Light Gravity - A Quantum Solution
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Transcript of Light Gravity - A Quantum Solution
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Light gravity A Quantum Solution
Bernard Paul Badham
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‘Fundamental problems require fundamental solutions.’
ISBN-13: 978-1480131552
ISBN-10: 1480131555
Published by
The Stables
White Horse Mews
Tenbury Road Bromyard
Herefordshire HR74LW UK
http://arkmedia.org
Copyright © 2012 Bernard Paul Badham. All rights
reserved. No portion of this book may be reproduced,
mechanically, electronically, or by any other means,
including photocopying without written permission of
the author.
4
Light Gravity
The Dynamic Casimir Effect and the Lamb Shift in Energy Levels of Atomic Particles
an Explanation for Quantum Gravity?
By
Bernard Paul Badham
15th
October 2012
Copyright Bernard Paul Badham 2012. All rights reserved. No
portion of this article may be reproduced mechanically,
electronically, or by any other means, including photocopying
without written permission of the author.
Abstract
In the light of the recent experiments carried out to demonstrated the dynamic Casimir effect, quantum gravitational flux theory is re-examined, concluding that gravity may be a quantum effect mediated by virtual and real light photons of the space vacuum, where relative acceleration between a mass and the space vacuum induces a mass-photon momentum exchange drag effect which we see as the force of gravity. The Lamb Shift that we observe in the energy levels of matter particles in a gravitational field may be evidence of light gravity at work.
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Introduction
In quantum gravitational flux theory (QGFT) postulated in my book ‘A Watched Kettle Never Boils’ it was explained that the space vacuum energy density is key to understanding gravity: it has been postulated that when a mass particle is accelerated though the space vacuum it experiences a Doppler Effect type of drag force on the particle and it is this resistance to acceleration which is seen as inertial mass of the particle, thus giving rise to Newton's Second Law of Motion (F = ma): Inertial mass (m) = Drag Force (F) of space vacuum per unit acceleration (a). Since the acceleration between the mass particle and the space vacuum is relative, then it must be that the weight of a mass particle at rest on the surface of a gravitating mass such as the Earth is also a result of a relative acceleration between the space vacuum and the stationary mass, thus gravitational force is an acceleration of the space vacuum through the stationary mass (W = mg): Stationary gravitational mass (m) = Drag Force (W) of space vacuum per unit acceleration (g)
Thus m = m
And F = ma = W = mg
6
Thus explaining Einstein’s mass equivalence: both inertial mass (m) and gravitational mass (m) are caused by the same effect: relative acceleration between the mass particle and the space vacuum. It has been discussed in these articles that the energy density of the space vacuum produces this drag force in accelerated motion and that the energy density is made up of real and virtual light photon pairs and real and virtual particles and antiparticle pairs. The energy density of the space vacuum in the form of these virtual particles approaches infinity and combined with the cold neutrino energy density form a space vacuum with transparent fluidic properties: transparent to normal matter undergoing constant motion but resistant to accelerated motion. In order to determine the magnitude of gravitational drag quantum effects on fundamental particles of matter, electron interaction with Lamb Shift wavelength microwave photons was investigated resulting in the following paper:
............................................................................
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START OF PAPER
Quantum Gravitational Field Theory
Acceleration of an Electron by Lamb Shift Photon
Absorption and Emission
Through Interactions with the Space Vacuum
Energy Density
Investigating a quantum gravitational field theory
and momentum exchange between photons at Lamb
Shift wavelengths and an electron at rest mass,
resulting in an acceleration of the electron.
by
Bernard Paul Badham
28th
June 2009
Copyright Bernard Paul Badham 2009.
All rights reserved. No portion of this article may be reproduced
– mechanically, electronically, or by any other means, including
photocopying – without written permission of the author.
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Abstract
In this quantum field theory of gravity it is postulated
that a mass particle accelerated by an external force
through the space vacuum energy density experiences
a drag force and it is this drag force which we see as
inertial mass (mi), likewise the theory postulates that
a mass particle placed in a gravitational field
accelerates in the direction of the field, this
acceleration of the mass particle results from the
drag force on the particle by the acceleration of the
space vacuum energy density and it is this drag force
on a mass particle in a gravitational field which we
see as gravitational mass (mg). The equivalence of
inertial mass, a particle accelerated through the
space vacuum, and gravitational mass, the
acceleration of the space vacuum through the mass
particle, is an explanation of Einstein’s mass
equivalence principle. Newton's Gravitational
Constant (G) is equated to Lamb Shift of electron
energy level (EL) in the hydrogen atom and (G) is
calculated using the Fine Structure Constant (alpha).
