### Archives For electromagnetism

EM and how we can generate EM from general relativity.

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

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

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

https://file.scirp.org/pdf/ACES_2013100819104983.pdf

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.

#### Abstract

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.

#### Introduction

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

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

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

#### de Broglie beats and the Compton frequency:

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

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

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.

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.

https://en.wikipedia.org/api/re
st_v1/media/math/render/svg/d50a640dc99823e7f650b0c2580ec3bc51ea7ddd

#### 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]

#### 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 1036 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:

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

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

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

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

#### Proton model:

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

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

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

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

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

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

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

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

#### The de Broglie frequency of the proton

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

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

John W Bush on de Broglie:

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

#### 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

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:cmprp ≈ hA quick trip to Wolfram shows  cmprp/h = 0.6 , so the correspondence is quite close. Plancks constant is of course the ‘quantum of action’ – so it should show no relation at all to the lowly proton – as the proton is ‘merely’ a composite particle, its mass or radius should have nothing to do with quantum mechanics. Unzicker’s coincidence will be revisited at the end of this work. In a past 2014 post I discussed an electron model in terms of ‘purely classical GR’.

# 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*E2 So at the Schwinger limit of 1.3×1018 V/m and with the constant ε being 8.854187817620… × 10-12 Farads/m, we get 1.5×1025 kg/m/s2. We have 200,000 metres per side, so there are 1.2×1041 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/(3e8m/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 2.3×1046 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.”

Thoughts:

Turbulence in GR is linear and hence does not give rise to cumulative gravitational effects. Indeed, the power that can be transmitted using GR as a factor of the ‘gravity caused’ is immense. For instance: at the power transfer of energy at the Schwinger limit (here I assume 3×1029 watts/m2), the non linear effect – the gravity term is very low.

Say (see http://arxiv.org/pdf/1007.4306v3.pdf) 3×1029 watts/m2 (at optical freq).\

Consider a 1 metre3 box with perfect mirrors at the schwinger limit – how much does that much radiation weigh?

I get 1×1021 Joules per cubic metre at any one time, so that’s 11.1 tonnes. (http://www.wolframalpha.com/input/?i=10%5E21Joules%2F%28c%5E2%29)

That seems like a lot of mass, but 11 tonnes in a cubic metre is not going to alter the static gravitational field much even in the low field limit like that of the earth.

That 11 tonne figure is interesting, as it is also the density of lead. Its strange (or not) that the Schwinger limit is also the density of normal matter.

From the book I am reading now: ( Fields of Color: The theory that escaped Einstein  — Rodney A. Brooks)

“… spin is an abstract mathematical concept that is related to the number of field components and how they change when viewed at from different angles. The more field components, the higher the spin.” 0  ,  1/2  ,  1  , 2  are the spin values so gravity has more field components. Can we mimic a field with a lower number of field components with one that has more field components? Yes. So we generate everything from gravity.

Einstein was of course worried about the electromagnetic radiation emitted from a classical Bohr atom. But I have also learned that he was worried about the GR radiation from that same atom that he claimed was ‘not observed’. I think that the waves would be of very low energy but I should work that out. (re – replenishment from the turbulent gravity).

Random Q: Were there about 5 times TOO MANY GALAXIES in the early universe – which would jive with my thought that dark matter is matter gone dark. In the early Universe matter was packed too tightly for there to be any dark stuff, so there was more galaxy formation. A: Possibly see for instance – http://astronomynow.com/2015/11/21/hubble-survey-reveals-early-galaxies-were-more-efficient-at-making-stars/

Random Q: Frame dragging. Would any other physics change over one of Tamjar’s rotating superconductors where he sees anomalous gravitational effects – i.e. look at decay rates of common isotopes, etc.

Random Q: There is the experiment in Italy where they see decay rates changing as the year advances, which is anomalous. Wonder if some frame dragging can take care of that.

### 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.
In PDF as a paper, or in as a poster I presented at EmQM15 in Vienna, published in IOP physics. http://iopscience.iop.org/article/10.1088/1742-6596/701/1/012023

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 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 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.

### 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 10−17m, 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.

I have been thinking about frame dragging and faster than light travel for a few days, and then about the fact that quantum collapse seems to take place ‘instantly’ (faster than light).

So then I read about the photon size for a 1MHz radio wave which is 300 metres – quite large.

So this huge wave has to refract as a wave and yet somehow instantly collapse into a very small area to be absorbed? Instantly? Insanity!

Wild thought: Frame dragging faster than light and gravitational shock waves to the rescue!

Answer: Collapse is a shockwave that causes frame dragging, allowing for ‘instant’ effects to happen (also EPR).

Frame dragging can in principle be used to travel faster than the speed of light. This is a known scientific fact that is thought to be non possible in practice due to all sorts of limitations. Science fiction of course loves it.

