REFLECTIONS ON GRAVITY
Part 3
Martin Gottschall  PhD © 2004

THE CURVATURE OF NATURAL LAW

General Relativity speaks of curved space-time, and a writer to be discussed later wrote of the "Curvature of Natural Law whose Radius is the Speed of Light". In PART 1 we introduced a theory of gravity and in PART 2 we derived its key equations. In future parts we will look at how these equations govern the inner processes of the densest of stars, and artificial gravity. Inside such stars the pressures are very intense, the temperatures or their equivalent very high, and an intense nuclear chemistry can take place.

Special Relativity considers the effects of motion, while General Relativity considers the effects of gravity. Our equations of gravity as outlined in PARTS 1 and 2 and the equations of Special Relativity share a peculiar feature that points to things beyond the familiar, which it is time for us to consider.

SPECIAL RELATIVITY

Albert Einstein published his Theory of Special Relativity in 1905. This theory took patterns which had already been recognized in Maxwell's electromagnetic theory by Lorentz and extended them into the "mechanical" world. From our perspective, the mechanical world of masses, motion, forces, stresses and strains, inertia and kinetic energy has a hidden electromagnetic foundation, so it is hardly surprising that this venture worked out so well.

The Mass of a Moving Object

A key proposition of Special Relativity was the idea that energy possesses mass or inertia, which is embodied in the equation:

        Y  =  m.c.c                    (32)

where "Y" is the total energy (we have already used "E" for the electric field, so we use "Y" to avoid confusion) of an object of mass "m", and "c" the speed of light.

We now take an object and act on it with a force so as to increase its speed, constantly imparting more and more energy to it, which becomes its energy of motion, or "kinetic energy". Since the energy imparted has mass, the accelerating object displays an ever increasing mass as its speed (and therefore kinetic energy) increases. The equation for the changing mass of the object can be expressed in the form:

                2            2
        (M/m)   +  (v/c)   =  1        (33)

where "M" is the mass of the object when at rest, "m" its mass when moving at a speed "v" and "c" is the speed of light. This equation graphs as a circle having a radius of 1 or unity. To "read" this formula and others like it, notice that on the left of the "=" we have two terms (numbers) which when added up, total unity. At values of "v" much smaller than "c", the speed of light, the "v/c" term is much smaller than unity, and so the "M/m" term must be very close to unity. This means that "M" and "m" are very close to equal. In other words, at speeds much smaller than the speed of light, the mass of the moving object is pretty much the same as its mass when at rest.

However, when "v" gets close to "c", it is the "v/c" term which approaches unity, and so the "M/m" term must be small. This means that "m" must be many times bigger than "M". FIGURE 8 is a graph of EQUATION (33) and gives us a more precise picture of the way in which "v" and "m" relate to each other. Firstly, notice that the graph is a circle. Secondly, notice that we are dealing with only two attributes, mass and speed. Finally, notice that our "variables" (things that take numerical values) are ratios of like things, mass divided by mass and speed divided by speed. These ratios are said to be "dimensionless", because regardless whether we measure speed in meters per second or feet per year, the ratio "v/c" will always turn out the same. Likewise, the unit of mass we use, whether kilogram or carat has no effect on the numerical value of "M/m".

When "dimensionless variables" are used, a single graph will convey the same information for which we might otherwise have to use many graphs. This practice comes from a discipline known as "Dimensional Analysis", which is a logical procedure for eliminating all irrelevant information which might otherwise confuse us, or cause us to repeat the same graph many times, under the delusion that each graph is telling us something new, when in fact it is only telling us the same thing in another guise.

Hence, FIGURE 8 contains the irreducible minimum of information about the relationship between the mass of an object and its speed of motion. The same will apply to the other circle formulas to be presented, since they use dimensionless variables too.

The Length and Rate of Activity of a Moving Object

Moving objects display two other strange properties not part of our everyday experience. They shorten in their direction of motion, and any internal activity in them slows down as the speed increases.

