Appendix

If a Black-Hole forms, gravity cannot disappear.

Method: Imagine an outcome contrary to a prediction made by the C-R theory, and see if we can catch conservation of energy being violated.

Experiment: Imagine that gravity disappears when a Black-Hole forms.

Goal: To demonstrate that Conservation of energy would be violated if gravity decreased when a Black-Hole occurred.

For the purpose of this thought experiment, we will assume that a large mass, M, exists. It is similar to our sun, and ready for our use. All non essential planets, asteroids, dust and debris have been removed to a far away location, and they will play no part in this experiment.

We will assume that only a comet, C, orbits this mass. The comet will follow an asymmetrical orbit between points P (perihelion), nearest the mass, and point A (aphelion), furthest from the mass.

The gravitational attraction between these masses causes each to possess identical but opposite momentum, with respect to the center of mass of the system.

The speed of the comet C will vary from maximum to minimum, between point P to point A, as was pointed out in Newton's third law. As Johannes Keppler stated, the area swept out by the comet orbiting the mass will be constant with time. This will cause the comet to have greater speed nearer the mass, but spend lesser time there, and be physically much closer to the mass. When it recedes, the comet will travel slower, spend a longer time in that part of the orbit, and be much further from the mass. The speed of the comet and its distance from the mass will be cyclical, but could take on any value between the maximum and the minimum for a randomly chosen instant of time.

For most practical purposes, if M>>C, that is if mass M is much greater than mass C, M could be considered the center of mass for the system.

As a condition of the thought experiment, we will require that, at some random time, all of mass M collapses under it's own weight, and forms a Black-Hole. To simplify the experiment further, assume that any heat or other energy/mass involved in the gravitational collapse remains trapped inside the Black-Hole.

(How this is accomplished is of no particular concern for this thought experiment. We simply imagine that it is possible.)

The density of mass M will become so great at the collapse that the gravitational escape velocity from the mass M will exceed the speed of light. No known particles can travel at this speed, and no known electromagnetic energy can exceed this speed. Because this is the case, as stated above in our original conditions for this thought experiment, let's suppose that gravity disappears. If it does occur, will conservation of energy be violated?

After the collapse, and the subsequent disappearance of gravity, notice that the velocity of comet C will be random with time. This also will be the case with the comet's kinetic energy. We obtained these results since we specified that we would choose any random time in the orbital cycle of the comet, C, to start the collapse. The comet will now be free to travel in a straight line until or unless some other gravitational influence is once again felt.

After an unspecified, random amount of time after the gravitational collapse, let us restore the Black-Hole back to it's original state. We will do so using conservation of energy. We specified in our starting conditions that all of the original energy and mass was to be conserved inside the Black-Hole. (Again, how the Black-Hole is to be restored is irrelevant to the experiment, we just require that it be restored).

Conservation of energy does not necessarily imply how, or even that we could restore the mass to it's previous state. There is nothing which would forbid it, either.

Once restored, we would find that the comet in our system had gained gravitational potential energy randomly, with time. If some other massive object had been in the vicinity, and caused the comet, C, to move in closer to the neighborhood of the Black-Hole, before we had restored the Black-Hole, our system would have randomly lost gravitational potential energy.

Therefore, our conclusion must be: Gravity cannot disappear when a mass collapses to form a Black-Hole, without violating conservation of energy.

Implication: For the same reasons that gravity could not disappear, gravity cannot decrease even slightly when a Black-Hole forms. If it did, conservation of energy, and conservation of momentum would necessarily be violated at each instance.

(Another thought experiment to follow will also address this question, if gravity can diminish partially when a Black-Hole forms)

QUESTION: How does gravity emanate from a Black-Hole?

Consider these Possibilities:

1. GRAVITONS ARE IMMUNE TO GRAVITY!

If this is the case, then gravitons, the hypothetical particles of gravitational interaction, must carry or cause the gravitational force. These "particles" must be immune to the force of gravity, since they must not be affected in the least by a collapse into a Black-Hole.

