 ...An Exact Classical Mechanics leads toward Quantum Gravitation... Contents
3.0 Does rest-energy vary with potential energy? Does it vary with binding energy?An electron accelerated by an electrostatic field provides a useful initial example. Any potential change Δψe is given by the work done in moving an object distance x against a field of force F from one position to another: i.e. Δψe = ∫ Fdx. If it is then released and allowed to accelerate freely in the field its potential will be lost as kinetic energy is gained. For example, an electron of m0 = 9.1091 × 10-31 kg is assumed falling through 106 volts. (1 electron-volt = 1.6021 × 10-19 joule) Equation[20] then shows energy ratio E/E0 = 1.957 and the electron will reach a value of v/c = .85958. It is now to be imagined that this high speed electron is allowed to slow down without change of electric potential. This can be done by allowing it to pass through a cloud chamber, for example, where it loses energy by knocking electrons off atoms to produce a trail of ions. We will suppose the electron is stopped. Its maximum kinetic-energy was E -E0 equal to Δψe but all this kinetic energy is subsequently lost. The final rest energy will be E - (E-E0): the original rest-energy has been recovered! Overall the rest-energy has not changed but potential has been lost: so rest-energy cannot be affected by electrostatic potential! A similar argument can be applied to the gravitational field. An elastic object is allowed to fall freely onto a rigid deflector inclined at 45 degrees to the horizontal. Its initial vertically downward velocity is converted to a horizontal one without change of kinetic energy. Its total energy E is then E0 + EK. Then it is stopped gradually by friction so that all EK is lost. Clearly the original rest-energy must be recovered. The same conclusion is reached if an object is considered lifted on a cable. The force of gravity is cancelled by the force on the cable so that, in lifting, zero work is transferred to the object. Its rest-energy must therefore remain invariant even though potential has increased. It follows that rest-energy must remain invariant in the gravitational field. Now we come to the nub of the issue. The foregoing conclusions mean that no binding energies, whether gravitational, chemical or nuclear, can be reflected as differences between the rest-masses of separated particles and their combined masses! It is true that atomic nuclei have different masses from the sum of the protons and neutrons of which they are composed. The difference, however, has to be due to loss of particles like photons or neutrinos associated with nuclear reaction: they cannot be equated with potential change! And binding energies are potential change. It follows that gravitational binding energies, contrary to established opinion, cannot be equated with change of mass. For example, Clifford Will(15), says on page 24 (of The New Physics edited by Paul Davies) when referring to the neutron star, "...the observed mass is less than the total mass of all the neutrons in the star, because of the sizeable negative gravitational binding energy". He was referring to the theory of general relativity which does not accept the existence of any real force of gravity. Instead objects move along geodesics in curved space-time and accelerate toward ponderous masses without a force being involved. On this theory it is true that some rest-mass has to transmute into kinetic energy as gravitational potential is lost. In this case, however, gravitation must be treated as totally different in nature from electromagnetism or the strong nuclear force because, as already proved, there can be no loss of rest-mass due to loss of potential if real forces are involved. Unfortunately theorists attempting to match general relativity to quantum theory obviously consider gravity as a real force as Chris Isham3 indicates. On page 87, of the same book, he shows how gravitons and gravitinos are postulated which interact with matter and themselves to produce a real gravitational force. They are copying the methods, developed so successfully by the late and famous Richard Feynman in his theory of quantum electrodynamics (QED), which considers electromagnetism as a real force. Clearly a total incompatibility exists which does not appear to have been recognised! In fact, if a neutron star were built entirely from accreted hydrogen, it would be heavier than its initial constituents owing to degeneracy pressure increasing electron velocities. If these fuse with protons to make neutrons, then a mass increase is again involved. This time it is because energy has to be added. This would derive from part of the excess kinetic energy which the hydrogen needs to shed on impact. Another concept needing to be assessed is the idea that, for the universe as a whole, its mass-energy is cancelled by its "negative gravitational potential energy". Clearly this idea is invalidated by the forgoing argument and something else needs to provide the balance. It is necessary to deduce the basic mechanics behind the concept of any type of potential energy but with curved space-time geometry disallowed, since it is not necessary, as §4 will demonstrate. In engineering mechanics, for example, total energy is defined as the sum of kinetic and potential energy, a useful concept because total energy can then be considered to remain constant. Potential energy is simply regarded as energy stored "somehow" in space due to the position of an object in the field of force. But how is it stored? Nobody ever seems to know: so let us probe deeper. A clue was given in my previous books(6, 7 & 8) and article(10 & 11). These showed how a sub-quantum fluid, now to be called the "i-ther" (intelligent ether), has to exist as a balance of positive and negative energies. These each comprise a seething mass of primary particles (primaries) constantly colliding like the atoms of a noble gas. An asymmetry has to exist in that the rest-energy of the positive primaries exceeds that of their negative partners with the latter having the greater kinetic energy (see §4.9). In consequence a small net negative pressure of the vacuum remains. Any density gradients result in net negative pressure gradients which act on positive matter to produce negative buoyancy forces. These are the source of the universal attractive force of gravity according to §4.9. For such a mixture the existing first law of thermodynamics is inapplicable. It is not wrong but has to be considered as a special case of a more general law which now reads, "Energy can only be created or destroyed in equal and opposite amounts". Hence both creation and destruction can proceed but only in such a way as to leave the net energy of the universe unchanged. Our special case has seemed to be universally applicable only because in most processes, such as chemical reactions, the negative component is not altered. But it does alter in free-fall! On this basis when a ball is thrown into the air it is losing energy by pure annihilation of amount equal to the product of the force of action of gravity and height moved. An equal positive force of reaction acts on the net negative kinetic energy of the i-ther and so does positive work on that fluid. But positive work done on negative energy is equivalent to reducing the quantity of negative energy. Hence both the object and the i-ther lose energy of their own kind in equal amounts by mutual annihilation. When the ball falls back again, mutual creation occurs, so restoring initial values. This, according to the present theory, is the real explanation for changes in potential not being reflected in changes of an object's rest-energy. Potential energy is not stored at all: it does not really exist! It has to be regarded as a pseudo-energy form: an artifice useful only for calculation purposes. The "total energy" of an object will, henceforth, be defined as the sum of rest and kinetic energies alone. Clearly, this sum will not be conserved in the potential field. | 
