MATTER-SPACE POTENTIAL

AUTHOR: ASAME IMONI OBIOMAH

COMMENTS

COMPLETION DATE: FEBRUARY 1997
MINOR EDIT: JANUARY 15-18 2001 (Minor textual changes)
MINOR EDIT: DECEMBER 02-04 2003 (Inclusion of Introduction, formatting)

Abstract: This paper tackles the problem of the gravitational interactions between matter and space.
It gives accurate solutions including a mathematical definition for inertia. It employs common sense potential field laws, Maxwellian electromagnetism and a space similar to (though independent of) that postulated by Dirac in his concept of the particle - antiparticle relationship. The reasons for the seemingly anomalous relations between matter and space are arrived at naturally and logically.

KEY WORDS: Matter, Time, Light, Mass

INTRODUCTION

This introduction will give a new insight to time and describe how identical equations to those of General Relativity can be derived without assuming a curved space or time as a fourth dimension. It is an overview for this treatise on the makeup and interactions of light and matter.

The equations in this chapter are denoted by a number followed by an asterisk - this is to seperate them from the the equations refered to in later chapters.

What is Time?
Time is the duration of an event. This duration is measured against periodic intervals that that are constant and can safely be used as standards, such as the average orbital period of the Earth around the sun (a year), the period of the Earth rotation about it's axis (a day). Where high accuracy is required, the periods of molecular and atomic vibrational movements are used as standards for time measurement, for example, an atomic clock in Greenwich (London, UK) sets the World standard time known as "Greenwich Mean Time" (GMT). This definition of time takes for granted that it's flow is unidirectional which negates the possibility of time travel.

Time tends to be addressed as a fundamental of nature, but for this to be so, time would have to have a beginning or a "zero" point. The concept of a zero point immediately throws up severe procedural problems for science. Mathematically, zero is either a starting point for a specific reference or it denotes nothingness. No science theory or observation has proven the existence of nothingness, indeed finding a reference point for the caliberation of nothingness will be impossible, yet present physical tradition would find a boon from such a rigid and impossible reference. As far as time is concerned, it is safe to summise thatr regardless of how it is measured, it can only be defined as the rate of flow of energy.

Energy can have no starting point and can never be null - there can only be equilibrium.

Indeed if we step outside of the mathematical mental bounds embodied in the concept of zero and in the concept of time, it becomes clear that the one universal fundamental is energy. All our standards - be they distance, force or time are mathematical conveniences for the description of energetic flows and interactions - they are abstracts that we have made our reality. This World view is essential to our understanding of Gravitation, Matter and Space.

Energy is the only physical fundamental in our World.

Strange Time Results
In 1887 when two physicists, A.A. Michelson and E.W. Morley performed an experiment that showed the speed of light to be remain the same relative to an observer, no matter the speed at which the observer moved. If the speed of light (approximately 3 x 10⁸ M/S) is denoted by C and the speed of the observer relative to a stationary light source is U, surprisingly

C - U = C

This is exactly the same result he would get if the observer was stationary.

The equation above shows that the time measured by the observer must slow down to counteract the effect of the observers motion for the observed result to be valid.
The incontrovertible result of the Michelson-Morley experiment threw the search for a medium for light waves into a quandary since no known material possessed the qualities that could "slow" time down. To solve the problem, Albert Einstein proposed a purely mathematical solution with the Relativity Theories. Whilst Relativity provides answers through sheer mathematical rigour, it is lacking the beauty of explanation.
Relativity is built on a new concept of time that makes it a 4th dimension of space (space-time) in addition to the known and intuitive length, width and height.
This rigid and unexplained mathematical solution has led to a lot of confusion accross mordern physics.

Certain nuclions are thought to borrow energy from space to maintain the nuclear bond. If there are interactions between an energy filled space and matter, we should be able provide insight by substituting an energy equilibrium where we would have placed a zero.

