THE BLACK HOLE ELECTRON
Author: D. Di Mario
d.dimario@infinito.it
Abstract: The theory presented
in this article introduces new unknown relationships that may shed new light on the nature of
matter. This theory allows the calculation of the gravitational constant (G) with a precision comparable to the other atomic constants, gives a direct
relation between mass and charge of the electron without the need of the
ubiquitous "classical electron radius" and generates a second fine structure constant
while also offering the disconcerting possibility of an anti-gravitational force.
Keywords: black hole,
electron, Planck charge, gravity, quantum physics.
Table of Contents
Foreword
Planck's
black hole
The
Planck charge
The
spinning black hole
The
quantum connection
The
electron mass
The
mystery of permittivity
The
swirling electron
The
bare particle
Quarks
and other particles
The
proton mass
The
gravitomagnetic effect
Closing
on antigravity
Measuring
antigravity
An
accurate constant of gravity
Conclusions
FOREWORD
The
electron, whether you like it as a well defined shape or as a (more likely)
hazy blob of wavelike matter, has not surrendered all of its secrets. The
quark structure is a comprehensive description of the possible excited states
of matter but has added little to the understanding of the intimate nature of
the electron. What we need is a leap forward enabling us to glimpse at the
core of this particle and find a viable relationship between what is supposed
to take place inside and what is measured outside. This is not as easy as it
sounds because the hypothesis put forward here is that the electron itself is a
miniature black hole analog. Besides, it would be highly desirable to define the black hole
with the Planck time and mass only and have all the electron properties of charge, mass, etc, without introducing any additional
parameters. In practice
we should be able to define the electron using only the constant of
gravitation, Planck's constant, and the speed of light.
PLANCK’S
BLACK HOLE
It is not difficult to devise a black hole
using some basic constants. The resulting object is rather meaningless until a
new interpretation is applied on the nature of the electric force and look at
it as a gravitational force changing with time, Planck's time, providing the
frame of reference is the black hole itself. A spinning black hole of this
kind would originate the electron mass and charge, the fine structure
constant, and eventually provide a link between electricity and gravity. In
order to create our model we first define Planck’s time t_{0}
as follows:
t_{0}
= ( p h
G / c )^{½}
/ c^{2} = 2.395x10^{-43} sec
where c = speed of light, h = Planck’s
constant and G = constant of gravitation. The numerical values used are the
ones currently available and, apart for a 2^{½}p
factor, it is the same as the Planck’s
time normally found in the literature. On the other hand, we do not know the
intimate structure of a black hole and its geometry is certainly different
from ours and the applicable time t_{0}
is not necessarily the one we normally calculate which is, after all, a purely
theoretical value. The Planck mass m_{0}
related to time t_{0}
is defined as h / t_{0}
c^{2} = 3.078x10^{-8} Kg. This particle with mass m_{0}
is considered as our
ideal
black hole. A black hole is not an ordinary body and the Planck’s black hole
defined above is all the more weird. Not only it is necessary to deal with the
distortion of the space-time continuum as in every black hole but, because of
the short time involved, it is not even sure it really exists. A possible way
out is to measure or predict some macroscopic effect, if any. One such effect
could be the ratio F_{g} / F_{e} of the gravitational to the
electric force between two electrons. This ratio is numerically very close,
around 0.2%, to the Planck time t_{0}
given earlier. The hypothesis put forward is that the small numerical
difference is due to the rotation of the black hole (with respect to a
stationary black hole that would show no difference) and the different
dimension between the above dimensionless ratio and t_{0}
depends on the fact that we will never be able to physically measure
t_{0}
because the latter is the ultimate quantumization of time. We will still have
the time dimension in our equations but we will not be able to experience the
temporal dimension associated to t_{0}.
The above considerations constitute the very essence of the black hole
electron.
THE PLANCK CHARGE
Although time t_{0
}and the small size of this black hole
are beyond our capacity of detection, we would expect to find a mass m_{0}
weighing around 30 micrograms. So far such a particle has never been found,
but are we looking in the right direction?
