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Pilot wave phenomena can build quantum mechanics out of nothing more than general relativity.

Rings coalescing

August 1, 2017 — Leave a comment

As someone pointed out on reddit, it looks like an inelastic collision.

Singularities, de Broglie and emergent quantum mechanics comes to mind for me.

The interaction causes a wave to propagate. After a time equal to the period of a wave on the ring, it separates into two.




The Atomic World Spooky? It Ain’t Necessarily So!: Emergent Quantum Mechanics, How the Classical Laws of Nature Can Conspire to Cause Quantum-Like Behaviour

by Theo van Holten

The hardcover is out – for example here:  or at Springerbut its coming out in paperback soon – . Its not coming in paperback, so I just bought the hard cover. Its ok if a paperback comes later but I can’t wait!

So what I’m saying is that I’m cheap enough to wait for the paperback, so I actually have not read the book, but it looks like its going to be a real addition to the field. Its aimed at people with at least a science background.

The book takes the discovery (by for example Couder/Bush) that quantum-like behaviour is not solely reserved to atomic particles one step further. If electrons are modelled as vibrating droplets instead of the usually assumed point objects, and if the classical laws of nature are applied, then exactly  the same behaviour  as in quantum  theory is found, quantitatively correct! The world of atoms is strange and quantum mechanics, the theory of this world, is almost magic. Or is it? Tiny droplets of oil bouncing round on a fluid surface can also mimic the world of quantum mechanics. For the layman – for whom the main part of this book is written – this is good news. If the everyday laws of nature can conspire to show up quantum-like phenomena, there is hope to form mental pictures how the atomic world works.

Here is an excerpt from the Preface to the book: (other tidbits can be downloaded from Springer)

To begin with a warning: the contents of this book may be controversial.

 The readers the author had in mind when writing this book are interested laymen, typically the kind of reader who searches bookshops for the latest popular-scientific books on developments in cosmology, on recently found fun- damental particles, or on the ever more magical findings of quantum physics. These readers presumably have some background of classical school physics (although most of it may have been forgotten). It is the kind of reader who does not like to be bothered with formulae or is even allergic to them, but who has the interest and tenacity to read sentences twice if necessary. But complete novices in the matters of the atomic world should be warned: the stories told in this book are not the same as usually found in books about quantum phenomena. This book does not give the conventional explanations. In order to read the usual stories, it is better to start in

one of the many other popular-scientific books.
 What then is this book about? This book certainly does not pretend to contain a

new theory of quantum mechanics, nor does it have the intention. Quantum theory in its present form is an almost perfect tool to calculate the behaviour of elementary particles. But the theory is “strange”, it is not something that intuitively can be understood. What this book tries to add are visualisations or mental pictures, closer to the intuition, because they are based on classical physics. However, the mental pictures in this book are not just half-baked analogies or metaphores, they are solidly founded on a large body of mathematical theory (for the diehards: the theory can be found in the appendix). This aspect makes this book different from other popular-scientific books.
Here is an excerpt from the book’s appendix. You can see that a mathematical treatment is supplied. This book is written for people who already know QM. I can think of some young physics undergrads I might buy this for!
I will do an in depth review when I’m able to get the book.
–Tom Andersen



An interesting popular article that I found in Quantum . My favourite quote:

But there’s another view — one that’s been around for almost a century — in which particles really do have precise positions at all times. This alternative view, known as pilot-wave theory or Bohmian mechanics,

New Support for Alternative Quantum View

An experiment claims to have invalidated a decades-old criticism against pilot-wave theory, an alternative formulation of quantum mechanics that avoids the most baffling features of the subatomic universe.

I really like this graphic – visit the story for more!
Emergent quantum mechanics comes in many forms: stochastic electrodynamics ( Ana María Cetto) , de Broglie – Bohmian mechanics (John W M Bush) , thermal models ( Gerhard Groessing ) etc. In many of these forms of emergent quantum mechanics, particles have a physical existence and experience sub quantal movement. The paper I have just posted looks at the gravitational consequences of this sub quantal motion. An interesting finding is that while a classical Bohr hydrogen atom has a lifetime of about 10^-11 seconds, it would take that same atom 10^40 seconds or so to radiate away a few eV of energy. This indicates that the stability of the atoms is not an indication that gravity needs to be quantized, which is antithetical to Einstein in 1916:
  • “…Nevertheless, due to the inner-atomic movement of electrons, atoms would have to radiate not only electro-magnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.” – Einstein, 1916
Einstein it would seem was wrong on the gravtitational side of this.
The paper looks at possible ways to see these tiny emissions (nuclear scale emissions are higher) and thus lays out a quantum gravity experiment achievable with today’s technology.
Parameter space for a quantum gravity experiment.

The experimental parameter space. Most important thing to note is that this is a quantum gravity experiment with an achievable parameter space!


Here is the paper…

Also see these references…


(This article is a work in progress…)

We posit that the de Broglie wave as a real physical wave produced by interactions between any massive particle and the gravitational background zero point field.


de Broglie waves are tied to momentum. They are associated with any free particle. For instance an electron or a Buckyball.  In my view they are some sort of beat phenomenon – doppler effect.

There is a huge background of Gravitational waves at some very large frequency – (perhaps Planckian).

How physically would waves associate with every single mass ? The only possible coupling is through mass itself.  So what is the result of something the mass of an electron on a homogenous gravitational wave background?

The mass will distort the background wave pattern.

From this distortion would come some sort of interference pattern. Think of the rubber mat analogy. There would be a dent for the electron in a sea of waves. Would this effect a much much lower frequency effect – de Broglie waves -?

If we take the mass of the particle as m, and the frequency of the background waves as 1.85e43 Hz. Perhaps this gives us the ‘dark energy’, along with quantum guidance rules.



The de Broglie wave is a wave that can be used to predict the quantum behaviour of particles. Its a wavelength that is tied to momentum.

The de Broglie wavelength is the wavelength, λ, associated with a massive particle and is related to its momentum, p, through the Planck constant, h:
\lambda ={\frac {h}{p}}.

This wave seems puzzling. Its tied to momentum, so for an observers travelling with different velocities will measure different de Broglie wavelengths. This is often taken as an indication of the non – reality of these waves. But there is a simple explanation for this – and its based on special relativity.

de Broglie beats and the Compton frequency:

"de Broglie made a second, less well known conjecture. If you combine 
the E=mc2 and the E=hf equations (where f is frequency), you arrive 
at the Compton frequency. de Broglie's conjecture was that the 
Compton frequency reflected, in the case of the electron (quarks 
were not yet discovered), some kind of fundamental intrinsic 
oscillation or circulation of charge associated with the electron. 
However it is now known that this presumed oscillation can also be 
interpreted instead as being externally driven by the zero-point 
fluctuations of the quantum vacuum (see chap. 12 of the monograph 
"The Quantum Dice" by de la Pena and Cetto).

Now comes a very intriguing result. One can easily show that if the 
electron really does oscillate at the Compton frequency in its own rest 
frame, when you view the electron from a moving frame a beat frequency 
becomes superimposed on this oscillation due to a Doppler shift. It turns 
out that this beat frequency proves to be exactly the de Broglie wavelength of a moving electron."

There is still a problem though. The de Broglie relationship holds for any object, experimentally measured up to a Buckyball with hundreds of component particles. Thus the de Broglie wavelength is some effect of mass combined with motion. The only effect that mass has on a purely classical geometric world is the Schwarzschild ‘indent’ on the background space time.

