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 10^{8} m/s
| ||

G | universal constant of gravitation |
6.7 x 10^{-11} m^{3} kg^{-1} s^{-2}
| ||

H | Hubble constant |
2.2 x 10^{-18} s^{-1}
| ||

R | radius of observable universe |
4 x 10^{26} m
| ||

M | total mass of the observable universe |
10^{53} kg
| ||

N | number of particles in the universe |
10^{80}
| ||

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 r^{2}.
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:

∫ {(G.m.a.4π.r

0 0

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.