1

2

Light gravity A Quantum Solution

Bernard Paul Badham

3

‘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

info@arkmedia.org

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.

5

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:

............................................................................

7

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.

8

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.

9

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.

11

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)

15

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

21

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

22

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

23

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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