What is Mass?

Don Herbison-Evans ,   donherbisonevans@yahoo.com
written 22 October 2015, updated 4 June 2017

ABSTRACT

This considers the possibility that rest mass energy of an arbitrary particle in our finite universe is just the sum of the energies of its gravitational interaction with all the other particles in its observable universe.

ASSUMPTIONS (approximations, from Wikipedia)
c    velocity of light    3 x 108 m/s
G    universal constant of gravitation    6.7 x 10-11 m3 kg-1 s-2
H    Hubble constant    2.2 x 10-18 s-1
R    radius of observable universe    4 x 1026 m
M    total mass of the observable universe    1053 kg
N    number of particles in the universe    1080
a    average mass density of the universe    kg/m-3
m    mass of an arbitrary particle    kg

DOMINATION BY THE MOST DISTANT PARTICLES

The assumption in this paper is that every pair of particles constitutes a system. There are thus N(N-1) systems in the universe. In this paper: the rest mass of any one particle as seen by any one of the other N-1 particles is assumed to be the mass equivalent of the sum of the energies of the N-1 other systems. Within any system, the gravitational mass of each particle is assumed to be the mass equivalent of the rest mass plus the kinetic energy from their relative motion. Outside that system, the system mass is assumed to be the mass equivalent of the rest masses of the two particles plus their relative kinetic energies less their potential energy.

It is interesting to note that the energy of the interaction between two particles separated by a distance 'r' varies as 1/r, whereas the number of particles in a shell of radius 'r' about a given particle, assuming a uniform random distribution, varies as r2. So that if the rest mass energy of a particle is determined by the sum of the gravitational energy of its interaction with all the other particles in the universe, most of the interaction will be from those particles that are nearest to the edge of its observable universe.

ASSUMING UNIFORM MASS DENSITY

Supposing that the rest mass energy of each particle is the sum of the gravitational energy of that particular particle with all the other particles in the universe, we may approximate this by the integral over the observable universe of the average observed mass density:

R                                                      R
∫ {(G.m.a.4π.r2)/r}dr = [G.2.π.m.a.r2] = G.2π.m.R2.a    J
0                                                       0
Equating this to the approximate mass energy of the particle : m.c2 = G.2π.m.R2.a = G.m.2π.3.R2.M/(4π.R3) = G.m.3.M/(2.R) which implies that: M = 2.R.c2/(3.G) ≈ 2.4.1026.1017/(3.7 x 10-11) ≈ 4.1054 This is similar to Hoyle's steady state equation, which is the same as Friedman's critical density equation, which imply that M = R.c2/(2.G) One may note that the values of the three constants on the right of this equation appear to have been determined quite independently of each other. The value of 'G' has been determined by local terrestrial experiments, often using lead balls. The value of 'c' is defined by counts of waves in space and time of particular radiations emitted by specific atoms. The value of 'R' has been determined from 'c' and the observed Hubble constant, H, using R = c/H where the value of 'H' has been determined using the spectra of distant objects.

Thus if this equation is true, it not only offers insight into Hoyle's and Friedland's dynamics of the universe, but also implies that the rest masses of particles may well reflect their interaction with the rest of the universe.

Whilst we define c to remain constant, it is less obvious that M, R, and H are constant. With a simple big-bang model, R is increasing, which implies that M may be decreasing as the most distant objects accelerate beyond our observable event horizon.

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