If the length of an object at rest is "X" and its length in motion at a speed "v" is "x" then:

               2           2
        (x/X)   +  (v/c)   =  1        (34)

where length is measured in the direction of motion. This means that not only does the moving object possess more energy than when it was at rest, but this energy is packed into a smaller space. This has a direct bearing on the ability of fundamental matter particles to resist intense collisions and the intense pressures that arise in such bodies as neutron stars.

If "N" is the frequency of some cyclic process in the object at rest while "n" is its frequency at a speed "v" then:

                2          2
        (n/N)   +  (v/c)   =  1        (35)

defines how the rate of activity slows with increasing speed. The significant thing is that the rate of activity can only slow down, not speed up above the rate at rest. It is as though there was a basic "rate' of time in our world which can be characterised by the speed of light, at which no other activity than motion, can take place, or by the rate of vibration, which is greatest at rest, when none of the innate capacity for action is expended on motion.

These equations show us that three quite different properties of an object are affected by motion in similar ways, which is in itself remarkable and must reveal something about the inner workings of matter.

Resistance to Pressure

EQUATION (34) can be used to describe how motion affects the volume of a particle, as noted above. Since it shortens while the transverse size remains the same, there is a decrease in volume. The energy density, Joules per cubic meter, of the particle has the units of pressure, and is a measure of the ability of the particle to resist external pressure and collisions with other particles. The variables M/X for the particle at rest and m/x for the particle in motion are proportional to its energy density or "internal" pressure. The ability of particles to resist pressure in high density stars has a bearing on the way in which these bodies can "burn" matter, and determines the ability of particles to survive a high energy collision. We obtain:

                                     2
        (M/X)/(m/x)   +  (v/c)   =  1    (36)

This equation will also graph as a circle if the horizontal axis is scaled as "v/c" and the vertical axis as the square root of "(M/X)/(m/x)".

INTERPRETING THE AXES OF THE CIRCLE DIAGRAMS

If we were to perform a series of experiments in which particles, say electrons were accelerated to various speeds and their mass then measured, we would plot a series of points on the circle of FIGURE 8. We could repeat the experiment with protons, ionized atoms and molecules, and even grains of sand etc. After a while it would become very apparent that all our experimental points fall onto just one quarter of the circle, from "A" around clockwise to "B", or in the first quadrant. This raises a question: "What kind of experiment would graph on other parts of the circle?".

Notice that in FIGURE 8 the horizontal axis or scale is labelled "v/c" and the vertical axis "M/m". The top half of the vertical axis and the right half of the horizontal axis are traditionally regarded as positive, and the other halves negative. Our question therefore reduces to deciding what the negative halves of these axes might mean. This meaning, whatever it may be, has to be the exact (or mathematical) opposite to the meaning of the corresponding positive half of the axis being considered.

For the vertical axis we already have a satisfactory answer. We can decide that the top half of the vertical axis relates to MATTER, since it is about masses, and then the bottom half must relate to ANTIMATTER, which is indeed the mathematical opposite of matter. Thus, if we were to repeat our experiment with a piece of antimatter, the result would graph into the fourth quadrant, the portion from "B" clockwise to "C".

The horizontal axis of FIGURE 8 is about motion. Without energy there can be no motion, in fact, without energy nothing can change. The concepts of "energy", "change" and "time" are closely linked in our thinking and experience. We therefore relate the right half of the horizontal axis to "energy" and the left half to "antienergy". We propose further that "energy" makes events progress forward in time, while "antienergy" makes the same events progress backwards in time.

IMPLICATIONS FOR COSMIC COMMUNICATION AND TRAVEL

These ideas have been explored in more detail elsewhere. Suffice to say that they lead us to a view of our universe as one which is created simultaneously in forward and reverse time. It is a dual universe each part of which exists in "time", but as a whole it exists out of time in a "now". In this universe instant travel, instant communication and time travel are possible.  Time can be stopped altogether as at points "A" and "C" of FIGURE 8. Notice that the equations of Special Relativity have led us to this perspective. When antimatter was discovered in the 1930's, anyone who graphed the equations of Special Relativity as circles, would have been led to these inferences about time, energy and the universe.

