A Matter of Gravity

Don Herbison-Evans


Newton made a good first approximation to the describing the effects of gravity out to interstellar distances with the formula

E = -GMm/r where E = the energy of the interaction,
M and m are the masses of the interacting objects,
r = their separation, and
G = the gravitational constant: ~ 6 x 10-11 MKS


Einstein made a brilliant second approximation by applying Occam's razor to create the axiom of the Principle of Equivalence: that gravitational mass is linearly proportional to inertial mass. This has extended our ability to describe the effects of gravity out to inter-galactic distances.

The Principle of Equivalence has been shown to be correct for Hadrons and Photons as far as experimental inaccuracies allow, but the evidence for its truth for Leptons is rather circumstantial. It would be nice if someone actually compared the molecular weights of say BeH2 and BeD2 with their molecular masses as determined by Mass Spectrometry, to see if the weights of the electrons equalled their masses in these molecules, although this would require chemical experiments at the limits of current precisions.

But the biggest problem with General Relativity is its use to interpret the observed Hubble Redshift of distant galaxies as Doppler shifts, and describing these as an expansion of space-time from a Big Bang. This implies that time is only semi-infinite, and this is intellectually distasteful.

Other interpretations of the Hubble Redshifts also have intellectually distasteful limitations, but perhaps it is time to reassess these.


Irrespective of General Relativity, if we interpret the redshifts as Doppler shifts, we may expand the formula for the energy of a gravitational interaction as a polynomial series expansion, as has has been done in many physical situations, perhaps with the simple form:

E = (-GMm/r)(1 + g1r + g2r2 + g3r3 ...) The effects of Hubble's observed expansion of the galaxies seems to start at a distance of about r1 = 100 Mpc, so we may calculate an approximate value for g1 using g1 =-1/r1 The data is probably insufficient at this stage to determine the higher order coefficients.


The redshifts can instead be interpreted as gravitational redshifts. with the light being emitted from galaxies the mass of which increase with distance. The more distant galaxies are seen at a younger stage of their development. For their light to suffer a gravitational redshift, these younger galaxies would thus seem to be heavier than the recent nearby older galaxies. There are several possible reasons why the the masses of younger galaxies may be larger than the masses of older galaxies.


Perhaps galaxies were at earlier times created from more matter, and the resulting depletion of of the condensing intergalactic clouds has led to lighter galaxies forming more recently.


Perhaps there are processes in galaxies that lose matter and/or energy and so they become lighter with time.


Perhaps the more distant galaxies are moving laterally at faster speeds approaching the speed of light, and so are appearing heavier.

written 28 April 2017, updated 6 October 2017
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