Time and Space
Firstly, it must be stated clearly that while the time of a given cycle might be slowed or speeded up, this effect is local (intrinsic) to that cycle only.
Compton's equations link light and mass with:

hf = MC² (1*)

rearranging

f = MC²/h, but f is the inverse of time t, so:

t = h/MC² (2*)

Equation 2* links the period of a light wave as it travels through "empty" space to it's perceived mass when it bounces off or is absorbed by an obstacle. The importance of this subtle link becomes obvious when we put aside our conditioning and notice that equations 1* and 2* are clearly unbalanced if we are to stick to present definitions - every factor in both equations is a measurement of an electrical quantity except for mass, M. There is an unexplored relationship between electromagnetic space and matter that defines the local or intrinsic time of a system (gravitational or electrical). Equations 1* and 2* hint at Space being an electrically conductive medium , however we cannot measure it's conductivity because we are at equilibrium with it - it is our zero point of reference.

re-ordering

Since kinetic energy W = QV/2, rearranging

The consequences of equations 1* and 2* above will be seen later in this paper when they are expanded and analysed in depth. For this introduction, we will now switch attention to gravitational systems which are are not only analogous, but also readily observable.

Fig 1 below shows a particle of mass m, orbiting a relatively massive particle of mass M. Note that while this illustration uses gravitational concepts (like the rest of the article) for explanatory purposes only to show the mechanism by which time acts "strangely". The system depicted could just as easily be an electrical one; the gravitational constant G is analogous to the inverse of the permittivity of space 1/4pe, which you can easily substitute (along with e/m where necessary) if you wish to gain much deeper understanding.

All measurements in our analysis below are taken by an observer on the orbiting mass m for the point in space, r_E. Our observer is ignorant of the laws of gravity and the existence of the greater mass M (just as we are ignorant of the make up of space and take it as a zeroth point of reference), yet what he is attempting to do, is measure the mass of his planet m, from the center of M, at a distance, r_o - using equations of translational motion.

For simplicity let's take the mass M to be equal to Nm (where N is a number).

The amount of energy needed to move the mass m from r_E (the surface of M) to an orbit r_o is given by:

Canceling out and rearranging:

Now r_o = GM / v² and r_E = GM / v_E², where v is the speed required to remain in orbit at r_o and v_e would be the speed required to "orbit" at r_E, so:

So,

or,

Since G = r_ov² / m and W = mv'², the last equation becomes:

rearranging,

Now, M = Nm so,

Remember that our observer is ignorant of gravitational law and the existence of mass M, so the term m (Nr_ov^{2 /} 2r_Ev'²) in the last equation is beyond him and would instead be interpreted as Dm (recall that he is attempting to measure the mass of his planet m). Fig. 2 denotes our observers perceptions of his planets dynamics (oblivious of M).

Thus, our observer would read the preceding equation as:

and,

This is identical to the equation for the variation of mass with velocity in General Relativity. Note that the above solution is valid for interactions between the mass m and a system of several other particles - perhaps microscopic - rather than just mass M.
It is interesting to learn that shortly after P.A.M. Dirac postulated the existence of antiparticles, he proposed a solution to particle-antiparticle interaction in which he postulated space to be jam packed with negative energy state particles.

Let us now derive the time equation for our observers orbit as he would calculate it from the center of mass M, at a distance, r_E!

Rearranging for Dm

But m = R²V/GT, similarly Dm must equal R²V/GDT since R, V, and G do not change, so

and

or

simplyfying

Here we again arrive at a solution similar a General Relativity equation; this time, Time Dilation. In the next chapters, we will apply our findings to the permittivity of space, e instead of it's gravitational analog G to build a framework of Matter-Space interactions that arrive at the General Relativity equations for time and mass naturally.

SECTION 1: MASS AND SPACE

There are two apparently independent physical bases for defining mass, inertial and gravitational. This hints at the existence of a single, more fundamental base from which the two above bases are derived. Here, we depart from the traditional definitions to take a closer look at the relationship between mass and electromagnetic phenomena.