Let us assume that the manifestation of mass
m_{0},
to an outside observer, is not gravitational as expected but of an electric
nature. As a consequence we should look for a charge Q_{0}
with an electric force equal to the gravitational force of mass m_{0}:
G m_{0}^{2}
= Q_{0}^{2}/
4 p e_{1}
this is the equation we would expect at the
Planck scale equating the gravitational and the electric force and could very
well represent the quantumization of both charge and mass of our black hole.
Outside the black hole we would have quite a different picture, derived from
the above, where we would experience a different mass and charge, the electron
in fact. The polarity of the charge, positive or negative, could be perhaps
related to the creation or annihilation of the gravitational force within time
t_{0}.
This process would originate a variable gravitational force but we would be
unable to detect such a variation and the only thing left would be a steady
field and a sign indicating the direction of the variation. The particle would
look like frozen in the moment of its creation. In practice, we have that no
phenomena dependent on time t_{0}
could be correctly detected and there might be a dimensional difference
between what the equations suggest and what we measure.
The
apparent dimensional difference between what we see in the equation and what
we actually experience is the key for the correct interpretation of
permittivity e_{1}
(more on this later):
e_{1}
= ( t_{0} /
4 p^{2}
)^{¼}
= 8.825x10^{-12} sec^{¼}
From our point of view we would physically
experience e_{1}
as a dimensionless number because we are unable to measure time t_{0}.
Once e_{1}
is known, it becomes easy to get the value
of charge Q_{0}:
Q_{0}
= m_{0}(4pe_{1}
G)^{½}
= 2.648x10^{-18}m(Kg sec^{¼}
m)^{½
}/sec
An observer far away from the black hole
would see charge Q_{0}
with the basic dimensions of time, length and mass similar to the cgs system,
but with numbers expected from the SI system. The introduction of the
dimension of Coulomb would "mask" the true nature of the charge.
It would be nice if Q_{0}
and e_{1}
would coincide with the known values of the electron charge and permittivity.
This is not quite so: although e_{1}
is only 0.3% different, we find Q_{0}
to be about 17 times larger than the electron charge. This is because no
rotation was taken in account. A very fast rotation should be considered
instead, and, in the case of a black hole, there would be only a small kernel,
probably surrounded by an intense energy field.
THE SPINNING
BLACK HOLE
The
fast rotation at speed u_{0}
of our black hole seems to be related to the fine structure constant a
in the following way:
a
/ 2 = 1 - u_{0}^{2}
/ c^{2}
This is a plain hypothesis but similar
relationships have been put forward by a number of researchers investigating the
intimate nature of fundamental particles and although the final equations were
to a certain degree different, the common thought was that there might be a link
between a and
u_{0}.
A complication arises here from the fact that we have to deal with the SI
dimensions without introducing the Coulomb, yet, the numbers are what we expect
from this system. To solve the problem we "scale" our charge and time
with respect to the unitary time (t_{u}
= 1) and charge (Q_{u} = 1). The result is an additional equation for a
= I_{u} /I_{q} where I_{u} = 4p^{2}Q_{u}
/t_{u}^{½}
and I_{q} = Q_{0}
/t_{0}^{½}.
The ratio I_{u} /I_{q} gives us the possibility to calculate a
out of the 3 basic constants only, i.e. c, h
and G with a result 0.02% close to the actual value:
a
= ( 2 p^{2}/
c ) ( p /
c )^{½}
( 2 G / h )^{¼}
( c / p h
G )^{1/16}
where 2p^{2}
is the quantity I_{u }/2. The fast rotation will tend to increase mass m_{0}
and the same will apply to charge Q_{0}
which will reach a final value Q_{f} at speed u_{0},
which is close to c. Q_{f} is a moving charge so we must expect also a
magnetic force F_{mag} opposing the electric force F_{ele}; both
forces are generated by Q_{f} but the magnetic force is slightly
smaller, as a consequence we will detect only a reduced electric force that we
identify as the electron force:
Q_{f}^{2}/ e_{0}
- m_{0}
Q_{f}^{2 }u_{0}^{2}
= e^{2 }/ e_{0}
An analysis of all forces involved will give Q_{f}
= Q_{0}
c/u_{0}
and an electron charge 0.01% close to the known value:
e = Q_{f} ( a
/ 2 )^{½}
= 1.602x10^{-19} m ( Kg sec^{¼}
m )^{½}/sec
Charge Q_{f} will set a new value for
the permittivity e_{0}
= Q_{f}^{2}/4 h c = 8.858x10^{-12} sec^{¼}
(0.04% off its real value) relevant to a rotating black hole. A strict
relationship is thus established between speed u_{0},
a and the
resulting charge e. It must be stressed that from our frame of reference e_{0}
would be a dimensionless number because we would not experience the sec^{¼}
dimension.