So a soliton forms and sweeps energy out of the wave and into the reception antenna.

If we could control this soliton collapse – we could perhaps harness it to perform faster than light communication and travel.

The soliton ‘shock wave’ is composed of gravity (as is light and everything else). It would have to have some very specific configuration.

Frame Dragging

Frame dragging occurs with linear effects too. My thought experiment on this is through a Mach – like view point. If you are inside at the middle of a very long pipe, which starts to accelerate, you will be dragged along. If the pipe stops at some velocity, you will approach that velocity eventually.

So space couples not to mass but to matter. If it just coupled to mass, you would not be able to tell if your neutron rope was moving or not. It couples instead to the actual bits of matter.

What about circularly polarized gravitational waves – timed so that the squished part is always in front and the expansion is behind the particle? So that’s 90 degrees from direction of travel of the waves – but perhaps they can be entrained as a soliton solution. Soliton

Would there be any consequences that we could measure?

http://physics.stackexchange.com/questions/178545/maximum-power-transmitted-using-general-relativity-waves-cf-schwinger-limit

For instance, there is an upper bound of the amount of EM energy that can be poured through a square mm of area – not predicted by Maxwell’s Eqn’s of course, as they are linear, but by quantum field effects. If we instead look at how gravitational energy we can pass through that same square mm, is it the same number of joules/sec? http://en.wikipedia.org/wiki/Schwinger_limit

Well there are a few problems with the Schwinger limit too:

"A single plane wave is insufficient to cause nonlinear effects, even in QED.[4] The basic reason for this is that a single plane wave of a given energy may always be viewed in a different reference frame, where it has less energy (the same is the case for a single photon)."

So according to QED, we can actually make a laser of any power – and as long as its in a vacuum, there are no non linear effects. Can that really be true?

The Schwinger limit is about 2.3 E33 Watts/metre^2.

I have calculated the limit of gravitational wave energy (which depends on frequency) to be

P (max gravity waves) = 3/(5pi)*c^3/G*w^2,

In Electromagnetism, QED says that the linearity of Maxwell’s equations comes to an end when field strengths approach the Schwinger limit. Its about 10^18 V/m.

What is the corresponding formula for gravitational waves. Since gravity is a non-linear theory, there should be a point where gravitational waves start to behave non linearly.

Here is my calculation, based on http://en.wikipedia.org/wiki/Gravitational_wave:

There is a formula there for the total power radiated by a two body system:
(1) P = 32/5*G^4/c^5*m^5/r^5 (for identical masses in orbit around each other)

Further down the same wiki page I see a formula for h, which has a max absolute value of (assuming h+ and standing at R = 2r away from the system, theta = 0):

(2) h = 1/2*G^2/c^4*2m^2/r^2

Things will be highly non linear at h = 1/2 (which is the value of h used in the diagram on the wikipedia page!). So lets set h = 1/2, and then substitute (2) into (1) to get the power as radiated by the whole system when h = 1/2 (use a lower value like h = 0.001 perhaps to be more reasonable, if you like). I am not trying to calculate where the chirp stops in a binary spin-down here, I’m looking for the maximum field strength of a gravitational wave.

I get for the maximum power from a compact source

(3) P = 64/5*c^3/4*m/r

That’s the total power radiated when h is well into the non linear region – you will never get more than this power out of a system using gravitational radiation.

The result depends on m/r , which makes sense as higher frequency waves with the same value of h carry more power.

Putting the result in terms of orbital frequency, w, we get (using newtonian orbit dynamics (http://voyager.egglescliffe.org.uk/physics/gravitation/binary/binary.html)

(4) Pmax = 16/5 c^3/G*w^2*r^2

That’s the max coming out of a region r across, we want watts per sq metre, so divide by the surface area of a sphere:

(5) Pmax/per sq meter = 3/(5*pi)*c^3/G*w^2

The maximum power that you can deliver at 10^14 Hz (light wave frequencies, so as to compare to the E&M QED Schwinger limit) is 10^65 watts/m^2 !

That’s a lot of power, dwarfing the Schwinger limit.

Is that about right? The max power scales as the square of the frequency, and is truly huge, reflecting how close to linear GR is over large parameter spaces.

w = frequency

So for gravitation, we have linear behavoir holds up until some fantastic power level:

http://www.wolframalpha.com/input/?i=c%5E3%2FG*%28%285*10%5E14%29%5E2%29%2Fsec%5E2

1e65 watts per sq metre at visible light frequencies is about the linear limit for gravitational waves at a frequency of 10^14 .

This means that gravity has ‘lots of headroom’ to create the phenomena of electromagnetism.

