In this two page paper, I look at how the relationship between the dimensions of a Kerr singularity and the strength of the electric Coulomb effect compare.

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Posts that can go on the front page.

#### Dark Matter – cuspy core problem.

Proposed solution is that dark matter wakes up, turns into matter and then self repels/forms stars, etc.This means no cusp is found.

Note how in the most tenuous gas clouds (well cold ones – the hot tenuous galactic halo does not count as its a supernova effect), the density is the exact same as the dark matter density?

From https://arxiv.org/pdf/1404.1938.pdf – note how dark matter is about about 0.2 protons per cm^3 (BR 13 measurement) . One would think that in the disk of the milky way, this close to the galactic core that the DM density is about as large as it gets. Which seems right:

The Dark Matter Halo of the Milky Way, AD 2013 – https://arxiv.org/pdf/1304.5127v2.pdf

We find that the cored profile is the preferred one, with a shallow central density of ρH ∼ 4 × 107M⊙/kpc3 and a large core radius RH ∼ 10kpc, as observed in external spirals and in agreement with the mass model underlying the Universal Rotation Curve of spirals.

From wikipedia https://en.wikipedia.org/wiki/Interstellar_medium

Note how the lowest density clouds are 0.2 – 0.5 protons/cm^3

**Why is this the same density?** Answer: The dark matter has a maximum density, if density gets higher it lights up and turns into protons/electrons/H – which results in WIM and WNM clouds. **Dark matter might be sleeping matter.**

#### There is a problem – what heats the Warm Ionized Medium?

Journal, T. A. (2000). EVIDENCE FOR AN ADDITIONAL HEAT SOURCE IN THE WARM IONIZED MEDIUM OF GALAXIES, (Rand 1998), 1997–2000.

Dark Matter waking up might naturally result in WIM over WNM.

Also see https://gravityphysics.com/2013/10/20/how-to-make-dark-matter/

–Tom

Read the following with the these two thoughts in your head first:

a) Quantum Mechanics emerges from General Relativity.

b) The Cosmic Censorship Conjecture is wrong.

Since the physical behavior of singularities is unknown, if singularities can be observed from the rest of spacetime, causality may break down, and physics may lose its predictive power. The issue cannot be avoided, since according to the Penrose-Hawking singularity theorems, singularities are inevitable in physically reasonable situations. Still, in the absence of naked singularities, the universe, as described by the general theory of relativity, is deterministic^{[1]}—it is possible to predict the entire evolution of the universe (possibly excluding some finite regions of space hidden inside event horizons of singularities), knowing only its condition at a certain moment of time (more precisely, everywhere on a spacelike three-dimensional hypersurface, called the Cauchy surface). Failure of the cosmic censorship hypothesis leads to the failure of determinism, because it is yet impossible to predict the behavior of spacetime in the causal future of a singularity. Cosmic censorship is not merely a problem of formal interest; some form of it is assumed whenever black hole event horizons are mentioned.

The above description is more or less the way that its viewed today.

If like me, you think that Cosmic Censorship is false, then the above reads as to how fundamentally acausal – ‘truly random’ events can emerge from a purely geometric universe. This does not sound like a catastrophe at all. It sounds like nature.

The Kerr solution plainly admits a > m . The number of papers trying to figure out how a > m cannot exist far surpasses the ones that simply explore the consequences of a > m naked singularities. These over spinning Kerr singularities are in fact fairly benign it turns out as they are impossible to hit unless one shoots a test particle along the exact equator – a set of measure zero. (Carter 1968).

Many of the papers concerning the non existence of a > m use a thought experiment along the lines of ‘starting with a ~= m, toss in a rock so that it looks like a > m will be the result’. They then go to great lengths to show that back reaction, etc will keep a <= m. That misses the point. There are also ways to construct a naked Kerr ring using wholistic methods like collapsing rings of matter, or colliding gravitational waves. Thus a > m can happen. See https://arxiv.org/abs/1509.05174 for example.

Get over it. Kerr spinning a > m solutions likely exist in nature.

#### Abstract

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 10^{36} force strength gap that separates gravity vs electromagnetism using only general relativity.

#### Introduction

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:

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:

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 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: https://arxiv.org/pdf/1509.05174.pdf 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

which at the location of B will represent a mass flow per unit area of *⍺𝛎m _{p}/(4πr^{2})* . Proton B with radius 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

*(4πr*. This results in a (peak per cycle) force felt by B of:

_{p}^{2})cThis 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 (~1×10^{23} Hz).