THE QUANTUM
CONNECTION
So far we have used only 3 basic
constants to derive all other quantities and it is tempting to think that it
might be possible to obtain the constant of gravitation G from other constants
which are known with great
accuracy. The advantage is that we would have G with a precision not possible up
to now. Of course we would always need an experimental confirmation but this has
already happened because this accurate G, first calculated already many years
ago, is in strict agreement with today's experimental results. In practice, the
value found for G is always decades ahead of the experimental confirmation. It
would be interesting to see if the same would hold true using some very old
data, from the pre-war era, and see if there is indeed a confirmation of the
theoretical result. The equation is arrived at by manipulating all the equations
we have seen so far and operating substitutions aimed at writing G using only
known constants:
G = c^{5}
a^{2}
( 2 -
a )^{2} ( e / 4
p^{2}
)^{4} / p
h
The result is 6.672918x10^{-11}
m^{3}/Kg sec^{2}. The quantity 4p^{2}
is the parameter I_{u} seen in the previous paragraph and the quantity a(2-a)e^{2}
is a constant, independent from speed u_{0}.
The other result, unexpected, is the fact that if we try to solve the equation
for a we
end up with two quantities: one is the classic fine structure constant a,
but there is also another value a_{q}
= 2-a that
might play a part in the modeling of another particle because it originates a
second lower rotational speed without any change in the charge value. The
particle that appears to emerge is the quark and a possible integration within
this framework is offered further on.
THE ELECTRON
MASS
The drawing below shows how the
difference of the squares of Q_{f} and Q_{0}
generates the electron charge (squared). The corresponding energy levels are M_{0},
m_{q }and
m_{e}
respectively, m_{e}
being the measurable electron mass. If the fine structure constant is set equal
to 2-a,
we have new values for Q_{f} and Q_{0}
but their squared difference is still the electron charge. From the energy point
of view, it is now the difference of the squares between M_{0}
and m_{e}
that generates the measurable mass m_{q}.
We will identify this new particle as the quark.
Normally,
the mass that we will able to measure in our frame of reference is the result of
the gravitational force taking place in the black hole within time t_{0}
and the rotational factor, which must be the same as the one used to get the
electron charge. If we apply these conditions to Planck's mass m_{0}
we have the electron mass m_{e}:
m_{e}
= m_{0}
( t_{0}
a / 2 )^{½}
= 9.1x10^{-31} Kg sec^{½}
This equation gives us the answer
on the link between the very heavy particle m_{0}
and the light electron mass. There is a time factor that we are unable to
measure directly but it is an integral part of the electron mass. If the
gravitational force of mass m_{0}
would exist only for the duration of time t_{0},
we would have a gravitational force F_{0}
= G m_{0}^{2}
t_{0}
but, for an outside observer, it will look like a steady, time independent,
gravitational force F_{0}
= G M_{0}^{2},
where M_{0}
= m_{0}
t_{0}^{½},
and finally, if rotation is taken in account we have the gravitational force of
the electron F_{g} = G m_{e}^{2}.
It is now possible to give an answer to the initial hypothesis about the ratio F_{g}
/ F_{e}: for a non-rotating black hole (charge = Q_{0}
and gravitational mass = M_{0})
the ratio of the gravitational to the electric force F_{0}
/ F_{q} is equal to t_{0}
both numerically and dimensionally. Again, we would not be able to measure time
t_{0}
and the ratio would look dimensionless. When rotation is brought in the picture,
we find that the change in the parameter values brings about a slight change in
the ratio that is now close, but not equal, to t_{0}.