So how can an indent give rise to a beat frequency?

This result may be generalized to include ZPF radiation from all other directions, as
may be found in the monograph of de la Pena and Cetto [5]. They conclude by stating:
“The foregoing discussion assigns a physical meaning to de Broglie’s wave: it is the mod-ulation of the wave formed by the Lorentz-transformed, Doppler-shifted superposition of the whole set of random stationary electromagnetic waves of frequency ωC with which the electron interacts selectively.”

Assume some white noise like stochastic gravitational wave spectrum as a background on that exists everywhere in the universe (as it undoubtedly does, with only the amplitude unknown). What is the result of viewing a truncated Schwarzschild solution moving (say slowly to ease the math at first) through this background?

One would expect lensing of this stochastic field. The field will refract modes that match its characteristic size. This size scales to its mass. First consider a particle at rest with respect to the observer. With the dent this causes in space time we see a time dilation which affects the waves cumulatively, causing an internal Compton frequency – which is a result of the

\nu ={\frac {mc^2}{h}}.

Another solution as explained by Rober Schuler

There is an obvious heuristic, however, which provides the needed frequency sum to a good
approximation. We need only assume that, like Schrödinger waves, de Broglie waves are related to the probability of finding a particle. Let p(A) be the probability of finding A, and p(B) the probability of finding B, and assume these meanings continue to hold if A and B are bound together. One of the interesting aspects of de Broglie’s paper (actually his thesis, which was printed in a journal), is a section treating bound particles where both are considered to be moving. [Ibid. 12] By contrast, when using Schrödinger’s analysis, stationary confinement boundaries and potentials are used (which would be associated with particles, e.g. a stationary nucleus, that have infinite de Broglie wavelength). Since we are only able to find the bound pair AB if we find both A and B, then the probability of finding AB must be p(AB) = p(A)p(B). If “p” is a sinusoidal function, then indeed the product of two such functions reduces by a common trig identity to a term involving the sum of the frequencies of p(A) and p(B), and a term involving their difference. The sum frequency corresponds perfectly to the frequency of the sum of the masses of A and B.
The only problem is what to do with the difference frequency? Wignall’s method was speculative, and we can’t use it anyway because he was not using probability, but complex valued functions. However, as an approximation we can observe two things. First, in the case of common nuclear particles, whether we treat them as hadrons (protons, neutrons), or quarks, the masses are approximately the same and the difference frequencies are therefore approximately zero. Second, in the case of the binding of electrons to a nucleus, the electron mass is to a good approximation negligible. It

Once this relationship is obtained, the de Broglie matter waves are a necessary conclusion, as the literature indicates.

So one is left with the task of showing that any truncated Schwarzschild solution will cause an internal frequency – a mode trap – when its sitting in a stochastic gravitational field.

The next step



Assume standing GR waves (in well defined the universal rest frame). 1.85e43 Hz. Then there is a Schwarzschild solution sitting in that standing wave bath.

Time dilation lapse function sqrt(1- 2M/r) becomes simply 1-M/r unless you are within 1e-30m of an electron. So that is the lapse function. What beat frequency does our planckian background generate ? – The compton frequency. Redshift. – there are

Take equation for z (r -> inf) and mult by the huge planck frequency. You then get the compton frequency. Solve the equation for the radius of the electron and get the planck length. (But this requires that the electron is quite small and that the buckyball is even smaller! – also this calculation is for a monochromatic wave – not a stochastic background).  What about using the width of the

So that is the size of the electron. One planck size will give you a gravitational (blueshift from outside) of the compton electron frequency.


Coulomb Attraction


de Broglie

The proton de Broglie frequency is about the exact same number –  2.3 x 10^23 Hz 

“He asserted that quantum mechanics was intrinsically relativistic and proposed that the pilot wave originates in internal particle oscillations at the Compton frequency, ωc =mc2/h ̄, at which rest mass energy is exchanged with wave energy. He proposed that the guiding wave field evolves according to the Klein-Gordon equation and consists of a monochromatic wave field in the particle’s frame of reference. The de Broglie relation, p = h ̄ k, then relates the particle momentum to the de Broglie wavelength, λdB = 2π/k. Finally, he stressed the importance of the harmony of phases, by which the particle’s internal vibration, seen as that of a clock, stays in phase with its guiding wave (de Broglie 1930, 1987). Thus, according to his conception, the wave and particle maintain a state of resonance.” [reference]

Take a ring of rotating matter.

No matter what frequency it rotates at, there is no General Relativistic waves emanating from it.

Now assume that the matter starts to clump up into two balls. NOW we have GR radiation.

Now run the camera in reverse.

What we have is an object that aggressively reflects (exchanges) GR radiation with other similar objects at the same frequency.

The rings I am talking about are the mass of an electron and very very small.

The classical gravitational radiation of Atoms:*(Gravitational+constant)%2F(45*(speed+of+light)%5E5)*(electron+mass)%5E2*((hydrogen+atom+radius)%5E4)*(compton+frequency)%5E6

Over the course of the lifetime of the universe, the Hydrogen atom releases 8 eV of energy as gravitational waves. So if its in a bath of these waves, then the loss would be much less – virtually zero.

For large atoms one would think that this energy exchange would be bigger. Of course ‘the actual path’ of the electron matters. The base energy level of an electron

Einstein in 1916 when wrote:

“Nevertheless, due to the inner-atomic movement of electrons, atoms would have to radiate not only electro-magnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.”

Why did Einstein worry about something that would effect the lifetime of an atom on time scales of the universe vs the tiny amount of time that a classical hydrogen at radiates EM energy?

Possibility of measuring something here.

  1. Get a lot of heavy atoms in ‘sync’ (NMR?)
  2. Radiating some amount of GR away, perhaps measure that on another bunch of similarly prepared atoms?
  3. ??? likely nothing…?

Also related — ? Thermal gravitational waves. 80 MW from the Sun, from atoms sliding near each other.

Its also easy to see that the resulting model is fully compatible with relativity and GR. Its after all made entirely out of gravity.

Calculation – watts emitted from one mole of uranium atoms (~200 grams of



  1. Use formula for watts emitted by a rod of mass m rotating at a frequency.
  3. So the uranium inner orbit has a velocity of 0.5c and a radius 1/8 that of hydrogen
  5. So we have 7.3e18 Hz and a radiative power of 10^-23 watts

Take this radiated power, and assume that uranium is thus in a bath of GR waves at 10^19  hz, so that it emits on average the same amount that it absorbs, (like SEDs only a lot easier   to imagine).

Experiment: Now take a semi-sphere of uranium and put a test mass in the middle. If its uranium (i.e. tuned to the neighbouring shell) it will feel some force, but if its something with a different material and hence different frequency pattern of gravitational waves, it will not feel the force from the shell. Better experiment: Two massive plates, one uranium or lead, the other with a different material of same mass but different inner orbital frequencies. Then hook up one of those torsion threads to two balls on an arm, one of each material, and look for a rotational force. (Using some with force materials).

Classical Nucleus – nucleus GW interaction.

Iron nucleus – speed of nucleons is (20 MeV kinetic energy) and say one pair is radiating Gravitational waves: r = 1 fm, so

I get about 1e-25 watts or so. (using this) . Model is that nucleons are moving about in the nucleus, and at times have a quadrupole motion, which is on the order of a bar of mass 2 nucleons, spinning about a fm apart at the 10^23 hz of the nucleon rotational period in a fermi gas model nucleus. (Note that the Sivaram and Arun paper about thermal gravitational radiation from neutron stars shows about a billion times less than this.