Perhaps one could dream up a super efficient way to generate ‘normal’ quadrupole gravitational radiation using some radio sources arranged in some way. Or a way to generate anti-gravity, etc.

GR certainly has a large enough range of linearity to power all of the EM we know today. Its also possible to generate monopole and spin 1 radiation from gravity, look up Brady’s papers on EM generation from simple compressible fluids, for instance.

Also do the joules/sec per square mm or whatever calc.

Also look at some other consequences in the dark recesses of the proton and electron (my models of them, or effects just based on size and field levels).  Would we start to get non-linear EM effects at what distance from the centre of an electron? Same for quarks?

http://en.wikipedia.org/wiki/Gravitational_wave

http://voyager.egglescliffe.org.uk/physics/gravitation/binary/binary.html

Ref http://www.jetp.ac.ru/cgi-bin/dn/e_038_04_0652.pdf

#### 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)

ν = 1.5×10^25 Hz

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.

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

The answer from physical theory is a resounding yes, but look at some first experiments along these lines:

### Bosons

Bosons obey boson statistics – which means they are not huge players in Quantum interactions. You can jam as many as you like into one state. In other words you can pile trillions of photons up in one place, they will all ignore each other.

### Fermions

Fermions are nice quantum particles. They don’t pile up on the nucleus and instead support the existence of matter with the pauli exclusion principle. All quantum level determining experiments are done with charged fermions. But are there uncharged fermions? (Yes – Neutrinos)

### Experiments that might show QM effects on non charged particles

Photon experiments. Experiments with light are pretty boring. Photons are bosons, or put another way, they simply do not interact with one another. The existence of the photon is always determined by an interaction with a charged particle. So no way to do a purely photonic QM experiment, I would think.

Neutrons: Uncharged and fermonic so it seems – but in reality Neutrons are composite particles made of charged quarks. There are no uncharged quarks.  So any experiment on QM that uses any charged fermion can’t be included.

Neutrinos: Well here we have an uncharged fermion, so that would seem to rule that there are quantum effects on non – charged particles. But of course neutrino experiments are very primitive and only concern neutrino – charged particle interactions. Its wildly impossible right now to do an experiment where neutrinos are say dropped into some potential well and we detect the pauli exclusion principle on them.

Gravitons and other bosons fall into the uncharged category for the most part, W bosons sticking in this regard. But I would bet that the QM nature of W+ interaction has not been experimentally studied.

I don’t know why the physics community has not spent more time on this. QM effects and charge seem to be locked together. A hypothetical all Boson universe would not need to use QM.

### Do Bosons Feel Quantum Mechanics?

More on this hypothetical bosonic universe. If we construct one where all fermions are missing, but the laws of physics are the same, would we need QM at all?

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 10100 when trying to calculate energy densities, etc.

Now I’m not sure that he is onto something real or not, although experiments are still being performed which detail positive results.

He does have some pretty convincing arguments about what happens to an object with a varying mass:

Let us suppose that, viewed in our inertial frame of reference moving with respect to the brick, when the mass of the brick changes, its velocity changes too so that its momentum remains unchanged. (The cause of the velocity change is mysterious. After all, driving a power fluctuation in the brick to excite a mass fluctuation need not itself exert any net force on the brick. But we’ll let that pass.) We see the brick accelerate. Now we ask what we see when we are located in the rest frame of the brick. The mass fluctuates, but in this frame the brick doesn’t accelerate since its momentum was initially, and remains, zero. This, by the principle of relativity, is physically impossible. If the brick is observed to accelerate in any inertial frame of reference, then it must accelerate in all inertial frames. We thus conclude that mass fluctuations result in violations of local momentum conservation if the principle of relativity is right.

Of course no ‘real’ physicist thinks that you can change the mass of something without a pipe of energy or mass leading into it, but that’s what he means here – some ‘magical’ varying mass. I assume that for my electron model, this varying mass is only a local effect – there is a secret topological ‘wormhole’ pipe that connects two electrons together, so the total mass is constant.

So does Woodwards insight give us any guidance with the effects of the resulting monopole gravitational waves on other varying masses? We can see right away that momentum conservation for such a topological system is only adhered to over a time average.

Look at the diagram from Woodwards article:

http://physics.fullerton.edu/~jimw/nasa-pap/

We see shades of my varying mass model. I am not saying that electrons can self accelerate, but more that the interaction of varying mass objects leads to entirely new physics, without introducing any new equations.

With monopole gravitational waves, the electron will feel a varying force, and the averaged momentum rule from Woodward would then imply that the net average acceleration on the particle is in one direction only, depending on the phase of the arriving wave. Of course these phases are what are called charge – the electron wants to maximize the acceleration, in order to go down the potential energy landscape in the best direction.

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

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

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

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

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

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

General Thesis?

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

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

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