We are now in the same exact situation described at the beginning where we had
the ratio F_{g} / F_{e} close to t_{0}.
With the manipulation of the equations we are able to write m_{e}
also in terms of charge Q_{0}
and hence in terms of the electron charge:
m_{e}
= (8 h^{3} / p
e^{4}) ( a
/ 2 )^{½}
/ (2 / a
- 1)^{2}
The result is always the same and
only 0.116% different from the real value. The difference reduces to 0.025% once
speed u_{0}
is adjusted as explained further on, or, in other words, using the current known
values.
THE MYSTERY
OF PERMITTIVITY
Permittivity e_{0}
is seen, in our equations and in our frame of reference, as a dimensionless
number. This should be expected because we are using the dimensions of length,
time and mass to describe the charge and the use of the SI system calls for a
dimensionless constant in order to return the correct numbers. The implication
is that there should be another constant v_{0},
a velocity, so that e_{0}
= v_{0}/c.
Numerically we recognize v_{0
}as the inverse of the resistance of
vacuum, nevertheless the dimension of permittivity requires the identification
of speed v_{0}.
The
electron energy m_{e}c^{2}
is often given as the ratio between its electric force and its radius, however
both charge and mass originate from mass m_{0}
and charge Q_{0}
and, as a consequence, we should be able to relate the electron energy to the
energy of m_{0}
or Q_{0}.
Because of the uncertainty principle, we will never be able to locate exactly
mass m_{0}:
it will move about at a certain speed v_{0}
so that its kinetic energy is m_{0}v_{0}^{2}/2;
this is the only energy level we would be able to measure and would correspond
to the electron energy:
m_{0}
v_{0}^{2}
/ 2 = m_{e}
c^{2}
The equation does not take in account the fact that the left term is
a non-rotating particle whereas the right term is a rotating particle. Even with
this limitation we get v_{0}
15% close to its expected value. Further elaboration of the above equation
yields:
G m_{e}^{2}
/ G m_{0}^{2}
= v_{0}^{4
}/ 4 c^{4} »
e_{0}^{4}
/ 4
The gravitational force of mass m_{0} could be written also in terms of Q_{0} or
the electron charge. In order to have a better value, we should consider both
particles m_{e}
and m_{0}
either rotating or non-rotating. If we adjust the equation such that only
rotating particles are shown, we get the following result:
F_{g} / F_{e}
» 4 p^{2}
e_{0}^{4}
» t_{0}
We see here that Planck's time is directly related to both permittivity and
to the ratio of the gravitational to the electric force in an electron. A very
accurate value for v_{0}
is obtained if we write it in terms of electrical quantities:
v_{0}
= e^{2 }/ 2 a
h
Numerically it is 2.654x10^{-3}
and appears to us as a velocity. The same is obtained also from Q_{f}^{2}/4h
or Q_{0}^{2}/2a_{q}h
and should not be difficult to identify it with experiments. It means also that
a dimensionless constant, numerically equal to
e_{0},
will appear in the cgs system once v_{0}
is found.
THE
SWIRLING ELECTRON
Further
manipulation of the equations leads to identify another factor that seems to
confirm that the electron is indeed a black hole. The Kerr-Newman condition is
satisfied because, for a non-rotating electron, we would have G M_{0}^{2}
= p
e_{1}^{3}^{
}Q_{0}^{2};
this equation is numerically and dimensionally correct despite its appearance.
For a rotating electron we would have a similar equation because
e_{0}
»
e_{1
}and M_{0}/m_{e}
» Q_{0}/e.
The result is a relationship which can be written with known constants albeit
with a 1% approximation because secondary effects of rotation are disregarded:
G m_{e}^{2}
»
p
e_{0}^{3}
e^{2}
A time dimension appears on
both sides of the equation but from our frame of reference we would experience
the classical gravitation force of the electron F_{g} without the time
dimension attached to it. The dimension of Coulomb cannot be applied to Planck's
level and a charge expressed only with the dimensions of mass, length and time
is a more suitable representation. Only in this way we are able to establish a
link between gravity and electricity: they are both of comparable magnitude when
they are confined within the black hole but the constraint of the time dimension
makes the gravitational force so much smaller when it is measured from our frame
of reference.