If the gravitons were particle-wave combinations, or components of gravity waves, they could not red-shift in gravitational fields. Otherwise, the strength of the gravitational interaction would be decreased as the gravitons were red-shifted.

In order to escape from the Black-Hole undiminished, the gravitons would almost certainly have to be massless and momentumless. They would follow straight lines, and they could not bend in a gravitational field, as would light (electromagnetic energy). {Given all of these conditions, it is hard to see how gravitons could exist at all.}

2. GRAVITONS TRAVEL FASTER THAN THE SPEED OF LIGHT (and thus they are free to escape from the black hole)

Another possibility is that gravitons travel faster than the speed of light, and so are not slowed down by the escape velocity speed-limit of the speed of light. If this was actually the case, consider this implication. For a sufficient density of mass inside the black hole, especially a point-like singularity, a suitable accumulation could still occur to force the escape velocity required to exit from the black hole to rise to some multiple of the speed of light. This "faster than the speed of light" escape velocity could rise above the speed of at least some of the gravitons. This would mean that gravity outside the black hole would decrease, and again, conservation of energy would be violated.

This case would also seem to violate the theory of relativity. How could these graviton "particles" travel faster than the speed of light, but still interact with regular matter?

3. GRAVITONS COULD USE A METHOD OF "TUNNELLING"

Gravitons could tunnel out from the singularity, across the forbidden area. Current theories would probably select this alternative. There are still many potential violations of conservation of energy which would occur, and I will be glad to touch on them briefly.

Assume that gravitons were permitted to tunnel directly from the singularity. Because they would emerge at different distances outside of the Schwarzschild radius, the gravitons would necessarily have different energies than they would have possessed without the forbidden zone. Some percentage of the gravitons would definitely miss their mark, and be momentarily forbidden from coupling across macroscopic distances. Some gravity might emerge from this type of a black hole, but anything less than a 100% tunnelling efficiency would seem to violate conservation of energy.

An alternate assumption on tunnelling is even more potentially ridiculous. This would require that the gravitons would be spontaneously created in equal and opposite pairs, somewhere outside the Schwarzschild radius. Within the time, energy, and momentum limits established by the Heisenberg uncertainty principle, this pair of gravitons would still need to be created from absolutely nothing. To avoid diminishing the gravitational field around the black hole, exactly the right number of gravitons would need to be created. From this exact matching amount of gravitons, exactly the right amount must then randomly tunnel into the black hole to annihilate their matching partners inside the black hole, and vanish into nothingness1. The remaining gravitons would appear to have been selected to "emerge" from the Black-Hole in undiminished numbers.

Even if this "tunnelling" scenario is the correct answer, there is a question whether the gravitons would red-shift as they emerged from the vicinity of the Black-Hole. If the gravitons could tunnel, and did tunnel, from a random height above the Schwarzschild radius, would this allow conservation of energy to be upheld?

The C-R theory would make the following suggestion, which should simplify matters greatly:

4. GRAVITONS ARE NON-EXISTENT

If gravitons are non-existent, then gravity would be a result from the property of the curvature or warping of space-time.

Gravity would not depend on the interchange of particles, as would an actual force. This implies that the curvature of space-time supersedes the speed of light escape-velocity limit established at the Schwarzschild radius. As a property of warped space-time, gravity would require neither mass nor momentum interchanges to make itself felt. There would be no continuous expenditure of energy necessary to continually make the presence of gravity felt.

Gravity itself would not curve under the influence of a mass, whether passing through the mass, or passing near it. The gravitational curvature of space-time would be identical at a larger distance for a collapsed mass, and for an uncollapsed mass. This would hold true even if we took a mass, and measured the gravitational curvature at a distance, both before and after we forced the mass to collapse. From any distance outside the Black-Hole, there would be no detectable difference, if this is indeed the case.

