THE THEORY OF GRAVITATION
Here we face the Ultimate Challenge: Explaining the value of G
as now measured in the year 2000
Copyright, Harold Aspden, 2000
Over the past 40 years I
have sought to interest the world of science in my theory of gravitation. It is
a theory based on interpreting the quantum activity which underlies our
immediate environment and pervades all space. There are energy transitions
involving what are called 'leptons', constantly occurring, even in the vacuum,
in an underworld scenario which some physicists refer to as the field of
'zero-point energy'.
My theory is a comprehensive 'unified field theory'
in that it explains gravitation as an electrodynamic process and is successful
in that it allows G, the Constant of Gravitation, to be determined
quantitatively and qualitatively in terms of the electric charge to mass ratio
of the electron.
The theory has developed in stages, but its
phenomenological basis, the link with electrodynamics, stands on the firm
foundations disclosed in the first edition of 'The Theory of Gravitation'
published in 1960. I wrote that text in the latter part of 1959 to put my theory
on record at a time when I had decided to make a career move by joining IBM in
England as a Senior Manager. I had not opted for an academic university career
following my Ph.D. research years at Cambridge. Instead I decided to develop
specialist skills concerning technological innovation and its protection in an
industrial environment.
The theory of gravitation was of interest to me,
essentially because my research had shown how the electromagnetic energy we
associate with magnetic induction is stored in what we term a 'field', whether
within solid matter or in vacuo. I could see a basis for connecting that with
the phenomenon of gravitation, but had come to see the need to believe in the
existence of a real aether, something of a 'taboo' subject in the world of
academic science. Physicists had come to accept the Einstein doctrine implicit
in his theory of relativity and the aether has no place in that doctrine.
'Four-space', a concept that defies visualization in physical terms, had
displaced the 'aether' and I well knew that, to project my theoretical notions I
would have to contest territory that was the exclusive province of the
physicists who were addicted to Relativity.
Over the years, I did update
the my theory of gravitation as it advanced step-by-step, notably in 1966, 1969,
1975, 1980 and 1996. [See book titles in list of references]
However, the
scientific community has remained unconcerned and has seemingly ignored my
efforts. So, with two new major advances of this the millennium year 2000, the
one reported in the preceding web page item and that I now present, I venture
now upon what I presume will be the culminating step, namely the task of
deriving G, the constant of gravitation, by theory which gives the precise value
in accord with the 1.5 part in 100,000 precision of the year 2000 measurement,
which has involved a quantum leap in the degree of experimental measurement
precision of this very-difficult-to-measure quantity.
Contrary to
conventional practice, and contrary to the natural and logical path I followed
in reaching the result, I will present the formulation first and then show how
it is derived. I want the numbers to point to the underlying physical picture,
because it is all too easy, if I start by portraying a physical scheme, for the
unbelieving reader to presume that that I rely on hypothesis and that the
assumptions implicit in that scheme were deliberately chosen to give the correct
numerical result.
Of course, even with this approach, critics will be
critical. They will suggest that I am merely playing with numbers, pressing the
buttons on a calculator until I find a mathematical relationship that gives the
right answer. However, I think the mathematical odds against finding the formula
I present below, as one fitting the known answer, are high enough to upset that
argument, but you must judge. I can only say that I have been guided by what I
see as the physics underlying the formulation and believe it portrays how Nature
regulates the phenomenon of gravitation.
The formula defines the action
of gravity as a quantum phenomenon, quantum in this case meaning 'as involving
discrete units of action'. Two distinct quanta are needed, as I shall explain
later, and these are odd integer numbers that signify a multiple of a unit based
on the form of the electron. These numerical quanta are denoted A and B,
respectively.
I shall formulate an expression for the square root of G,
which I express as Gr, the reason being that I see the action as
between systems each involving the same two basic quantum units, each such unit
comprising one A quantum and two B quanta, for reasons that I shall explain in
detail later. Then, without further ado, I present the formula:
Gr =
(4π/3)(4.8032x10-10)/(108π)3(A)4(9.10939x10-28)X
where:
X = [1 + 2(A/B)3]/[1 + 2(B/A)]
Now, if you use
your calculator and substitute the numbers 5061 and 3485, for A and B,
respectively, you will discover that G has the value 6.67435x10-8 and
I ask you now to compare this with the latest, year 2000, value of the Constant
of Gravity G reported in SCIENCE, v. 288, p. 944 (2000), which is
6.67423+/-0.00009 times 10-11
N.m2.kg-2.