Taking 1e-25 watts – which is 10e-7 eV/second I can calculate the pressure between two 10kg masses 0.1 metres apart, I get 10^-10 newtons. This is about the right amount of effect to mess up all the newtonian gravitational constant experiments.

Using Pressure = E/c , where E is in Watts/metres^2 and 1e-25 watts per nucleon emitted, assume complete absorption. (not cross section is assumed about the physical size of the nucleon, which is also the gravitational wavelength). Then we get the 10^-10 newtons.

Gravity force between 2 10kg masses at 0.1 apart is 6.7e-7 Newtons.

This force is not the nuclear strong force or the electromagnetic force, (which are stronger) but simply assuming that the nucleus can be treated classically for gravitational waves. The nucleons generate GWs which are can be absorbed by another nucleon of the same kind.

Cavendish Experiment*(Gravitational+constant)%2F(45*(speed+of+light)%5E5)*(electron+mass)%5E2*((hydrogen+atom+radius)%5E4)*(compton+frequency)%5E6*(6.022×10%5E23)


A proton model is presented where a mechanism for charge, electromagnetic and quantum effects are generated from pilot wave phenomena. The pilot waves are constructed from nothing more than gravitational effects. First a simple model of a proton is discussed. The physical consequences of such a model are explored, showing that this model can generate large proton – proton forces, which are then identified with the Coulomb force. Further, quantum mechanical effects are also shown to emerge from this model. Using canonical untuned parameters, the model generates a Coulomb strength force between two protons that is within a factor of 5 of the actual force, thus bridging the 1036 force strength gap that separates gravity vs electromagnetism using only general relativity.


General relativity is often thought of as the smallest force – a perturbation on the quantum field theory that can safely be ignored on the microscopic scales of elementary particles. The most recognized illustration of this ‘fact’ is given by the ratio of the gravitational to Coulomb force between two elementary charged particles. For protons:

R_{(Proton EM/Gravity)} = \frac{k_{e}e^2}{Gm_{p}^2} = 1.236\times10^{36}  

Yet gravity is also in many ways thought of as the strongest force, as for instance when the nuclear strong force keeping a large neutron star from collapsing is overwhelmed by some additional mass and gravity takes over, forming a black hole. Another very recent display of the ultimate strength of general relativity is the observation of gravitational waves from 1.3 billion light years away – the gravitational wave event GW150914. In the GW150914 gravitational wave production zone, the peak energy density of the wave energy was about 15 orders of magnitude stronger than the strongest electromagnetic field possible via the Schwinger limit. General Relativity can dwarf all known fields in strength.

General Relativity – “Einstein’s aether”  – is very stiff and has a huge range of linear behaviour, far outstripping electromagnetism in terms of maximum power it can push through a square metre of space, along with a much larger linear range of behaviour. It has been verified to work over a very large parameter space. Its also inviscid in that it allows objects to pass through it almost unhindered: no one talks about friction in empty space.

With the huge energy densities and extremely large linear range of gravitational wave phenomena, one is led to investigate gravitational waves and interaction strengths of smaller entities such as those that are the mass of the proton and other elementary particles. For a compact gravitational entity of the mass of a proton, one would expect that gravitational waves at a frequency dictated by the size of the entity might come into play.

Proton model:

An proton is modelled as a small region of space which has a varying mass. The origin of this varying mass is energy exchange with other protons (or other charged particles). The mass of the proton is given by the following ansatz:
m_{p}(t) = m_{p}((1 - \alpha) + \alpha sin(\nu t))
where 𝛎 is some frequency, and is the proportion of mass that is varying, so is in the range 0 –> 1. The cause of this varying mass is in this model due to the emission and absorption of large amounts of gravitational wave energy, as in the phenomenon of \alpha  \sim  1 tuned superradiance/absorption. The exact geometric/topological structure of this proton model is not known or modelled, but could be a naked Kerr like ring ‘almost singularity’ undergoing deformations from the gravitational wave background. The singularity in the Kerr solution is known to be unstable – this means that when a ring singularity exists in a natural, noisy environment, that the structure of the singularity is wildly varying, likely negating many of the concerns that led to Hawking and Penrose’s singularity conjecture. One more point on the ring singularity’s innocuous effects is the fact that only a set of geodesics of measure zero will hit (those geodesics coming in on the equator). If one looks at the paper here: you can see that running time backwards – turning figure 1 in that paper upside down.

Coulomb Attraction

First recall that we are dealing only with classical general relativity. Electromagnetic effects are generated using general relativity.

So how would two of these time varying mass protons interact?

Call the two protons A and B, and calculate the force that B feels from A at a distance r apart . Proton A exchanges mass at a rate peaking per cycle

  \frac{ d m_{p}(t) }{ dt }|_{max} = \nu \alpha m_{p}

which at the location of B will represent a mass flow per unit area of ⍺𝛎mp/(4πr2) . Proton B with radius r_p will absorb this mass flow at a rate controlled by its area (the cross section for gravitational wave absorption at a resonant frequency is very high) of (4πrp2)c. This results in a (peak per cycle) force felt by B of:

dp/dt = (4 \pi r_{p}^2) c * \alpha \nu m_{p}/(4  \pi r^2) = \alpha c \nu r_{p}^2  m_{p} / r^2

This force scales with the frequency 𝛎.  Evaluate this equation by equating it with the electromagnetic force for two protons at a distance r, assume that the fraction  = 1/137, and solve for the remaining free parameter – the frequency of the mass exchange effect 𝛎. This gives a frequency that corresponds to about the light travel time across the proton, and is closer still to the nuclear strong force interaction time (~1×1023 Hz).

 \alpha c \nu m_{p} r_{p}^2/r^2 = k_{e}q^2/r^2   =>    \nu =   8 \times  10 ^ {22} \text{Hz}     [calculation]

The force in this simple model as it stands at this point does not (yet) represent a Coulomb force, as this generated force, while large varies between a push and a pull, averaging to zero. The magnitude looks very tantalizing however as this shows that a purely geometric model can produce forces equivalent in magnitude to electrostatic forces. Various pilot wave theories come to mind, such as de Broglie – Bohm Mechanics or even the macroscopic hydrodynamic quantum analog experiments of John W Bush. And yes this means that I think that quantum mechanics and electromagnetism are closely related.

So we assume that there is some mechanism holding the protons in a phase such that the force is purely repulsive. (AKA surfing, John Bush math on walkers, etc)

The de Broglie frequency of the proton

The proton de Broglie frequency is almost the same frequency  as the calculated frequency above which was not used to get the frequency correct for the electromagnetic force. Yet the de Broglie wavelength is a quantum notion, and so should not be related to an electromagnetic field strength effect.

Proton de Broglie frequency =  2.3 x 10^{23} Hz

John W Bush on de Broglie:

“He asserted that quantum mechanics was intrinsically relativistic and proposed that the pilot wave originates in internal particle oscillations at the Compton frequency, \omega _{c} = m c^{2}/{\hbar} , at which rest mass energy is exchanged with wave energy. He proposed that the guiding wave field evolves according to the Klein-Gordon equation and consists of a monochromatic wave field in the particle’s frame of reference. The de Broglie relation, p = \hbar k , then relates the particle momentum to the de Broglie wavelength, \lambda_{dB} = 2\pi/k  . Finally, he stressed the importance of the harmony of phases, by which the particle’s internal vibration, seen as that of a clock, stays in phase with its guiding wave (de Broglie 1930, 1987). Thus, according to his conception, the wave and particle maintain a state of resonance.” [reference]


If the proton is indeed some sort of geometric  object operating in a gravitational superradiant regime, then delicate phase considerations come into play, reminiscent of bouncer – walker systems (and QED).  See for example Bush 2016 for terminology and background.

