Freeman Dyson: Is a Graviton Detectable?

NEOCLASSICAL PHYSICS AND QUANTUM GRAVITY
Imagine that nature emerges from a Euclidean 3D void space populated with immutable oppositely charged Planck spheres, which we call the electrino and the positrino. These are the only carriers of energy, in electromagnetic and kinetic form. They observe classical mechanics and Maxwell’s equations. Nature overlays Euclidean space (Map 1) with a lightly interacting Riemannian spacetime æther (Map 2). 𝗡𝗣𝗤𝗚 is compatible with GR, QM, and ΛCDM observations, while providing a superior narrative that explains nature and the universe.
For 𝗡𝗣𝗤𝗚 basics see: Idealized Neoclassical Model and the NPQG Glosssary.

In honor of the 90th birthday of Freeman Dyson, the Institute of Advanced Studies at Nanyang Technical University in Singapore held a symposium in 2013 at which Freeman Dyson gave a talk titled “Is a Graviton Detectable?” In this post, I’ll edit YouTube’s auto-generated transcript for correctness, grammar, and brevity. I’ll also add in relevant formulas shown on the slides. Lastly, I’ll discuss how Freeman’s thoughts relate to NPQG. I’ll put my comments in a red font so they stand out from the transcript which I will show in italic font. Freeman also published an accompanying paper with more details : Is a Graviton Detectable.

So, good morning everybody and thanks to everybody who had a hand in inviting me here and thanks to all of you who took the trouble to come. […]

[2:00]It all starts with this wonderful paper of Bohr and Rosenfeld in the year 1933 which was a very famous piece of work. This was the finest example of Bohr’s style. The title was “On the Question of the Measurability of Electromagnetic Field Quantities.” It’s the foundation of the field of quantum electrodynamics. It’s the paper in which Bohr found the precise physical basis for the quantum treatment of electromagnetism, showing that if you had electromagnetic waves interacting with material objects, and if the apparatus behaved by the rules of quantum mechanics, then the rules of quantum electrodynamics were a necessary consequence. That is what Bohr and Rosenfeld established.

What I’m trying to do today is to discuss the same problem for gravitation. So how about gravitation? Is gravitation in fact like electrodynamics? In electrodynamics we have the classical theory of Maxwell, and we have the quantum theory, which started with Einstein, the theory of the photon which is the particle of electromagnetism. The classical and the quantum picture are linked together by this subject of quantum electrodynamics. Does the same thing hold for gravity? That is the big question which we don’t yet know how to answer. There’s been a great deal of talk, and a great deal of philosophizing, and not very much detailed science. I shall try to talk about the detailed science today.

NPQG teaches that gravitation is based on electrodynamics. The key is that NPQG imagines fermion particles as a composite payload of electrinos and positrinos, corresponding to the fermions in the standard model, surrounded by a neutral shell composed of ‘rotating’ electrino/positrino dipoles, often traveling rather rapidly in their wave equation. These neutral shells do not establish the larger more persistent electromagnetic fields like the payload, but rather fluctuate at a very low level that propagates spherically at \mathbf{1/r^{2}} , like an electromagnetic wave, but which practically serves to only slightly influence neighboring shells energy in an ebb and flow. I suppose to make an analogy, a charged payload produces a direct electric field, and if it is moving, a direct magnetic field, while a shell produces an alternating electromagnetic field of much smaller magnitude. There is a second effect, that the shell radius decreases as a function of composite particle energy. It is this radius decreases that implements the Lorentz function which causes space to curve. Thus NPQG imagines gravitation as a electromagnetic and kinetic effect, which will hopefully turn out to be a grand simplifying factor, and you will see that arise in areas discussed by Freeman, such as whether electromagnetic waves and gravitational waves propagate at the same speed. They do, although here NPQG models the speed of electromagnetic propagation, c, as a local property dependent on the energy of the spacetime æther.