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 =

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, , 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, , then relates the particle momentum to the de Broglie wavelength, . 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]

#### Discussion

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.

#### Conclusion

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 https://gravityphysics.com/2016/07/25/the-physics-behind-de-broglie-waves/ – the reference to http://www.calphysics.org/mass.html

https://arxiv.org/abs/gr-qc/9906084

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

#### Appendix

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:

*cm*A quick trip to Wolfram shows cm

_{p}r_{p}≈ h_{p}r

_{p}/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’.

A couple of months ago I read Jim Baggot’s Farwell to Reality. I was very impressed. I won’t go into details, but the book takes the eminently reasonable suggestion that 11 dimensions, uncountable infinities of universes and other mainstream theoretical physics subjects are “fairy tale physics”. Physics really needs people like Jim Baggot, Peter Woit, and Lee Smolin to show that the emperor has no clothes. But what if things are far worse than these authors report?

So I went looking for other writing critical of modern physics. Did I find it. I read two of Alexander Unzicker’s books. The Higgs Fake and Bankrupting Physics. They are a great read, whether you agree with him or not(caution – unintended hilarity). As if to underline the mindset of the physics community at large, after writing these two books Unzicker had trouble with arXiv, and has several more stories about the negative reaction of this closely knit society to outside criticism. One fact about criticism is that people get most upset when the criticism strikes close to the truth. Peter Woit’s criticism of Bankrupting Physics revolves around trying to classify Unzicker as ‘a garden-variety crank’ – which of course then makes Woit’s job easy as it automatically discounts everything he says (unless he is in agreement with Woit of course). My take is simpler: Woit’s book and blog regularly complains about string theory and the multiverse being bunk, which in my opinion is something like 99.9999% likely to be true, while Unzicker’s assertions are ‘only’ 10 – 99.9999% likely to be true. Contrast that with the 50,000 papers on supersymmetry – each one of which is a 100% waste of time according to both Woit and Unzicker. Peter Woit can be wrong too. There *are* other areas of physics that smell as bad as String Theory.

Physics is broken. Worse than we think.

# Eureka!

The Ligo measurement is the greatest thing to happen in Physics and Astronomy for decades. Amazing work. It was about 50 years ago that the first gravitational wave detector was built by Weber. It took 50 years of refinement, many PhDs postdocs and full careers, but the LIGO team did. it.

I will assume that you have already read the paper and other popular sources on this observation, so I will jump into what excites me about this observation:

### The enormous gravitational wave energy emitted.

How much energy? Three solar masses worth of gravitational waves were emitted over just a few tenths of a second. The paper reports a peak gravitational energy emission of 200 solar masses per second! See the paper for errors on this estimate but its accurate to within 20%. The really amazing thing though is that this emission took place from a region only about 200 km across. The frequency of the waves at peak emission is (from the paper fig 1 – bottom row) 120 Hz or so.

Lets look at that amount of energy in terms of another form of energy that we are more comfortable with – electromagnetic waves – light. I want to compare this to the “Schwinger limit” – which is the maximum electromagnetic field that can occur before quantum pair creation effects take over. The Schwinger limit controls the maximum power that a region of space can transmit through itself (via opposing overlapping lasers say).

Say we had standing radio waves at 120Hz in a 200km on a side box, how much power could such an area radiate if it were only limited by the Schwinger limit? (i.e. ignore the mechanism by which such spectacular amounts of energy could be turned into radio waves).

The formula for energy density given an electric wave is quite simple: See for instance this hyper physics page:

Total Energy density = ε*E^{2} So at the Schwinger limit of 1.3×10^{18} V/m and with the constant ε being 8.854187817620… × 10^{-12} Farads/m, we get 1.5×10^{25} kg/m/s^{2}. We have 200,000 metres per side, so there are 1.2×10^{41} J (joules) in a 200km on a side box at the Schwinger limit.

How many joules of gravitational wave energy were held in a 200km box around GW150914? Well at 200 solar masses per second emitted, we need to take the size of the box and use light travel time to determine the amount of energy in the box at any one time: So 200 solar masses per second. Light travel time is 200km/(3e^{8}m/s) = 6.7×10^{-4} seconds. So if that volume emits 200 solar masses of energy per second, then that is 0.13 solar masses worth of energy at any one time in that volume, or 2.3×10^{46} Joules! This is some 5 orders of magnitude above what can be emitted by this same region using electromagnetic means!

