Broken Maxwell EM ?

[Mikey]

Two years ago I also came across Bearden. I am grateful for this topic because of the hint that it is most probably disinformation. Anyhow I want to share my experiences:
I bought two of his books "Energy from the Vacuum" and "Gravitobiology" and some DVDs (Tom talks Tesla, Secret Soviet EM Weapons, Floyds Secrets) where he covers the theories of Tesla. I read only about 100 pages from the books, because I was not attracted from the material as I initially expected. I simply tried to understand what he did have to say and compare it to the knowledge from my studies. I could never verify some of the statements because I do not have the post graduate knowledge to do that. On one DVD he showed a supposedly free energy device run in a garage of an individual. Besides the poor filming quality there was only sketchy technical smalltalk in the interview with the builder, nothing tangible or even usable.
When I was busy with this material I showed the DVDs a friend, who was also interested in these topics. Now, as I read material which arguments against Bearden's theories, I find it interesting to witness that I was also part of a disinformation process. Needless to say, I am going to retrieve the damage at the next occation.

 

[Newton]

Recently my attention was drawn to the "European Ufo Survey", and in particular to a paper written by their onboard theoretical physicist Phillippe Gaugain: "Unified Dirac-Maxwell field as space-time portal". Three of the important references in this paper are papers by K. J. van Vlaenderen on "Tesla waves", "scalar fields" etc. In his papers Koen van Vlaenderen is using quaternions (more precisely: bi-quaternions), quotes Tom Bearden etc. His papers have been criticised by Gerhard Bruhn.

In fact the use of quaternions only obscures the subject and makes it difficult to see what is the real content and what are the problems.

All the content of Maxwell's equations in vacuum can be summarized in just one line:

*d*d A = J

where A is the electromagnetic potential, J is the electric current, d is the exterior derivative, and * is the Hodge star operator. Koen van Vlaenderen proposes to replace them by a more symmetric one

(*d*d + d*d*)A = J.

Note: *d*d + d*d* is known as Laplace-Beltrami operator.

And that is all. But he is not able to express his idea in such simple terms. Now, when you see the above simple form - you instantly see the problem. The electric charge is not conserved in this "theory with scalar waves". While in the original Maxwell theory we automatically get charge conservation, that can be written as d*J=0, in the modified theory electric charge is not conserved.

Paul Gaugain, in his paper, is not concerned with this problem, he does not correct it. It is not a good visit card for the European Ufo Survey!

I'm new to this forum, but this topic is a great interest to me.

First, are you sure your Laplacian with the differential and codifferential wrt <,> is called the Laplace-Beltrami operator? The Laplace-Beltrami is the so called 'rough Laplacin' and your form is usually called the Laplace-de Rham operator (also refered to as the de Rahm-Kodaira-Hodge Laplacian) in differential geometry.

Actually my interest is in SP(4) manifolds and solving irreduceable 2 order (on-linear) PDEs. And of course the assocated Lie algebras. Why do I mention this interest in this topic? Well quarternions (bivectors) seem to be the enabling technology... And interestingly problems involving Hamiltonian flows just don't seem tractable in Gibb's vector forms, that is 3-D orthogonal representations. But 4-dimensional non-independent quaternions (generalized coordinates) seem to be natural in generating the proper torsion free symplectic (state-space) manifolds.

In general, Gibbs arguments fall apart for a wide range of interesting problems, like Navier-Stokes, Bosonic strings, spherical gyro, etc... In short, all those problems that involve those nasty torsion-free spin manifolds.

So it looks like Gibbs may have set back mathematical-physics a century.

Newton

 

[ark]

First, are you sure your Laplacian with the differential and codifferential wrt <,> is called the Laplace-Beltrami operator? The Laplace-Beltrami is the so called 'rough Laplacin' and your form is usually called the Laplace-de Rham operator (also refered to as the de Rahm-Kodaira-Hodge Laplacian) in differential geometry.

Yes, I am sure, you may like to check S.I. Goldberg, "Curvature and Homology", p.78.

In general, Gibbs arguments fall apart for a wide range of interesting problems, like Navier-Stokes, Bosonic strings, spherical gyro, etc... In short, all those problems that involve those nasty torsion-free spin manifolds.

So it looks like Gibbs may have set back mathematical-physics a century.

Newton

Can you give just one detailed example when "Gibbs arguments fall apart"? And what are Gibbs arguments anyway? Never heared of such?

 

[Newton]

You'll notice that the Laplace-Beltrami operator is only equal to the Laplace-de Rham operator when there is no curvature.

When there is curvature, the two operators differ by Ric o X on a Riemannian manifold (I believe this is pretty well known). This is a very common error, but I'd be surprised if it's actually wrong in Goldberg.

 

[Newton]

The 'Gibbs argument' is the argument that he had with Heavyside in the late 19th century regarding using a simplified vector space in EM theory (vs Clifford algebra or Hamilton's quarternions).

What was lost (unknown at the time) was special relativity, Bosonic strings and other dynamics on torsion-free manifolds (aka - spin manifolds, SP(4), symplectic manifolds, etc)

 

[ark]

You'll notice that the Laplace-Beltrami operator is only equal to the Laplace-de Rham operator when there is no curvature.

