Unification of Quantum Mechanics and General Relativity with a Particle Theory
David W. Talmage
University of Colorado Denver
Using a causal model of reality General Relativity (GR) and Quantum Mechanics (QM) can be unified with the hypotheses that all the forces that affect matter particles are the result of a change in the precise amount of energy required to form the particles and that a gradient in the density of short lived or virtual bosons is directly or indirectly involved in effecting this change. However, it is proposed that there are two different mechanisms whereby the bosons change the energy requirement of matter particles. Accepted theory holds that with electromagnetism and nuclear forces the energy requirement is changed by an exchange or sharing of short lived bosons. But with gravity and inertia it is proposed that the bosons (gravitons) change the energy requirement of matter particles indirectly, through a change in the speed of light. In order to explain inertia it is proposed that the gravitational field of gravitons derived from the universe forms an undetectable preferred frame, in which the speed of light is isotropic. These hypotheses bridge the gap between GR and QM by producing an equivalence between the curvature of space described by GR and the gradient in the density of virtual gravitons required by QM.
The
Particle Energy Requirement Force Theory
or PERFT was developed through a
qualitative analysis of well confirmed observations and not by mathematical
derivation. Thus, PERFT is a
qualitative or causal model of reality.
It is compatible with both General Relativity (GR) and Quantum Mechanics
(QM) and thus unifies them with a single view of reality. Just as the qualitative model of Copernicus
preceded the quantitative models of Kepler and Newton, a correct qualitative
model of forces is a prerequisite to a successful quantitative model.
The first observation that forms the basis of
PERFT is that energy and mass are interchangeable. The amount of energy released through atomic reactions is equal to the loss
of mass times the square of the speed of light. This is Einstein’s famous equation (1), E = mc2, which
is the basis for the atomic bomb and the production of energy by the sun. This equation describes but does not explain
why all matter particles consist of trapped energy, which can be released upon
the annihilation of the particles (with
antiparticles) or by rearrangement of particles in atomic reactions that
results in the loss of mass.
The second observation is that all electrons are the same. When we observe the high definition of pictures on the screen of a television set we are unwittingly observing the evidence that all electrons are the same. If electrons varied only slightly in their mass or charge television pictures would be blurred; the more variation in electrons the more blurring would be present.. Similarly, all protons are the same. Although protons are not used to produce television pictures, they are accelerated to high speeds in particle accelerators. The protons are guided around the circular path of the accelerator by magnetic fields. If there were any variation in the mass or charge of the protons, it would be impossible to keep the protons together. All the protons increase in mass as they are accelerated and the magnetic fields have to be carefully adjusted for this change to keep the protons together on their predetermined path.
Why is it important that all electrons are the same and all protons are the same? This is important because it indicates that a precise amount of energy is required to make the particles stable. Electrons and protons are the only two stable particles that make up matter. Each proton has approximately 1836 times as much energy as each electron and there are no known stable particles with amounts of energy between that of the electron and proton. A neutron has slightly more energy than a proton but a neutron is stable only when it is incorporated into an atomic nucleus in close association with protons and other neutrons. In this context all neutrons are the same. The result is that all atoms and molecules of matter that have the same number of each of the three particles behave exactly alike. Thus, all molecules of water are the same.
PERFT is based on the observation that the precise amount of energy that matter particles contain varies with their relationship to each other. Thus, protons and neutrons contain less energy and less mass when they are packed in an atomic nucleus than when they are separated. The energy that is released when the particles come together is known as the strong nuclear force. Energy is also released when an electron moves from one orbit in an atom to another that is closer to the protons in the nucleus. And the falling of water on a turbine produces energy that can be converted to the electric energy that lights our homes. The very small change in mass of a molecule when its electrons change their orbits has not been measured but the standard theory of electrodynamics assumes that both the nuclear and electromagnetic forces are due to an exchange of short lived or virtual bosons. Thus, it is reasonable to conclude that if the strong nuclear force derives its energy from a change in mass then the electromagnetic force also derives its energy from a change in mass and energy requirement.
The gravitational force is much weaker than the electromagnetic force by a factor of approximately 1037. Thus, it is impossible to measure the change in mass of material objects that are moved from one altitude to another on the earth. The potential energy that is released when an object falls from space to the earth is approximately one billionth of its rest mass-energy. The source of this potential energy has never been determined but the following are two reasons for thinking that the potential energy is derived from the matter particles because of the change in their energy requirement in a changed gravitational field.