In this model G is shown to be a ratio of electron
Lamb Shift energy to the total mass-energy of the
electron. It is noted that EL wavelengths falls within
the CMBR spectrum. Finally base units for G are
shown to be equivalent to the rate of change of
volume (of space) per unit mass, demonstrating that
gravity may be an accelerating flux of the space
vacuum energy into a mass.
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Introduction
Postulate 1. The acceleration of the energetic space
vacuum into a gravitating mass is hypothesised as
resulting from the Lamb Shift energy jitter of mass
particles immersed in the space vacuum sea of virtual
and real photons and particle, anti-particle pairs.
Postulate 2. Newton’s gravitational constant ‘G’ is
derived from the Lamb Shift Energy (EL) equation
and is shown to be related to the fine structure
constant (). Therefore a new formula is derived
without the use of ‘G’ to determine the strength of a
gravitational field around a gravitating mass. This
formula links gravitational field acceleration ‘g’
directly to known quantum mechanical effects, thus
unifying quantum mechanics and gravitational field
theory.
Postulate 3. Einstein’s space-time curvature is thus
seen as an acceleration of the space vacuum energy
density into a gravitating mass. This acceleration of
the space vacuum and hence space time curvature
following an inverse square law is modelled by a
shrinking and accelerating spherical volume of space
vacuum energy around the gravitating mass.
Postulate 4. The units of ‘G’ are shown to be space
vacuum volume/s2 per unit of gravitating mass. G is
10
thus a ratio of the quantum energy fluctuations in
matter to the mass-energy of the matter itself.
Postulate 5. It is the absorption of the space vacuum
energy and consequent emission spectra at microwave
wavelengths by the energetic jitter of matter particles
which causes the acceleration of the space vacuum
energy.
Postulate 6. It is postulated that not only does this
space vacuum energy density flow into matter cause
the energetic jitter of mass particles above the ground
state, but also sustains the ground state of matter
particle standing waves.
Postulate 7. The absorption of the photon energy
from the space vacuum and subsequent emission in a
spectrum of wavelengths is compared to the spectrum
of CMBR and thus may be its cause or source of
energy.
Postulate 8. Since dynamic flow of gravitational
space vacuum energy into a mass results in
microwave emissions by matter, then it is postulated
that this may be the primary cause of planetary and
stellar heating particularly if there is a metallic core,
such as in the Earth, Jupiter and our own sun. It is a
known effect that microwave radiation induces
electromagnetic effects in metals by induced currents.
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Postulate 9. Any mass particle placed in the space
vacuum energy flow will experience a drag force
which will cause its acceleration with the space
vacuum towards the gravitating mass.
Postulate 10. Since the drag force is proportional to
mass all masses will accelerate at the same rate as the
collapsing space vacuum.
Postulate 11. A mass particle in free fall in a
collapsing sphere of the space vacuum will be at rest
with the surrounding space vacuum and therefore
weightless.
Postulate 12. The real and virtual photon radiation
pressure and virtual and real particle and anti-particle
energy pressure of the space vacuum, akin to the
Casimir Effect, is the driving ‘force’ behind the
gravitational space vacuum energy flow into matter,
thus sustaining matter particle standing wave vortexes
in the ground state and energetic jitters in shifted
energy levels above.
Postulate 13. It is the subsequent leak of this space
vacuum energy above the sustained ground state
energy of matter that is seen as a spectrum of
microwave energy at around CMBR temperatures and
wavelengths and which may thus be responsible for
planetary and stellar heating.
12
Postulate 14. The accelerating collapse of the sphere
of space vacuum energy around a gravitating mass
follows an inverse square law giving rise to Newton’s
and Einstein’s gravity equations.
Postulate 15. The collapse of the space vacuum
energy sphere around a gravitating mass following an
inverse square law thus increases the energy density
near the gravitating mass and gives an explanation for
the effects on space, time and light in General
Relativity theory.
Postulate 16. Increases in the energy densities of the
space vacuum due to mass particle velocities also
gives rise to the known effects of contracted space
and time dilation in Einstein’s Special Theory of
Relativity.
