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.

Continue Reading...### Archives For general relativity

#### 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 don’t divulge the recipe until later, lets start with the most undark matter we can find – CERNs protons.

CERN has proton – antiproton collisions going on at 7 TeV. There are collisions that generate up to a few TeV of photons.

Lets look at that from a viewpoint of classical physics, with some General Relativity added in the right place.

We have a few TeV of photons, these are generated in an extremely short period of time. We have two protons approaching and hitting (basically head on to get 2TeV of gammas). They are travelling at c. So that’s an interaction time of 2fm/3e8 m/s – 1.5 e-24 seconds.

So what happens gravitationally?

I have recently read a paper Monopole gravitational waves from relativistic fireballs driving gamma-ray bursts by Kutshera (http://arxiv.org/abs/astro-ph/0309448) that talks about this effect for, well exploding stars.

We have in a small area a mass of 7 TeV, of which about half leaves via gammas, the rest is in ‘slower’ particles like those higgs bosons, etc. This drop in mass results in a monopole gravitational wave. How big:

The force of Gravity is usually determined by the masses of the objects involved. But gravity is a local phenomenon (Einstein’s vision, not Newtons), and the field is actually a gradient of the potential.

So we have a potential change from 7 TeV to 5 TeV as seen by an observer near the collision as 2 TeV of gammas go whizzing by in a time span of 10-24 secs. Lets take the observer to be just outside the interaction area, say 10 fm away.

The gradient of the potential changes as the mass changes, which means its time dependent. We need the gradient.

Look at the Gravitational potential of the observer before and after the wave passes.

Before G(7 TeV)/10fm and after we have G(5 TeV)/10fm. So that’s an potential difference of G(2TeV)/10fm acting over a time of 1e-24 seconds, which means that we have a gradient of (some math. )SI units! Observer is a proton 10fm away,

I get 8.1×10-20 Watts – i.e. the observer proton sees its energy rise at a rate of 10-19 watts for 1e-24 seconds, it gets a boost in the away from the interaction, which raises its energy by a mere 5e-25eV.

Not much. But what I think is missing is that this sort of effect has to be looked at on a much smaller scale, and repeating, in that this monopole gravitational energy is coming in – then bouncing back out. The proton is thus an engine to this coherently at 1e40Hz or more, which makes other protons/electrons feel a force (they are bouncing this gravitational monopole radiation back and forth too) of the same size as the coulomb force. So this is the coloumb force. Electromagnetism as a phenomena of General Relativity. If you re-do the math with 10-47 or so seconds as the period then you start to see coulomb level forces at play. (Taking away accelerator energies ‘only’ adds a few zeros to the huge frequency requirement for mass exchange.)

The coloumb force rides above this – its a meta field ontop of this gravitationally built monopole system.

I think that electrons do this in a native, compact manner, likely using topology, while protons employ a complicated-ish ‘engine’ built of springs and struts made of GR that produce the same force as an electron. The strength of this force is determined by a feedback mechanism to balance that of the electrons.

Could dark matter be unlit(inactive/relaxed) protons? In other words protons that are not near an electron, and thus stop vibrating and being a charged particle. No near electron means no feedback means no charge. So perhaps looking for dark matter using a dense matter system like a block of germanium is bound to fail. We need to look using some sort of empty space experiment that gets to the vacuum conditions of interstellar (as we know dark matter exist on an interstellar scale).

An experiment might be to create a very hard vacuum starting with a hydrogen plasma, then as you pump down, look for some sort of indication that the charge of the remaining protons and electrons in the gas has gone down. You might look at the response of the p/e left in the chamber to photons – there will be less scattering as you pump down, but if the scattering falls off a cliff faster than your pumping rate you have made dark matter.

What is the distance at which this effect might happen at? In other words how far apart do electrons and protons have to be before the charge effect starts to stall? I am not talking about the range of photons – that’s infinite, but about the range of this effect – where will protons start to lose the signal from electrons, and calm down? 1m, 1micron? What is the density of gas in quiet parts of the galaxy? Intergalactic space is 1 atom/m3, I would say 1e6x this level is likely for some wastelands in the milky way. (we need dark matter in the milky way to get our velocity curves right!) So that’s 1 per cm3.

What’s the best vacuum you can make?

Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth (10^{−12}) of atmospheric pressure (100 nPa), and can reach around 100 particles/cm^{3 }

That’s about the right density. So has anyone ever measured laser scattering in such a chamber as a function of pressure? Corrected for pressure, we would get a horizontal line in a suitable graph. Boring stuff, it would seem, so likely not measured. The mean free path is 40km in these chambers.

**Some problems solved by this ‘dark matter is matter gone dark’ hypothesis:**

1) Early universe. It has been determined that the early universe must have had a mass that was much larger than the observed mass today. This is solved with dark matter, but that dark matter would have had to take part in things. If it were instead all just regular matter, there is no problem.

2) Early universe clumpiness: Its been really hard to come up with galaxies born so quickly. Yet they can be seen with telescopes. With all the matter in the early universe taking part, clumps are easier to make.

3) The lack of dark matter peaks at galactic cores. This one stumps the experts – physicists were sure that dark matter would accumulate at galactic cores, but it does not. If you have matter lighting up as it moves close to the core, then the radiation given off by this newly lit matter would keep things expanded, furthermore it is seen at the core, and so does not count as being dark. (http://www.cfa.harvard.edu/news/2011-29)

**Early universe CMB**

This is the way things are thought to work.

