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Light gravity A Quantum Solution
Bernard Paul Badham 2
‘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. 3
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. 4
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 5
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. 8
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 9
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.
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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, 12
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 13
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) 14
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 15
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 = 2c2 + m2c4 (8) Since a photon has no rest mass: m = 0 Therefore: E2 =2c2 Thus: E = c (9) Giving the same equation as (4) for the momentum of a photon: = E/c Mechanisms of Photon Exchange 16
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 17
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 18
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 19
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 20
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 22
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 = - Eď §/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 23
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 24
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 25
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. 26
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 = 5mec2 (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:
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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 = 5mec2 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 10-24J This comes every close to the latest measured value of the Lamb shift: EL = 5.415393396 x 10-24J. 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 28
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 = - Eď §/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: ď ˛e = mev = 9.1094 x 10-31kg x 9.81m/s ď ˛e = 8.9363 x 10-30kgm/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: 29
EL = Gmec2 = 6.67259 x 10-11 x 9.1094 x 10-31 x (2.998 x 108)2 EL = 5.4632 x 10-24J (Slightly lower than that measured for the simple hydrogen atom) Lamb Photon Momentum: = EL/c = 5.4632 x 10-24J/2.998 x 108m/s = 1.8223 x 10-32kgm/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
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* Number of Lamb Shift Photons to produce g for unit mass: NLe1kg = NLe x 1kg/me = 490.386 x 1kg/9.1094 x 10-31kg 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 = 5mec2 x kL Then: NLe = mevc/5mec2 x kL = mev/5meckL Cancelling me and since v = g NLe = g/5ckL 31
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 32
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 10-24J
2. Lamb Shift photon frequency: fL = EL/h = 5.4632 x 10-24/6.626 x10-34 fL = 8.245 x 109Hz 33
3. Lamb Shift mass: mL = EL/c2 = 5.4632 x 10-24/(2.998 x108)2 mL = 1.8284 x 10-40kg
4. Lamb Shift wavelength: L = c/fL = 2.998 x 108/8.245 x 109 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: 35
G = kg.m.m.m/kg.kg.s2 Thus G = m3/kg.s2 Since m3 is volume and s2 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 coworkers 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 38
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 39
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, 40
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. 41
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 1032 Kgm/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) 42
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. 43
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