In the case of gravitation you have the classical theory of Einstein, general relativity, which describes gravitation beautifully as a classical phenomenon in the classical world. Waves of gravitation propagating through a universe with equations which have enormous elegance and enormous predictive power and have been verified by observation. So it’s a firmly based classical theory. On top of that you have what’s called quantum gravity, which is the notion that actually there exists a particle called the graviton which has the same relation to classical gravity as the photon has to the Maxwell theory. But there’s no observational evidence for the graviton. Do gravitons actually exist? We don’t know. Nobody has ever seen a single graviton. That’s the subject which I’m going to discuss.

In NPQG Einstein’s curvy abstract geometrical spacetime is implemented with a particulate æther. So as not to overstate the case for NPQG, a broad set of possible particles are considered potential constituents of spacetime æther, much as air contains many constituent and transparent gases. Spacetime æther may be comprised of gravitons, axions, photons, neutrinos, and perhaps other exotic particles we have not yet imagined.

Roughly speaking there are three possible alternatives which might describe the universe we live in. There is first of all what I would call the the Orthodox view, the view of all the experts, which is that quantum gravity is a good theory just like quantum electrodynamics. That in fact that there do exist gravitons, and that they obey the equations of quantum gravity, and they have the same kind of behavior as the photon except that it’s harder to observe. That’s the first possibility

The second possibility is what I call concealment. It is that quantum gravity exists but it can never be detected, in the same way that the quark particle exists, which everybody believes is real but it can never be observed. That has turned out to be a very fruitful concept in particle physics and it is called quantum chromodynamics, which is the theory of the strong interactions. The quark is a quantum field which has all the properties of a quantum field except observability, such that you can never see a quark by itself. All you can see is confined systems in which the quarks are hidden. That’s why we call it confinement. That’s the second possibility, that quantum gravity is real but unobservable.

The third possibility is that quantum gravity is nonsense. That in fact there is no such thing as quantum gravity. That gravity is a purely classical phenomenon and the alleged effects of quantization are for some reason absent. If that were true gravitation is a classical phenomenon. It is some kind of statistical property which only belongs to matter in the large, and not to matter in the small. So there’s no such thing as a gravitational field of an electron and it’s only a collective property of matter in bulk.

Those are the three possibilities. The question which I’m asking is what is the evidence? What can we actually say from what we have observed? There are four subjects I’m going to discuss.

First of all what happens if you try to apply the Bohr-Rosenfeld argument to gravitation? That’s essentially just mathematics and it has an interesting answer.

The second subject is a particular kind of gravitational observation which is actually being done in the real world. It is called LIGO which stands for laser interferometry gravitational observatory. It’s a long vacuum pipe with a mirror at each end and light bouncing up and down. LIGO measures very precisely the phase of the light as it comes back and forth and is reflected at the mirrors. That’s a very precise measurement of the distance between the two mirrors. When a gravitational wave comes by, the gravitational wave is a distortion of the space and it produces a very small change in the separation of the mirrors as it was measured by the light. The purpose of the apparatus is to detect classical gravitational waves coming from astronomical sources. […] Could an apparatus of that kind detect a graviton? The answer is no. That’s my first piece of evidence that in principle that kind of an apparatus would be incapable of detecting a graviton, even if it were as sensitive as it’s possible to be, and even if the universe were totally quiet with no background incidental noise. It would still not be possible to detect a single graviton. That’s quite a strong statement. That’s evidence in favor of unobservability of gravitons.

In a gravitational wave produced in an extreme energy event, such as those now detected by LIGO (subsequent to Freeman’s 2013 talk), the electromagnetic energy spike is so high that as the wave progates spacetime æther energy changes so much that the æther particles shrink according to the Lorentz factor. There is also a complimentary kinetic energy effect whereby æther particles translate as in a sea where particles move up and down and side to side. Now as to the question of could a LIGO-like detector be designed to detect a single graviton delta in spacetime is still interesting and we’ll need to examine Freeman’s argument to see if his logic still holds.

The third subject is another kind of detector consisting of a single atom. That’s the analog of Einstein’s photoelectric effect. Einstein invented the photon by considering what happens when an electromagnetic wave knocks an electron out of an atom. You can ask the same question about a gravitational wave. Suppose when a gravitational wave hits an atom it can also can knock out an electron or it can knock out a proton or a neutron. That also could be observed so that’s another kind of graviton detector. The answer is ‘maybe.’ You can’t prove that it doesn’t work but there’s fairly strong evidence that it doesn’t work.

