The Subquantum Plenum 
(c) Robert Neil Boyd

DeBroglie Waves as a Convectional Propagation of Subquantum Particles

DeBroglie waves can be explained as a convectional process involving subquantum particles which can travel FTL. (Again, there is no upper limit to the velocity of convectional processes.) It may be that these subquantum entities flee before the disturbance created by the larger entity, e.g. an electron, conveyed by convectional processes. Implicit in this view is the conjecture that subquantum entities are not involved with standard relativity limitations and the Planck considerations of QM, such as the Plank length, and that such entities may thus be allowed to propagate at FTL velocities, all due to the smallness of these particles. It is also possible that since charge is normally considered in its quantized form that charge quanta may be divisible just as photonic quanta are divisible. See for information on the division of quanta in relation to the quantum Hall effect. Given this situation it is possible to conceive of subquantum entities which have the quality of charge, which might sum according to some rule related to the Planck constant to create the form of charge we are most familiar with, such as the charge of an electron.

The problems with the AB effect seem to go away when one ignores relativistic considerations and contemplates the effect as being due to subquantum particles, rather than "virtual" particles. The equations will work pretty much the same way if we replace these "virtual" particles with subquantum entities.

Convection, again, is the process of one object bumping into another object, which bumps into another, etc. This can happen whether the objects involved are linked directly or non-locally. In this sense, a convectional wave looks the same as a "mass wave" which is similar to a DeBroglie wave. This is not to say that the AB effect is exclusively due to DeBroglie waves. This is simply another example of evidence supporting the existence of subquantum entities and their effects, which define the "physical vacuum" or plenum, in this case, the AB effect. By Einstein and Bohm, these sorts of activities are termed "osmotic", and proceed at " osmotic velocities", which can be superluminal due to non-local connectivity amongst the involved particles. Osmotic velocity of charged particles in free space is given as

mu_o = -e / 2 (lamda / v)

In the case of interactions involved with a gravitic field, this becomes

mu_o = -G / 2 (lamda / v)

Here acceleration due to osmotic velocities is given by

m v_n = -grad_n (V + Q)

where Q is the non-local quantum potential.

(See 'The Undivided Universe" p 201-203)

[Potentials proceeding according to the Dirac delta function, which have negligible duration and infinite height at t = 0, are most interesting with regard to osmotic accelerations.]

See Volume I of James Clerk Maxwell's Treatise on Electricity and Magnetism at articles [44], [55], [238], and [248] for information on convection. See [36], [37], [61], [111], [295], [329] and [334] for descriptions of the "electric fluid". See article [64] for electrical density. Article [314] regards the electrical conductivity of a medium in which small spheres of another media are distributed. (I bring Art. [314] up because I think that it is possible that there are several sizes of particles involved in the subquantum domains.)

By the Eikonal equation we can determine the speed of sound in the media as a function of mass density per unit volume, relative to the granularity of the media, which is related to the size of individual elements in the media. The Eikonal equation implicitly implies infinitesimally small element size as well as the infinitely large. Infinitesimally small elements in a unit volume can imply an infinitely dense medium. The velocity of sound in an infinitely dense media is ________ ?


Bernhard Riemann showed the passage of electric potential as a modified form of Poisson's equation where the Poisson equation takes on the same form as descriptions of the propagation of waves and other disturbances in an elastic media.

Also, please remember that it is well known that propagating electromagnetic fields have a linear momentum P given by

P = Integral v { ( eta_0 [E X B] dv) }


P = Integral S/c^2 dv, where S is the Poynting vector

This E/M field carries as well, a momentum density given by

(P_1) field = S/c^2

One may ask then, what is actually responsible for these known properties of momentum of electromagnetic propagations, if this momentum is not carried as the result of the motion of massive particles?

Further, the vacuum has many physical properties which imply a substantive media. For example, the vacuum has :

A modulus of elasticity 
A stress tensor 
A sheer tensor 
Magnetic permeability coefficient 
Magnetic susceptibility 
A bulk modulus 
A modulus of conductance 
A modulus of coercivity 
A characteristic E/M wave impedance of 377 Ohms

It is certain that the vacuum has other known and measurable physical properties which are not found in the above list. All these measurements, and others, strongly imply the existence of a substance. Indeed, were one given the parameters of the substantive vacuum without being informed as to what was being measured, it would be easy to think that some sort of material was being described, rather than a "vacuum".