1. The fractional change in the clock rate of matter particles that are moved from one altitude to another above the earth is exactly equal to the fraction of total mass energy that is converted from potential to kinetic energy by a fall between the two altitudes(2-7). If potential energy were supplied from a source other than the particle there would be no explanation for this correlation.
2. The equivalence of gravitational and inertial masses in all matter particles suggests that gravity and inertia have a common cause (5). An increase in the mass of accelerated particles is well established. Thus, it seems likely that gravity, like inertia, is based on a change in the energy requirement of matter particles.
Despite the previous conclusion that all five forces
involve a change in the energy requirements of fundamental particles, PERFT
proposes that there are two different mechanisms by which the energy
requirement is changed.
As mentioned above the standard model of electrodynamics assumes that the nuclear and electromagnetic forces are produced by an exchange of virtual bosons (8). However, PERFT proposes that the changes of energy requirement for gravity and inertia are based on a different mechanism than the other three forces, namely by a change in the speed of light (4-7).
This is the most unique feature of the theory and the proposal that gravity is the result of a change in the speed of light is based on the following:
1. A unification of Einstein’s General Relativity Theory with Quantum mechanics has never been achieved (9,10). PERFT suggests that this is because the possibility of a unique mechanism for gravity has not been considered.
2. Unlike electromagnetism gravity cannot be absorbed by the masses it attracts. PERFT explains this as being the result of the fact that the gravitons do not react directly with matter particles but act indirectly through a change in the speed of light.
3. The change in the speed of light in a gravitational field has been observed by Shapiro’s experiments measuring the round trip time of light bounced off of Venus when the light path skirted the edge of the sun (11).
4. The bending of star light around the sun is equal to the amount of bending that can be calculated from the assumptions that the speed of light is reduced in the gravitational field of the sun and that light follows a least time path (4,11,12). QM requires that light follow a least time path.
5. Despite its weakness the gravitational field is the only force field that affects the speed of light.
6. The observed fractional reduction in light speed in a gravitational field is twice the observed fraction of energy released and twice the observed reduction in clock rate. This correlation, which is predicted by General Relativity (13), is perhaps the strongest argument for a causal relationship between the speed of light and the energy content of matter particles.
Because the equivalence of gravitational and inertial masses indicates a common cause for the two forces, inertia, like gravity, must be based on a change in the speed of light. This can only be true if there is a preferred frame in which the speed of light is isotropic.
The preferred frame is undetectable in laboratory experiments for the reason proposed by FitzGerald, Lorenz and Poincare (14), namely that changes in clock rate and distance cancel all observable effects of motion. The law of inertia states that every change in the direction or velocity of a material object is the result of a force, which implies that energy is either added to or subtracted from the object. Only if the direction or velocity of an object is changing relative to some preferred frame could there also be a coincident change in the speed of light relative to that object. Non laboratory evidence for a preferred frame is found in observations of the cosmic radiation (15) and in observations of double stars (16). The latter observations indicate that the motion of the source of light has no effect on the velocity of light. Thus the speed of every photon correlates perfectly with the speed of every other photon and there must be a common cause, which PERFT proposes is the preferred frame.
PERFT proposes that both gravity and inertia are the result of a gravitational field that is produced by the virtual bosons derived from all the energy of that part of the universe to which the observer is central. The gravitational potential and the speed of light are both inversely proportional to the density of the field, which is the integral of the quotients (mass divided by distance) of all the matter and energy of the universe. This must be true if, as Newton showed, the gravitational force is inversely proportional to the square of the distance. Thus, gravity is the result of a gradient in the gravitational field which produces a gradient in the speed of light, whereas inertia is a result of the motion of the object relative to the gravitational field, which forms the preferred frame in which light is isotropic. In both cases the effect is due to the change in the speed of light relative to the object.
Discussion
GR is based on an equation that describes a curvature of space surrounding any massive object such as the sun or the earth. This equation has been very successful in predicting the curvature of star light around the sun, changes in clock rate in a gravitational field and the advance of the perihelion of Mercury. Einstein spent many years in an unsuccessful attempt to use this approach to describe the electromagnetic force and thus unify the latter with gravity. On the other hand numerous unsuccessful attempts have been made to apply the successful method of quantum electro dynamics to a description of gravity (9,10). Thus the gap between gravity and electromagnetism has not been bridged from either direction.