Postulate 17. The presence of the space vacuum
energy around a gravitating mass and its varying
density: increasing as a particle approaches the
gravitating mass: gives rise to general relativistic
effects such as contraction of space along the radial
density field, reduction in the speed of light and since
the speed of light governs time: thus time dilation
(Shapiro Effect), where because the speed of light is
reduced, time runs slower.
Postulate 18. Near a gravitating mass where the
collapsing sphere of space vacuum energy is
increasing in density as it collapses towards the mass,
13
this inverse square law curvature of the energy
density causes an effect on light similar to an optical
mirage, where the light is refracted towards the mass
due to the increasing optical density of the space
vacuum energy, thus we see that light is curved
around a mass as described in Einstein’s General
Relativity Theory.
Postulate 19. The flatness of empty space devoid of a
gravitational field and hence of uniform space
vacuum energy density explains the constancy of the
speed of light in a vacuum and since any changes in
the space vacuum energy density due to a gravitating
mass or particle velocities gives equal length
contractions and speed of light time dilations, thus
maintaining the constancy of the speed of light for the
observer in the field or at velocity.
Postulate 20. Lamb Shifts in the energy of electrons
is recalled as being caused by photon interactions
with the space vacuum. This jitter in the energy levels
of the electron is likened to Brownian motion of
smoke particles in air and since this is taken as
evidence for the existence of air particles, the Lamb
Shift jitter of electrons is taken as proof for the
existence of space vacuum particle and anti-particle
pairs.
Postulate 21. A formula is derived which links
electron recoil acceleration (g) after spontaneous
emission of Lamb Shift radiation with the constant
14
which determines the strength of electromagnetic
interactions: the fine structure constant ()
Lamb Shift
The Lamb shift is a tiny change in certain atomic
energy levels. It occurs because the atom is
interacting with the empty space surrounding it by
absorbing and emitting ‘virtual’ photons. Discovered
in 1947 by the American physicist Willis Lamb, the
shift provided important experimental evidence for
the then emerging theory of quantum electrodynamics
(QED), which describes the interaction of charged
particles in terms of the exchange of photons.
Equations for Calculating the Momentum of
Particles and Photons
* The momentum ( of a mass particle:
= mv (1)
Where (m) is the rest mass of the particle and (v) is
its velocity.
* The momentum of a light photon:
E = mc2
(2)
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Where (E) is the energy of the photon and (c) is the
velocity of light in a vacuum.
Therefore: m = E/c2
(3)
Substituting m into equation (1) gives: = Ec/c2
Since for a photon velocity v = c
Then the momentum of a photon is given by:
= E/c (4)
* The De Broglie wavelength of a particle:
Since the energy (E) of a photon is Planck’s constant
(h) times its frequency (f):
E = hf (5)
We can substitute E of equation (5) into equation (4)
and get:
= hf/c (6)
Since the wavelength () of the photon is given by
rearranging the wave speed equation: c = f:
= c/f
16
Therefore f = c/
Substituting (f) into equation (4) we get:
= h/
Thus giving the De Broglie equation (7) for the
associated momentum and wavelength of a particle.
* Relativistic mass particles:
The energy of particles with relativistic mass as a
result of travelling at speed is given by:
E2 =
2c
2 + m
2c
4 (8)
Since a photon has no rest mass: m = 0
Therefore: E2 =
2c
2
Thus: E = c (9)
Giving the same equation as (4) for the momentum of
a photon:
= E/c
Mechanisms of Photon Exchange
17
In my quantum field theory of gravity I state that
what we see as a gravitational field is the acceleration
of the space vacuum energy density into a gravitating
mass and as a result any mass placed in this
accelerating energy density will experience a drag
force and will thus itself be accelerated along with the
space vacuum, this is what we see as ‘free fall’ where
the falling mass is at perfect rest because it is being
equally pushed and pulled by the flow – it is therefore
weightless, just like a ball thrown into a river it is
taken along with the flow and at rest with the
surrounding water, likewise a mass particle in ‘free
fall’ is at perfect rest with the surrounding space.
When the mass particle is obstructed by the surface of
a fixed object such as the earth it experiences weight
because the accelerating space vacuum still exerts its
drag. The fixed object is holding the mass particle
against the flow of the space vacuum and thus this
space vacuum drag on the mass particle produces its
weight, it is no longer at rest with the space vacuum.
This is analogous to the ball in the river being stuck
on a rock as the water flows over it and keeps it stuck
to the rock.