It may be found that the scalar Helmholtz equation will apply to the vacuum medium in terms of a displacement gradient which will give us a relation between a compressional wave in a fluidic or superfluidic media and the DeBroglie relations, where wavelength is defined in terms of momentum and frequency in terms of energy. It is true that DeBroglie speculated that material particles were associated with these "matter waves" and were a hitherto undetected oscillatory phenomenon.

The connection between the scalar Helmholtz equation and the DeBroglie relation should be based on the classical relation, E = p ^2 /2m. For the DeBroglie relation, this develops as

i h_bar @psi / @t = h_bar ^2/ 2m @^2 psi/@x^2 
(@ denotes the partial derivative)

The Helmholtz equation depends on the material displacement gradient, grad_q so that we have

grad^2 p omega + omega^2/ c_f^2 p omega = 0 
(omega is the frequency)

Here, c_f is identical to (B/p_o)^1/2 where B is the bulk modulus of the medium.

I am in the process of working out the results of combining the Helmholtz fluidic equation with the DeBroglie relation. Then I will discover how far the results actually correspond to observable reality. Superficially, this idea seems to have some merit, so far. I will let you know what becomes of the notion.

The dielectric constant of the substantial vacuum, eta_o, is approximately 10 e-9 /36 pi farad/meter.

Magnetic permeability, mu_o, is identical to 4 pi (10 e-7) henry/meter.

Origination of the E field is

grad dot E = p/ eta_o, 
where p is the scalar charge density in coulombs per cubic meter

The origination of the B field is

grad cross B = mu_o J + eta_o mu_o @E/@t, 
where J is the vector current density in amperes per square meter.

Here, the second term is almost identical to Maxwell's "displacement current" which is a movement of charge, which leads us to further examine the possibility that origination of charge is due to some inherent element of the substantial vacuum and not necessarily innate to the elemental particles themselves, except as they might be comprised of [smaller] (subquantum) elements of the substantial vacuum.

The above also implies that the magnetic field results from the vectored displacement of charges moving in the inertial frame of the substantial vacuum. Since the elemental particles all have a magnetic moment and the property of angular momentum, it is fairly easy to deduce from the above that the elemental particles may be comprised of vortices of charged (subquantum) entities swirling about to make the coherent structure that is the elemental particle.

This further implies the existence of charged subquantum entities and further supports Aspden's hypothesis regarding the substantial nature of the vacuum. This also aligns with Tony Smith's "Compton radius Kerr-Newman vortex" model of the electron.

Along with this, remember the experimental series at Fermilab which has gathered data which could be interpreted as evidence for the existence of a new level of matter. In an article titled "DO QUARKS HAVE SUBSTRUCTURE?" as shown at , first published in

Physics News Update 
The American Institute of Physics Bulletin of Physics News 
Number 258 February 13, 1996 by Phillip F. Schewe and Ben Stein ,

their results imply that quarks, themselves have constituents. These findings were dramatic enough to cause one of the experimenters to exclaim, "Is there no end to the smallness of particles?"

An interesting aside here is the fact that, as you were alluding to yesterday, the characteristic velocity of the media, C_v is found by placing

C_v = 1/ (eta_o mu_o) to the one half ,

which comes out as approximately 2.998 X 10 e8 m/sec., the speed of light in the media. However, this is only the characteristic velocity of Lorentzian E/M propagations in the media, and has nothing to do with subquantum matter transports in the media, which should proceed according the DeBroglie relation regarding "matter waves" in the case where the subquantum species so transported are possessed of the property of charge. For those species which do not have charge, the DeBroglie relation will not hold. In these situations we will probably need to resort to representations of behaviors exclusively in terms of mass transport equations through an anisotropic superfluidic media. For cases where such mass transport of neutral subquantum species is in the form of waves, the Helmholtz scalar ought to be useful. For shock front propagations, a separate treatment will be required. For convection-type mass transport, a continuity equation will need to be developed to express the continued existence of the massive neutral elements of the subquantum fluid as they move about. Something like

@p/ @t = - grad dot pV

where the term pV is the vectored mass flow of the substance and p is its density.

We could also have something like

grad ^2 (the laplacian) pV = eta_o mu_o (@^2 pV/@ t^2)

to show 3D spherical mass transports. (Note that here, C is not a limiting velocity.)

Perhaps we might be able get Aspden to become more interested in developing such ideas.