### Discussion

The mechanism by which one arrives at the Schwinger limit is conceptually simple – ‘QED non linear photon – photon scattering’ involving electron – positron pair creation. (See the wikipedia article for a start).

Is there a corresponding quantum ‘Schwinger limit’ for gravitational waves (gravitons)? Well there is of course a limit in place due to classical general relativity, which is well known. In this case we are close (gravitational *h* is about 0.001 or so?) of the classical limit, which is basically that you can’t pile anything up so that the density would cause a black hole to form. But is there a feynman diagram for graviton – graviton scattering – well of course there is – it should behave like real classical gravity! I guess what I am wondering – is there another pathway where graviton scattering would take place and according to QM make the GW150914 ‘impossible’?

Does the observation of gravitational waves 5 orders of magnitude stronger than the strongest possible electromagnetic wave mean that we can finally stop calling gravity the weakest force? Yes to that!

My take as anyone who reads any of this site will know is that electromagnetism, quantum mechanics and the nuclear forces are all emergent phenomena from classical general relativity (see my poster). To me this observation is another hint at what general relativity can do.

As a further note, this corresponds to 0.018 watts per square metre at the 1.3 billion LY distance of the earth! That means that the earth had 2.3 Terawatts of gravitational energy passing through it on Sept 14 2015, just from this one event. Yet this massive amount of power is barely within observational limits of LIGO. LIGO sees only nice correlated bumps (with only 2 detectors its not really built to look at the background of gravitational wave energy), so we could easily have this much energy passing through the earth in the form of these stochastic low frequency gravitational waves all the time, and LIGO would not be able to detect it.

Gravitational waves make the perfect sub-quantum excitation – they can carry very large amounts of energy without anything but a carefully designed detector being able to pick them up.

### What would be an ideal detector for LIGO frequency waves?

Other than the actual LIGO observatory of course (which I argue below may not be the ideal gravitational wave detector).

A nice isolated black hole maximally spinning at near a = 1, and of the same approximate mass as the GW150914 emitter would exchange a substantial amount of the incoming wave energy into motion – and it would pick up something like 0.2 GW of power for a fraction of a second, which would likely be observable since this hypothetical black hole is sitting so nice and quiet, a GJ of energy exchange would cause small (since the thing is so heavy) but measurable effects.

Say we don’t have a nearby system (we would need varying sizes to couple to the frequencies we wish to monitor) of quiet black holes to listen to. What else could we build? The ideas opens up if one assumes that matter and light are both gravitational phenomena. What would be ideal is something that mimics a tuned superradiant like interaction with gravitational waves, but it trillions of times lighter and made of ‘ordinary matter’. What makes super radiance work?

“What happened is that because this Rydberg atom stayed very high excited, but up there the energy levels are very-very close together. What does that mean? The transitions have very long wavelengths. So basically every sample that you can have is very small compared to these long wavelengths. And so superradiance is actually quite likely in these cases. And this is actually exactly what happened. As I said, it was an accident, I don’t think it could have been done such an ideal experiment on purpose in this case.”

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

*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.*

tom@palmerandersen.com, 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 10^{42} 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 (10^{14}Hz), for GR the maximum energy transfer rate be- fore non linear effects start to dominate is tremendously high – about 10^{65<}^{sup>W/m}^{2}. Compare that to electromagnetism, where we have to appeal to something like the Schwinger limit which is only 10^{30W/m}^{2}. 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^{−65}s, 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^{−65}s 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 1.2×10^{20}Hz. 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.

### Discussion

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^{−17}m, Occam’s razor perhaps suggests that we prove that general relativity is not the sub-quantum medium before a new field is invented.