In order to explain why the mass particle is taken
along with the flow of the space vacuum we must
look at its interaction with the space vacuum and this
is clearly an exchange of momentum between the
mass particle and the space vacuum energy density.
In the case of the ball in the river it is being equally
pushed and pulled by the water molecules. So what is
18
pushing and pulling the mass particle in an
acceleration of the space vacuum? The answer to this
must lie in the momentum imparted to the mass
particle by the substance of empty space.
*It is an important point to remember at this stage that
a particle will only experience a drag force from the
space vacuum if it is accelerating through it as in
Newton’s Second Law: F=ma or if the space vacuum
is accelerating through it as in Newton’s: W = mg. It
is only this differential of velocities (disturbed
equilibrium of photon exchange between the particle
and the space vacuum) or relative acceleration
between the mass particle and the space vacuum, that
a particle experiences a drag force. This may be
likened to Doppler effects between the standing
waves of the matter particles and the standing waves
of the space vacuum virtual particle pairs. At a
relative constant speed the mass particle experiences
no drag force (Newton’s First Law) because it is in a
state of equilibrium with the space vacuum.
The space vacuum is filled with virtual particle pairs
and virtual photons all interacting with a mass particle
by absorption and emission, thus there is a continuous
exchange of energy between an electron and the sea
of virtual particles and photons in which it is
immersed. These emissions and absorptions cause
tiny changes in the energy levels of an electron –
these energy shifts are what we see as the Lamb Shift.
Each time an electron emits a virtual photon or virtual
19
particle by the law of the conservation of momentum
it ‘jitters’ i.e. recoils like a gun firing a bullet and
likewise when it absorbs a virtual photon or virtual
particle it also recoils just like a skater on ice catching
a ball. Normally of course this jitter is in random
directions for a particle at rest (equilibrium) in a sea
of virtual photons and virtual particles which is also
at rest, so although in this case the electron does not
move in any fixed direction it is still jittering in this
sea as a result of all the random absorptions and
emissions.
If the space vacuum sea of virtual particles and
photons surrounding the electron is moving in a fixed
direction then this will result in a net drag force acting
on the particle in the direction of motion of the space
vacuum sea of virtual particles and photons. It must
be remembered that the existence of these virtual
particles and photons is due to the quantum
fluctuations in the space vacuum which can be
likened to an energetic sea of almost infinite zero
point energy (ZPE). The space vacuum today is
recognised as an almost infinite source of energy, a
seething sea of short lived virtual particle pairs
coming in and out of existence, such as an electron
and positron pair which can quickly annihilate one
another forming two virtual photons. This energy
quickly returns to the space vacuum zero point
energy, thus by Heisenberg’s uncertainty principle
does not violate any laws of energy conservation. The
elastic electromagnetic properties of the substance of
20
the space vacuum are reflected in the electric and
magnetic constants μ0 and ε0, where:
c2 = 1/μ0ε0 (10)
If the electromagnetic density of space is increased,
the magnitude of these constants increase which in
turn reduces the speed of light.
The tiny shifts in the energy levels (jitter) of electrons
in orbit around atoms, what we call the Lamb Shift is
evidence of the existence of this seething sea of
energetic virtual particles and photons – virtual
because they are short lived and exist on borrowed
energy. An analogy to this energetic jitter of electrons
immersed in the seething sea of the space vacuum is
the Brownian motion of visible smoke particles
immersed in the random movements of invisible air
atoms.
We must also realise that although the quantum
fluctuations of the space vacuum even occur at a
temperature of absolute zero (0K, -273oC), space
itself is never under these conditions, the cosmic
microwave background radiation give space a
temperature of 2.725K thus making it energetic. We
must also remember that there is radiation pressure in
our universe (a sea of photons as a result of the ‘Big
Bang’ and the billions of years of the radiative
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processes of stars, pulsars, neutron stars etc). Stars
also pump out billions of tiny particles into space,
protons, electrons and a radiant stream of the almost
mass less particles, neutrinos. The neutrino density of
the space vacuum has built up over billions of years
and although these were once ‘hot’ when created in
the nuclear core of stars and travelling at near light
speeds, there must now be a neutrino population in
our universe which is now ‘cold.’ They may still, by
their infrequent collisions with matter, have lost
kinetic energy and have slowed down to a sea of
‘stationary’ particles or simply decayed into
something else, either way even without zero point
energy the space vacuum is an electromagnetic
energetic entity and it is certainly not energy less or
empty.