Note that my derivation, as formulated,
involves the old-fashioned cgs system of units, as applied to a vacuum assigned
unity permeability and permittivity. I prefer that because the vacuum is my
reference base and the numbers are easier to work with if one bases the units on
that as reference, given that the object is to understand physical phenomena
occurring in vacuous space, rather than find a convenient way of dealing with
practical problems by avoiding numerical expressions that put 4π into the
calculation.
Those G values differ by very slightly more than one
standard deviation of the year-2000 measurement. That is more than one order of
magnitude more precise than any previous measurement of G.
So, I claim
that my formula, as just presented, has something to say about the nature of the
force of gravity, subject of course, to it having a true physical
basis.
Well, first of all, if you are astute on matters relating to
physics, you will already have noticed that the electron charge/mass ratio
features in the equation for Gr. The charge of the electron in cgs
esu is 4.8032x10-10 and the mass of the electron is
9.10939x10-28 gm.
So here is that 'Unified Field Theory'
connection. The mutual force of electrodynamic attraction between two discrete
electrical charges separated by unit distance is equal to the product of their
charge values in esu, if they are moving mutually parallel at the limiting speed
governing electromagnetic wave propagation in vacuo. That, in physical terms,
raises certain questions, because we see particles generally as being close to a
position of rest in the electromagnetic frame of reference. However, note that I
am using the electron as a unit only. I do not say that gravitation stems from
the interaction of electrons. Instead, I say that it arises from interactions
between what I call gravitons, a kind virtual lepton that lives in a world that
is ever moving at the speed of light, c, relative to the frame occupied by
matter.
You see, the quantum energy activity underlying everything
imparts a universal motion to matter (physicists call it the Zitterbewegung), a
jitter associated with Heisenberg's Principle of Uncertainty. That system of
matter in motion in an inertial frame defines the local electromagnetic frame of
reference, and so the material universe would be dynamically out-of-balance
inertially, were it not for a hidden counterpart system of gravitons moving in
juxtaposition about the inertial frame. The relative motion, as between
that graviton system and the matter it balances, is the speed of light c.
However, we are dealing here with a system that is kept in step by synchronizing
actions which override certain considerations that govern material particles
moving linearly at high speed through the electromagnetic reference frame. The
gravitons do not gain kinetic energy in the context of the relativistic mass
increase that applies to material particles. I accept that this may seem a
little complicated, but it is fully explained in my published works and here I
am intent on justifying the numerical formulation just presented.
The
formula contains four other quantities, namely 4π/3, 108π, 5061 and
3485.
As to 4π/3 you can guess that this is the numerical coefficient
used to derive the volume of a sphere from the radius. So we are concerned with
units of electric charge that sit within a spherical unit of space, or,
alternatively, that, as part of a uniformly dense system of charge, are excluded
from a spherical space.
Note then that 108π appears as a cubed
expression. This also suggests a volume measure, where 108π is proportional to a
side dimension of a cubic form. You will further notice that it has the effect
of very substantially weakening the mutual attraction force implied by the
interaction of two electrons. However, the force of gravity as based on the
interaction of two electron masses is still far weaker than that reduction would
imply. So we look, not to the unit charge of the electron, but rather to the
unit charge excluded from a spherical form on the basis that the charge density
is determined by e, the electron charge, as distributed uniformly over a cube of
size involving that expression (108π)3.
Here I am going to
digress for a moment to refer to a paper published in Physics Letters,
41A, 423-424 (1972), which I co-authored with Dr.D.M.Eagles. It was
entitled 'Aether Theory and the Fine Structure Constant'. The fine-structure
constant is a numerical quantity linking the three properties of the aether,
namely c, the speed of light, e, the charge of the electron and h, the symbol of
the energy quantum, Planck's action constant. Measurement indicates an
approximate relationship:
hc/2πe2 = 137.0359and, back in 1972, based on the
development of my theory pertaining to gravitation at that time, I discovered
the physical basis of this numerical quantity. My formulation was:
hc/2πe2 = 108π(8/1843)1/6
That number
1843 was determined by an energy minimization argument, subject to energy not
becoming negative, but with the physical quantity represented by that 1843
number being the number of electrons and positrons that could fill the volume of
space occupied by one unit charge particle in the aether. The number had to be
an odd number. Its value was derived by rigorous analysis from first principles,
as that paper shows.