In the language of bouncer walkers, this system exhibits incredibly high memory (but not infinite!) and thus various QM like effects could emerge from these interactions. The electromagnetic effects are then ‘side effects’ of the gravitational pilot wave interaction.

One is then left with a geometric unification plan where gravitation is the ultimate base interaction with electromagnetic, quantum and other force effects resulting from the small scale interaction of high frequency gravitational waves with the particles that produce and interact with them.

Thus the various forces and QM may be found to emerge from purely classical geometric effects.


Protons made with nothing more than classical general relativity thus exhibit the expected forces of electromagnetism, without introducing a separate electric field. Electrical behaviour is then seen as a phenomena of Gravity, rather than its own field.
These protons also behave according to the laws of QM, all by generating QM effects using pilot wave mechanics.

This I believe shows a possible way to unify Electromagnetism, General Relativity, and Quantum Mechanics.

–Tom Andersen
July 1 , 2016

Addendum: Nov 20 2016.

I am working on a computer program to model a positron – electron hydrogen like system starting with only equation on varying mass, and the laws of motion for the electron – which sees not only the waves from the positron – but also waves from itself – the memory effect. (indeed how would an electron tell waves from itself apart from those of others?). The memory effect is limited for positronium to the volume of space  that an atom takes up. I think that the solution to the non-local Bell’s theorem type of things is retarded and advanced fields – re (Wheeler’s delayed choice or Wheeler Feynman advanced/retarded fields). All or nothing G = T, but T is all GR, so really G = 0. Look at Grossing as well, some math might be handy from him and also John Bush.

See also the boxed quote in – the reference to

kerr ring weith lartge blobs weill rsadiate using eddington blob formula like bar or blob. has to.

ring is unstable . Blobs appear . must radiate . Radiation wil bring back ring so its a feedback processs



Oza, Harris, Rosales & Bush (2014), Pilot-wave dynamics in a rotating frame
MIT site: John W.M. Bush
Is quantum mechanics just a special case of classical mechanics?
Monopole GR waves
Other posts on this site as well..
A few times in Alexander Unzicker’s books he mentions the following coincidence:cmprp ≈ hA quick trip to Wolfram shows  cmprp/h = 0.6 , so the correspondence is quite close. Plancks constant is of course the ‘quantum of action’ – so it should show no relation at all to the lowly proton – as the proton is ‘merely’ a composite particle, its mass or radius should have nothing to do with quantum mechanics. Unzicker’s coincidence will be revisited at the end of this work. In a past 2014 post I discussed an electron model in terms of ‘purely classical GR’. 


Can a sub-quantum medium be provided by General Relativity?

Thomas C Andersen, PhD
As a personal note of celebration, Art McDonald, the director of the Sudbury Neutrino Observatory has won the Nobel Prize in Physics. I worked on SNO for 8 years for my masters and PhD. The Sudbury Neutrino Observatory also shared the Breakthrough prize in Fundamental Physics! The breakthrough prize is awarded to the whole collaboration (26o or so of us). It was a real treat to work on the neutrino observatory.
Screen Shot 2016-07-16 at 2.21.12 PMIn PDF as a paper, or in as a poster I presented at EmQM15 in Vienna, published in IOP physics., Ontario, Canada. (Dated: October 19, 2015)

Emergent Quantum Mechanics (EmQM) seeks to construct quantum mechanical theory and behaviour from classical underpinnings. In some formulations of EmQM a bouncer- walker system is used to describe particle behaviour, known as sub-quantum mechanics. This paper explores the possibility that the field of classical general relativity (GR) could supply a sub-quantum medium for these sub-quantum mechanics. Firstly, I present arguments which show that GR satisfies many of the a priori requirements for a sub-quantum medium. Secondly, some potential obstacles to using GR as the underlying field are noted, for example field strength (isn’t gravity a very weak force?) and spin 2. Thirdly, the ability of dynamical exchange processes to create very strong effective fields is demonstrated through the use of a simple particle model, which solves many of the issues raised in the second section. I conclude that there appears to be enough evidence to pursue this direction of study further, particularly as this line of research also has the possibility to help unify quantum mechanics and general relativity.

The Sub-quantum Medium

In emergent QM the sub-quantum medium is the field out of which quantum behaviour emerges. Most, if not all EmQM theories published to date do not explicitly define the nature of the sub- quantum medium, instead quite reasonably they only assume that some underlying field exists, having some minimum set of required properties, for instance some sort of zero point field interac- tion.

There have of course been investigations into the physical make up of a sub-quantum medium. Perhaps the most investigated possible source is stochastic electrodynamics (SED)[5]. Investigated on and off since the 1960s, SED posits the existence of a noisy isotropic classical radiation field as the zero point field (ZPF). stochastic electrodynamics as a sub-quantum media has many desirable properties. As an example of progress in stochastic electrodynamics Nieuwenhuizen and Liska[12] have recently used computer simulation techniques to build an almost stable hydrogen atom.

Yet classical electrodynamics has a few problems as the sub-quantum medium. Davidson points out that

”A particle in SED gains or loses energy due to interaction with the zero point field. Atoms tend to spontaneously ionize in SED as a consequence. … The spectral absorp- tion and emission lines are too broad in simple calculations published so far to come anywhere close to fitting the myriad of atomic spectral data.”[4].

Other sub-quantum medium proposals include Brady’s compressible inviscid fluid – an entirely new classical field that is posited to underpin quantum mechanics and electromagnetism.[1]

This paper proposes a sub-quantum medium that is already experimentally confirmed and is somewhat surprisingly stronger and more flexible than usually thought – general relativity (GR). Using GR as the sub-quantum medium as presented here assumes only classical GR. Other pro- posals that are similar in some ways are Wheeler’s geons of 1957 – constructed of source free electromagnetic fields and gravity under the laws of standard QM[11] and Hadley’s 4-geons[8]. Hadley’s proposal is perhaps the most similar to that here, but Hadley assumes the independent reality of an electromagnetic field. This paper instead uses only GR as the fundamental field.

General relativity has some qualities that lend itself to consideration as a sub-quantum medium:

1. Frictionless (inviscid):

The movement of objects through empty space is observed to be frictionless, as waves and objects can travel long distances without measurable hindrance. GR’s ether (such that it is) behaves as an inviscid media in its linear regime, allowing for this. Importantly, there is friction in situations such as Kerr hole frame dragging.

2. Covariant: Manifestly so.

3. Non Linear:

This non – linearity allows for a rich variety of behaviour at small scales – a minimally explored, flexible platform to construct particles.

4. Coupling:
General relativity couples to all material, uncharged or charged.

Potential Problems

How can general relativity form a basis for quantum mechanics, given the following: 1. Gravity is weak.