Notice the simplifications:

• Gravity does not decrease when a Black-Hole forms
• No new forces need to await discovery.
• Conservation of energy still reigns supreme.
• A singularity, -a physicists nightmare-, is not needed.
• Tunnelling, with it's dependence on provident probability is not needed.
• All of the incongruities and improbabilities of tunnelling are also done away with
• A Black-Hole becomes "Humanly understandable" (It didn't have to be so nice for us)
• Gravity becomes the "effect" observed, not the underlying cause, of planetary motion and everyday falling down.
• Multi-Universe, wormhole-bridges caused by Black-Hole singularities are not possible, and are not needed. (WHEW!)
• Red-shifting in the universe has an alternate, gravitational explanation.
• Time-inactivation of electrical charges, and mass-sifting by Black-Holes become real, viable concepts.

IMPORTANT IMPLICATION:

Since we have hypothesized that gravity can emanate from a Black-Hole to influence masses outside the Schwarzschild radius, this implies that masses outside the Schwarzschild radius can create conditions of tidal shifting of the inactivated masses while they are still inside the Black-Hole. If the curvature locally can go below "c", this can lead to re-activation of the mass and energy trapped within the Schwarzschild radius, in the volume in space that the C-R theory would call the Neutral Zone.

Lesser Implication:

If our universe is entirely within the inside region [the Inner Active Zone] of a Black-Hole, the gravitational influence of this universe will be felt outside the boundaries of this universe.

Just in case the above examples of our thought-experiments were not enough to convince you that gravitational particles, or gravitons, do not exist, let us beat the dead horse of gravitational particles even further to death.

QUESTION: Could gravity be caused by gravitons?

Assume again that gravity is caused by the interchange of hypothetical particles called gravitons.

OBJECTIVE: Demonstrate that this interchange of gravitational particles again will seem to result in violations of conservation of energy. We will do this by demonstrating that, if matter is indeed influenced by gravitational particles, then, even under normal orbital conditions, gravity should decrease, due to a gravitational shadowing effect. This shadowing effect would violate conservation of energy.

Thought Experiment: IMAGINE THAT GRAVITONS BEHAVE LIKE PHOTONS

(for descriptive purposes only)

To better visualize how this partial gravitational influence might be encountered, let us describe gravity and gravitational interaction in terms of light, so that:

Brilliance of light = gravitational attraction = (emission of gravitons)

Decreasing Transparency = Increasing Density and Mass

In this thought experiment, we will specify one sun, one earth and one moon. Each will be partially luminous, to simulate their "output" of gravitons, and each will also be partially opaque, to indicate their "capturing-of" or their "reception-of" gravitons. We would then have the following description of the system.

In this imaginary system, the moon orbits the earth, and the earth-moon pair orbits the sun. Since glow will simulate gravity emitted, we could describe this sun as glowing brighter that this earth, and this earth as glowing brighter than the moon.

In addition, the moon would be more transparent than the earth, and the earth would be less transparent than the sun. This would simulate the increasing "interception" of gravity, with an increase of both the density and mass from the moon, to the earth then to the sun in our imaginary example.

In this example, the light from the sun would "attract" the earth and the moon (simulating the pull of gravity). The earth would glow less brilliantly than the sun, but still brighter than the moon. The moon would be attracted to both the earth and the sun, but would orbit the earth. The earth moon pair would then orbit the sun together.

In this example, the moon would spend more time in the earth's shadow, and the earth's shadow would be comparatively darker than the moon's shadow. Since the moon would be attracted to the sun only by the light from the sun, and the light emitted by the earth with the sun shining through the less transparent earth would be less than the light emitted by the sun directly, the moon would gain some amount of orbital distance from the sun every time the moon "hid" in the earth's shadow.