With the ability to choose the direction of time and to stop time altogether, it is possible to conceive of methods of space/time travel which are a match for the stupendous size and age of the universe. This overcomes the often stated view that the universe is just too big and the speed of light limit too slow for useful communication or travel except perhaps to our nearest stellar neighbours. By manipulating time in the right way, our spacecraft can move at a speed less than the speed of light and yet arrive at its destination anywhere in the universe at the moment of its departure or even before its departure.

Historically scientists have been in the forefront of skepticism over claims of ET visitation to this world. They have found it particularly inconceivable that there should be anything approaching the reported frequency of ET craft and encounters that witnesses have claimed. From their perspective, space travel was too costly, too hard, too dangerous and just took too long to be anything but a rare event. It is ironic that Special Relativity, one of the foundations of Physics, should have built into it the signposts which point to this scientific viewpoint being completely wrong, narrow minded and parochial.

As said elsewhere, we rarely find things which we are not looking for, and especially if our mind-set is against that thing. If the scientists who presently are so sceptical about UFO's and ET visitation were to look at the accumulated evidence and to search for the kind of evidence they find more persuasive, who knows what they might find? I know that I found what I was looking for, and many others have too.

THE GRAVITY EQUATIONS IN CIRCLE FORM

In PART 2 we derived equations describing the effect of gravity. EQUATION (15) defines the speed of light in a gravity field. In a circle format this equation would take the form:

               2
        (c/C)   +  (2.P/(C.C))  =  1     (37)

This equation is graphed in FIGURE 9. In accordance with accepted practice, we graph the causal variable horizontally and the "dependent" variable vertically. Note that we must scale the square root of the gravity term on the horizontal axis in order to generate the circle graph.

The equation for the rest mass "Q" and "q" would be:

               2
        (Q/q)   +  (2.P/(C.C))  =  1     (38)

and the equation for rest energy "RE" and "re":

                  2
        (re/RE)   +  (2.P/(C.C))  =  1   (39)

While the equation for the frequency "N" and "n" of cyclic processes is:

               2
        (n/N)   +  (2.P/(C.C))  =  1     (40)   
       
In each of EQUATIONS (37) to (40), the leading term is scaled on the vertical axis, and they are all regarded as matter properties.

The similarity of the equations describing the effects of motion, and those describing the effects of gravity can hardly be due to some kind of meaningless chance. It is not due to faulty logic or mathematical errors, as these have been eliminated by deriving the equations in different ways, from different starting points, and independently on numerous occasions. Besides, errors tend to destroy patterns, not create them. This similarity is worth exploring further, and if we find a way to "explain" it, we will doubtless have made some very significant discovery.

For the moment, we can say that since we have taken the view that inertia is an attribute of the electromagnetic structure of all matter and energy, and gravity acts only on this same structure, this similarity tends to confirm our  proposition. Indeed we can combine the effect of motion and the effect of gravity on matter into a single equation which graphs as a three dimensional object.

A NEW CONCEPT OF TIME

EQUATION (35) shows how the frequency of internal processes in a moving object decreases as its speed increases, ceasing altogether at the speed of light. This equation seems to imply that there is an upper limit to the capacity for activity of bodies, and this capacity can either be directed to internal processes (vibration) or an external process (motion), or some combination of both, but increasing one requires that the other must decrease, since the two measures of activity must add up to a fixed total rate of activity.

Although EQUATION (35) was derived originally for an object outside a gravity field, it will be valid in a gravity field also, the difference being that the speed of light will be the value in that field. The rate of vibration at rest "N" will also be the rate which EQUATION (40) gives for the relevant gravity potential. These two equations can be combined to eliminate the values of "N" and "c" in the gravity field, and yield the Equation:

               2           2
        (n/N)  +  (v/C)   +  2.P/(C.C)  =  1     (41)
 
in which "N" and "C" are the values at rest and at infinity (when "P" is zero). It will be shown later that gravity is itself the product of an electromagnetic vibration, and hence is a kind of activity. EQUATION (41) seems to be telling us that the activity of vibration plus the activity of motion plus the activity of gravity add up to a constant total for all matter at all times, and the changes which we observe are simply different proportions of these three things, in such combinations that their total is always the same.