It is interesting to consider the idea that gravitons might propagate with high speed when they have high energy. NPQG has not yet taken a position on this. This is the flip side of the question of what happens when a photon reaches extremely low energy. Does a very low energy photon still travel at c or is there some point where it slows down? Presumably the gravitons at the low end of the temperature spectrum in free space and low gravity environments like earth are moving very slowly. There is some reason to believe the gravitons of spacetime form a Bose-Einstein condensate over a wide temperature range. A Bose-Einstein condensate behaves as if it is a single entity – so I don’t know what it would mean for gravitons to have kinetic vector motion in that state. Well this is certainly food for thought – imagine that similar to the many neutrinos that permeate everything, including you and me, that high energy gravitons in far greater numbers are also flying through us. I suppose it doesn’t really matter to us if it is so, for just as with neutrinos, it appears to be harmless. Furthermore, NPQG already imagined that everything is permeated with gravitons anyway, so what difference does it make if there are some going the speed of light?

The fourth subject I will discuss is another way of detecting gravitons which is based on the coherent conversion of photons into gravitons. This is an interesting process invented by a Russian called Gertsenshtein in 1962 in a paper about wave resonance of light and gravitational waves. Gertsenshtein showed that in classical gravitation electromagnetic theory there is a process of conversion of gravitons into photons or photons into gravitons, which you can calculate. This gives you a method of detecting gravitons if this actually happens. It’s rather like the oscillation of neutrinos which was recently discovered. There are three different kinds of neutrinos and they also can convert into each other by the same kind of coherent process. It happens whenever you have two linear fields which satisfy a bilinear coupling equation so they can convert coherently one into the other.

The idea of converting photons into gravitons and gravitons into photons makes sense in NPQG, where a photon is a 6/6 composite shell and a spacetime particle is a 12/12 composite shell. In NPQG, spacetime particles are also ingredients in pair production. This lends support to the idea that spacetime particles are dominated by gravitons.

There are all together four different arguments and in the end the question remains open.

\mathit{\Delta E_{x}\left(1\right)\Delta E_{x}\left (2\right)\sim \hbar\left | A\left ( 1,2 \right ) -A\left ( 2,1 \right )\right |\; \; \; \; \; \; \; \; \; \; \; \; \left ( 10 \right )}

Equation (10) is the Bohr-Rosenfeld argument about the uncertainty relation for observations of electric and magnetic fields showing that they had to be consistent with quantum electrodynamics. \mathbf{\Delta E_{x}\left(1\right)} is the uncertainty of a measurement of electric field in some spacetime region 1 and \mathbf{\Delta E_{x}\left(2\right)} is the uncertainty in the measurement in another spacetime region 2. The Heisenberg uncertainty relationship says the product of the uncertainties of the two measurements is at least as great as this quantity on the right which is a purely classical quantity. A(1,2) is the electric field averaged over region 1 induced by a classical dipole in region 2 and A(2,1) is the other way round, it’s the electric field in region 2 induced by a classical dipole in region 1. You take those two classical dipoles and subtract them and that gives you the uncertainty in the measurement. That was the result of the Bohr-Rosenfeld argument which was sort of a verification that quantum electrodynamics had to be true if the classical apparatus used for the measurement obeys the rules of quantum mechanics.

What happens when you apply that to gravitation? The mathematics looks so much the same. You have a similar sort of an equation with the uncertainty of measurement of gravitational fields with classical gravitational quadrupoles in this case. So it looks as though it should be the same.

But if you look carefully at Bohr’s argument you find there’s one place where it’s very tricky. The argument in fact requires a particular physical device (Apparatus 2) which is the compensation for the induced currents and charges (caused by Apparatus 1). Bohr is imagining you have the classical charges and currents of the measuring equipment (Apparatus 1). They move in response to the electric field that you’re measuring. But of course when those classical charges move, they in fact induce further fields which you cannot control. Those are the other fields you’re trying to measure and that messes up your measurement. In order to make the measurement as precise as possible, Bohr imagines that those induced charges and currents in the fields you are trying to measure are compensated by another set of charges and currents exactly opposite to the ones you are using for the measurement. This enables the measurement to be as precise as it should be. That compensation requires that you have this other piece of equipment (Apparatus 2) which carries charges and currents precisely opposite to the ones you’re using for the measurement.