When there is curvature, the two operators differ by Ric o X on a Riemannian manifold (I believe this is pretty well known). This is a very common error, but I'd be surprised if it's actually wrong in Goldberg.

No, this is not an error. Different mathematicians use different names for the same object. For example in the monograph of F.W. Warner "Foundations of differentiable manifolds and Lie groups", Ch. 6.1., you will find the same definition of Laplace-Beltrami operator as in Goldberg. Some monographs call it simply "Laplace operator" or "Laplacian". Some call it Laplace- de Rham. The meaning should always be read from the definition or from the context in which it is used.

 

[Newton]

You'll notice that the Laplace-Beltrami operator is only equal to the Laplace-de Rham operator when there is no curvature.

When there is curvature, the two operators differ by Ric o X on a Riemannian manifold (I believe this is pretty well known). This is a very common error, but I'd be surprised if it's actually wrong in Goldberg.

No, this is not an error. Different mathematicians use different names for the same object. For example in the monograph of F.W. Warner "Foundations of differentiable manifolds and Lie groups", Ch. 6.1., you will find the same definition of Laplace-Beltrami operator as in Goldberg. Some monographs call it simply "Laplace operator" or "Laplacian". Some call it Laplace- de Rham. The meaning should always be read from the definition or from the context in which it is used.

Here's an excellent paper, http://arxiv.org/PS_cache/math/pdf/9807/9807078.pdf using the most recent and industrial strength differential geometry.

Usually (where I come from), del-squared is the Laplace-Belrami operator. See what you think aobut the paper- It's a good read if you're into non-linear PDEs.



How do I get hyperlinks in this editor? Edit: Ah, they're almost automatic...

 

[ark]

I am not into PDE and/or into hydrodynamics, as they have little to with quantum theory. and quantum theory seems to be an important part of our understanding of the workings of Nature. As for "industrial-strength", it is a subjective term. Some people will call it "industrial-strentgth", some will just check whether the paper is right or wrong, some will just look whether it is important or not (again it is all subjective).

Not all mathematics is relevant for our understanding of the Universe around us. It may be interesting as an intellectual adventure, but I care for a somewhat more "practical" things, namely things that address in some constructive way the 100 years of standoff of theoretical physics.

 

[Newton]

There seems to be quite a few references to the work of Tony Smith. What I find scary is that Smith is almost always right or at least always has the big picture right. And he always references the exact right sources, for example Kac at MIT for gauge theories.

My background is in mathematical-physics, but I'd bet most physicists (especially QM types) think he's wrong and/or crazy.

So here's the question to forum members - do you think Tony's Voodoo Unified Theory model (theory based on the exceptional Lie groups) is correct?

 

[ark]

So here's the question to forum members - do you think Tony's Voodoo Unified Theory model (theory based on the exceptional Lie groups) is correct?

Probably it is incorrect, but it may have interesting insights. It is probably incorrect because he is not able to derive quantum theory, explain the nature of the apparent randomness in quantum events - as far as I know. Perhaps one day someone will find out how to make sense of Tony's ideas and will build a real, good, theory.

 

[Ruth]

Not all mathematics is relevant for our understanding of the Universe around us. It may be interesting as an intellectual adventure, but I care for a somewhat more "practical" things, namely things that address in some constructive way the 100 years of standoff of theoretical physics.

Hi Ark, could you please explain (for all us non-matheticians) what the 100 years of standoff in theoretical physics is all about? I would be very interested in hearing about this problem, especially as it seems to have lasted so long. I would appreciate it if you could explain in simple language and not use maths symbols (because I don't understand that language, or is it a science?). Thanks.

 

[John G]

So here's the question to forum members - do you think Tony's Voodoo Unified Theory model (theory based on the exceptional Lie groups) is correct?

Probably it is incorrect, but it may have interesting insights. It is probably incorrect because he is not able to derive quantum theory, explain the nature of the apparent randomness in quantum events - as far as I know. Perhaps one day someone will find out how to make sense of Tony's ideas and will build a real, good, theory.

Tony does get the Dirac equation from a random walk through his 4-dim hyperdiamond Feynman Checkerboard.

http://www.valdostamuseum.org/hamsmith/USGRFckb.html

Also from Tony's site: The zero-sum rule, like Valentini's equlibrium, produces the Born rule. Perhaps Valentini's non-equilibrium violations of the Born rule in the early inflationary universe may be related to non-zero-sum processes such as particle creation; and Perhaps maverick-world deviation from the Born rule for a finite number of trials may be related to the difference between a Poisson distribution (approximation to Binomial distribution accurate for low probability, near the tail) and a Gaussian distribution (approximation to Binomial distribution accurate for many events, near the center).

I think Tony's model is correct but I'm just an electrical engineer and programmer with E8 root lattice geometry as a hobby. He of course can and has changed details related to his model.