- [1] Robert Brady. The irrotational motion of a compressible inviscid fluid. page 8, jan 2013.
- [2] Robert Brady and Ross Anderson. Why bouncing droplets are a pretty good model of quantummechanics. jan 2014.
- [3] Richard Brito, Vitor Cardoso, and Paolo Pani. Superradiance, volume 906 of Lecture Notes in Physics.Springer International Publishing, Cham, jan 2015.
- [4] Mark P. Davidson. Stochastic Models of Quantum Mechanics A Perspective. In AIP ConferenceProceedings, volume 889, pages 106–119. AIP, oct 2007.
- [5] L. de la Pena and A. M. Cetto. Contribution from stochastic electrodynamics to the understanding ofquantum mechanics. page 34, jan 2005.
- [6] William E. East, Fethi M. Ramazanolu, and Frans Pretorius. Black hole superradiance in dynamicalspacetime. Physical Review D, 89(6):061503, mar 2014.
- [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] 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] 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] J. Maldacena and L. Susskind. Cool horizons for entangled black holes. Fortschritte der Physik,61(9):781–811, sep 2013.
- [11] CharlesWMisnerandJohnAWheeler.Classicalphysicsasgeometry.AnnalsofPhysics,2(6):525–603,dec 1957.
- [12] TheoM.NieuwenhuizenandMatthewT.P.Liska.SimulationofthehydrogengroundstateinStochasticElectrodynamics. page 20, feb 2015.
- [13] WILLIAM H. PRESS and SAUL A. TEUKOLSKY. Floating Orbits, Superradiant Scattering and theBlack-hole Bomb. Nature, 238(5361):211–212, jul 1972.

For my Masters and PhD I worked on the Sudbury Neutrino Observatory, where I worked on the water purification team and also the computer simulation of the detector. It was a great time and I learned a lot from my Supervisor John Simpson at the University of Guelph in Canada.

The papers below are SNO collaboration papers, in addition to papers in journals like NIM, where our lab published the details of our ultra low level radon counting experiments.

I maintain a list on Research Gate of my publications.

#### The Speed of Light

The speed of light limit is at this point a postulate of physics, which is necessary as:

- Electromagnetic Radiation travels at c.
- Maximum speed of particles is c. (Lorentz equation).
- Relativistic QM – depends on c as a postulate.
- Strong force.
- more…

These are in the Standard Model disparate fields and laws. Why do they all share the same speed ‘c’? The only real answer right now is ‘because’. Hence the speed of light is a postulate. In modern physics this fact is acknowledged by saying that its not the ‘speed of light’ but rather the ‘fundamental speed’.

Postulates are never a good thing. Much of our understanding of the physical world comes from explaining away what we thought were arbitrary rules using more fundamental principles. We do need postulates, but its a good thing when we can lower the count. The Standard Model + QM have many tens of postulates (rules, particle masses, coupling constants, etc etc).

Now look again at a universe made of only GR. The speed of light becomes the speed of gravity – a ‘mere’ bulk propagation constant – the speed of Einstein’s Aether.

If one were to then build out other fields and physical effects (e.g. emergent quantum mechanics) using GR as a base, the speed of light is not needed as a postulate. It then becomes transparent as to why the speed of light is the same as the speed of gravity, and why the equations of relativistic QM are littered with the symbol ‘c’. Some ideas of how to build todays physics from GR are outlined in other posts on this site, but also see Brady and Anderon’s paper.

#### Lorentz Transformation

The behaviour of particles and clocks at velocity is dealt with using Lorentz transformations. These same transformations arise when looking at emergent phenomena such as Brady’s sonons travelling through an inviscid medium with a sound velocity. Thus Lorentz contraction can be thought of as arising from the bulk properties of the GR field.

#### Consequences

Removing the speed of light as a postulate would be a good thing, but are there any measurable consequences? In other words, if there is some truth to this theory is there any experiment that might be done to show that the speed of light is merely a bulk property of an all encompassing field that creates all matter, fields and forces?

Look at the speed of sound on Earth. This speed forms a barrier to objects moving faster than sound. But jets and asteroids can move faster than sound. So maybe analogously we can find a way to break the light speed barrier? Its not as simple as breaking the sound barrier though, as GR is an extremely strong field with a truly huge range of perfectly linear behaviour. To get an idea of its strength, consider that a mass of the Earth formed into a black hole is only about a cm in size, and so GR behaves linearly up to within a metre or so of that incredible field strength. But experimenters have access to extremely accurate clocks, huge collision energies and lots of computational power.

Once its accepted that the the speed of light might not a postulate, experiments are possible. There are actually quite a few people already measuring the constancy of the speed of light.

#### Conclusion

The fact that the speed ‘c’ is ingrained in all of physics and that General Relativity has this speed built in at a fundamental level is a huge clue as to the underlying makeup of the world around us.

My take: Its all GR.

–Tom Andersen, July 1 2015

Yves Couder’s (and others) experiments with small (in the human sense) and absolutely huge (in the quantum sense) silicon oil droplets and baths have proven to be a wonderful analog for quantum mechanics.