Matter seems to have a fixed capacity for action. We will define this "capacity for action" as a measure of the "rate of time" which characterises our observable universe. This rate of time is the same for all matter in our universe, at all times, everywhere in space. It is a "universal constant" much as the speed of light is in Special Relativity.

In Special and General Relativity it has been customary to describe the slowing of the internal activity of objects by speed or gravity as a slowing of "time". This is incorrect in our view and creates a paradox. For example, consider the well known "thought experiment" in which one of two twins embarks on a cosmic journey at close to the speed of light. He returns to Earth ten years later in Earth time, having "aged" only two years. The paradox is that the twin remaining on Earth can not see or interact with people from eight years in his past, and yet he is supposed to be "simultaneous" with his twin brother who has aged only two years and is therefore eight years in his past.

Although we traditionally used clocks and celestial events to measure time, the true "rate of time" according to our definition, is measured only approximately by clocks. Under ordinary conditions of speed and gravity, "clock time" is a good approximation to "time", but in principle, clocks do not measure time exactly, and what they do measure is always less than time.

So far our various equations have graphed as circles. EQUATION (41) has three independent variable, one more than the previous equations. It has three axes and graphs as a sphere, FIGURE 10. The points on the surface of the sphere represent every possible combination of vibration, motion and gravity potential. The axes can be regarded as the energy/antienergy, matter/antimatter and gravity/antigravity axes. An exploration of their meaning will be deferred till later.

   
THE RATE OF TIME AND MULTIPLE UNIVERSES

The rate of time (or capacity for action as we have viewed it) is still a mystery. Motion and gravity can slow activity, but they do not speed it up. We have argued that all matter and energy which we can sense must remain simultaneous with us and must therefore have the same "rate" of time, regardless of the rate of its internal activity as determined by its speed and/or gravity potential. We need a "universal" rate of time if we are to avoid time paradoxes.

Our universe has a particular rate of time which is represented by the "1" of EQUATION (41). Are faster or slower rates possible? If so, they would have to lie outside our observable universe, since we could not be simultaneous with any event having a different rate of time.

We can define a "rate" term "r" which may be less than or greater than unity. We can then multiply any one of our circle/sphere equations by this rate term. Thus, EQUATION (41) for example becomes:

                 2             2                    2          2
        (r.n/N)   +  (r.v/C)   +  2.P. (r/C)    =    r          (42)

This equation will graph out as a series of concentric spheres of different radii, FIGURE 11, according to the value of "r", which has been normalized to our rate of time. It suggests that there exist a whole family of "physical" universes, each of which has a specific rate of time, for which the speed of light and the internal details of their matter and energy are different one from the other. In general, for "r" exceeding unity, the speed of light will be higher than the value we experience, and the mass or inertia of corresponding particles will be less, and vice versa for "r" less than unity. It also means that the rate of corresponding vibrations will be "r" times higher.

Despite such differences as the speed of light and the masses of particles, the universes characterised by the different values of "r" must have similarities also, since they possess the same attributes which interrelate in the manner of the circle/sphere equations. At this stage of our development we have only begun to explore our half of our universe. We have yet to accept the existence of its reverse-time counterpart, and we are even further away from exploring those other universes which operate at different rates of "vibration". These have been explored in metaphysics, but not the so-called "natural" sciences.

Experience teaches us again and again that we can fail to recognize the evidence for the existence of something if our minds are not open to the possibility of that thing existing. Therefore to say for example that reverse time and other universes as defined here, cannot exist because our science has not discovered them, only has a degree of validity if that science was not in denial of such a possibility, and would have recognized any evidence for it had it been available.

GEORGE HUNT WILLIAMSON

Williamson wrote The Saucers Speak. It was published in 1963 by Neville Spearman, London, but was published in the 1950's also in the United States. It was a diary of communications between a human and an ET contact group. On page 83 of that edition we find an ET message dated 19 September 1952, 6.30 pm:

"Zo again ... The Four Great Primary Forces are: Static Magnetic Field; Electro-Static Field; Electro-Magnetic Wave; Resonating Electro-Magnetic Field. Your scientists do not understand the last one mentioned. ..."