Electron Photon Emission
The electron (if initially in an excited state by
absorption of a photon from the space vacuum) will
in a very short time (a few nanoseconds) emit a
photon and recoil in the opposite direction:
e
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This obeys the law of conservation of momentum, the
sum of the initial momentum of the electron and
photon is zero since initially neither has velocity in
the linear direction shown. When the photon is fired
they move in opposite directions and therefore the
sum of the final momentum is still zero.
* The recoiled electron has momentum: e = mev
* The emitted photon has momentum: = E/c
Therefore by the law of conservation of momentum:
mev + E/c = 0
mev = - E/c (11)
The negative value just shows that they are moving in
opposite directions. The recoiling electron has
momentum equal and opposite to the photon. In this
case the photon is emitted to the right and the electron
recoils to the left. Initially in an excited state, the
electron drops to a lower energy state in a series of
emissions or it may even by one emission drop to the
ground state. Certainly for the electrons surround an
atom in different orbitals and energy levels, there will
be a spectrum of energy levels possible as it returns to
the ground state and therefore a spectrum of photon
emission energy levels. In this study, for the time
being, we will assume that the energy absorbed in one
photon is the energy emitted by one photon i.e. the
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electron jumps from ground state to excited state and
then immediately back to the ground state.
Electron Photon Absorption
The electron, if initially in the ground state by
absorption of a photon from the space vacuum, will
recoil in the opposite direction:
e
The electron initially at rest has a momentum of zero.
The recoiling electron having absorbed the photon
will have a momentum equal to the initial momentum
of the photon. Assuming that the mass gained by the
electron from the photon is negligible compared to
the mass of the electron:
mev = - E/c
In both cases, whether absorption or emission the
electron mass particle recoils with a momentum equal
to the momentum of the photon. If the incoming
photon is from the right the electron recoils left and if
the emission is to the right, the electron again recoils
to the left. Liken this to a skater on ice throwing a ball
to another skater and then catching the ball as it is
24
thrown back, he will recoil to the left at each throw
and catch he makes. The electron in a seething sea of
virtual (and real) photons and particles with a
spectrum of energy levels and therefore will recoil for
each photon or particle absorption and because the
absorptions and emissions are in random directions
and momentum it will jitter about in the sea in
random directions and velocities, just like the smoke
particles in air.
If a mass particle is immersed in a moving
(accelerating) sea of virtual and real photons and
particles it will be carried along with this seething see
by an imbalance of electromagnetic interactions
between their charges and it will jitter as it moves.
Any obstacle preventing the movement of the mass
particle will experience the electromagnetic drag
force of the sea on the particle. This we liken to a
gravity field where the space vacuum is flowing into
a gravitating mass, a mass particle placed in this
accelerating flow will be carried along with the flow.
If the space vacuum sea is stationary as in a zero
gravitational field it will remain at rest unless acted
on by an external force, in this case moving
(accelerating) the mass particle through the space
vacuum by a force will disturb the equilibrium and
therefore there will be a drag force equal and opposite
to the applied force.
Note: a mass particle which is stationary or moving at
a constant speed through the electromagnetic space
25
vacuum will not experience a drag force, it is only in
accelerated motion is the electromagnetic equilibrium
disturbed and a drag force initiated, this is possibly
due to Doppler shifts of the waveform of the mass
particle. As long as the particle remains at rest
relative to the background of the space vacuum it will
experience no drag force, as in the case of free fall in
a gravitational field when both mass particle and
space vacuum are moving or when both are at rest in
a non moving zero gravitational field.
This gives us the mass equivalence principle where to
move an inertial mass through space:
F = mia = Drag of space vacuum
And when space is moving through a fixed
gravitational mass:
W = mga = Drag of space vacuum
Concluding that:
mga = Drag of space vacuum = mia
This explains Einstein’s mass equivalence principle
and why there is no distinction between a mass at rest
in a zero gravitational field and a mass in free fall in a
gravitational field, in both cases the mass is at rest
26
with respect to the background space and therefore
weightless.
Summary
It takes a force (F = drag) to accelerate a mass
through space, then a fixed mass in a gravitational
field experiences weight (W = drag) because the
space must be accelerating though the mass. A
gravitational field is the acceleration of the energetic
space vacuum into a gravitating mass.