There are many researchers who think that these experiments show something much more – they hint at what the microscopic quantum world is really like. The quantum like effects occur when the driving force and frequency of the system are carefully tuned. When the conditions are right, the drops interact with their own waves – long after the waves have been emitted. Couder calls this behaviour the ‘high memory regime’ – its where all the quantum like behaviour emerges.

So the question becomes – what is the memory of a real quantum system? The answer to that question is surprisingly simple. Its infinite. Quantum states can entangle and ‘live’ forever. This fact is the foundation of Quantum Computing, the Many Worlds Theory and many other absurdities (Schrödinger’s cat…). Indeed the only point in QM where memory is not complete and infinite is at the point of measurement. But measurement is in the eye of beholder, and thus we need not worry about the measurement problem here. Or rather we will attempt to solve the measurement problem with a new hypothesis – that the memory of real quantum systems are limited, and that this limit is responsible for the collapse of the wave function.

This of course could kill or seriously limit the reach of quantum computing, and would provide a quick end to the Many Worlds Theory, and many many other consequences of quantum mechanics. Indeed Hilbert Space itself would lose its ‘reality’ – becoming nothing more than a mere mathematical trick for ‘memory intact’ (AKA pre-collapse) states.

What is the form of the memory? In Couder’s experiments its simply the range of an emitted wave in meters. Since his test trays are small, this means that the waves can bounce off the walls and interact with the emitter again.

We can look at such a system as a particle in a well. In Couder’s experiments you can see excited states decay after a time, and this time is increased as the memory of the system is increased.

So if we look at the simplest physical analog of this – a particle in a well that can quantum tunnel out – we have Alpha – emission. These particles are trapped in the nucleus, but sooner or later they tunnel out.

Thus tunnelling is a collapse of the wave function – these alpha particles leave fossil traces in rocks for instance, so they have been emitted in a very real sense.

Of course the pure QM follower will tell you that each emitted alpha is just another cat in a box - and that the entire history of the world hinges on you (or is that any smart person?) looking at the actual billion year old track - only then does the linear superposition of uncountable 10^{Millions}of state vectors collapse. Kind of hilarious, but that is what a truly linear system will do to you if you push it!

What causes the emission? The wave function has presence inside and outside of the barrier, so it can ‘feel’ that there is a lower energy state out there waiting for it. In a real pilot wave sense the pilot wave extends into the region beyond the barrier. We have a series of waves inside a femto metre sphere or so, and they bounce around for a few years (or 10^{24}) years, or 10^{-6} seconds.

So a large variation of lifetimes – yet the playground is almost the same size, its the energy levels that are different, but only by a small factor. The greater amount of the wave function that is outside the nucleus, the shorter half life.

What really happens? Is it that the particle keeps inside the nucleus, and as soon as it randomly happens to walk out it is released? In ‘real QM’ the wave function only gives a probability for finding the alpha outside the nucleus, so in some sense its ‘constantly’ out there. But in a realist theory the alpha has a real velocity inside and around the nucleus. This could perhaps be a real difference – perhaps if we postulate a fixed speed of the alpha on a random walk through the probability field, we can connect the lifetime to the percentage of the wave function that is outside the nucleus. See

Unpredictable Tunneling of a Classical Wave-Particle Association

So if a certain percentage of paths is outside, and the particle covers … do the calculation – random walk – step length is some distance much less than the nucleus size, speed v, then typical time to get out would be defined. perhaps with the speed held constant, we can determine step length by looking at the size of the region of probability outside the nucleus, we can determine the speed/step length that is implied. Someone must have done this?

http://demonstrations.wolfram.com/GamowModelForAlphaDecayTheGeigerNuttallLaw/

So in the playtime circa 1900 flat spacetime where QM currently works, there are no non – local effects and QM makes sense. This is why most theorists like the quantization of gravitation program – it would bury the annoying real 4D version of spacetime underneath many levels of obscure mathematics.

## The Aether

#### Einstein:

*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:

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 1.2356×10^{20} 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.