Well that (compensation) you cannot do with gravitation. In the case of gravitation you have to use masses to induce the gravitational forces that you’re trying to measure, but there’s no such thing as a negative mass so this kind of a compensation cannot be done. For that reason the Bohr-Rosenfeld argument simply doesn’t apply to gravitation. It may be true the quantum gravity has the right commutation rule so it may not fail, but you can’t prove it as Bohr did with the Maxwell equations.

In NPQG there is no separate force of gravity. Gravity is caused by a very small alternating electromagnetic interaction of the electrinos and positrinos in particle shells. Particle shells are net neutral, but there are still interactions between all the electrinos and positrinos in the shells according to Maxwell’s equations. Those interactions cause an energy wave that propagates spherically through spacetime æther particles and the shell of any other particle encountered. Furthermore, the shell energy required to maintain stability of a particle is a function of the payload matter-energy and the velocity of the particle relative to spacetime æther. The shell energy is how mass is implemented. Equation (m:E) shows Einstein’s mass-energy relation for a particle at rest (i.e., not moving relative to spacetime æther). Equation (E:p) shows the energy-momentum relation for a moving particle. As the energy of the payload increases due to composition and kinetic motion, the shell energy must increase to compensate. Shell energy increases by increasing the velocity of the electrinos and positrinos in the shell and by contracting the shell according to the Lorentz equation.

\mathit{m_{0}= \frac{E}{c^{2}}\; \; \; \; \; \; \; \; \; \; \; \; \; \; \left (m:E \right )}

\mathit{E^{2}= \left ( pc \right )^{2}+\left (m_{0}c^{2} \right )^{2}\; \; \; \; \; \; \; \; \; \; \; \; \; \left ( E:p \right )}

Therefore, NPQG is not constrained by the ‘negative mass’ issue that Freeman Dyson raises. That said, we still need to understand the electromagnetic Bohr-Rosenfeld argument with respect to NPQG for all particle types, not just gravitons. To prove that there exists a spacetime æther particle, it may be possible to show gravitational attraction to the isthmus of heated spacetime æther between two equal massive bodies. Imagine the line between the centers of two equally shaped massive spheres. Now, draw a second line perpendicular to the first that intersects the first at the midpoint. Place a test object on the second line, slightly offset from the first line. We would expect a vector component of attraction from both test bodies that would cause a force towards the first line. However, there should be an additional gradient of spacetime energy attracting the test body towards the intersection point of line 1 and 2. The only remaining experimental question is to determine if equipment could be sensitive enough to measure that additional convective force.

[19:30]The second subject is LIGO. Here I can actually prove a theorem. It’s the only really strong statement I can make. It is actually a theorem that a detector of the design of a LIGO, that’s two mirrors measuring the gravitational wave as it comes by, cannot in fact work for a single graviton.

\mathit{E= \left ( \frac{c^{2}}{32\pi G} \right )\omega ^{2}f^{2}\; \; \; \; \; \; \; \; \; \; \; (1)}

“If you look at equation (1) for the energy density of a gravitational field in which \mathbf{\omega} is the frequency and f is the fractional change in distance that’s measured in consequence of the distortion of metric space by the gravitational field. f is a pure number – it’s the fractional gravitational expansion or contraction of the space measured. Then the energy density of the wave is given by this formula with the square of velocity of light c and the Newton’s constant G. The remarkable thing is the square of the speed of light which is an enormous factor. It says that a very very small distortion of the space produces a large energy density so the exchange ratio between the observed distortion and the energy it takes is very large.

NPQG will have a different formula, at the least because the speed of light c varies as a function of the energy, i.e., temperature, of the spacetime æther. This varying speed of light is caused by the change in permittivity and permeability of spacetime æther with energy. The more energy carried by each spacetime æther particle (graviton) the less the energy gap to the Planck energy. Of course in free space and on Earth, gravity is so low that spacetime æther is near 0 Kelvin and equation (1) applies within the limits of measurability by GR-QM era test equipment.

