Symmetry, Gravitation and Inertia

(Response #1 by L D Howe to Prof. W Kuijk-Grünbauer's letter entitled "A Re-dimensionalization of Physics holding unified Physical Fields producing a purely gravitational Lorentz Force")

Abstract

This letter offers a way to support the detailed analysis of Prof. Kuijk-Grünbauer, while explaining well documented experimental facts. Although Newton was able to unite gravitaional mass with inertial mass, this can only apply in a universe where there is no symmetry between charge and mass. The development of Prof. Kuijk-Grünbauer's analysis leads naturally to three sets of Maxwell equations.

The mathematical analysis that you have used offers a practical way to overcome the asymmetry associated with "normal" physics. However, there is a set of physical observations that it does not appear to explain and, indeed, are counter to your arguments. That does not mean that the analysis is wrong, only incomplete. To illustrate the problem let me describe a physical experiment. For simplicity I have used a thought experiment, but it reflects a real, physical situation.

Consider three pairs of particles, such that the particles in each pair are identical to one another. Let the pairs be characterised as follows:

Table 1: Particle pairs for the thought experiment

These could represent respectively, protons, alpha particles and stripped carbon nuclei, such as those produced in a tandem Van der Graaff generator. Assume the particles are initially held at rest and then allowed to accelerate under electrostatic repulsion. The observed acceleration on each particle for each pair would be respectively, 13.8 ms^-2, 13.8 ms^-2 and 41.3 ms^-2. This corresponds to the equation

(1)

where a is the acceleration and the other symbols have there usual meaning. Now, in Newtonian mechanics, force is normally defined as the product of mass and acceleration. The dimensions of acceleration, a, are [L] [T]^-2. Thus the dimensions of permittivity are [L]^-1 [T]² [C]² [M]^-1 [L]^-2 = [L]^-3 [M]^-1 [T]² [C]² or m^-3kg^-1s²C². The reason for the problem is that mass, in its gravitational force meaning, has been convoluted with the inertia associated with the amount of substance. If we separate out these two meanings into two separate entities, one associated with the gravitational "charge" and the other associated with the amount of substance, then we arrive at the perfect symmetry of your proposal by inserting an extra dimension, [I] for inertia, into the dimensions of all three laws, as follows:

(2)

(3)

(4)

where sp, the dreaded spon, is the unit of inertia (numerically equal to mass for "pure" positive mass, but NOT for negative or mixed masses). So in all three cases, the dimension of K is a new Newton (N_n) with dimensions sp.m.s^-2. All three laws remain mathematically the same as you have stated, only the dimension is changed, but it preserves your assertion that in all cases, K has the same dimension. In this new world, we can have charge without mass (i.e. without gravitation), but NOT charge without inertia (otherwise acceleration would be infinite and the speed of light would be meaningless).

I conjecture that your three formulae for E now become (with having the usual meaning of a unit vector in the direction of r):

(5)

The dimension of E in all three cases is now new Newton's per source unit. It is the natural dimension, because the electric field acts on an electric charge, the gravitational field acts on a gravitational "charge" and the hybrid field acts on a hybrid "charge". This now fully preserves your symmetry, but allows the effect of charges to act on masses, as in the thought experiment above. It also fits exactly with established electric field theory.

The hybrid field would only be observed to be of any significance where there are relatively large masses together with small charges. Calculations suggest that, for two identical particles with positive mass (where inertia is numerically identical to gravitation), a mass to charge ratio of 1.16 x 10¹⁰ kg/C gives an equal contribution to acceleration from all three laws (this is equivalent to ). If the mass to charge ratio is much greater, Newton's law dominates and if it is much smaller, Coulomb's law dominates. Of course, for like charges and like gravitation, the components from Newton's law and Coulomb's law would be opposite and therefore cancel. So the question is (that we have not yet addressed) "what is the sign of the force associated with the hybrid law?" Remember that the sign for Newton's law (for repulsion) is negative, while that for coulomb's law is positive (vice versa for attraction). That is to say, for gravitation, like charges attract and unlike charges repel, whereas for electric charges, unlike charges attract and like charges repel. Because of the square roots in the hybrid law, does this mean that the force is imaginary and therefore tangential?

Going back to your equations (6) we now get:

(6)

Where the bracketed expressions are (dimensionless) scalars. This corresponds exactly to your equations 6. Note that we can also write a corresponding set of transposition equations for K, which explain the calculated mass to charge ratio for a pair of identical particles, as noted above:

(7)

When we get to your Equation 7, I see a deeper problem. Let us consider two charges, q₁ and q₂ and two observers O₁ and O₂. Let q₁ move at velocity v with respect to q₂, and assume that O₁ is moves in the same frame of reference as q₁ while O₂ moves in the same frame of reference as q₂. Now, from the point of view of O₁, the B field for q₁ will be zero and the B field for q₂ will be non-zero, whereas for O₂, the B field for q₂ will be zero and the B field for q₁ will be equal in magnitude and opposite in direction to that observed by O₁ for q₂. B₁ does not, of course, depend on q₂, but it does depend on the relative motion of O₂, moving in the same frame of reference as q₂. This may be an artefact of Einsteinium relativity, which I feel we must address at some stage.

Using my proposed dimensionality, the dimension of is . Without this dimension it is not possible to explain the effect of the mass (inertia) to electric charge ratio under the influence of a magnetic field, such as within a mass spectrometer or a bubble chamber. This leads to the set of equations:

(8)

All three will be equal if the mass to charge ratio (with positive mass, where inertia is numerically identical to gravitation) is 1.347 x 10²⁰ kg.C^-1, which is equivalent to , as you correctly assert. Consequently, this leads to a triplet of equations for the Lorentz force (F):

(9)

Note that the dimension of F is the same in all three cases, namely sp.m.s^-2.

I now propose three sets of equations:

The Electric Equations

IE (The "First Gauss Law")		with each term of dimension sp.C-1.m-1.s-1
IIE (The "Second Gauss Law")		with the "charge density" of dimension Cm-3 and overall dimension of terms sp.C-1.s-2
IIIE (The "Faraday-Henri Law")		with overall dimension sp.C-1.s-2
IVE (The "Maxwell-Ampère Law")		with the "electric current density" of dimension C.m-2.s-1; each term of dimension sp.C-1.m.s-3

The Gravitational Equations

IG		with each term of dimension sp.kg-1.m-1.s-1
IIG		with the "gravitation density" of dimension kg.m-3 and overall dimension of terms sp.kg-1.s-2
IIIG		with overall dimension sp.kg-1.s-2
IVG		with the "gravitational current density" of dimension kg.m-2.s-1; each term of dimension sp.kg-1.m.s-3

The Hybrid Equations

IH		with each term of dimension sp.()-1.m-1.s-1
IIH		with the "hybrid density" of dimension .m-3 and overall dimension of terms sp.()-1.s-2
IIIH		with overall dimension sp.()-1.s-2
IVH		with the "hybrid current density" of dimension .m-2.s-1; each term of dimension sp.()-1.m.s-3

I think these represent, respectively, what you call "the Maxwell equations for the electric platform", "the Maxwell equations for the gravitational platform", and "the Maxwell equations for the hybrid platform".