The 108π term has the following meaning. The unit
charge particle sat in a cubic volume of space with its charge balancing the
opposite polarity of a uniform charge density filling that space. The aether is
electrically neutral on a macroscopic scale but has electrical structure on a
microscopic scale, as needed to account for Maxwell's displacement
currents.
Analysis, based on explaining the energy quantum of the photon
and deriving the action underlying Planck's radiation law, which includes h,
told me that the side dimension of a unit cube of space is 72π times the
classical radius of the electron, the latter being
e2/mec2 in cgs units. Here you see that
charge/mass ratio of the electron mentioned above. Now, the so-called classical
radius of the electron is a notion only. In fact, the correct formulation of
electron radius is that advocated by J.J.Thomson, which is two-thirds of the
value of the classical radius. So one can say that the unit cube side of the
space occupied by one aether charge e is actually 108π times the actual radius
of the electron. You can, by cubing this quantity, and dividing by 4π/3 obtain a
measure of the unit volume of a cubic cell of the aether in terms of electron
volume.
It is, simply, 9,324,644, but one needs to divide this by that
number 1843 to get a measure of the volume of that unit cube in terms of the
volume of the unit aether particle that sits in that cube. The result is
5059.49. That explains how I first began to see something special about such a
numerical quantity pertaining to the aether. You see, I could work out the
electrical charge density that filled those cubic units of space, and I
suspected that units of a spherical particle form in dynamic balance with matter
would displace a tiny amount of charge owing to their finite volume, and I
simply worked backwards on the assumption that this would account for gravity to
estimate the physical size of that particle. I found that, using the J.J.Thomson
formula, it would have a mass of approximately 5063 times that of the electron.
Hence my interest when I saw that analysis of the photon by deriving the fine
structure constant had led me to that 5059.49 quantity.
So I come to that
5061 term which appears in the gravity formula to a fourth power. The fourth
power arises because, in electron unit terms, a non-composite particle of charge
e that is N times the mass of the electron, has a volume that is 1/N3
that of the electron. Then, since volume determines the electrical charge
involved, but gravitational action, in the Gr context, is scaled
according to mass, we need to adjust that by the factor 1/N to obtain
1/N4 as the appropriate term to use.
Now, why have I used
5061, rather than 5059 or 5063? This is the real breakthrough in the development
of my theory, guided now by this new year-2000 report of the latest G
measurement.
The answer to this is that my theory has evolved in stages.
Initially I was concerned with how gravity could arise from the influence of
very tiny masses and yet satisfy the same constant of gravitation that applied
to large masses. Even the energy content of electromagnetic waves gravitate,
because we see them deflected in a gravitational field and I say this in the
firm belief that Einstein is wrong in declaring that this arises because space
is curved. My case, based on aether theory, is that the aether medium can offer
the same G response to large systems of mass as it does for tiny units of mass,
meaning the mass-equivalent of energy. [I note here that I adhere to an
interpretation of the basis of the formula E=Mc2 as justified
historically by energy conservation theory in classical electron theory, again
rejecting the Einstein theoretical doctrine.]
The outcome of these
considerations led me to picture a graviton system in which a component of unit
charge of higher mass was partnered by a pair of unit charges of equal mass
somewhat lower than that of their companion. The idea was that, consistent with
quantum electrodynamic principles, the charge pair could be leptons which could
mutually annihilate to vacate space and shed energy as needed should the
populace of the particles of higher mass have to adjust slightly in volume to
keep the energy balance and assure that the volume to mass ratio remains
constant. The latter is essential for G to be a constant.
The simple
equation governing G is:
G = (σV/M)2where σ is the electric charge density
filling those cubic cells of space and V/M is the volume to mass ratio of the
graviton-lepton system that provides the dynamic balance for any matter
present.
On this basis a mass M sitting at rest in the electromagnetic
reference frame (the E-frame) has angular momentum owing to its motion about the
inertial frame (I-frame) and its centrifugal action needs to be balanced by a
corresponding mass M of gravitons and leptons of a gravitational frame (G-frame)
moving with that frame in juxtaposed relationship.
So we can determine
V/M if we know the mass values of the gravitons A and the leptons B in terms of
units of electron mass. For a system with twice as many leptons B as gravitons
A, one can calculate the volume V of charge they displace as:
V = (1/A)3 + 2((1/B)3in electron charge
volume units. Similarly, one can calculate the their combined mass M as:
M = A + 2Bin terms of the unit of electron mass.
The
ratio V/M becomes:
V/M = [1 + 2(A/B)3]/[(A)4][1 +
2(B/A)]which one can see has the form needed to justify the remaining
components of our basic formulation for the value of the square root of
G.
