#### 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

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: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’.