\mathit{c= \frac{1}{\sqrt{\epsilon \mu }}}

NPQG has not yet determined a formula for G as a function of spacetime æther temperature, nor how \mathbf{\omega} and f behave in high temperature spacetime æther. Suffice it to say that high energy (temperature) spacetime æther is very dense and and that gravitational waves near a black hole would be extremely high energy.

\mathit{E= \hbar\omega}

\mathit{c= \omega\lambda}

\mathit{E_{s}=\left ( \frac{\hbar\omega^{4} }{c^{3}} \right )\; \; \; \; \; \; \; \; \; \; \; (2)}

Equation (2) is for a single graviton with a frequency \mathbf{\omega} . The energy of a graviton is \mathbf{\hbar \omega} according to Planck. The cube of the wavelength \mathbf{\lambda} is roughly the minimum volume that the graviton could occupy so the energy density of a graviton is at most this quantity \mathbf{E _{s}} . If you put those two things together and you say equation (1) is equal to equation (2) then you’re talking about the distortion of space corresponding to a single graviton is this quantity f in equation (3).

\mathit{f= \sqrt{32\pi}\left ( L_{p}\omega/c \right )\; \; \; \; \; \; \; \; \; \; \left ( 3 \right )}

\mathit{L_{p}=\sqrt{\frac{G\hbar}{c^{3}}}= 1.4\; x\; 10^{-35} meters\; \; \; \; \; \; \; \; \; \; \; \; \; \left ( 4 \right )}

The quantity which comes in there is the Planck length \mathbf{L _{p}} and because of the large velocity of light the Planck length is a very very small number, 1.4 times 10 to the minus 33 centimeters. That is then the standard distortion f produced by a single graviton. It’s the fact that it’s so small which makes a graviton hard to observe. The logic is very simple. If you wanted to disturb a single graviton we would have to measure the separation between these two mirrors with an accuracy which is equal to delta which is just proportional to the Planck length and nothing else. See equation (5).”

\mathit{\delta= \left ( \sqrt{32\pi} \right )L_{p}\; \; \; \; \; \; \; \; \; \left ( 5 \right )}

I suspect Dyson is missing something in this equation because a graviton in NPQG would be a small particle but not Planck scale. After all, as a graviton heats up (gains energy) it must shrink according to the Lorentz equation in order to implement the characteristics of spacetime such as length contraction and time dilation. Aha, here is the error: “The cube of the wavelength \mathbf{\lambda} is roughly the minimum volume that the graviton could occupy so the energy density of a graviton is at most this quantity \mathbf{E _{s}} .” This is a common error in GR-QM era physics because of a lack of understanding of the physical implementation of wavelength. In NPQG, wavelength is the distance a particle travels during which the electrinos and positrinos in the shell travel their wave equation and return to symmetry with the starting point. The graviton is a spin 2 particle, so it only needs to go through 180 degrees to return to symmetry. In any case, the distance traveled is not necessarily related to the size of the particle. Gravitons typically move very slowly in free space.

[23:50]Now comes in quantum mechanics for the apparatus. The apparatus is just a mirror which has a mass M. Equation (6) is a consequence of quantum mechanics. If you have a mass M it has an uncertainty in position and it also has an uncertainty in velocity. If you try to hold it still for a length of time T it will wobble around. It will have quantum fluctuations which are of order \mathbf{\delta } and that’s the equation for the quantum fluctuations of the mirror.

\mathit{M\delta ^{2}\geq\hbar T\; \; \; \; \; \; \; \; \; \; \; \; \; \left ( 6 \right )}

\mathbf{M \delta ^{2}} is at least Planck’s constant times the time. That’s the best you can do for determining the position of a mirror over a time T. The time T is at least the time it takes for the light to go from one mirror to the other which is at least the wavelength of the graviton you’re trying to observe. If you put equations (5) and (6) together the answer in equation (7) comes out that the distance D between the mirrors has to be less than \mathbf{\frac{GM}{c ^{2}}} .