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:

- Cannot use already built CFD codes, as they are not built for the high dynamic range ‘Couder like memory’ like I am looking for.
- However Euler equations and physical setup is trivial for a CFD problem.
- 1000 resolution seems high enough.
- Two ‘electrons’ (one out of phase so will be a positron, or perhaps heavier and a proton) will be modelled as a point like particle that provides expansion/contraction of the aether, while at the same time each of these masses responds (‘surfs’) on the generated field.
- The goal then is to create a model of the hydrogen atom (or positronium).
- The electron should orbit the proton with Bohr like energy levels, determined numerically without recourse to QM.
- Photon/Atom interactions could also be modelled – photons should emit from the assembly when its started with ‘too much energy’.
- http://web.cse.ohio-state.edu/~busaryev/Projects/Smoke%20Simulation/
- http://obswww.unige.ch/lastro/conferences/sf2013/pdf/lecture5.pdf
- http://plutocode.ph.unito.it/
- http://www.astro.uu.se/~bf/course/numhd_course_20100124.pdf

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 *v*_{1}/*c* where *v*_{1} is the velocity of the electron in the first circular Bohr orbit and *c*is 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.

#### Cosmic Censorship:

Weak or strong, the cosmic censorship conjecture states that naked singularities can’t be seen, otherwise everything will break down, it would be really bad and worst of all theorists would be confused.

But it turns out that singularities very likely don’t actually exist in a real universe governed by GR. Any lumpy, non symmetric space time can have all the spinning black holes it wants – at any angular momentum, even with **a > m** (angular momentum greater than the mass in suitable units), as the Kerr solution + bumps (bumps are incoming GR full bandwidth noise), will have no paths leading to any singularity! So the *curtain can be lifted*, the horizon is *not* needed to protect us.

#### Cosmic Serendipity Conjecture:

In any sufficiently complex solution of GR, there exists no singularities. I am not talking about naked singularities here, I mean any and all singularities.

The complex nature of the interaction of GR at the tiny scales where the singularity would start to form stop that very formation. In other words, the singularity fails to form as the infalling energy always has some angular momentum in a random direction, and ruins the formation of a singularity.

In all likelihood actual physical spinning black holes in a turbulent environment (normal space) will have no singularity.

I will let Brandon Carter speak now:

“Thus we reach the conclusion that at timeline or null geodesic or orbit cannot reach the singularity under any circumstances except in the case where it is confined to the equator, cos() = 0…..Thus as symmetry is progressively reduced, starting from the Schwarchild solution, the extent of the class of geodesics reaching the singularity is steadily reduced likewise, … which suggests that after further reduction in symmetry, incomplete geodesics may cease to exist altogether”

Kerr Fields, Brandon Carter 1968.

Not cosmic censorship, but almost the opposite – singularities can’t exist in an GR universe (one with bumps) because there are no paths to them.

We have all been taught that singularities form quickly – that when a non – spherical mass is collapsing, GR quickly smooths the collapse, generating a singularity, neatly behind a horizon. Of course that notion is correct, but what it fails to take into account is that in a real situation, there is always more in falling energy, and that new infalling energy messes up the formation of the singularity.

While there may be solutions to Einstein’s equations that show a singularity (naked or not), these solutions are unphysical, in that the real universe is bumpy and lumpy. So while the equations hold ‘far’ away from the singularity, the detailed Gravity in the high curvature region keeps it just that – high curvature as opposed to a singularity.

The papers of A.Burinskii come to mind, e.g.:

Kerr Geometry as Space-Time Structure of the Dirac Electron

#### Conclusion

I am willing to bet that this conjecture is experimentally sound, in that there are no experiments that have been done to refute it. (that’s a joke I think).

On the theory side, one would have to prove that a singularity is stable against perturbation by incoming energy, which from my viewpoint seems unlikely, as the forming singularity would have diverging fields and diverging response to incoming energy, which would blow it apart. Like waves in the ocean that converge on a rocky point.

–Tom

#### Abstract

An electron model is presented where charge, electromagnetic and quantum effects are generated from pilot wave phenomena. The pilot waves are constructed from nothing more than gravitational effects. First the general model of the electron is proposed. Then the physical consequences are laid out, showing that this model can generate large electron – electron forces, which are then identified with the Coulomb force. Further, quantum mechanical effects are shown to emerge from this model.

#### Electron model:

An electron is modelled as a small region of space which has a varying mass. The origin of this varying mass will not be discussed here. The mass of the electron 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 very large changes in gravitational potential – essentially *the time derivative of the mass will be a potential that has a slope proportional to the frequency*. Assume that this frequency is very high, and you can see potential for some huge effects to come into play, as compared with the tiny gravitational field of a normal mass the size of an electron.