Electron Lamb Shift Photon Interaction Number
to Produce g
Calculation of Lamb Shift Energy
In this investigation into the number of photon
absorptions and emissions needed to accelerate a free
electron by g = 9.81m/s2 we will assume that the
energy of the photon is equal to the Lamb Shift
energy required to produce the universal gravitation
constant G.
In another paper a value very close to G, the universal
gravitation constant, was derived from the Lamb Shift
energy of a hydrogen electron in the 1s-2p state.
27
Assuming that G is the result of an average energy of
all Lamb Shifts of matter particles immersed in the
ZPE of the space vacuum and that the measured value
for G is the ratio of the average of the Lamb Shift
energy (EL) to the mass-energy (Ee) of the electron:
G = EL/Ee
Since Ee = mec2
Then:
G = EL/mec2
Remembering that Lamb Shift energy of an electron
in orbit around an atom depends on its orbital
quantum numbers and the size of the charged positive
nucleus the electron surrounds:
EL = 5mec
2 (k)
Where k is a value which depends on the orbital
quantum numbers and varies from: k (n, 0) is a
numerical factor which varies slightly with n from
12.7 to 13.2
Let us now use this formula to calculate the Lamb
Shift for the hydrogen atom (Electron shell 1) where
n =1 and Lqn = 0:
28
First of all we will take an average value for k (n, 0)
equal to 12.95 and assign a value to the multiplying
constant [k(n,0)/4n3] in the equation and call this kL:
kL = [k(n,0)/4n3]
= 12.95/4
kL = 3.2375
Therefore:
EL = 5mec
2 x kL
= (7.2974 x 10-3
)5 x 9.10938215 x 10
-31kg x
(2.99792458 x 108m/s)
2 x 3.2375
EL = 5.485054 x 10-24
J
This comes every close to the latest measured value
of the Lamb shift: EL = 5.415393396 x 10-24
J. If we
calculate the value in this case of k(n, 0) using the
measured value for Lamb Shift it comes to 12.7854
giving kL equal to 3.19635.
The constant ) is the fine structure constant which
determines the splitting of the lines of hydrogen
spectra due to these Lamb Shift interactions with the
space vacuum ZPE. These interactions of the electron
with the space vacuum are via virtual photon
emissions and absorptions. The fine structure constant
29
determines the strength of these electromagnetic
interactions and itself is a constant without units
because the fine structure constant is a ratio of the
ratio of the velocity of the electron in the Bohr model
of the atom to the speed of light.
*Momentum of Electron Accelerated to g
Using the derived equation (11) we can see the left
hand side represents the momentum gained by the
electron on photon emission and the right the
momentum of the photon:
mev = - E/c
If we want the electron to accelerate from rest by (g =
9.81m/s2) then its final velocity (v) after one second
equals 9.81m/s. The momentum gained by the
electron:
e = mev
= 9.1094 x 10-31
kg x 9.81m/s
e = 8.9363 x 10-30
kgm/s
* Momentum of a Lamb Shift Photon
Using the gravitational constant (G) as the being
generated by matter particle Lamb Shifts, then the
photon energy:
30
EL = Gmec2
= 6.67259 x 10-11
x 9.1094 x 10-31
x (2.998 x 108)2
EL = 5.4632 x 10-24
J
(Slightly lower than that measured for the simple
hydrogen atom)
Lamb Photon Momentum:
= EL/c
= 5.4632 x 10-24
J/2.998 x 108m/s
= 1.8223 x 10-32
kgm/s
* Number of Lamb shift Photons to produce g in
an electron:
NLe = e/
= 8.9363 x 10-30
/1.8223 x 10-32
NLe = 490.386
Per unit acceleration = 490.386/9.81 = 49.9884
31
* Number of Lamb Shift Photons to produce g for
unit mass:
NLe1kg = NLe x 1kg/me
= 490.386 x 1kg/9.1094 x 10-31
kg
NLe1kg = 5.3833 x 1032
Per unit acceleration = 5.487564 x 10-33
*Relationship of Photon Absorption Number to
the Fine Structure Constant
Since NLe = mev/EL/c
Where EL is the Lamb Shift photon energy, where EL
= 5mec
2 x kL
Then:
NLe = mevc/5mec
2 x kL
= mev/5meckL
Cancelling me and since v = g
NLe = g/5ckL
32
Per electron: g = NLe 5ckL
Per unit 1kg mass: g = NLe 5ckL/me
Summary Conclusions
It can be seen that the acceleration (g) of a mass
particle is directly proportional to the fine structure
constant () to the power of 5. This makes sense
since alpha is the constant which governs the strength
of the electromagnetic photon interactions between
matter particles and the energy of the space vacuum.