This gain of gravitational energy, simulated in this example with light and transparency, {for visual purposes only}, would violate conservation of energy. If gravitons exist, they must self-condradictingly pass through nearer masses unaffected, so as not to decrease gravity for masses at a further distance, while still interacting with those closer masses at the same time.  

Otherwise, we are left with the choice that masses at a distance will randomly gain some gravitational potential energy depending on whether randomly distributed nearer masses create a gravitational "shadow" effect. We are once again led to the conclusion that gravitons, if they exist, must create violations of conservation of energy. This is hardly a reliable theoretical endorsement of gravitons, when conservation of energy must fall by the wayside in order to allow gravitons to exist. A much more logical conclusion is again, gravitons do not exist, and cannot exist. Some other method of explaining gravitational interactions must be needed.

(How convenient of the C-R theory to come along and do just that for us.) See C-R theory assumption A, in chapter 1.

Another Thought Experiment on the Nature of Gravity

Assume that all of the mass in the entire universe is concentrated in one bundle.

Leave this bundle of mass to sit by itself for a very long time.

Imagine the differences which would occur when gravity was caused by gravitons, and when gravity was caused entirely by the curvature of space-time.

If the force of gravity was caused by gravitons, then we would have this entire mass of the universe (our given starting condition for this thought experiment) emitting gravitons, and receiving none in return. If this is to be the case, then at some point, we would expect the number of gravitons emitted to decrease to some level less than half of the original starting graviton output.

If we were to arrange for a smaller mass to be brought into the universe at this time (How we could do this would not be of great concern, just imagine that this was possible.), we would notice that the gravitational output would be less than we would expect.

We would notice that the newly introduced mass would attract the older, gravitoned-out mass with less intensity than the freshly-introduced (graviton rich) mass. If this was the case, then both conservation of energy and conservation of momentum would be violated.

On the other hand, if all of the mass in the entire universe were packed into a singular mass, and that mass obeyed the C-R theory, this contradiction would not arise. Since the gravitational field would be created strictly by the curvature of space-time, and this steady curvature would require no constant replenishment of energy, the gravitational field would retain it's intensity clear to infinity, with no apparent contradiction.

Just in case there would be those who would claim that spontaneous creation of virtual particles, especially gravitons would solve this dilemma, let us consider this.

The creation of spontaneous particles (supposedly allowed within the time-energy or momentum-position limits set by the Heisenberg Uncertainty Principle, would possibly create gravitons. If the virtual particles were created, then we would expect the most spontaneous creation to occur near the highest energy, or highest curvature parts of the universe. Since only the gravitons created outside of the singular mass would aid in reducing the overall deficit in graviton emission, we would expect some gravitons to be created, in pairs, near the outer edges. Even though some of the gravitons could find their way back into the singular mass, to ease it's chronic deficit of gravitons, there would then be extra gravitons left outside of the mass, chasing after other emitted gravitons. The allowable uncertainty in the time/energy parameters is unlikely to allow any virtual pairs of gravitons emitted to help the overall situation.

From an external point of view, we would find that the number of gravitons emitted was greater than the number of gravitons received, and something would have to come from nothing on a consistent basis for this to occur. If this was the case, then we would expect conservation of energy to be violated again.

Therefore, we have concluded that the creation of virtual graviton particles outside the mass would not aid the overall situation. There might be more gravitons apparently emitted which would be detectable at a point far away, but the imbalance between gravitons emitted and gravitons received could be substantial in the length of time this experiment could run.

(Consider an experiment with all the mass in the universe concentrated into two lumps. One lump would be a billion times as massive as the second lump. Separate these lumps by the diameter of the universe, one at each edge. Leave the masses alone for billions of years. Eventually, bring the small mass near the larger mass at a rapid speed. The larger mass should be gravitoned-out or gravitonally depleted compared to the smaller mass.) The gravitons emitted by the smaller mass should be more plentiful than those emitted by the larger mass. If so, at least for a while, conservation of energy should be violated.