GR is often thought of as a weak force, after all the electromagnetic force between two electrons is some 1042 times that of their gravitational attraction! But for the purposes of a sub-quantum media we are interested in large energy transfers (e.g. Grssing’s[7] thermal ZPE environment), not the weak effects of gravitational at- traction. Instead of 0Hz attraction effects, consider gravitational waves. Looking at optical frequencies (1014Hz), for GR the maximum energy transfer rate be- fore non linear effects start to dominate is tremendously high – about 1065<sup>W/m2. Compare that to electromagnetism, where we have to appeal to something like the Schwinger limit which is only 1030W/m2. Thus GR has plenty of room to host strong effects.

2. Gravity has a weak coupling.

In order to model a quantum system (say a hydrogen atom), we require the quantum forces to be much stronger than the electromagnetic forces. Yet the coupling of gravity to the electron is much weaker than even the electromagnetic force. The solution to this problem lies in realizing that gravity can couple not only through ’0Hz’ effects but also through the exchange of wave energy. The Possible Mechanisms section below outlines how this could happen.

3. Gravity is quadrupole (spin 2).

If we are to also generate EM from GR, we require a spin 1 field to emerge. Emergence is the key – underlying fields can give rise to apparent net fields of different spin. E.g. Monopole gravitational waves[9].

4. Bell’s theorem and hidden variables.

Using GR as the underlying medium to emerge quantum mechanics from would seem to have to satisfy Bell’s inequalities – and thus disagree with current QM theory. Maldacena and Susskind’s EP = EPR paper[10] is an example of a solution to this.

Possible Mechanisms

Here I investigate some consequences of purely classical geometric particle models that are the mass of the electron in a universe where the only field is classical general relativity. The exact micro structure of a particle is not of concern here, instead I look at some tools and building blocks with which to build elementary particles from nothing more than classical GR.

An electron like particle is modelled as a small region of space which has some geometric microstructure that results in a particle with the correct mass and spin. I will point out here that a Kerr solution with the mass and spin of an electron happens to have a (naked) singularity at virtually the Compton radius (1/13 the Compton wavelength).

Whatever the exact microstructure of an elementary particle, there is certainly extensive frame dragging occurring. Frame dragging is the ’handle’ to which gravitational wave energy exchange can grip. As Brito et al. start their comprehensive ’Superradiance’ paper:

”Superradiance is a radiation enhancement process that involves dissipative systems”[3].

Superradiance in GR was introduced by Press and Teukolsky’s 1972 paper Floating Orbits, Super- radiant Scattering and the Black-hole Bomb[13].

This paper posits that EmQM’s sub-quantum ZPF might be a run away superradiance effect (limited by non linear mechanics). Is the universe a black hole bomb?

This superradiant (and highly absorbing – see figure 1) energy exchange of the particle with its surroundings causes the particle to be subjected to huge forces – superradiance for example allows for a substantial fraction of the mass of a rotating black hole to change over time scales a few times the light travel time across the of the hole. The recent paper by East et al. studies black holes undergoing superradiance using a numerical method.[6]. It seems that the superradiance is on a knife edge with absorption – these effects happen at only slightly different frequencies.

While the time scale for a black hole with the mass of an electron is a tiny 10−65s, it seems reasonable to assume that the frequency for superradiance is tied to the distance scales involved in the particles structure, so there could be superradiant effects happing on different timescales. For instance, an effect at 10−65s could be holding the particle together, while the forces of EM and the actions of QM might take place using waves closer to the electron Compton frequency.

Look now at a Compton frequency superradiant process. We have an energy exchange of some fraction of the mass of the electron happening at 1.2×1020Hz. The maximum force an effect like this can produce on an electron mass particle is of order 0.01 Newtons! Forces like this are surely strong enough to control the movement of the electron and phase lock it, giving rise to the sub-quantum force.


FIG. 1: From East[6]: Top: mass change over time, for incident gravitational waves with three different frequencies. ω0M = 0.75 is superradiant, while ω0M = 1 shows complete absorption. Bottom – shows the effect of the wave on the shape of the horizon – so the entire wave packet can be visualized.


There is also a mechanism by which electromagnetic effects can emerge from such energy ex- change. See Brady[2] section 4 for one simple method of calculating an electromagnetic force from mass exchange.


The sub-quantum medium, whatever it is, has to behave so that quantum mechanics can arise from it. I hope that this paper has shown that General relativity covers at least some of the requirements for a sub-quantum medium. In order to fully test this idea, there might likely need to be an actual geometrical model of the electron found. The techniques of numerical general relativity could be the best tool to study these interactions in detail.

If the pursuit of an emergent quantum mechanics is to prove fruitful, then the idea that a field like general relativity does not hold on the microscale may have to be re-considered, as with EmQM there is no overarching ’quantum regime’. With general relativity still on the stage at 10−17m, Occam’s razor perhaps suggests that we prove that general relativity is not the sub-quantum medium before a new field is invented.

  1. [1]  Robert Brady. The irrotational motion of a compressible inviscid fluid. page 8, jan 2013.
  2. [2]  Robert Brady and Ross Anderson. Why bouncing droplets are a pretty good model of quantummechanics. jan 2014.
  3. [3]  Richard Brito, Vitor Cardoso, and Paolo Pani. Superradiance, volume 906 of Lecture Notes in Physics.Springer International Publishing, Cham, jan 2015.
  4. [4]  Mark P. Davidson. Stochastic Models of Quantum Mechanics A Perspective. In AIP ConferenceProceedings, volume 889, pages 106–119. AIP, oct 2007.
  5. [5]  L. de la Pena and A. M. Cetto. Contribution from stochastic electrodynamics to the understanding ofquantum mechanics. page 34, jan 2005.
  6. [6]  William E. East, Fethi M. Ramazanolu, and Frans Pretorius. Black hole superradiance in dynamicalspacetime. Physical Review D, 89(6):061503, mar 2014.
  7. [7]  G. Gr ̈ossing, S. Fussy, J. Mesa Pascasio, and H. Schwabl. Implications of a deeper level explanation ofthe deBroglieBohm version of quantum mechanics. Quantum Studies: Mathematics and Foundations,2(1):133–140, feb 2015.
  8. [8]  Mark J. Hadley. A gravitational explanation for quantum theory non-time-orientable manifolds. InAIP Conference Proceedings, volume 905, pages 146–152. AIP, mar 2007.
  9. [9]  M. Kutschera. Monopole gravitational waves from relativistic fireballs driving gamma-ray bursts.Monthly Notices of the Royal Astronomical Society, 345(1):L1–L5, oct 2003.
  10. [10]  J. Maldacena and L. Susskind. Cool horizons for entangled black holes. Fortschritte der Physik,61(9):781–811, sep 2013.
  11. [11]  CharlesWMisnerandJohnAWheeler.Classicalphysicsasgeometry.AnnalsofPhysics,2(6):525–603,dec 1957.
  12. [12]  TheoM.NieuwenhuizenandMatthewT.P.Liska.SimulationofthehydrogengroundstateinStochasticElectrodynamics. page 20, feb 2015.
  13. [13]  WILLIAM H. PRESS and SAUL A. TEUKOLSKY. Floating Orbits, Superradiant Scattering and theBlack-hole Bomb. Nature, 238(5361):211–212, jul 1972.

The Aether


We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an aether. According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it. [1]


Brady, in the paper “The irrotational motion of a compressible inviscid fluid” hypothesizes something different – that the universe is made of a non – relativistic compressible fluid, and that this fluid generates General Relativity.