PERFT is based on the most fundamental concept of realism, that there is an objective reality that is independent of our ability to measure it. The observation that the measurements of the speed of light yield constant results is not considered evidence that the speed of light is in reality constant, because of the observations that the clocks with which the measurements are made vary with both motion and changes in the gravitational field. Thus Shapiro’s observation that light pulses that pass near the rim of the sun are delayed is considered evidence that the speed of light is reduced in the gravitational field of the sun. This is the only interpretation of Shapiro’s experiments that is compatible with the requirement of QM that light follow a least time path. The fact that the measured round trip speed of light is the same in all directions on the earth is attributed to a change in clocks and measuring rods that exactly cancels any real difference in the two one way speeds.
PERFT accepts the reality of the quantum world, although some aspects of it are difficult if not impossible to comprehend, such as non-locality and the production of virtual bosons that tunnel through anything at great distances. The observations that support quantum mechanics are too many to ignore. There are two important advantages to this approach. The first is that it provides a preferred frame, which is necessary to explain inertia, without postulating the existence of an aether for which there is no evidence. And second, it gives a quantum explanation of the predictions of GR by dividing the production of gravity into two steps. By postulating that the primary effect of the gradient in the gravitational field is a change in the speed of light, the gradient in the density of virtual gravitons produces effects that are equivalent to the curvature of space postulated by GR (6).
One may reasonably ask how a change in energy requirement produces a force. The force that we are most familiar with is gravity. Assume that it takes less energy to form an electron on the floor of this room than it does at the ceiling. Why does that difference cause the electron to fall from the ceiling to the floor with an acceleration of 10 meters per second per second (assume the electron is in a vacuum tube). PERFT proposes the following explanation: The quantum uncertainty of position permits the electron to move in all directions but with different probabilities. The length of time it can stay in any altered position is inversely proportional to the amount of energy required for the particle to exist in the altered position.. Therefore, the most probable altered position is straight down where the energy requirement is the least. And the change in energy requirement is zero if the velocity of motion straight down produces an increase in the inertial energy requirement that is exactly equal to the decrease in gravitational requirement. Once the electron starts down it must continue down at an accelerated pace to preserve its energy. On the surface of the earth this requires an acceleration of 10 meters per second per second.
A problem with the Standard Model is the absence of mutual repulsion by different parts of the electron. According to PERFT the force that an electron responds to is a gradient in the energy requirement to make an electron. The electron is made of energy and the individual quanta of energy that make up the electron do not respond to that gradient. Therefore there is no reason for the individual parts of the electron to repel each other.
A theory or model should not only be consistent with all known observations, but must also have the possibility of being refuted by future observations (7). Any one of the seven following observations would refute PERFT:
1. Any departure from an exact equivalence of the inertial mass of a particle of matter, including the mass derived from its kinetic energy, and its mass as determined by its production of a gravitational field or its response to that field. Thus, an effect of temperature on the orbit of an object circling the earth would refute our model.
2. Any demonstration that the framework of space at any point is not determined by the total gravitational potential of the universe, which is the integral of the quotients of all its particles of energy divided by their distance from that point. The Stanford gravity probe is designed to test this point.
3. The demonstration of a gravity boson such as the postulated graviton that acted directly on matter particles.
4. Any lack of correlation between the change in the speed of light, the change in clock rate and the energy derived from a gravitational fall.
5. Any evidence that the gravitational force can be absorbed.
6. A demonstration that the curvature of starlight around the sun is not the least time path.
7. A demonstration that the one-way speed of light is isotropic on the earth’s surface.
A Possible Experimental Confirmation
If the framework of space is determined by bosons derived from all forms of energy in the universe, a bright beam of light should alter the framework of space within its boundaries. The brightest beam of light we have available is sunlight. Although the amount of energy in a sun beam is infinitesimally small compared to the energy of the universe, it could have a measurable effect on the velocity of light because the distance from the test beam to the sunbeam is small compared to that of the universe and the sunbeam’s velocity is great. Thus, the sunbeam could have a detectable dragging effect on the preferred frame within its boundaries.
I propose the following experiment. Place two atomic clocks (accurate to 3 ps) approximately 100 km apart, in a direct line of sight and in a line with the rising or setting sun. Synchronize the clocks, using a laser beam and the Einstein convention, before and after sunrise or before and after sunset. If the postulate is correct, and the dragging effect of the sunbeam is greater than 10-8 then an alteration of the apparent synchrony of the two clocks should be detectable in a very specific manner.
If the clocks are synchronized before sunrise, then when the sun rises the Western clock should appear to be retarded compared to the Eastern clock because the synchronizing signal will arrive sooner than expected if the signal goes faster in the presence of a sun beam going in the same direction than in its absence. If the sunbeam has a dragging effect on the light signal then it must have an equal dragging effect on itself.
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Major questions raised by PERFT