It is the product of the number of these photon
absorptions with
5 which governs the recoil
acceleration.
A mass particle moved through the space vacuum
energetic sea of virtual and real photons will interact
with it by Lamb Shift absorptions and emissions and
if there is an acceleration of this ZPE flow through
the mass particle the electromagnetic interactions
governed by the strength of the fine structure constant
will cause the mass particle to accelerate with the
space vacuum.
It is the resultant of the recoils of absorption and
emission and the relative acceleration of the mass
particle to the medium which will determine the
33
strength and direction of the drag force (F) on the
mass particle.
As before we can liken this mass particle photon
interaction with the space vacuum ZPE to a smoke
particle jittering in air with Brownian motion, when
the air is still we just see the recoil jittering of the
smoke particle, if the air is moving the smoke particle
moves with it.
Further Calculations & Discussion
1. Lamb Shift photon energy:
EL = Gmec2
= 6.67259 x 10-11
x 9.1094 x 10-31
x (2.998 x 108)2
EL = 5.4632 x 10-24
J
2. Lamb Shift photon frequency:
fL = EL/h
= 5.4632 x 10-24
/6.626 x10-34
fL = 8.245 x 109Hz
34
3. Lamb Shift mass:
mL = EL/c2
= 5.4632 x 10-24
/(2.998 x108)2
mL = 1.8284 x 10-40
kg
4. Lamb Shift wavelength:
L = c/fL
= 2.998 x 108/8.245 x 10
9
L = 0.03636m
L = 3.636cm
It is clear that when an electron interacts with the
space vacuum via photon emissions and absorptions
that the wavelength of these exchange photons is in
the microwave region of the electromagnetic
spectrum. The wavelength of the Lamb Shift photons
falls within the spectrum of Cosmic Microwave
Background Radiation (CMBR).
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5. Temperature of Lamb Shift Radiation:
TL = 0.002898/L
= 0.002898/0.03636
TL = 0.0797K
The temperature of the Lamb Shift photon radiation is
below the peak wavelength of the CMBR radiation
spectrum with a Wein’s Law temperature of 2.725K.
Newton’s Universal Gravitational Constant (G)
Newton’s gravitational constant (G) is a constant
which determines the strength of a gravitational field,
in base units:
Since F = GMm/r2
Then G = Fr2/Mm
= N.m.m/kg.kg
Since F = ma
Then N =kg.m/s2
Substituting the base units for newtons (N) we get:
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G = kg.m.m.m/kg.kg.s2
Thus G = m3/kg.s
2
Since m3 is volume and s
2 rate of change then:
G = Volume/s2
per unit mass
Indicating that this gravitational constant is related to:
The rate of change of volume (of space) per unit
mass
This demonstrates that base units for G are
equivalent to the rate of change of volume (of space)
per unit mass, suggesting that gravity may be an
accelerating flux of the space vacuum energy into a
mass.
END OF PAPER
............................................................................