Einstein’s inertial medium behaves as a nonrelativistic barotropically compressible inviscid fluid.[2]

Although my model of the electron and quantum effects is very similar to Brady’s, I diverge with him on the essence of the aether. I hypothesize that Brady and Einstein’s ether are the same thing, so that instead of Brady’s concept of generating GR from aether, we instead start with Classical General Relativity (with ‘no matter’, so the stress tensor T = 0), and then  create Sonons as solutions of GR. The aether is that of Einstein’s GR.

Einstein’s Aether in Fluid Dynamics terms

Einstein’s aether is inviscid – which means it has no viscosity (rocks travelling through empty space experience no drag…). Is it compressible? Certainly – this is what constructs such as black holes are. Is it irrotational? – that is a not a property that we need to determine, since without viscosity, an irrotational flow will stay that way.

Truly Inviscid?

No. GR is non-linear, which makes the inviscid property only an approximation – it’s a good approximation, though! Waves generated on an ocean or an oil puddle in a lab travel a limited distance, while the waves of GR can easily travel the universe. But they don’t travel ‘forever’.

Consider now the construction of a Brady like sonon out of pure GR. We follow Brady’s paper until section 1.1, where he states:

When an ordinary vortex is curved into a smoke ring, this force is balanced by Magnus forces (like the lift of an aircraft wing) as the structure moves forward through the fluid [10]. However a sonon cannot experience Magnus forces because it is irrotational, and consequently its radius will shrink, causing the amplitude A in (5) to grow due to the conservation of fluid energy. Nonlinear effects will halt the shrinking before A reaches about 1 since the density cannot become negative.[3] 

Intriguing. Look now at a completely classical general relativistic object – a spinning  Kerr solution. We have a tightly spinning GR object that can shrink no further.  Since we are trying to model an electron here, we use the standard black hole values (for an electron model this is a ‘naked’ a > m Kerr solution [6])

Brady’s sonons interact with the surrounding aether – how would that work in GR? We are after all taught that all GR objects like black holes have no hair. But of course they can have hair, its just that it will not last long. That’s the point here. Sonons can and will stop interacting if the background incoming waves die down below a certain point. But above a certain point black holes become perturbed, and things like ‘superradiance’  as Teukolsky and others discovered come into play.

Indeed, as long as there are incoming waves, it seems that objects made of GR are highly reactive, and not boring at all.[4][5]

So pure GR has at least the ability to interact in interesting ways, but are the numbers there? What frequencies do we need for Brady like Sonons constructed from GR (I’ll call them geons from now on) to get to the point where there are electromagnetic strength interactions are taking place?

Bradys interactions occur with mass transfer – the compressible fluid carries away mass to and from each Sonon in a repeating manner. Not a problem for any GR ‘blob – geon’.  If they interact, then energy must be flowing in and out – that’s the definition of interaction.

An Electron Model

A previous post here – An Electron Model from Gravitational Pilot Waves  outlines the process.

We take a small region of space (e.g.  containing a Kerr solution) and assume that this region of space is exchanging gravitational energy with its surroundings.  Call it an geon-electron.

Assuming that the exchange takes place in a periodic fashion, the mass of this geon-electron (energy contained inside of the small region of space) is given as

me(t) = me*((1 – f) + f*sin(vt))

where v is some frequency, and f is the proportion of mass that is varying, so f is from 0 –> 1.

This varying mass will give rise to changes in the gravitational potential outside the region.  But gravitational effects do not depend on the potential, rather they depend on the rate of change of the potential over spacetime intervals.   So it’s not the potential from this tiny mass that is relevant, it is the time derivative of the potential that matters.

Potential = -G*me(t)/r

Look at the time derivative of the potential

dP/dt = -G*me*f*v*cos(vt)/r

This gradient is what one can think of as the force of gravity. This force rises linearly with the frequency of the mass oscillation.

The EM force is some 10^40 times that of gravity, so we just need to use this factor to figure out an order of magnitude estimate of the frequency of this geon mass exchange rate.

This is detailed in the ‘Coulomb Attraction’ section of an earlier post.

Using de Broglie’s frequency – he considered the Compton value of 1.2356×1020 Hz as the rest frequency of the internal clock of the electron, one arrives at an electron model with these properties:

  • Entirely constructed from classical General Relativity
  • Frequency of mass exchange is the Compton frequency
  • Electromagnetic effects are a result of GR phenomenology
  • Quantum effects such as orbitals and energy levels are a natural result of these geons interacting with their own waves, so QM emerges as a phenomenon too.


Einstein’s Vision:

“I published the paper on the relativistic dynamics of the singular point indeed a long time ago. But the dynamical case still has not been taken care of correctly. I have now come to the point where I believe that results emerge here that deviate from the classical laws of motion. The method has also become clear and certain. If only I would calculate better! . . . It would be wonderful if the accustomed differential equations would lead to quantum mechanics; and I do not regard it as being at all out of the question” (Ref: Miller, 62 years of uncertainty)

The State of Physics today ————————– Obviously a sea change in fundamental physics would be needed to allow for anything like these ideas to be considered. In fact its not that the ideas here might be correct – but rather that Brady and others who toil on actual progress in physics are sidelined by the current ‘complexity is king’ clique that is the physics community today. The physics community is more than it ever has been in the past, a tightly knit clique. This may be the fault of the internet and the lock in group think that instant communication can provide. This clique gives rise to ideas like ‘quantum mechanics is right‘ and other absurdities, such as the millions of hours spent on String Theory, when it’s ‘not even wrong‘.

Tests and Simulations

Given the entrenched frown on the subject of alternative bases for the underpinnings of our physical world, we need to look for experimental evidence to support these kinds of theories.

The work of Yves Couder and his lab in one kind of essential experiment. They have shown conclusively that quantum like behaviour can emerge from classical systems.

Another path – one that in my opinion has been somewhat neglected in this field is that of numerical techniques.

Here I outline some steps that might be taken to construct a GR based model of an electron. Excuse the more colloquial manner, I am making notes for a future project here!

Numerical Plans

There are only about 22 Compton wavelengths within the Bohr radius. So if one goes to a 100 Compton wavelength simulation zone, with 1000 grid points on a side, thats 1e9 grid points, and each point needs only four 8 byte doubles, so 32 bytes, so 32 GB.

The equations to solve on this simple grid are those of fluid dynamics: Compressible Isothermal Inviscid  Euler equations.  : As from I do like CFD.

Screen Shot 2014-07-14 at 10.08.23 PM


With a 32GB data set, 1e9 data points, and about 1000 computer FLOPs per visit, we have 1e12 FLOPs per time step, and an algorithm that gets 10GFlops, I get about a minute per time step.  Each time step needs to cover about 1/100th of the Compton time, or about 1e-22 secs, and we need to let light cross the atom (3e-19 secs) hundred times to get things to converge, or about 3e-17secs, so 300,000 time steps. (Better speed up the algorithm! Should be easy to get 20GFlops over 8 processors, and perhaps cut Flops/grid point down, which could mean a day or so on a 8 core Intel).

Computer Model:

Note on the Fine Structure Constant (useful in a numerical model)

The quantity  was introduced into physics by A. Sommerfeld in 1916 and in the past has often been referred to as the Sommerfeld fine-structure constant. In order to explain the observed splitting or fine structure of the energy levels of the hydrogen atom, Sommerfeld extended the Bohr theory to include elliptical orbits and the relativistic dependence of mass on velocity. The quantity , which is equal to the ratio v1/c where v1 is the velocity of the electron in the first circular Bohr orbit and cis the speed of light in vacuum, appeared naturally in Sommerfeld’s analysis and determined the size of the splitting or fine-structure of the hydrogenic spectral lines. [*]

See also the Wikipedia physical interpretation section.