THE BARE PARTICLE
All calculations were executed with
a high precision program. Yet, the numbers we get are very close but definitely not within
the uncertainty of known values. Speed u_{0} is responsible for the discrepancy. If we would be able to slow
down this speed by 111.0728 m/sec we would have the right numbers, with the exception of
the electron mass that would show still a minute difference. There could be a number of
reasons for the slow down but the concept of bare particle seems the most promising: what
we have been calculating so far refers to a bare particle but the polarization of vacuum
brings about a screening effect on the charge resulting in a lower measurable value. We
could think that the polarization induces a "speed drag" of exactly the required
amount with the results given in the table below where the numbers show the difference in
ppm with known values:
param. |
bare particle |
with drag |
a |
- 203 |
0 |
e_{o} |
+ 405 |
0 |
m_{e} |
- 1164 |
- 251 |
e |
+ 101 |
0 |
The remaining difference in the electron mass could be
explained as the energy necessary to set up the polarization of the vacuum: calculations
indicate that this will account for about 80% of the difference. This means that there is
probably another unknown mechanism that takes care of the residual 20%.
QUARKS AND OTHER PARTICLES
The value for the fine structure constant is
related to the mass of the particle through the rotational speed. If the rotation of the particle is pushed to the limit
of the speed of light, we would be left with a massless and chargeless particle. It is not difficult to see the neutrino in the description
of this particle.
Also the
second value of the fine structure constant a_{q} seems to generate another basic particle rotating at a
different speed. The resulting entity has a mass m_{q}
and a charge identical to the electron:
m_{q
}= m_{e} ( a_{q} / a )^{½} = 1.5x10^{-29 }Kg = 8.44 MeV
This value is within the range of the D (down) quark.
Due to the lower rotational speed and the stronger fine structure constant (a_{q} is 273 times a) we should expect this particle to be particularly reactive, so
reactive in fact that it could be found only in its excited state and in combination with
other particles. There is an interesting consequence for the model adopted so far
concerning the charge: a temporary variation of the rotational speed may generate a
fractional charge but it is not clear how it relates to mass and permittivity.
An excited state of particular interest is the r (Rho) particle; its mass is calculated using the empirical factor
2/3a:
r = m_{q }2 / 3 a = 771.4 MeV
The value is in line with experimental data and seems to
play an important part in the determination of the proton mass.
THE PROTON MASS
The
hypothesis for the proton is that the combination of 3 excited quarks m_{q} originates a stable
configuration at an energy level given by the factor 2/3a for each individual quark. The proton mass m_{p} is then given by the
combination of 3 r (Rho)
particles:
K_{0} m_{p }= m_{q} 2 / a
Where K_{0} is an unknown factor, expected to be 1 but in actual fact it must
be around 2.5 in order to return the correct numbers. On the other hand, if we accept the
idea of the quark structure and knowing that the mass is inversely proportional to the
fourth power of the charge, we may write the following relation:
( m_{p
}/ 3 m_{q} )^{¼} = K_{0}
With the above equation it was attempted to relate the
equivalent proton charge to the equivalent charges of the three quarks making up the
proton: we did not get the expected result of 1 but it is now possible to combine the two
equations thus originating a relationship for the proton/electron mass ratio:
m_{p
}/ m_{e} = 3^{1/5} ( 2 / a )^{4/5} ( 2 / a - 1)^{½}
The resulting number is only 125 ppm
different from the known ratio. It is likely that the difference is due to some additional energetic process that might be
typical of the proton structure.