It follows that we can say that we have here a theory that can account
for the precise value of G, the Constant of Gravitation, guided by the empirical
data that A has the value 5061, meaning the graviton has a mass of 5061 times
that of the electron, and B has the value 3485, which says that the lepton has a
mass that is 3485 times the electron rest mass.
Now, again I digress,
this time to explain that there are in physics essentially three basic forms of
lepton that have mass. They are the (a) the electron, which in my theory has a
prominent role in the E-frame, as part of matter, (b) the muon, which in its
virtual form, has a major role to play in my theory by sitting in the I-frame
and functioning as an omnipresent energy source and (c) the taon (the
tau-particle), which, in its virtual form, and being the only remaining lepton,
has to be the lepton form B that sits in the G-frame.
The theory
developed from the initial calculation of the energy content of the aether
particle that sits in every cubic cell of the aether. Using the J.J. Thomson
formula:
E = 2e2/3afor the electron of mass-energy E and
charge e, a is electron charge radius, but applying this same formula to the
aether particle, the energy scales by the factor (1843)-1/3 to a
lower value. Here I am using the fact that the aether particle has a charge
volume that is 1843 times that of the electron, as I knew from the photon theory
mentioned above that gave the fine-structure constant. I regarded this energy of
the aether particle as determining a pressure in the aether medium which
signified a uniform energy density. Accordingly, I deduced the energy content of
the unit cubic cell of aether, because I knew, as shown above, that the volume
of that cell is some 5059.49 times that of the aether particle. Note then that:
(5059.49)(1843)-1/3 = 412.6656
In energy terms,
as units of electron rest-mass energy, this is the energy needed to create two
virtual muons, the leptons of the I-frame. Here was the component building block
from which Nature creates protons and I did decipher that process by 1975, three
years after the publication of that Physics Letters paper on the aether
derivation of the fine-structure constant. It was duly published by the Italian
Institute of Physics in Il Nuovo Cimento, v. 30A, pp. 235-238 (1975). It
is entitled: 'Calculation of Proton Mass in a Lattice Model for the
Aether'. The proton/electron mass ratio was found to be:
1836.1523a value that was one part in two million too high
according to measurements of that period, but which fitted even closer to the
eventual measurements using a new direct method rather than merging two
separately measured quantities.
The next advance relevant to this account
was the discovery by which I deciphered the process of creation of the tau
particle. It evolved from a sequence of reactions in which mesons are created,
the subject of my paper in Hadronic Journal, v. 9, pp. 153-157 (1986).
The paper is entitled:'An Empirical Approach to Meson Energy
Correelation' Here I had shown that the common building block, the virtual
muon, from which protons and tau-particles develop, gave simple formulated
relationships from which one can deduce that the tau particle has a mass energy
that is greater than that of the proton by a factor of
37/12.
This was a curious result, but, given that theoretical
proton quantity 1836.1523, it told me that the tau particle should have a value
close to 3485.21 in electron rest-mass energy units. Here, then you can see how
I arrived at the odd integer value 3485 as used in the above gravity
formula.
But still, what about that 5061 value? Here I struggled with a
dilemma for quite a while, given that I had derived that value of 5059.49 from
basic aether theory and the empirical evidence, also from certain particle decay
reactions, was telling me that a particle form of that mass in electron terms
had to exist in Nature, whereas I knew that the 5063 value had a link with
G.
The latter connection arose because I presumed that such a particle
existed in the G-frame and worked out that, if it expanded slightly to increase
a certain amount in volume, that would increase its gravitational effect. I
argued that it would thereby shed a commensurate amount of energy, which, since
energy is conserved, would assume material form in the E-frame. The
corresponding mass added to the E-frame would then have the gravitational
property set up by the effect of that volume change in displacing charge in that
G-frame. Now, you can easily work this out yourself. Given a particle satisfying
the J.J.Thomson formula and having a certain V/M ratio as applies to its whole
spherical form, how does a small increment of V relate to a change of M? The
answer is that it is minus three times the V/M ratio.
Now, what this
means is that, whereas the graviton A in the G-frame can engage in energy
fluctuations as between itself and matter in the E-frame, and keep things in
order gravitationally, there has to be a process by which, given a steady state
matter presence in the E-frame, creation of the latter is accompanied by
creation of the lepton-graviton form in the G-frame. The latter must comply with
the V/M ratio. The volume V comes into being as M is created.