Compton Frequency Mass Exchange…

de Broglie

His original conception, his “double-solution theory” (de Broglie 1956), involved two waves, a real pilot wave centered on the particle and the statistical wave predicted by standard quantum theory. He asserted that quantum mechanics was intrinsically relativistic and proposed that the pilot wave originates in internal particle oscillations at the Compton frequency , ωc =mc2/h at which rest mass energy is exchanged with wave energy. He proposed that the guiding wave field evolves according to the Klein-Gordon equation and consists of a monochromatic wave field in the particle’s frame...[Bush 2015]



“De Broglie’s law of motion for particles is very simple. At any time, the momentum is perpendicular to the wave crests (or lines of constant phase), and is proportionally larger if the wave crests are closer together. Mathematically, the momentum of a particle is given by the gradient (with respect to that particle’s co-ordinates) of the phase of the total wavefunction. This is a law of motion for velocity, quite unlike Newton’s law of motion for acceleration. “ –

Antony Valentini, Beyond the Quantum

So are the GR constructs that I espouse in these posts able to naturally create such an effect?

We have monopole waves….


I start with a screen grab from the video below. Yves Couder and friends are clearly looking at hidden variable theories:

Screen Shot 2014-03-10 at 8.40.20 AM

Screen Shot 2014-03-09 at 6.46.17 PM

Here is a 3 minute movie with the above slide:

The pilot-wave dynamics of walking droplets

Here is a paper about eigenstates, etc… Self-organization into quantized eigenstates of a classical wave driven particle  (Stéphane Perrard1, Matthieu Labousse, Marc Miskin, Emmanuel Fort, and Yves Couder).

Compare that with my hastily written post.

See also (pointed out by  Warren Huelsnitz) :

 “Why bouncing droplets are a pretty good model of quantum mechanics

Yves Couder . Explains Wave/Particle Duality via Silicon Drop

“Couder could not believe what he was seeing”.

Here it was sort of a eureka moment at home on a Sunday afternoon.

Here is a link to the whole show.(45 mins)


Valentini (along with me) thinks that QM is wrong, in that its not the ‘final layer’. His de Broglie arguments are powerful and hit close to home for me. I have read most of David Bohm’s papers and books since discovering him as a 4th year undergrad back in the 80s. Bohm’s ideas launched mine. Note that much of physics is built on the assumption that with QM somehow ‘this time its different’ – that any future theory will need to be QM compliant or it is wrong. As if QM was somehow as certain as the (mathematical and hence solid) 2nd Law or something. This leaves no room for argument or dissent. Perfect conditions for a paradigm change!


This is the presentation that outlines things as he sees them. I see things that way too, although I am of the opinion that the pilot waves are GR ripples.

Is Quantum Mechanics Tried, True, wildly Successful, and Wrong?

Quantum Theory at the Crossroads
Reconsidering the 1927 Solvay Conference

A relaxing read:

Not even wrong. Why does nobody like pilot-wave theory?

“De Broglie’s law of motion for particles is very simple. At any time, the momentum is perpendicular to the wave crests (or lines of constant phase), and is proportionally larger if the wave crests are closer together. Mathematically, the momentum of a particle is given by the gradient (with respect to that particle’s co-ordinates) of the phase of the total wavefunction. This is a law of motion for velocity, quite unlike Newton’s law of motion for acceleration. “

Antony Valentini, Beyond the Quantum

Take a ring of some material (in my thinking its likely a construct of some compact gravitational solution, like a Kerr singularity with a >> m).

This ring is rotating a some huge speed, with a frequency of nu_e.

Along comes an incident regular gravitational wave, with the roughly same frequency as the rotation of the structure, nu_w ~ nu_e.

What will happen?

Look at what happens with the ring (which is assumed at least somewhat pliable and soft), is not spinning.

The gravity wave simply interacts with it causing a change in its shape from circular to an ellipse.


Make the ring a spinning entity, – (so that the dots above are rotating) and what happens: The ring becomes an emitter of gravitational radiation – it scatters the incoming waves.

Why – well its easy to imagine that the ring has some properties like tension and stiffness, due to rotation. Then as the ring is turning  its shape shifting will turn with the ring, making a new gravitational emitter. In other words the ring gets deformed, rotates to a new position, and then un-deforms – radiating the gravitational energy it has stored.

With systems like this in the normal world, we know that when the frequencies of the spinning object is comparable to the frequency of the incoming radiation, we get resonant tuning – the ring will maximally scatter incoming radiation.

What are the numbers?

Looking at energy radiated, need to start over again, but

10-60 watts. Is that enough for an electron?*G**4%2F%28c**5%29%29%2F%28planck+length%29**5*%28%28electron+mass%29**5%29

Electrons exist as small black hole – like things which turn on and off at huge frequencies, and Birchoffs theorem is used to create electrostatics (indeed electrodynamics) using nothing but monopole gravitational waves. (see previous post).

So there exists a field of vibrating humps of gravitational potential (a.k.a dark energy or dark matter?) that fills space. It is at rest in the universe, and forms a frame of reference – not really an ether, as relativity still works fine. More like the cosmic microwave background.

Protons are different
So electrons repulse each other. How do protons work?. They are massive, 2000 times heavier, and have a known size of about a fm (10-15 meters).

So given this hilly landscape of varying potential, is there any other way to get purchase? In other words how do you do what an electron does given that huge radius and 2000 times the mass?

The frequency of the field can be approximated in the following way:

Involve the two constants ‘G’ and ‘Q’. You get a frequency along the lines of 1065 Hz

for two electrons separated by d:

me2G/(2d2)*K = Q2/(4*pi*E*d2),

where we know that K – the ratio of gravity to electric force on electrons is about 8.3×1042. K is unitless. suppose K is actually w*r/c, where r is some nuclear radius. With an radius r of about a fm, we get a frequency of 1065 Hz. Another way to think of this is that the light travel time across a black hole the mass of an electron is also 10-65 seconds.

This huge frequency implies a wavelength of a tiny 10-57 meters. So in the diameter of a proton, we have 1042 waves. There are an incredible number of these waves boiling inside the proton.

The proton needs to ‘latch’ onto these waves, with the same force as an electron, but it does it in a completely different manner – it uses not a disappearing act, but some mechanism that keeps the mass elements of the proton preferentially in the wells – which has the same effect as the electron’s disappearing act, but much harder to achieve, and thus requires 2000 times the mass. In fact the proton only has to do things 1/2000 as well as an electron per unit mass – so the effect can be quite weak, (e.g. hit 2001 times and miss 2000 times).

So the proton uses a factory technique, where all the parts (how many.?) move around so as to be in the right place at the right time, slightly more often than not.

Why is the charge so balanced then? A question for another day.

Thought experiment, that is…

Take a gravitational well created by any object. Simple Schwarzschild solution. There is a test particle at some distance r away from the source.

Now imagine that the source disappears. Really just ‘goes away’ – violating the conservation of stuff. (The source mass of course could be going away for a temporary time,  quantum – style, or could be using a wormhole device to disappear – I’m not concerned here with the how or why this would happen).

The source disappears over a short time. (This would create a monopole gravitational wave).

