Archives For Particle Structure

Particles have structure. I think its all geometry.

The Tully-Fisher relation (aka Baryonic TFR) is remarkable. As the diagram below shows, the relationship between Vand the baryonic mass of galaxies is just too finely tuned to be caused by dark matter. Something is up. Vis the stellar orbit velocity in the galactic halo. For more details see the paper by Lelli, McGaugh and Schombert .

Screen Shot 2018-02-24 at 5.34.29 PM

MOND (MOdified Newtonian Dynamics) is one explanation for the Tully-Fisher relation. It posits that the force towards the centre of a galaxy at large distances is not simply that of Newton, but is modified with the a0 of  1.2×10-10m/s2 in all galaxies in addition to the usual force predicted by standard Newton or General Relativity’s gravity. LCDM Dark matter is a clumsy explanation for the BTFR, as it needs fine tuning for every galaxy (or every galaxy type) in order to make that straight line be so, well, straight.

There is another way to generate an inward acceleration.

We need a force on each nucleon that changes with how much matter is inside the radius where the particle is. It somehow ‘knows’ the gravitational potential at R, and has a force that depends on that!

What I have so far on this is something to do with dark energy being more concentrated in galaxy cores, so the particle feels this dark energy slope and responds to it.

NOTE: This needs to include a dependence on the enclosed M (ie enclosed Dark Energy inside R).  I call this emission based acceleration ‘Anomalous radial nucleonic radiation’  (ARNR). MOND tells us that particles in the galactic halo can ‘weigh’ the galaxy. They have that information. So there must/might be something like dark energy concentrated in the galaxy and the particles react to this, pushing radiation outward and reacting inward. Note in the galactic core the divergence of the DE is 0 – so no extra force on the particle in the middle of the galaxy.

It might seem strange to have this concerted outward radiation pattern though! Here are some possible explanations for an outward constant radiation by the halo constituents.

    • I’m a fan of super high (nuclear and above) frequency gravitational wave (HFGW) emission/absorption in atoms and nuclei. So we might have some sort of stimulated emission from nucleons based on the outward flow of HFGW out of a galaxy.
    • Dark Energy has a value of about 1GeV/m3 . If this energy is concentrated by the galactic core, then maybe some the nucleon has a force toward the centre of the galaxy in response to the divergence of the DE field.  (i.e. lower radiation resistance in the outward direction). This Dark Energy may be some new field, (or HFGW).
    • Some other mechanism. We don’t have to know the mechanism to predict some consequences.

People don’t generally like the MOND theories because general relativity (GR) in its usual form is so well tested and accurate. LCDM is disliked by many because of the fine-tuning required in order to get everything to match observations.  ‘Anomalous radial nucleonic radiation’  (ARNR) allows GR to exist as is.

Consequences of ARNR

If nuclei really do radiate continuously, (perhaps in violation of quantum – mechanics) then there will be experimental consequences. These consequences may be largely hidden from earth-based experiments, as the emission would be isotropic and take place in some field (such as gravitational waves)  that is hard to detect with current instruments.

There may be other places where cosmological or galactic cluster observations might note this energy output.

In other posts, I have wondered if dark matter is ‘sleeping regular matter‘ and I still think that it may be a viable option, but it seems like any explanation in terms of dark matter may need to be fine-tuned to match observations.

Also, see:





(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 

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.


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)









Proton model:


Coulomb Attraction


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









The de Broglie frequency of the proton



John W Bush on de Broglie:










–Tom Andersen
July 1 , 2016

Addendum: Nov 20 2016.


See also the boxed quote in – the reference to





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..


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.

Lets look at an early universe model made entirely of classical General Relativity. Multiply connected, very lumpy, with energy across huge bandwidths.

Lots of energy – some 10^80 nucleons worth, all in some region with small finite volume. How would this smooth itself out as time evolves?

Are fundamental particles at their core an echo of the conditions at the big bang? In other words the density of energy in g/cm^3 of the core of an electron is perhaps the same energy density at which electrons were formed.

Crazy thought:

I think that electrons are much much smaller than quarks, and as such formed earlier in the big bang.  This was the start of inflation. The universe consisted of electrons + other chaotic GR mess. So we have incredible expansion as the electrons repel each other ferociously.

Then as time passed, and the universe approached the meter size, quarks and nucleons organized to quench the repulsion.

According to the standard model of inflation, (see below) that means that electrons are about 10^-77 m across while quarks are larger, more like 10^-27 meter.  (not sure I did the math right?)

So inflation is a phenomenon of the creation of charge in the Universe.

Reading a little on this – its at odds with the current theory (no doubt !) – in that the current theory has inflation coming when the strong nuclear force is separating out. But perhaps that’s another way to look at it – there are no forces other than random chaotic ones, and electrons give quarks a reason to be created – to soak up the energy of ( or  quench)  the inflation.



– electrons and quarks apply brakes to inflation as they condense.

