An approach to particles from relativistic kenetic energy (draft)

Copyright (c) Warren Frisina 2019

    CONTENTS

1.  Introduction

2. Energy, momentum and Force

3.  The Hubble parameter in acceleration units

4.  Planck's constant, and particle mass 

5.  The (sub-atomic) relativity/quantum bridge, and the gravitational coupling constant

6.  Isolated particles and the Strong force

7.  The unit charge (electron charge)

8.  The zero rest mass particle, and the Weak force

1. Introduction

With the exception of loop quantum gravity this study outlines the reverse of the standard approach -- this approach begins with gravity (relativity) then derives quanta in an effort to lead to a seamless unification. While the first premise is an offshoot of general relativity, the approach proceeds from the real and complex forms of special relativity, which are not as resistant to the inclusion of Planck's constant. While special relativity is not ordinarily associated with gravitation, it is restricted here to the subatomic scale prior to non-zero rest mass particle establishment. The complex form is also restricted to certain conditions, so that there is also no conflict with general relativity. Under no circumstances is negative Newtonian (baryonic) type mass, nor tachyons considered.

Similarly "... magnetism and the magnetic field can be considered a relativistic consequence of the electric field."*

The premises follow.

1. Spacetime is identical with the pure gravitational field.

2. This field has no net energy nor momentum.

3. Classical physics is assumed.

4. The Hubble law is assumed.

DEFINITION: A particle precursor is apparent if a finite region of spacetime is curved.

2. Energy, momentum and force

Rephrasing E = mc^2, in a finite curved region

E = xc^2 + (y-x)c^2

where y = precursor to particle total mass

x = precursor to particle rest mass

(y-x)c^2 = relativistic kenetic energy = E(s)

xc^2 = 0 throughout (rest mass is to be replaced by

said relativistic energy);

specifically E(s) = (y-x)c^2 (1)

where y = x(1- v^2/c^2)^-1/2 c^2 (2)

y = -ix(v^2/c^2 -1)^-1/2 c^2 (3)

When the ordinary form of the relativistic velocity term is apparent, v < c; when the complex form is seen, v > c; the latter velocity interval is to be clarified -- it does not refer to tachyons. To repeat, under no circumstances is Newtonian (Baryonic) type mass considered negative. It will be seen that "v>c" refers to "v different from c in expanding spacetime" (not v greater than c); similarly "v<c" refers to "v different from c in contracting spacetime" (not v less than c). Combining these relations for consistency throughout,

E(s) = xc^2(1- v^2 / c^2)^-1/2 -1) (1a)

E(s) = -xc^2 -ixc^2(v^2 / c^2 -1)^-1/2 (1b)

so that global energy remains at zero. These two particle precursors can be termed spacetime waves, to contrast with classical gravity waves where v=c.

Similarly, for momentum,

p(s) = (y-x)v (4)

= xv((1- v^2 / c^2)^-1/2 -1) (4a)

= -xv -ixv(v^2 / c^2 -1)^-1/2. (4b)

And force F(s) = dp(s) / dt (5)

= xa{((1- v^2 / c^2)^-1/2 -1) + (v^2 / c^2)(1- v^2 / c^2)^-3/2} (5a)

= -xa - ixa((v^2 /c ^2 -1)^-1/2 + (v^2 / c^2)(v^2 / c^2 -1)^-3/2). (5b)

While special relativity is not ordinarily applicable in instances of acceleration, this instance does not yet include a non-zero rest mass particle.

3. The Hubble parameter in acceleration units

While (5b) indicates non-uniform acceleration in general, sufficiently far from light speed the velocity term nears a constant -- indicating the suitability of special relativity under this condition (also, it will be seen that acceleration "a" is close to zero under this condition, so that special relativity is still applicable). That v may be a multiple of c in this context is physically conceivable in that a light speed barrier has not been crossed; the field is being unstressed as v increases.

Note that the v>c equation form is consistent with the Hubble Law for sufficiently high v while the v<c form is not, regarding consistency with special relativity. For example, when two galaxies are far enough apart to have a relative velocity near light speed, the v<c form breaks down.

(See the following article "Generalizing Newtonian Gravity ..." for a derivation of H in acceleration units in the real mathematical domain, which is more accurate, taken from direct observation.)

This parameter can be employed from observation as a=45 km/s per 10^6 LY) = H. The uniformly accelerated motion equation becomes

a = [(600045 km/s)^2 - (600000 km/s)^2] / (2*10^6 LY) = H (lemma)

with appropriate conversion factors for SI units. The velocities are estimated from a plot of the variable term of (5b) where the slope abruptly approaches a constant asymptotically at v about 2c. The value of "a" is taken to be the Hubble parameter, H, in acceleration units, provisionally replacing "a" in Equations (5a) and (5b).

4. Planck's constant and particle mass

Consider

L(s) = L(1- v^2/c^2)^1/2 (6)

= iL(v^2/c^2 -1)^1/2 (6a)

where L(s) is a particle precursor wavelength, L to be determined (as with x).

Spacetime wave frequency would be

V(s) = v / L(s) (7)

Substituting (6) or (6a) into (7), V(s) increases with v --> c, so that frequency appears directly related to energy,

K = E(s) / V(s)

= xLc v -- > c (8)

which is indeed a constant if precursor wavelengths are rest values. Since precursor velocity is near light speed here there could be sufficient relativistic kenetic energy to produce a non-zero rest mass particle, in that the velocity terms have cancelled. It might be suspected that L is a Compton wavelength, if K = h and x is a rest mass.

Given the equivalence of gravitational and inertial effects

F(g) = F(s)

where F(s) is (5a) and F(g) is Newtonian gravity, where the distance between two particle masses is assumed constant at the value L of Equation (8); F(g) is provisionally multiplied by the relativistic velocity term of (5a) because of the two-particle proximity and interaction implying special relativity effects; all masses are equal. Then

particle mass = [(H/G)(h/c)^2]^1/3 kg (11)

suggesting a stable bound quark. It might now be indicated that L in (8) is a Compton wavelength, x is a rest mass and that K is Planck's constant, h.

(continued in the following post)

_

* The Great Design, Robert K. Adair, Oxford University Press, N.Y., Oxford, 1987, P. 62