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NEW EVIDENCE
The Dynamic Casimir Effect
In a recent article published in Nature: 'Scientists create light from vacuum' it was discovered that via the Dynamic Casimir Effect light could be extracted from the vacuum: ‘The experiment is based on one of the most counterintuitive, yet, one of the most important principles in quantum mechanics: that vacuum is by no means empty nothingness, in fact, the vacuum is full of various particles that are continuously fluctuating in and out of existence. They appear, exist for a brief moment and then disappear again. Since their existence is so fleeting, they are usually referred to as virtual particles. Chalmers scientist, Christopher Wilson and his co-workers have succeeded in getting photons to leave their virtual state and become real photons, i.e. measurable light. the physicist Moore predicted way back in 1970 that this should happen if the virtual photons are allowed to bounce off a mirror that is moving at a speed (accelerating) that is almost as high as the speed of light. The phenomenon, known as the dynamical casimir effect, has now been observed for the first time in a brilliant experiment conducted by the chalmers scientists..... “the result was that photons appeared in pairs from the vacuum, which we were able to measure in the form of microwave radiation.” What
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happens during the experiment is that the ‘mirror’ transfers some of its kinetic energy to virtual photons, which helps them to materialise.’ This experiment demonstrates the following important properties of the space vacuum and its relevance to QGFT: 1. Virtual Photons shown to exist in the space vacuum 2. These virtual photons become real photons when a mass accelerates through the vacuum 3. Energy is transferred to the virtual photons from the accelerating mass. 4. The accelerating mass (the mirror) loses energy by changing the virtual photons into real photons 5. This loss of energy can be viewed as a drag force from the vacuum; hence a Newtonian force is required to maintain constant acceleration. 6. The creation of photons becomes significant at speeds near the speed of light - this and the energy loss may be linked to an increase in the drag force at relativistic speeds and thus an increase in relativistic mass. 7. The photon energy levels created from the space vacuum is in the microwave region and is analogous
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to QGFT Lamb Shift radiation and Cosmic Background Microwave Radiation. If the above reported experiment proves to be correctly interpreted then it brings new light in understanding the nature of quantum gravity. Reminding ourselves of the important principles we have: A mass particle in relative acceleration with the space vacuum experiences a drag force; this is experienced as an energy loss, where the energy lost by the mass particle is imparted to virtual photon pairs which carry off this energy as a paired of real photons. In the case of the oscillating mirror above the frequency of the mirrors oscillation (f) imparts to each photon of the real photon pairs with frequency (f/2). In this particular experiment it was reported that the mirror achieved 5% of the speed of light and that the mirror was oscillating at 11GHz. This would give each real photon of light a frequency
of 5.5GHz and wavelength (of:
= 2c/f
= (2 x 2.998 x 108m/s)/(11 x 109Hz)
Photon wavelength = 0.05451m = 5.451 cm
This places the photon radiation from the accelerating mirror in the microwave part of light’s electromagnetic spectrum. Microwaves range from: 1GHz to 170GHz,
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a wavelength range of 30cm to 1.7mm. In the above paper Lamb Shift photons were calculated to be in the same part of the spectrum: frequency 8.25GHz and wavelength 3.64cm. Relating these two wavelengths with the Cosmic Microwave Background Radiation of peak frequency 160.2GHz and peak wavelength 2.73cm:
Relative Acceleration Conclusions
In the paper above the acceleration imparted to a mass was via the force of a Lamb Shift photon, emission or absorption of the photon involved exchange of momentum, like a gun firing the mirror recoils when the photon is emitted or absorbed. The magnitude of the photon momentum was equal to EL/c.
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In the dynamic Casimir experiment the mirror loses where energy losses to the virtual photon pairs to make them real photons, where the energy loss is equal to:
Where f is the frequency of the mirror:
Photon frequency = f/2
Photon energy = hf/2
= 6.626 x 10-34kgm2s-1 x 11 x 109Hz/2
EC = 3.6443 x 10-24J
The momentum imparted to the mirror per Casimir photon:
PC = E C/c
Momentum of Casimir photon = 1.21558 x 10-
32Kgm/s
If we assume that the mirror is of unit mass, then the number of such photons to produce an accelerating force of g would be:
N = Momentum of 1kg mass at 9.8m/s divided by the
momentum of a Casimir photon
N = mv/Pc
= (1kg x 9.8m/s)/(1.21558 x 10-32Kgm/s)
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N = 8.062 x 1032 photons
This comes close to the number of Lamb Shift photons
needed to accelerate a 1kg mass to g: NLe1kg = 5.3833 x
1032
. This is not unexpected since both types of light radiation fall at the same end of the microwave spectrum. In either case, whether by emission or absorption or creation of virtual light photons cosmic microwave background radiation, Lamb Shift and the Dynamic Casimir effect may be related to each other and the gravitational effect of the space vacuum on a mass when they are in relative acceleration.
In fact it may be the case that what we see as the gravitational force on a mass is none other than the quantum exchange, absorption, emission and creation of light photons with the space vacuum energetic sea of virtual particles. Gravity mediated by light.
When a mass (inertial) is accelerated through the space vacuum light photon exchange between the mass and the vacuum exerts a drag force on the mass due to mass-photon momentum exchange, similarly, when a mass (gravitational) is at rest, the relative acceleration of the space vacuum through the mass exerts a similar drag force via photon-mass momentum exchange.
The Lamb Shift that we observe in the energy levels of matter particles in a gravitational field may be evidence of light gravity at work.
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Copyright © 2012 Bernard Paul Badham. All rights
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the author.
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