\mathit{D\leq \frac{GM}{c ^{2}}\; \; \; \; \; \; \; \; \; \; \; \; \; \left ( 7 \right )}

Planck’s constant has disappeared and you have an equation or inequality for the separation of the mirrors. The mirrors have to be close together depending only on their mass to make the measurement possible. The quantity \mathbf{\frac{GM}{c ^{2}}} is the Schwarzschild radius corresponding to the mass of the mirror. It’s the radius of a black hole of a mass equal to the mass of the mirror. The mirrors are that close to each other it means that each is attracted to the other with an irresistible force and they both collapse into a black hole. That’s what nature does to prevent you from making the experiment. Nature forbids the experiment by this very crude mechanism. You are forced to make the mirrors so heavy to make the quantum fluctuation small, that they collapse into a black hole. It turns out that the you can actually prove mathematically that the apparatus is not going to work.

This argument so far assumes the mirrors are suspended in space as free objects. That’s the best you can do. The alternative would be to have them supported by some kind of elastic framework, but then it has to have a finite sound speed in the mechanical framework. Then if you take a mechanical support you get equations of the same kind with the sound speed replacing the light speed so that actually makes things even worse. If you have a mechanical structure supporting the mirrors you get an even stronger inequality GM over C squared is greater than ratio of light to sound velocity times the separation. The conclusion is still true. You can prove that there is no possible gravitational wave detector of that kind which will detect single gravitons.

Let’s go on then to a more hopeful kind of gravitational wave detector which is the single atom with the gravitoelectromagnetic effect. We’re looking at a single atom and a gravitational wave comes in and another particle, either an electron or a neutron or anything else, is kicked out. You can calculate by quantum mechanics the rate at which this will happen. The gravitational wave is a quadrupole so the matrix element for transition of the electron from state a to state b (equation 11).

\mathit{D _{ab}=m \int \psi _{b} ^{*}xy \psi _{a}d\tau \; \; \; \; \; \; \; \; \; \; \left ( 11 \right )}

\mathbf{\psi _{a}} is the wave function of the initial state \mathbf{\psi _{b}} is the wave function of the final state and x and y are the two coordinates of the electron at right angles to each other. That’s a particular quadrupole with polarization at 45 degrees to the XY axis. You could take the other polarization and it would give the same result. Then the cross section for kicking out the electron is given by equation (12) which is the standard formula from quantum mechanics for a quadrupole radiation process. G is the coupling constant of gravitation which comes out of the Einstein equation, \mathbf{\omega} is the wavelength, c is velocity of light, D is this matrix element, and then you have a delta function for energy conservation since the graviton energy \mathbf{h \omega } is equal to the difference between the two states energies, so that’s the cross-section.

\mathit{\sigma \left ( \omega \right )=\left ( 4\pi ^{2} G \omega ^{3}/c^{3}\right )\sum_{b}\left | D_{ab} \right |^2 \delta\left ( E_{b}-E_{a} -h \omega \right )\; \; \; \; \; \; \; \; \; \; \; \left ( 12 \right )}

Well that’s of course a complicated thing to calculate. It doesn’t look very promising but you can make a very strong argument by writing down an exact sum rule. A sum rule in quantum mechanics is a wonderful device for getting simple consequences from complicated equations. You sum over all the frequencies and everything comes out very simple.

\mathit{S _{a}= \int \sigma \left ( \omega \right ) d\omega / \omega \; \; \; \; \; \; \; \; \; \; \; \; \left ( 13 \right ) }

This quantity \mathbf{S _{a}} is the logarithmic average of the cross-section averaged over energy but with \mathbf{d \omega / \omega } . It’s the logarithmic average of the cross-section and that you can calculate very beautifully from this formula if you integrate over \mathbf{\omega} and the delta function disappears and you get products of matrix elements which become matrix products and in fact you get a double commutator of this quadrupole with the Hamiltonian and so everything becomes simple and the result is \mathbf{S _{a}} , the logarithmic average cross-section, turns out to be just this quantity in equation (14) that’s an exact sum rule. It’s a very very simple but powerful equation.