Throughout this paper only classical physics will be used, and on top of that, the only field used will be that of gravity (GR).

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?

I will use the 2014 paper “*Why bouncing droplets are a pretty good model of quantum mechanics*“ as a starting point.

Please open up that paper and have a look:

In section 4.3 – 4.4, the authors use analogy of two vacuum cleaners(!) to come up with a mechanism for an “inverse square force of attraction between the nozzles”.

Where ρ is the density of air and Q is the volume of air flow at each nozzle. I will use this train of thought to come up with a similar inverse square relation for my electron model.

In the equation above, ρ*Q gives the *mass* intake of one nozzle. In my model ρ*Q is thus the same as time rate of change of the mass of the electron, which averages out to f*me*ν, where

f = fraction of electron mass that is varying (f = 1 – me(min)/me)),

me == rest mass of electron,

and

ν = frequncy (greek nu).

So we have f*me*ν == ρQ, substituting into (8) from Brady and Anderson, we get

dp/dt = f*me*ν/(4πr^2)*Q

Where Q is still some volume flow, in m^3/sec. What, though is the volume flow for an electron – its not sucking up the surrounding air! One possibility is to model Q for my electron model as a spherical surface at some ‘electron radius’, with a speed of light as the velocity. So we have Q = 4πre^2*c and we get the force equation:

dp/dt = f*me*ν*(4πre^2*c)/(4πr^2)

This is the force on an electron nearby another electron at distance r in the model.

This should equal the Coulomb force law: (ke is the coulomb constant)

f*me*ν*(re^2*c)/(r^2) = ke*q*q/r^2

f*me*ν*(re^2*c) = ke*q*q

Now the fraction f, the frequency ν and the re are all unknowns. But lets use the classical electron radius for re, and a fraction f equal to the fine structure constant. Then we get solving numerically for ν the frequency… which is about 1000 times the Compton frequency. (So close to it in some ways)

There are of course other options, as the effective radius of this electron is not known and also the mass fraction is unknown. So this result is more for scale’s sake than anything. Still I will use these numbers for the rest of this paper.

Also interesting is to derive the value of the coulomb force between electrons – simply calculate (leave f alone for now),

f*me*ν*(re^2*c)

This gets to about a factor of 1000 or so away from the correct answer for ke*q*q. But not bad considering that I present no reason why to choose the Compton values for radius and frequency, other than a first jab in the dark.

In section 4.5 – 4.10 the authors show how these pulsating bubbles follow Maxwell’s equations to a good approximation. In the model of the electron presented here, that approximation will be orders of magnitude better across a very large parameter space, as the GR field is much better behaved than bubbles in water, to put it mildly.

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

#### Quantum Mechanical Behaviour

The electrons modelled here, which only contain a varying mass, can produce electrical effects that exactly match that of the electric field. As the Brady and Anderson paper continues in part 5, so will we here.

In actual fact, since these electrons have been modelled using the same sort of pilot wave phenomena as Brady and Anderson use, there is not much further to do. QM behaviour erupts from these electron models if you follow sections 5, 6 and 7.

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

#### Conclusion

Electrons made with this model exhibit all the expected forces of electromagnetism, all without introducing electric fields at all. Electrical behaviour is then seen as a phenomena of Gravity, rather than its own field.

These electrons also behave according to the laws of QM, all by generating QM effects using pilot wave mechanics.

From the Brady and Anderson conclusion:

“These results explain why droplets undergo single-slit and double-slit diffraction, tunnelling, Anderson localisation, and other behaviour normally associated with quantum mechanical systems. We make testable predictions for the behaviour of droplets near boundary intrusions, and for an analogue of polarised light.”

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

#### Appendix

There would be much work to do to turn this into a proper theory, with some things needed:

1) What happens with multiple electrons in the same region? A: I think that the linearity of GR in this range assures that the results are the same as EM. It would show a path to finding the limits of EM in areas of high energy, etc.

2) How do protons/quarks work? A: It would seem that quarks might be entities with more complicated ways of breathing mass in and out. This is something that is apparent from their larger actual size, which approaches the maximum size allowed to take part in the geometrical pilot wave, which may run at the compton frequency.

3) Why is charge quantized? A: To me, it seems that the answer to this may be that electrons have quantized charge and protons/quarks are using feedback to keep to the same charge. What about electrons, why are they all the same? I think that’s a puzzle for another day, but perhaps a wormhole model of the electron could be made where the frequency and magnitude of the varying mass would be set from GR considerations.