1. When an atom is excited its mass increases, it then ejects the excess mass in a photon. The interaction that excites the atom is purely electromagnetic, yet it gives birth to mass.

A photon is mass less until its velocity is slowed (as in a deflection) or it is brought to a halt (as in the creation of a particle and its antiparticle). Conversely, when a particle and its antiparticle annihilate, photons are created.

The above are examples of the generation of mass and photons

(in each instance, one from the other), thus they must both be, on a fundamental level expressions, of one and the same entity.

2. consider the following equation:

The left hand side of equation 1 contains factors that pertain to matter alone (in a gravitational field and in a photon), while the right hand side describes a purely electromagnetic wave. This seeming asymmetry leads not only to the inter- convertibility of matter and electromagnetic energy, but also to the precise definition of mass or matter and its interactions with space as arrived at below.

3. Electromagnetic waves obey the inverse square law (an impossibility in an empty space).

Postulate's:

1. Space is filled with mass less negative electrical charges

2. the dynamics of these mass less electrical charges are similar to the dynamics of an ideal gas with the conditions:

(a) a mean velocity numerically equal to the speed of light C,

(b) a mean free path or wavelength W,

(c) a frequency f!,

(d) a negative electric charge -e!,

(f) they are governed by the inverse square law for force on electric charges:

3. Planck's constant holds in space with the relations:

4. Newtonian gravitation is valid.

5. Matter consists entirely of stationary waves.

SECTION A: MASS

The mass less negative electrical charges that fill space are from now referred to as "space charges".

From the first postulate and equation 2, the kinetic energy of a single space charge is:

-k.E = -e!C²/2

and since W = C/f!

e!C²/2 = -hf! (4)

so,

substituting this in equation 1 yields: 

or,

Equation 6 shows mass as a frequency "defect" in the space charge field. What this means is that, the property we call mass is simply a measure of how far space charges stray from the fundamental frequency f!. Thus, matter consists of bundled waves, not particle's.

Since the energy within matter (internal energy and total energy - hf) is not propagated relative to any reference frame, it exists as a stationery wave. The negative sign on mass in equation 6 is due to the negative electrical charge of the space charges.

For all known forms of matter hf is less than hf! for any given volume. Matter, thus contains less energy per unit volume than surrounding space - in a way similar to the phenomenon of vortices.

The impact of this definition of mass becomes apparent in the next section, gravitation.

SECTION B: GRAVITATION.

We start considerations on the above topic by deducing the effect of a gravitational field on a clock.

(A) DEFINING THE CLOCKS PARAMETERS

For our clock we employ a space charge with a frequency defect, f, a wavelength or "radius" L, an electric charge e! and a mass given by, -m = -e!f/2f!. The concept of matter as a stationary wave leads to the consequence that its wavelengths can only occur in integral multiples of L, only wavelengths of L, 2L, 3L, 4L.....nL, are allowed.

For any mass type M*, therefore, R = NnL, where N is a constant particular to M*. By the same wave concept, L = n W.

The gravitational constant as derived from this defect is thus:

Where V is orbital velocity at L. From equations 2 and 3:

since -G = -2LV²f!/e!f (equation 7),

but V = 2pLf so,

rearranging to find L²,

using C = W f! and -e = -e!/W³ f!² to manipulate the previous equation for V² we get:

V² = 4p²(Lf)² (10)

THE CLOCK IN A GRAVITATIONAL FIELD WITH POTENTIAL, S

If our space defect is at a distance r in space from another relatively massive space defect with mass -M = -ne!f/2f! (where n is the number of space charges making up wavelength R).

The velocity S, the space defect would have to move at, to remain in orbit at R would be: S = Ö(GM/R)

The mass -M is our frame of reference and its gravitational parameters - S, and R are thus, constant. Every measurement taken at its surface is logically constant.