\mathit{S_{a}=4 \pi^{2} L _{p} ^{2} Q\; \; \; \; \; \; \; \; \; \; \; \left ( 14 \right )}

[32:25] “This capital Q is then a property only of the initial state. The sum over the final states has disappeared. That gives you a matrix product. You get just the expectation in the initial state of this differential quantity. The amazing thing is that all the constants have disappeared. The mass has disappeared. The potential has disappeared. The charge of the nucleus has disappeared. It no longer depends on anything except just the shape of the wave function and nothing else. Q is a pure number. If you take the simple case where you’re talking about a spherical wave function, that’s just an ordinary bound state of an electron in an atom which you’d expect to be the one which would react most strongly to gravitation, then everything becomes absurdly simple and you can prove just by simple algebra that this capital Q is a number of the order of one which is at least three-quarters. If you take the simple model for the wave function which is typical of a strongly bound particle like a ground state of an atom or a ground state of a nucleus so r to the minus n where n is some positive power times an exponential that’s a typical wave function for a bound particle then q is 1 minus n over 6 so it’s very close to 1. Q is just a number which for ordinary atoms and nuclei is close to 1. The final result of this whole discussion is that the logarithmic average of the cross-section equation (14) is just equal to the Planck length squared and that’s all it is. The Planck length squared is a very very small area of the order of 10 to minus 65 square meters so there’s nothing you can do to change that. It doesn’t matter what kind of an atom you’re using or whether you’re talking about nuclear forces or electromagnetic forces. The best you can do is a cross-section of 10 to minus 65 square meters. I can’t any longer prove a theorem. I can’t say this measurement fails for fundamental physical reasons. It fails for practical reasons.

Let me just talk about gravitational thermal generators that were worked out by Stephen Weinberg a long time ago. The Sun is a wonderful source of gravitons with observable energy. In the core of the Sun the average energy of the particles is of the order of ten kilovolts. With electrons and protons colliding together all the time very hard they will be generating gravitons and that’s about the best source of gravitons that you can imagine. It’s producing huge numbers of gravitons all the time and they all escape from the Sun because the Sun is transparent to its own gravitons. That turns out to be seventy-nine megawatts for the Sun. It’s a large amount of energy by human standards but very small by astronomical standards. It turns out four times 10 to the minus four gravitons per centimeter squared per second. If you multiply that by the cross-section and imagine the whole earth is used as your gravitational wave detector then during the entire lifetime of the Sun you should on the average detect four gravitons so it’s just barely possible.

Anyhow that’s not very encouraging. You can imagine better sources than the Sun. You can imagine moving around the universe looking for better sources of gravitons. There are hot neutron stars which are much more actively radiating than the Sun. They have very much higher average thermal energy. They radiate maybe ten to the ten times more strongly than the Sun. Neutron stars don’t live so long. The total amount of energy in the form of gravitons is not all that much greater than the Sun. In the case of the neutron star it comes out faster but you don’t gain all that much. You can imagine a detector which is bigger than the earth maybe closer to the source. In principle maybe you could do somewhat better but not very much. The most is that perhaps ten to the ten gravitons could be detected during the lifetime of the source. Then there comes the argument about backgrounds. Any source of gravitons of that magnitude producing gravitons of the kilovolt range also produces neutrinos and the neutrino background turns out to be enormously large in comparison. Neutrinos have enormously stronger interaction than gravitons by something like twenty powers of ten and they emit much more copiously. Also the detection probabilities for neutrinos are much larger. You get something like thirty powers of ten favouring neutrinos against gravitons so any conceivable graviton detector looking for thermal gravitons has to deal with this overwhelming background of neutrinos. From a practical point of view that seems to make the thing pretty hopeless, but it’s not so satisfactory a conclusion as you had for the LIGO.

Well the final set of detectors which I’ll talk about very briefly are the coherent detectors. Those are non-thermal detectors which are then the thing that Gertsenshtein proposed first forty years ago. That comes from this process of coherent conversion of gravitons into photons. Equation (24) is just a coupling of the gravitational field amplitude which is Hij which is the Einstein tensor multiplied by the electromagnetic energy tensor Tij which is a combination of a classical magnetic field B and the quantum magnetic field b. You get a mixing of classical and quantum magnetic fields. The interaction finally gives you a bilinear term, linear in gravitation and also linear in photon field, multiplied by the classical background field. Now imagine your detector consists of a long long magnet with a strong classical magnetic field and you put in photons at one end and out come gravitons at the other end or vice-versa.