THE GRAVITOMAGNETIC EFFECT
The satellite
Gravity Probe B is set to
measure the feeble gravitomagnetic field induced by a rotating mass: the Earth in this
case. In this theory we find the same effect in the electron itself. If we
look carefully at the equation giving the electron force we find that the magnetic force F_{mag}
is also generated by the rotation of Planck's mass m_{0} at speed u_{0}:
F_{mag} = G m_{0}^{2} u_{0}^{2} / c^{2} = G
m_{0}^{2} ( 1 - a / 2)
This means that the quantity m_{0} Q_{f}^{2 }u_{0}^{2}/4p could be replaced with the equation shown above without any difference. As a
consequence the electric force of the electron could be calculated also in the following
way:
G m_{0}^{2} - G m_{0}^{2} ( 1 - a / 2) = G m_{0}^{2} a / 2 = e^{2 }/ 4 p e_{0}
What the equation says is that the force acting between
two rotating masses m_{0} is identified by our instruments and in our frame of reference as
the electric force between two electrons and measured as such. Definitely not a
gravitational force. In light of this last finding, we are able to propose a consequence
that covers the intriguing possibility of an antigravitational force.
CLOSING ON ANTIGRAVITY
As far as the gravitational force
is concerned, time t_{0} is
the quantity that represents the transition from the black hole frame of reference to
ours. If we apply this concept to the equation relevant to the rotating mass m_{0} we
would have the following relation:
G m_{0}^{2} t_{0} - G m_{0}^{2} t_{0} u_{0}^{2} / c^{2} = G m_{e}^{2}
This is, in practice, the same equation we found for the
electron mass but now we see that its gravitational force is actually composed of two
terms and the second one is in opposition to the first one: in other words, the
equation shows that the faster the mass rotates the weaker its gravitational force
becomes. If this line of reasoning could apply to every mass we should expect that Gravity
Probe B will surely measure a gravitomagnetic force but it will also find that this
force is contrary to the normal gravitational force. What is more, as the
quantity G m_{0}^{2}u_{0}^{2}/c^{2} is a force of magnetic origin, we should expect that
the antigravity effect is further enhanced if the rotating mass generates a powerful
magnetic field as well. Maybe the reported gyroscopic anomalies and the
debated Podkletnov experiment have a
common ground after all. It must be said also that it is not clear if a fast rotating mass is, on its own,
also a screen against an outside gravitational field or the effect is limited only to a
decrease of its gravitational force. In any case, this theory should be regarded only as a
first step towards the unification of forces that will surely lead to a better
understanding of gravity and, as a consequence, pave the way for a theory on antigravity.
MEASURING ANTIGRAVITY
It appears that a rotating mass m_{r} would
undergo a weight reduction when it rotates at speed u so that its final mass m_{f}
is:
m_{f}^{2} = m_{r}^{2}_{
}- m_{r}^{2} u^{2} / c^{2}
This is deduced from the equation giving the
electron mass. Unfortunately any experiment aimed at finding a reduction using the above
equation will not be able to detect the infinitesimal change of mass unless the speed is
substantially increased with the result that the device will shatter to pieces long before
reaching any measurable change. Maybe the situation is different when we are dealing with elementary particles. From a
theoretical point of view, if we would manage to rotate a given mass at the speed of
light, we would be left with an object with no measurable weight.
The situation improves if we endow the rotating
mass with a strong magnetic field. The equation would look now as follows:
m_{f}^{2} = m_{r}^{2}_{
}- m_{r}^{2} B_{k} u^{2} / c^{2}
Where B_{k} would be a
dimensionless term
related to the magnetic field strength of the rotating mass. In this case there is no need
to rotate the disk at prohibitively high speed, the weight reduction should be now within
reach of our instruments. The reduction could be so strong to render mass m_{r}
weightless, not only, but we could reach a point where, at a certain rotational speed, the
right term of the above equation would become negative hinting at the possibility of a
real antigravitational force. Recent experiments with superconductive rotating disks, or
rings, seem to point to the right direction but further efforts should be made in order to
find a weight reduction of the rotating device. Mr Podkletnov with his first Tampere
experiment, and his more recent paper (link no longer present as of 3/2003), was the first to report a gravitational
anomaly although subsequent tests have given
conflicting results probably because one did not know what to look for, i.e. any
experiment should measure a weight reduction of the rotating disk rather than an elusive
shielding effect.