From Newtons laws of gravitation, the gravitational field with potential S behaves as if all its generating mass is concentrated at the centre of M. As a result of this the potential, S varies with mass per unit length at a point r = R + x according to:

S = Ö(GM/r) = Ö(GM/R+x)

If s is known, the value of the mass M can be calculated at any point in space, r away from its surface. The value of S depends only on mass per unit length and not on radius, R. Indeed any mass with value M and radius, a (where a < R), would give the same result for S. For a mass with variable radius, R (where R is always less than r), there must be a compensating change in the local properties of the surrounding space for the same value of S to be returned for each variation of R.

We conclude that for any mass of value M, at a point in space r, potential, S is constant regardless of R.

From our considerations so far the relation for the gravitational constant -G in equation 7 can be written:

From equation 6, -M = e!f/2f!. Since rS² is constant for the case being argued, for the same values of M to be given at r for different values of R, there is a change in the local value of f!. This change is reflected in a compensating change to f so that equation 6 always gives the correct value of M. Measurements taken with normal space parameters of (W)(f!)= C would record a frequency at point r of Df!, making equation 6:

-M (at point r) = e!Df/2Df! (6b)

Measurements taken at point r or any other, would however appear to be the same as given by equation 6 due to the dependence of f on f!. The value of Df! rises to a maximum at the point where the difference between it and f! are negligible. Beyond this point, the gravitational field logically ceases to exist. 

THE INTERNAL ENERGY RELATIONSHIP OF THE CLOCK AND ITS POSITION, r IN A GRAVITATIONAL FIELD WITH POTENTIAL, S

Now, the gravitational constant due to the space defect is:

-G = -2LV²f!/e!f , = -LV²/m

Note: the negative sign on G is due to the negative charge of the space charges.

so,

or since M = ne!f/2f!,

but V² = 4p²L²f² and

so:

from equation 3, -e = -e!/W³ f!² , thus:  

but f! = e!f/m equation 6 therefore,

Now

from equation 6, m = -e!f/2f! so S² is:

but W = C/f!, therefore:

but from equation 6, -m = e!f/2f! giving:

with L = n W as mentioned above, from equations 3 and 4, e = ne!/RC², also r = DR, so:

applying the logic of equation 6b:

where is the apparent permittivity at r measured by the space defect

or,

GMr/R² = DfC²/f (12)

This is one of the consequence's of the General Theory Of Relativity, but in obtaining this result, we have used the classical gravitation equations, only modified by the proper definition of mass. This result, as well as those below can be obtained by likening space to an ideal gas,using two density functions, (a) - rW² = -1/m and (b) -1/rf! = e . We will, however keep interpreting the classical gravitation equations which are familiar and instantly recognizeable. Here it must be stated, that since space is negatively charged, all matter, including laboratory equipment is in equilibrium with it and so reads this charge as neutral. Matter is a wave defect in this sea of negative charge.

Matter-Space Energy Potential Of A Mass In Motion.

Replacing -M in equation 12 with -hf/C² yields:

Rearranging to solve for -G,

To effect a change of sign on -G (anti-gravity), the stationary wave type or the charge sign on the space charge would have to be changed. From Maxwell's electromagnetic theory, C² = 1/m e , substituting this in equation 13 gives:

from equations 2 and 4, -h = e!C W/2 and -m = W/e! so,

From gas dynamics - the pressure due the gas molecules impinging on a wall is dependent on the inverse of the area of the wall. Similarly, a space defect with a radius L, takes part in a different number of collisions as compared with a normal space charge, due to its new momentum, e!Lf as against e!W f!. It thus has a different kinetic energy value from the surrounding space charges with which it must collide and exchange momenta until they collectively form an equilibrium system.

If the above system is isolated, the total potential is an algebraical summation of the potentials of the enclosed entities.