Elsewhere in various other communications it is made very clear that the last member of the above list is the gravity field.

When we discuss the nature of the gravity field, we will propose that each particle of matter creates a radial electromagnetic standing wave field centred on the particle and diminishing with increasing radius. This standing wave energy is not emitted as photons and remains attached to its central particle. Since gravitating bodies comprise vast numbers of particles, the standing waves associated with each of them are equally vast in number. Their combined effect is to change the value of "e" and "u" of space, as described in PART 1 of this series. The above phrase "resonating E/M Field" is a wholly apt description of our notions about gravity.

DANIEL FRY

Fry was an electronics engineer engaged at White Sands Proving Grounds in instrumenting test firings of rockets. On July 4 1950 he missed the bus he had intended to catch to a nearby town to celebrate the day, and was walking in the desert at night when he saw a discoid object land nearby and a voice engaged him in conversation. That night he was taken on a flight in this craft to New York and back, that took about half an hour. In the following months Fry had numerous conversations with the ET controlling that craft (who was not in it). This ET discussed scientific topics with Fry and used the phrase "The curvature of Natural Law, whose radius is the speed of light". He also gave Fry an explicit description of a method for creating artificial gravity. I quote:

"You are familiar enough with electrodynamics to know that a moving electron creates a magnetic field. The tremendous surge of electrons through the force rings produces a very strong magnetic field. Since the direction and amplitude of the flow can be controlled through either ring, and in several paths in a 'single' ring, we can produce a field which oscillates in a pattern of precisely controlled modes. In this way we can create magnetic resonance between the two rings, or between the several segments of a single ring."

"As you know, any magnetic field which is changing in intensity will create an electric field which, at any given instant is equal in amplitude, opposite in sign, and perpendicular to the magnetic field. If the two fields become mutually resonant, a vector force will be generated. The effect is similar to, and in fact, identical with a gravitational field. If the centre of the field coincides with the craft's centre of gravity, its only effect will be to increase the inertia or mass of the craft."

"If the centre of gravity does not coincide with the centre of the force, the craft will begin to accelerate towards the centre of the field. ..."

Fry gives us more information about "artificial", (perhaps "anti-") gravity, than does Williamson. However there can be no question that both messages could well be describing the same phenomenon.

CONCLUSIONS

We have explored the "Curvature of Natural Law", and found that the effects of both motion and gravity are such that the equations describing them graph out as circles. We have also combined both effects in a single equation and found that this equation graphs as a sphere.

We began by exploring the effect of motion and gravity on matter and energy, and having found out the nature of this effect, we have come to the realization that these equations were defining the rate of time as a constant in our universe.

In attempting to understand the "other half" of the axes of our diagrams we were led to the concepts of "antimatter", which was already a known entity,     "antienergy" which activated reverse time and "antigravity" which we have yet to explore in more detail. Reverse time implies the existence of a sister universe created together with our universe, the two together constituting a mysterious timeless entity.

By considering the possibility that the rate of time may have a number of values, we have opened the door of our minds to the possibility of a number of universes whose "spaces" may overlap with little or no interaction, each containing energy and matter of its own kind which may have little or no interaction with matter and energy of different rates of time.

The usefulness of a theory is often measured by its predictive power. We started by trying to understand gravity and stumbled upon a whole array of notions pointing to the universal role of electromagnetic fields in all matter and energy, the existence of two opposed timestreams and their associated composite universes and finally a hierarchy of composite universes characterised by different rates of time or action, having different values for the speed of light and the other parameters of the various circle equations.

We have answered some questions about our world, and ended up with other questions that we could not even have formulated before answering those initial questions. This paradox is surely the enduring human experience of the quest for understanding.

In the remaining parts we will "come down to earth" or at least to our visible universe to explore the more immediate consequences of our theory of gravity.

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