This is
what we see with pair creation and annihilation in quantum-electrodynamics and I
imagine a scenario where a pair of tau leptons group with a graviton, so that
the tau leptons can feature in matter creation and annihilation reactions,
whereas the gravitons serve in regulating minor energy fluctuations.
In
any event it then becomes possible, owing to that minus three factor, to
calculate the ratio of the mass g of the graviton to the mass τ of the tau
particle. The ratio is simply that obtained by solving the equation:
(g/τ)3 - 3τ/g -1 = 0which gives;
g = 1.452627τ
Given adoption of 3485 as the odd integer
value of B based on the tau mass-energy calculation, one finds, using this
formula, that g has to be close to 5062.4, but since A must be an odd integer
and particle creation involves energy requirements that can exceed but not fall
short of what is required, we need to opt for the next lower odd integer value,
namely 5061 as the value of A.
Accordingly, I have, in physical terms,
justified the values of A and B as used in the formulation of G, the Constant of
Gravitation.
Before ending this summary discourse updating my theory of
gravity, I need to clarify one important point that has crept into my writings
over the years.
The question at issue has been the effect of an electric
charge sitting in a surrounding sea of charge having a uniform charge density σ,
given that the charge has a significant volume. I knew that the aether has a
charge density that can be expressed as e/d3, where e is the charge
of the proton and d is the side dimension of a cubic cell of aether. This
assumes that the aether particle that sits in that cell and neutralizes that
charge continuum is a negative charge of magnitude e that we associate with the
electron. Above we have seen that knowledge of d allows one to calculate that
charge density and we found that the volume of that cubic cell was 9,324,644
times the volume of the electron charge or 5059.49 times the volume of that
aether particle. It follows, therefore, that the effect of a charge e sitting in
what is, in effect, a hole in the continuum of charge density σ, will exhibit a
net effect that is modified by the presence of that hole, meaning the absence of
charge that otherwise would fill the space defined by that hole.
So I
wondered if the calculation of the value of σ would need adjusting by one part
in 5059 or so to keep the charge balance. I saw this as implying that I might
need to increase the value I calculated for G, as a squared effect in terms of
σ, by a factor of 2/5059, or 0.000395, which was enough to change a G value of
6.6700x10-8, say, to a value of 6.6726x10-8, which is an
appreciable difference given that the standard deviation or degree of
uncertainty recorded for G in tables of physical data was
0.00085x10-8 until this recent and far more precise measurement of G
was announced.
It is necessary now to settle this issue. Note, however,
that it really has little bearing upon the actions of charged particles of
higher mass than the electron or the discrete aether charge sitting in the cubic
cell of aether. The σ charge background would affect the electron charge by one
part in ten million and so affect the fine-structure constant evaluation by 2
parts in ten million. The G calculation is where we see the primary effect of
this problem.
Now, we take e as the unitary charge value by assumption
and without thinking of any background charge continuum effects. Given no charge
continuum in the background of space and ignoring the reality of Maxwell's
displacement currents and their need to have a charge source, one can readily
assume that a proton charge is equal in magnitude to the charge of an electron,
but opposite in polarity. However, if we say there is that σ continuum present,
then we should be declaring instead that the net effect in electric and magnetic
field action stemming from the fundamental unit charges of opposite polarity is
the quantity to be equated in magnitude. In other words, a positive charge of
nominal value e and volume V sitting in a positive σ background really has a
charge value equal to e plus σV because, when offset by the effect of the hole
it occupies in the continuum charge, it is seen at a distance as having a net
effect of a charge e. In contrast a negative charge of nominal value -e and
volume V must really have a charge of minus e plus σV, but will be sensed at a
distance as having the net charge -e.
Then, when the two charges are
involved in a mutual annihilation process, given the slightly different values
of their actual charge, they create a charge residue of 2σV which fills the 2V
volume of the vacated space.
As to the neutral balance of continuum
charge and the discrete aether charge sitting in one of those cubic cells of the
aether, this then gives the relationship:
σ(d3-V) + (-e+σV) = 0from which we see that:
e = σd3
Accordingly, it was rigorously correct to
use this latter relationship in the formulation of G, without making any
correction for the finite form of the discrete aether charges sitting in those
cubic cells of the aether.
REFERENCES
[1] The Theory of Gravitation, 2nd. Ed., (1966)
[2] Physics without Einstein (1969)
[3] Gravitation
(1975)
[4] Physics Unified (1980)
[5} Aether Science Papers
(1996)
********H. Aspden August 29, 2000
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