In reaching equilibrium, the space charge clocks energy changes, so that its frequency becomes Df!. For a space charge, therefore, equation 14 becomes:

The gravitational potential energy of the mass, -M is (according to Newtonian gravitation): 

y being a dimentionless constant dependent on shape. Putting -M = -hf/C²,and substituting -G for its value in equation 15

gives:

but -e = -1/mC² so,

Now -e! = -W/m so, 

since -2hf! = -e!C²,

We have seen that a space defect distorts the space around itself in reaching an energy equilibrium. When a space defect moves with a velocity V, relative to the point at which it attained energy equilibrium with space charges with velocity, C, it does work against the system. Using e!C/2 and noting from equations 2 and 3 that W has a value of 0.2357 x 10- ²³, it can easily be deduced that space contains more energy per unit length than any form of matter including the nucleus. In the matter space system, therefore, matter is treated in exactly the same way as we would treat a satellite under the influence of a much more massive body. When a mass moves with a velocity V, therefore, equation 17 becomes: 

but from equations 3 and 4, e! = We C², substituting this in equation 18 gives:

The factor -e!(C²-V²) in equation 18 accounts for the phenomenon, inertia. This is simply an effort at remaining in equilibrium and thus reluctance to move, since moving at a velocity, V increases the kinetic energy of the matter - space system. Any change in speed reduces the potential energy of the equilibrium system in the very same way as a satellite in earth orbit, firing a burst from an onboard thruster to increase speed, loses potential energy.

As a consequence of its new velocity, the mean free path of the space defect changes and therefore its frequency. Its mass being dependent on its frequency must also change.

Rearranging and multiplying both sides of equation 18 by 1/C² to obtain the new mass -Dm:

but,

\ -m = -Dm Ö(1 - V² /C²) (20)

Effect Of Motion On Time (Frequency)

Mass is defined by equation 6 as: -M = e!f/2f!, however, as seen above, mass in motion increases its value. The explanation for this is a Doppler effect for potential energy through permittivity. Since space is filled with charges which move at the speed of light, C and have a frequency f! relative to one another, a mass in motion at a speed other than C, experiences an apparent frequency f!", rather than f!.

From the equation preceding equation 20

cancelling out and manipulating equation 16 for -DU, gives:

The term, -U / f!²(1 - V² /C²) is apparent frequency squared. It is from now denoted by the symbols, f!" and f".

From equation 6

f = 2Mf! / e!

thus when in motion it becomes:

f is directly proportional to the other frequencies found in matter through the fine structure constant and so they are also proportionally dilated.

Length Contraction

Due to its motion,the mass also measures an apparent space charge wavelength, W", therefore, relative to itself, the speed of light, C becomes

When -M is in stationary equilibrium, its gravitational potential energy is -U and its total energy is,-hf = -MC² . In motion its potential energy is -DU, with its total energy, -hf"= -DMC"².

Now -DU/U = 1/(1 - V² /C²), thus, the apparent speed of light

-M experiences is:

and

Like f!", X" is directly proportional to, and dictates the other wavelengths that occur in matter. For example, the Bohr radius is given by:

Acknowledgements

Einstein, Albert. (1916). The Foundation of the General Theory of Relativity, (Annalen Der Physik, 49, 1916.) Cf. The Principle of Relativity: A Collection of Original Papers On The Special And General Theory Of Relativity. Page 111. [Dover Publications Edition, 1952].

Isaac Newton. (1687). The Mathematical Principles of Natural Philosophy, trans. A. Motte (London, 1729).

James Clerk Maxwell. (1873). The Scientific Letters and Papers of James Clerk Maxwell [SLPM] edited by P. M. Harman (Cambridge University Press 1990).

Max Planck. (1906). M J Klein, Max Planck and the Beginnings of Quantum Theory, Archive for History of Exact Sciences 1 (1962), 459-479.

Niels Bohr. (1913). Levine, Ira N., Quantum Chemistry, Prentice Hall, Englewood Cliffs, New Jersey, 1991

Compton. (1923). A.H. Compton, The Spectrum of Scattered X-Rays, Phys. Rev., 22:5 (Nov. 1923), 409-13.

Technical College - Bourgas,

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