AN ACCURATE CONSTANT OF
GRAVITY
The first result of this study was a theoretical constant of
gravitation in 1980. The result was a numerical value of 6.673019(127)x10^{-11} (between
brackets the uncertainty of the last digits). The calculation was based on the accuracy of
data available at that time. We have an improved precision of 6.672918(2)x10^{-11} if we use
the most recent Codata
values. The number for the constant of gravitation G mentioned in the same Codata list is
6.673(10)x10^{-11}. This number is actually a magnitude less accurate than the
previously given value of 6.67259(85)x10^{-11}. It was found that some of the measurements carried out in the past
exclude each other and the National Institute of Standards and Technology (NIST) had no
better choice than to increase the uncertainty in order to gather for all the
measurements. It is hoped that new experiments based on quantum effects will give a
conclusive answer but there are now underlying doubts on the numbers given by present
experiments based on classic methods.
At the present there are several
experiments being tested in labs around the world, some of them are rather
ingenious, all aimed at improving the precision and accuracy of the value of
the constant of gravitation. a preliminary value of 6.6739x10^{-11}
with an uncertainty of 0.0014% was recently obtained by a group of the
university of Washington. These measurements, once refined, should
reduce the uncertainty by 10 times.
CONCLUSIONS
When we start to investigate the realm of the
Planck mass we experience a collapse of the time dimension. Certain quantities
no longer have the dimensions we are used to and this has a ripple effect in our
macro world where we find numerically valid results but with an apparent
dimensional mismatch. However hard we try, we cannot bring the Planck mass in
our world if we do not consider the collapse of time near the black hole. We
could probably devise some esoteric and complex transformations in order to
justify the results but the approach of retaining the known SI numerical values
offers us a solution immediately applicable to our daily experience.
The precise and accurate value for the constant of
gravitation is being confirmed by experiments and it is likely that future, more
accurate measurements will fully confirm the calculated value. The ratio of the
proton to the electron mass, though only accurate to 0.01%, is given by an
astounding simple equation based only on the fine structure constant. The
electron mass can be calculated by means of other quantum constants and its
gravitational force can be related directly to the electron charge and
permittivity. Even the fine structure constant can be calculated straight from
the three initial basic constants: G, c and h.
The scientific community has had a difficult time
to find a link between the very heavy particle
m_{0}
(the Planck mass) and the very light atomic and subatomic particles that we find
in nature. The solution was the
introduction of a new constant, the strong gravity constant, which is
merely a mathematical artifact devised for the sole purpose of providing the
missing link. The solution offered by this theory is to see the Planck mass as a
black hole and derive all the basic particles from a description of its
peculiarities. We have seen that there is no need for the strong gravity constant
because the particles themselves, including the electron, are in fact tiny black
holes.
References:
Di Mario, D. (1997) Electrogravity: a basic
link between electricity and gravity. Speculations in Science and Technology,
vol. 20, issue 4, p. 291-296. Chapman & Hall, London.
Schiller, C. (1996) Does matter differ from
vacuum?
http://xxx.sissa.it/abs/gr-qc/9610066
Oakley, W.S. (1995) Gravity and Quarks.
Speculations in Science and Technology, vol. 18,
issue 1, p. 44-50. Chapman & Hall, London.
Spaniol, C. and Sutton, J.F. (1992)
Classical electron mass and fields, Part II, Physics Essay, vol. 5(3),
p. 429-430
Di Mario, D. (1980) Inertia of the
electron, letters. Wireless World, vol. 86, December, p. 85. IPC
Business Press Ltd. London.
Sivaram, C. and Sinha, K.P. (1979) Strong
spin-two interaction and general relativity. Physics Reports, vol. 51,
p. 113-183
Sivaram, C. and Sinha, K.P. (1977) Strong
gravity, black holes, and hadrons. Physics Review D, vol. 16
(6), p. 1975-1978
Motz, L. (1972) Gauge Invariance and the
quantization of mass. Il Nuovo Cimento, vol. 12B (2), p. 239-255
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