially, one needs “torsion” as well. Torsion in both space and time. I prefer to reserve the word “field” to refer to the electromagnetic field, and not confuse it with tension and compression in the structure of space-time. Further there are other ways of storing energy in space time in the new theory than tension, compression or “torsion” for which we do not even have an accepted name, though they are related to the “quantum spin” degree of freedom. These are things such I have called the “hedgehog and the quedgehog – because they are three and four dimensional directed volume elements. The algebra of space-time is not complex, it is hypercomplex. To get the underlying algebra of reality right one needs quite a lot more complexity than the merely complex. This is where Dirac’s relativistic quantum mechanics breaks down. Dirac makes the mistake of attributing different things squaring to negative unity to the same thing, especially in his treatment of the underlying commutation relations he used (which were also too simple in that they did not exhaust that needed for the implicate order). This then leads him to thoroughly confuse himself which, being Dirac, he was honest enough to say this explicitly, even in his textbook (see the top of page 265 in the 4th edition, section 70 after equation 34).

So, in summary, one can indeed start with light and get a long way, also taking Maxwell as a basis. One has then assumed the Maxwell equations and their underlying standard (3D!) vector mathematics as a given. Big mistake! Not for Maxwell per-se, as the vector maths parallels the Clifford maths quite beautifully, but in any further extension of Maxwell into the realm of an improved relativistic quantum mechanics such as contained in the kinds of theories I’m now developing (I hope!).

One can also start by forgetting about light and Maxwell electromagnetism and just start with charges and the retarded potentials. One can get a long way with this too, though one has put charge in as a given. Ok, for photons one has put photons in as a given, and the fields (do not forget). One has to start somewhere. For me, while this once was a good starting point, I think one can go deeper and derive this from the proper properties of space and time.

For me, and to re-iterate, I am not starting with a given set of equations but with the underlying nature of space and time with four dimensions, two parameters and a similar definition of multiplication and addition to that in the Maxwell equations, though a more sophisticated treatment of division. This treatment of division leads to a definition of a differential which then leads, on introducing root-mass stuff, to a set of equations identical to the Maxwell equations. Unlike mere Maxwell, however, the new theory has solutions which look more like quantised photons in that they have a fixed angular momentum and an integral energy given by E = h nu, in any frame. Also, the new theory admits self sustaining vortex solutions and gives the forces needed to confine them. If the photon has integral spin, these have half-integral spin. They are also, neccesarily, charged, as this is the minimum energy configuration of such topologies. The charge one calculates has a range, containing the observed value, and for very simple assumptions is very close to the elementary charge (see Martin and my 1997 paper).

I think a further point is in order. If I am right, and everything is made of space-time and root energy, then this means, if Wittgenstien and his followers were right, that it would not be possible to say anything from within the system about the external nature of the system. If we are creatures made of space and time and of their excitations, then, without a tool composed of something outside of space and time, we have no means to measure their properties. All our rulers and clocks are also made of space time. Deform it from outside how you will, our measuring instruments deform too! The new theory describes fields, charge, light (as photons) and spin. All of these are made of the fabric of space and time as well. None are sufficient, then, to look outside the space-time box. Recent experiment has also shown conclusively that gravity is of the same stuff too. There is no measure we have to get outside the system (unless you can suggest one!). One may then be able to show that one has the minimal and best possible set of starting parameters, iff (if and only if) the theory then defines everything one observes, just and no more. Not there yet, but working on it!

That is the task.  Space and time may not, of course BE the proper starting point. I am working on a level yet deeper (for fun) but am not ready to talk about that yet.  Perhaps one should start with light. Perhaps one should start with charge. Maybe one needs six leptons a dozen quarks in three flavors each, QED QCD, Maxwell Einstein, relativity. Who knows, maybe one needs strings or membranes. Maybe, but I do not think so. I think we can, and will, do better than that.

To come back to your question, however, I think one can derive space-time and energy, given a different starting point. For example assuming all of the properties of light one could argue (and I have in the past) that space and time are what you would observe, given such a system. One then has to take on board all of the properties of light as a starting point, which then themselves become the basis about which one can say nothing within the framework adopted. At the moment I prefer to take space time and root energy as the basis, rather than the fields and the quantisation of light as in the Maxwell equations, as a given. Why? Because I think one ends up with a much more simple, much more compact view of the underlying nature of reality.

Cheers, JGW.
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From: General [general-bounces+john.williamson=glasgow.ac.uk at lists.natureoflightandparticles.org] on behalf of Dr Grahame Blackwell [grahame at starweave.com]
Sent: Sunday, November 05, 2017 6:48 PM
To: Nature of Light and Particles - General Discussion
Subject: Re: [General] Maxwell's

Dear John W,

I'd be very interested to see your derivation, not of Maxwell's Equations, but of the nature of space, time and energy that you use as your platform for deriving Maxwell's Equations.

I'm not clear how it would be possible to derive a robust well-evidenced model of space-time-energy that:
(a) doesn't reference (directly or indirectly) Maxwell's Equations or any findings derived (directly or indirectly) from those equations or any of the previously-derived electrical and magnetic relationships from which Maxwell compiled his well-structured summation of those relationships;
(b) doesn't draw on any form of post-hoc rationalisation or circular argument;
but yet
(c) provides a basis for formulation of a set of electromagnetic field interrelationships.

One concern in particular (though not the only one) is how one defines a model of space-time-energy that (presumably) makes no use of prior findings on electricity or magnetism but yet is able to provide a basis for deriving relationships between electricity and magnetism.  Specifically, how does one _define_ the terms 'electricity' and 'magnetism' (or 'electromagnetic') without reference to any of that prior work?

Thanks,
Grahame
----- Original Message -----
From: John Williamson<mailto:John.Williamson at glasgow.ac.uk>
To: Hodge John<mailto:jchodge at frontier.com> ; Nature of Light and Particles - General Discussion<mailto:general at lists.natureoflightandparticles.org>
Sent: Sunday, November 05, 2017 11:26 AM
Subject: Re: [General] Maxwell's

Dear all,

Please remember I have derived the Maxwell equations, and more, from just the nature of space, time and energy.

Relativity, in the sense that Andre has talked about as the transformations of energy and momentum, are then derived from this in both the modified theory I am working on now and in the two SPIE papers in 2015.

Regards, John.
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