 

[Newton]

I happened to see Tony's work and noticed that the mathematics (Lie algebra) was right on for Bosonic strings (SP(4)), ie Fourier wave optics with three Fourier pairs - time, frequency, and phase. BTW, these three yield both EM theory and special relativity, where the constraint c, the speed of light, forces each Fourier dual manifold to 'warp' from Euclidean (unconstrained) to symplectic (constrained).

And also noticed that spin(6) manifolds are very very special as he pointed out (the product of two bivectors). When two Bosons interact combination manifold is spin(6) with a scalar (constant acceleration -Gravity?) But those two Bosons are on torsion-free manifolds (knots in the projection) and the result (some sort of Fermion) is knot free (Euclidean space) but quantized. The wave would be a soliton - the solution to a irreduecable 3 order PDE. (Note that all higher order PDEs reduce to zero through third order PDEs, Bott's contribution to PDE theory)

It appears that spin(6) interaction manifolds are analogous to Kahler manifolds (Riemann-symplectic) but are simultaneously symplectic and octonion.

And all this is deterministic - all Hamiltonian flows (as in theoretical mechanics).

The question is: how do two Bosons interact so that they bend each other into opposing (?) direction circular orbits - integer wavelengths in circumference?

My conclusion is that Tony's work is 'String Theory' not 'Quantum Mechanics'! And I believe most, it not all of it, is correct.

 

[ark]

Tony does get the Dirac equation from a random walk through his 4-dim hyperdiamond Feynman Checkerboard.

Dirac equation is not the same as quantum theory. And Born's rule is not the same as quantum theory. Many people derive different aspects of quantum theory form these or that assumptions, assumptions that are being made just to derive what they want to derive. I am not saying that such exercises are not interesting. Sure they are. But I have my own starndards as to what I consider a "theory". What Tony offers are, according to my standards, interesting ideas. But this is not a "theory". For instance I am not at all convinced that Tony's recast of Wyler's "derivation" of the formula for the fine structure constant explains it. I had quite a few interesting exchanges with Tony on this subject, but they did not help me to change my mind. A breakthrough is needed, and Tony is just going there, but not being there yet. And I am not sure if his way is the way in the right direction. Perhaps it is. Perhaps it is not.

 

[John G]

A breakthrough is needed, and Tony is just going there, but not being there yet. And I am not sure if his way is the way in the right direction. Perhaps it is. Perhaps it is not.

Tony calls his model a work in progress, there are certainly more things Tony would like to know. For example:

... just as in 2-dimensions the Wei Qi boark has 4 (square/diamond) links from each vertex to a nearest neighbor. Conway and Sloane (in their book Sphere Packings, Lattices, and Groups, Third Edition, Springer 199) say on page 119: "... Formally we define Dn+ = Dn u ( [1] + Dn ). ... Dn+ is a lattice packing if and only if n is even. D3+ is the tetrahedral or diamond packing ... and D4+ = Z4. When n = 8 this construction is especially important, the lattice D8+ being known as E8 ...".] ...
... and [here is] a web page with links to some (Macintosh) 3-D Go programs http://www.asahi-net.or.jp/~hq8y-ishm/game.html and here is a web page about diamond Go http://www.nrinstruments.demon.co.uk/diamond/diamintro.html and here is a page with a .exe type 3-D Go program http://www.nrinstruments.demon.co.uk/diamond/diamprog.html I would like to see, but have not seen, 4-D and 8-D programs with hyperdiamond boards, since I think they may be related to generalized Feynman checkerboards and spin networks. ... One more comment is that I prefer the Chinese name Wei-Qi, but I realize that the Japanese term Go is more prevalent in Euro/American circles (and Japan). (In Korea, it is Baduk.) ...".

Maybe you should make an 8-dim Wei Qi board and let Laura play with it (I'm only half kidding)

What Tony offers are, according to my standards, interesting ideas. But this is not a "theory". For instance I am not at all convinced that Tony's recast of Wyler's "derivation" of the formula for the fine structure constant explains it. I had quite a few interesting exchanges with Tony on this subject, but they did not help me to change my mind.

I think Tony's main theory is the A-D-E series and all the conformal transformations/complex domains/wavelets that occur as you go up the A-D-E series. I don't know the math of course and you certainly do being Tony's reference for this stuff but in my simple terms the Wyler stuff gets particle masses and force strengths and the fine structure constant (kind of a strong gravity vs EM force strength ratio) as diffusion equations through complex domains kind of like lattice gauge theory mass calcualtions represent diffusion through a lattice spacetime. At D4, Tony has an SU(5) GUT-like theory, at D5 he has an SO(10) GUT-like theory, at E6 Tony has an E6 GUT-like theory that Witten wanted for string theory. At E7, Tony has a Susskind-like Bosonic M-theory and at E8 a Jose M Figueroa-O'Farrill-like Bosonic F-theory. Going from D3 to E8, gets you from gravity to string theory and from the Wheel of Life/Circumplex to the Sri Yantra/Enneagram (my true area of expertise most related to this stuff are circumplexes and Enneagrams not electrical engineering and programming
http://tap3x.net/EMBTI/j6dialogues.html).