There are two potential energies for the test mass – the potential energy when its in the well, and then the potential energy when the well is gone. The difference is of course just G*MsMt/r. During the disappearance of Ms (source mass) the total energy of the test particle would remain the same, so the kinetic energy of the test particle would rise as the PE tended to zero.

So that’s 1/2MtV2 = GMsMt/r

V = sqrt(2GMs/r) – the escape velocity – makes perfect sense. (it would be towards the place where Ms was, but everything here is talked about in such a short period of time that the test particle never gets to move much)…

So now, imagine that the source mass (Ms) appears again. If you left everything else alone, the test particle would of course slow back down and again be parked stationary in the potential well.

So lets change that. Say, in this world of disappearing masses, that now, in an act of symmetry, the test particle has taken its turn and has now ‘gone away’ during the re-inflation of Ms. So now you have Ms back, and the test particle magically appears in the well. Lets not worry about the energy needed to get back into the potential at this point.

Of course, now we are back at the initial conditions, and we repeat:

  • Ms – disappears.
  • Mt has a KE boost of the escape velocity.
  • So Mt is getting a KE boost of the escape velocity at each cycle.

In fact, repeat the whole process at about 1065 hz. (see this post for a calculation of this frequency) (2014 edit – Perhaps this frequency is way off… see May 2014).

Then you have the capability to produce an acceleration of 1042 TIMES the normal classical gravitational acceleration on an object. Take Ms and Mt to both be the mass of the lightest charged particle, the electron. In the example above, I guess one of the particles is a positron since there is a net attraction. Attraction vs repulsion is a phase thing here. If both particles disappear and re-appear at the same time (well with speed of light taken into account between them), then you would have repulsion.

This is the source of the electric charge: the Coulomb field is a consequence of Gravity – a phenomenon, not a fundamental field.

Obviously not a complete model at this point!

Here are some nice things about this:

  • Obviously covariant, GR friendly (as long as you can stomach the varying mass thing).
  • If correct, things like the Maxwell equations should drop out. That would be a telling feature.
  • It forms a way to unify gravity with the other forces of nature.
  • It does not use the well worn QFT as a starting point, which has never really amounted to much.
Maxwell Equations
We now have a coulomb strength field with repulsion and attraction (caused by different phase locking). This is set in a covariant GR framework. Maxwells equations can be determined from Coulomb’s law and Special Relativity : see for example this paper by Richard E Haskell.
  • Why the phase lock?
  • What about QED and its exact predictions?
  • What is the mechanism that controls the mass swings?
  • What about the ‘other’ properties of the electron – the gyromagnetic ratio, etc.
  • Can this model be used for nuclear forces as well?
  • What about quantum effects? Can time and energy be used at these scales?
Hints to answers:
  • Perhaps phase lock is the wrong way to think about the interaction, and something more like QED provides a better way to think about repulsion vs attraction, etc.
  • QED is modeled with the exchange of precisely timed phase clocks – the physical model of this may be the pulse exchanges outlined above.
  • General Relativity does not tell us how space is connected. It may not be simply connected.
  • The gyromagnetic ratio of the electron can be found to be 2 from several papers on gravitational models of the electron – those papers assume a classical model for charge, but still may hold. The extremely high frequency of this effect means that on a scale of even femtoseconds we have 1028 oscillations – likely can ignore many effects, and again treat the electon as if it has a classical charge.
  • Nuclear forces may be a result of real, actual,  particles interacting at distances close enough that non – linear effects and the full theory of General Relativity need to be taken into account. Perhaps get numerical relativists to work on this.
  • Quantum mechanics may be a phenomenon of a multiply connected GR universe, with all the fast clocks and wormhole like behaviour providing enough room to create a (now extant) hidden variables theory of QM.
  • Perhaps the Proton participates in this dance with a much more complicated set of machinery – and is – say not multiply connected, or has a different structure, etc.
Obviously a big pill to swallow. But it does head down the road to integrating the forces of nature.
Tom Andersen
Meaford, On Canada
October 16, 2011 (with personal notes from 1995 – 2011)

I will show with a few simple equations how it could be that electrons and electromagnetic theory can be constructed from GR alone.

1) The electron is some sort of GR knot, wormhole or other ‘thing’, which has one property – its mass is moving from 0 to 2*me in a wave pattern. Well actually, the mass does not have to all b oscillating, it only changes the math slightly.

2) Due to the birkhoff theorem, the gravitational potential at any time is given by the amount of mass inside a certain radius.

3) Due to 2) above, we can use the simple gravitational formula to describe the potential.

\Phi(r,t)=2\frac{m_eG}{r}sin(\omega t)

This potential exerts a force that depends on the frequency of the varying mass, taking the derivative to get the slope of the potential holding r steady:

\frac{\partial}{\partial t}\Phi(r,t)=2\omega\frac{m_eG}{r}cos(\omega t)

With the mass changing, we have monopole graviational waves emanating (and incoming, since the universe is not empty), from such a structure.

The big assumption here is of course the varying mass of the electron. Where does the mass go? The obvious answer is through some sort of wormhole, so perhaps there is another electron somewhere else with the opposite phase of mass. Shades of the Pauli exclusion principle.

There are lots of places on the internet where one can find electron models where the the electron is modeled on some standing wave, which is what this really amounts to, since electrons would have a huge force on them if the incoming and outgoing are not balanced.

According to the accepted theories of physics, this question is not in good taste. An electron is described by charge, mass, and a few other parameters. But there are no ‘whys’. Why do electrons have a charge of 1? or a mass of 0.511 MeV? No one knows. Most physicists will not think or worry about this.

There are lots of theories about electron substructure out there. Here is mine.

The electron is a knot, pattern, or whirligig built of ‘standard general relativity’.

How could this possibly work? I really don’t have all the answers – or even all the questions yet, but there are some details that I want to share.

Basically, an electron is a construction of GR, where (here is the leap of faith part) the mass of the electron varies in an even sine wave cycle at an enormous frequency – 10^60 Hz or so. This ‘varying mass’ creates monopole gravitational radiation. The net effect is that there are forces between neighbouring electrons that scale in strength with the frequency of this pulsating mass.

Example Detail
So how could something like charge be generated by classical general relativity? Gravity is 10^42 or some factor like that weaker than the electrostatic force. It turns out to be not all that hard to accomplish, at least in broad strokes. Basically the frequency of the varying mass creates via the slope of the gravitational potential, a net force on any neighbouring similar structure that also has a varying mass.

General Thesis?

First this: General Relativity alone is sufficient to create a pretty complex interacting world of ‘stuff’. I guess almost anyone would agree with this statement, as a fictional universe built of rotating, coalescing black holes has plenty of interaction, energy exchange, and other qualities. But it is not this world.

My theory, however strange it may sound is exactly that -we are living in a world described only by GR. All the interactions, fields, quantum phenomena and the rest can ultimately be described via plain old General Relativity. Plain except for the massively interconnected topology.

This is not an ‘end of physics’ argument, for if my theory is ‘true’ all I think it means is that we have found a new problem set – GR is not easily solvable, linear or predictable. In other words, a GR – only universe can be ‘almost anything’ according to the math – it may mean that new theories as important and different from the ‘base GR’ will be needed. Example: Cartesian – Newtonian space is the base for theories such as Newtonian Gravity, thermodynamics, etc. Common belief is that these theories are constructed using a Euclidian coordinate system as only a ‘part’ of the theory – it is my belief that, for instance, Newton’s Gravity does not so much use cartesian coordinates, as it is cartesian theory.