-cosmological constant is bound up spring like effect of noisy GR wave energy piled to the limit of curvature. Once we start to drop density, density drops faster and faster as GR is non linear, so there is less to keep it together. This is the origin of the cosmological constant, which powers inflation:


This steady-state exponentially expanding spacetime is called a de Sitter space, and to sustain it there must be a cosmological constant, a vacuum energy proportional to \Lambda everywhere. In this case, the equation of state is \! p=-\rho. The physical conditions from one moment to the next are stable: the rate of expansion, called the Hubble parameter, is nearly constant, and the scale factor of the Universe is proportional to e^{Ht}. Inflation is often called a period of accelerated expansion because the distance between two fixed observers is increasing exponentially (i.e. at an accelerating rate as they move apart), while \Lambda can stay approximately constant (see deceleration parameter).


The basic process of inflation consists of three steps:
  3. This action generated a repulsive force that drove the portion of the Universe that is observable to us today to expand from approximately 10−50 metres in radius at 10−35 seconds to almost 1 metre in radius at 10−34 seconds.

Koide and Compton

The Koide formula is a remarkable equation relating the masses of the 3 leptons. When it was first written down, it did not in fact predict the mass of the tau to within experimental error. Turns out though that the experiments were wrong. A decade or two passed: it turns out that the Koide formula is extremely accurate.

The Koide formula has been compared to Descartes theory of circles: One can see that the two relationships bear a resemblance. Jerzy Kocik, in his paper called “The Koide Lepton Mass Formula and Geometry of Circles” uses this correspondence to determine that the Koide formula looks like a generalization of Descartes Circle equation – with a characteristic angle of about 48 degrees.

Kocik's generalization of Descartes' circle formula

If one uses this formula, then the radius of the electron is actually the biggest, and tau smallest, (with a further particle having no or almost no mass…-  ν  ?).

Large electron a result of this. We have Radius proportional to 1/mass.

So are there any physical models that work well with the lightweight electron being large?

The Koide Lepton Mass Formula and Geometry of Circles

Koide – 2012 geometry paper – uses inverse mass as Descartes curvatures, so electron bigger than muon.

Gravity vs. Quantum theory: Is electron really pointlike?

Alexander Burinskii  – posits these same radii for the electron, muon and tau, using the Kerr Neumann formula r = J/m = hbar/2m. Note that I would use only the Kerr formula (same answer for large a)

Implies huge electron, but as Burinski points out, this might not be the size we see when accelerated, etc.

So if the Koide formula is real, then it describes some relationship between the areas (using the geometry paper) where they overlap at some 48 degree angle (look at diagrams).

The naked kerr solution describes a wormhole like situation, so we could get the mass oscillation that I am looking for.

Also – is a kerr solution with a so high really a naked singularity. The ring would look like a straight line (use cylindrical coordinates) – like a line of sharwshild solutions moving in space – would this make an horizon again? (I am thinking of a tubular horizon…)

1112.0225.pdf (burininski)



Electron model:






I said that the mechanism for this time – varying mass will not be discussed, but here are two possibilities. One possibility is that electrons are some sort of wormhole, with some portion of their mass disappearing into and out  of this wormhole, like some mass bouncing between two open throats. The other more simple way this could happen is if the electron was simply losing mass off to infinity – and getting it back – in a periodic fashion.

Coulomb Attraction

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


Please open up that paper and have a look:


Screen Shot 2014-05-17 at 11.48.22 AM




me == rest mass of electron,


ν = frequncy (greek nu).










ν = 1.5×10^25 Hz 







Quantum Mechanical Behaviour



Pilot wave behaviour is outlined in the Brady and Anderson paper.




From the Brady and Anderson conclusion:









See also
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..

–Tom Andersen

May 17,  2014



So can one construct a machine that behaves like a dipole?

Take a canonical dipole. Two radio antennas, both vertical, one transmitting, the other receiving. The question then is, can we make a mass (or more likely a Rube Goldberg system of masses) bob up and down by the action of another mass-system moving at some distance away? if we can, then we have constructed a ‘spin one’ field from gravity, in much the same way that one can build something that is more than its parts.

The underlying field would of course be spin 2, but the field interpreted from the motions of our mass systems would look like a covariant, fully geometric compliant spin 1 field. It would in fact be a spin 1 covariant field.

Contraptions and questions come to mind right away. How do normal gravitational waves radiate as the eccentricity of an orbit approaches 1? What about a similar structure but with say a small particle orbiting a slender rod along the long axis. Not looking for stable orbits here at all. Just a mechanism to transfer a dipole motion across empty space to another construction of masses.

It seems more than possible that such an arrangement exists.



I read this paper today like a breath of air.



From Intrinsic Charges and the Strong Force by Bo Lehnert


Have a look at the image on the right. We see a ‘strong’ force holding these particles apart.

Could this be an actual model for real particles? I don’t think that the author of the paper intends for this model to be taken literally, but it certainly has some obviously interesting properties. Intrinsic Charges and the Strong Force.


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…





So that’s 1/2MtV2 = GMsMt/r





  • Ms – disappears.
  • Mt has a KE boost of the escape velocity.




Obviously not a complete model at this point!

Here are some nice things about this:

Maxwell Equations
  • Why the phase lock?
  • What about QED and its exact predictions?
  • What is the mechanism that controls the mass swings?
  • Can this model be used for nuclear forces as well?
Hints to answers:
Tom Andersen
Meaford, On Canada


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.