I don’t expect this model to be instantly accurate, or to answer all questions right away, but the draw to unify EM, QM and Gravity is strong. Any leads should be followed up.

###### See also

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..–Tom Andersen

May 17, 2014

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

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)

https://www.youtube.com/watch?v=KByhu3HKy5s

## Valentini:

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!

http://www.perimeterinstitute.ca/search/node/valentini

EG:

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.

http://streamer.perimeterinstitute.ca/Flash/3f521d41-f0a9-4e47-a8c7-e1fd3a4c63c8/viewer.html

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*

Can’t be done, it would seem, since gravity is spin 2.

Well, electromagnetism is spin 1, but we have tech gadgets and a billion transistors on one chip.

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.

What if the electron is not a single negative charge, but rather an onion

like arrangement of charge, with an excess of 1 unit negative?

Same for the neutron and proton (instead of 1/3 charged quarks).

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.

# How is that even a question?

Previous posts have all not mentioned quantum effects at all. That’s the point – we are building physics from General Relativity, so QM must be a consequence of the theory, right?

Here are some thoughts:

QM seems to not like even *special* relativity much at all. It is a Newtonian world view theory that has been modified to work in special relativity for the most part, and in General Relativity not at all.

There are obvious holes in QM – the most glaring of which is the perfect linearity and infinitely expandable wave function. Steven Weinberg has posted a paper about a class of QM theories that solve this problem. In essence, the solution is to say that the state vector degrades over time, so that hugely complex, timeless state vectors actually self collapse due to some mechanism. (Please read his version for his views, as my comment are from my point of view.)

If one were to look for a more physical model of QM, something along the lines of Bohm’s hidden variables, then what would we need:

**Some sort of varying field that supplies ‘randomness’:**

- This is courtesy of the monopole field discussed in previous posts about the proton and the electron.

**Some sort of reason for the electron to not spiral into the proton:**

- Think De Broglie waves – a ‘macroscopic’ (in comparison to the monopole field) wave interaction. still these waves ‘matter waves’ are closely tied to the waves that control the electromagnetic field.
- Put another way – there is room for many forces in the GR framework, since dissimilar forces ignore each other for the most part.
- Another way of thinking about how you talk about multidimensional information waves (hilbert spaces of millions of dimensions for example), is to note that as long as there is a reasonable mechanism for keeping these information channels separate, then there is a way to do it all with a meta field – GR.

**Quantum field theory:**

- This monopole field is calculable and finite, unlike the quantum field theories of today, which are off by a factor of 10
^{100}when trying to calculate energy densities, etc.

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.

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:

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.

History has showed us that all physical theories eventually fail. The failure is always a complete failure in terms of some abstract perfectionist viewpoint, but in reality, the failure only amounts to small corrections. Take for instance gravity. Newton’s theory is absurd – gravity travels instantly, etc. But it is also simple and powerful, it predictions working well enough to put people on the Moon.

Quantum Mechanics, it would seem, has a lot of physicists claiming that ‘this time is different’ – that QM is ‘right’. Nature does play dice. There are certain details of it yet to be worked out, like how to apply it to fully generalized curvy spacetimes, etc.

Lets look at what would happen if it were wrong. Or rather, lets look at one way that it could be wrong.

QM predicts that there are chances for every event happening. I mean in the following way – there is a certain probability for an electron (say) to penetrate some sort of barrier (quantum tunneling). As the barrier is made higher and or wider, the probability of tunneling goes down according to a well defined formula: (see for example this wikipedia article). Now, the formulas for the tunneling probability do not ‘top out’ – there is a really, really tiny chance that even a slowly moving electron could make it through a concrete wall. What if this is wrong? What if there is a limit as to the size of the barrier? Or put another way – what if there is a limit to probability? Another way to look at this is to say that there is a upper limit on the half life of a compound. Of course, just as Newton’s theory holds extremely well for most physics, it may be hard to notice that there is not an unlimited amount of ‘quantum wiggle’ to ‘push’ particles through extremely high barriers.

Steven Weinberg has posted a paper about a class of theories that try to solve the measurement problem in QM by having QM fail. (It fails a little at a time, so we need big messy physics to have the wave collapse). I agree fully with his idea – that we have to modify QM to solve the measurement problem.