“The beauty of that is since the process is coherent the probability of conversion goes as the square of the length. The probability of conversion is actually this equation (29) which says probability of conversion is B squared, the square of the magnetic field, times D squared, which is the length of your magnet, divided by the fourth power of this velocity of light. It’s always the velocity of light which kills you. The probabilities are amazingly small and again this is a purely classical effect. Planck’s constant has disappeared. It’s a classical mixing of gravity with photons. The conversion length L is 10 to the 25 centimeters which is of the order of a kiloparsec in astronomical units divided by the magnetic field in gauss.

So it means for any conceivable magnet the probabilities are very small. It looks as though in principle it might perhaps be feasible. But then there comes a fatal flaw into this argument too – nonlinear electrodynamics. It turns out that the Maxwell field after all is not linear and this was in fact a discovery of Euler and Heisenberg already in 1936. It’s one of the most beautiful things that Heisenberg did when he was still a scientist. Heisenberg and his student Euler worked out the theory of the polarization of the vacuum produced by pair creation, that is electrons and positrons popping up and down in the vacuum produced this fourth order term in the Maxwell equations. The Maxwell equations are inherently nonlinear when you allow the Maxwell field to interact with electrons and positrons. This is the Euler-Heisenberg nonlinear electrodynamics which tells you that in fact the speed of light in a classical magnetic field is less than it would be in a vacuum.”

From an NPQG perspective, a magnetic field carried by the spacetime æther must also increase the energy of the spacetime æther particles. NPQG already teaches that the speed of light through spacetime æther varies with the energy of spacetime æther according to the changes in permittivity and permeability caused by the increased energy.

\mathit{g=1-\left ( v/c \right )=\left ( k \alpha B^{2}/360 \pi ^{2}H ^{2} _{c} \right )\; \; \; \; \; \; \; \; \; \; \left ( 35 \right )}

[45:00]Equation (35) is the amount that the speed of light is reduced in a magnetic field. B is the classical magnetic field. Hc is the critical field which is 5 times 10 to the 13 Gauss which is actually about what you get astronomically in a pulsar. A pulsar is a magnetized neutron star which typically have fields which are just about equal to the critical field so this in a pulsar these numbers can be quite large. The Maxwell field becomes strongly nonlinear. That tells you then this coherent conversion doesn’t work. If you have graviton and a photon going at different speeds they’re not going to be coherent with one another so the coherent conversion simply fails and so that happens then to be true in a neutron star.

In NPQG, the speed of light and the speed of gravitation are the same locally. Therefore Freeman’s argument is not correct.

“If you imagine a detector in which your magnetic field is more of a reasonable terrestrial magnetic field of the order of 10 Tesla or something of the kind that was used the way the people at CERN actually used this as a device for detecting axion’s. There was an experiment at CERN looking for the coherent conversion of photons into axions. Axions being a hypothetical particle with mass zero which might exist and be detectable in this way. They did the experiment and also got a null result. Of course they were not looking for gravitons. If you took an experiment of that kind with an unreasonably long magnet of the order of say a hundred million kilometers or so, it still turns out that the coherent conversion doesn’t work. The nonlinearity of the Maxwell equation is enough to defeat you so it seems this kind of detector also doesn’t work.

I’ll leave the subject there. I don’t want to get drowned in details. The final conclusion is that the promised possibilities remain open that quantum gravity may be in fact correct as all the experts believe or it may be correct but with confinement so that gravitons are always confined and not visible or it may be that gravitons don’t exist. We can’t yet decide that but I think it’s an interesting subject and certainly there is the possibility of pushing these arguments very much further. Thank you.”

I found this talk to be wonderful. I really enjoy Freeman Dyson’s presentation style. It is pleasant, paced at the speed of my current cognition (i.e., relatively slow), and explanatory. I can also see how much of his thought process relates to NPQG and provides a pathway for study that will help me understand prior assumptions and thoughts, and then adapt or revise them for NPQG. My guess is that scientists moved away from the classical world and have never envisioned a way that classical fundamental particles could produce the observations they have made in experiments.

J Mark Morris : San Diego : California : February 12, 2020 : v1

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