If all the matter was lit, then the He4/Li levels would be not what is observed. ==> Some kind of non interacting matter was needed.

The CMB is too smooth. Dark matter is needed to make galaxies:

Dark matter condenses at early epoch and forms potential wells, the baryonic matter flows into these wells and forms galaxies (White & Rees 1978). (Ref: http://ned.ipac.caltech.edu/level5/Sept09/Einasto/Einasto4.html)

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.

The title about says it.

I have been thinking and reading a little about the electromagnetic potential and it gauge invariance lately. In simple, but absolutely correct terms, you can think of Gauge Invariance like this:

Electrons only respond to the slope of the voltage potential, and not the absolute value. So if you take any circuit, experiment, etc, planet, etc and add a million volts everywhere, no one will be able to tell, except people who look in from outside the circuit or planet.

This fact led physicists to renounce the potential as something real, and instead pronounce it as only a mathematical tool, useful for getting the field, which is the ‘real thing’. So in other words, ‘Voltage is not real’. Sure feels real to me when I get a shock from static or touching the wrong wire! But physics says its the potential difference that matters, and not the potential iteself. Point taken.

Then along comes the Aharonov-Bohm Effect (David Bohm is one of my heroes in physics). It describes an experiment where electrons can detect a change in the potential – where the changes result in no fields. In other words it seems that electrons can see this potential. To me, this is a sign that this potential is real. To others of course, its not.

Richard Feynman seemed to think more along the lines of the ‘potential is real’ camp.

So if its real, what gauge did nature choose? In other words what is the voltage of the universe? I of course don’t know, but if we assume that there is some real fixed gauge, then what could be the consequences?

1) No consequences for local experiments, etc.

2) Perhaps there are things on a larger scale that do arise from this permeating ‘potential’ everywhere. Could this potential (i.e. voltage) be real in the sense that it is made out of something? That is the crux. Its certainly *not* made of photons, like the electric field. My thinking of course is that it is made of gravity – standing wave patterns in space that make it possible for these varying mass electrons to communicate (feel force) from other electrons and particles operating at the same (super high 10^50Hz) frequencies.

Could this potential, if its real, *be* Dark Energy?

— Tom Andersen

See also

http://arxiv.org/abs/1208.3224

http://arxiv.org/abs/0905.2589

Ref:

Feynman, R. *The Feynman Lectures on Physics* **2**. pp. 15–5. “*knowledge of the classical electromagnetic field acting locally on a particle is not sufficient to predict its quantum-mechanical behavior.* and *…is the vector potential a “real” field? … a real field is a mathematical device for avoiding the idea of action at a distance. …. for a long time it was believed that A was not a “real” field. …. there are phenomena involving quantum mechanics which show that in fact A is a “real” field in the sense that we have defined it….. E and B are slowly disappearing from the modern expression of physical laws; they are being replaced by A [the vector potential] and [the scalar potential]*“

# 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.

Take this size of an electron as the ‘black hole’ size. That is about 10-55 m I think. Then for a solid, we have about 3.35*10^{28} molecules water per m cubed, h2O, so 7e**29 electrons / m**3 – say 1e30 electrons per cubic metre. With a 1.48494276 × 10-27 m / kg conversion constant for the Schwarchild radius of an object measured in kg, and an electron mass of 9.10938291(40)×10−31, we get diameter of 2.6 10-58m, so cross section is 7e-116 and then the total area of a cubic metre of water is about 1e-85 m**2/m

So what is the neutrino cross section.

Say neutrinos only interact with electrons when they hit the actual black hole part. Also assume that neutrinos are much smaller than electrons.

How many meters of water would a ray penetrate before hitting an electron within its -black hole radius?

1e-85 m**2, which works out to a coverage of one part in 1e85, so 1e85 meters would ensure a hit. This is vastly larger than the real distance, which is only a few light years, 1e17 m or so.

So I guess that this idea is very wrong on some counts.

If you use the radius of the electron as a kerr naked ring singularity, you get 1e-37 metres, or **1.616199 × 10 ^{-35} meters, ie te planck length. **

Then with these planck length sized electrons, you get about 1e-70 – which is about 1e-40 m**2/metre of water, still not enough, but closer.

Funny how the kerr radius of an electron mass naked singularity is the planck mass.

Trying a compton size of 2e-12m instead of 2e-56, makes the

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

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

**Protons are different**

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

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

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

Involve the two constants ‘G’ and ‘Q’. You get a frequency along the lines of 10^{65} Hz

for two electrons separated by d:

m_{e}^{2}G/(2d^{2})*K = Q^{2}/(4*pi*E*d^{2}),

where we know that K – the ratio of gravity to electric force on electrons is about 8.3×10^{42}. K is unitless. suppose K is actually w*r/c, where r is some nuclear radius. With an radius r of about a fm, we get a frequency of 10^{65} Hz. Another way to think of this is that the light travel time across a black hole the mass of an electron is also 10^{-65} seconds.

This huge frequency implies a wavelength of a tiny 10^{-57} meters. So in the diameter of a proton, we have 10^{42} waves. There are an incredible number of these waves boiling inside the proton.

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

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

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

Thought experiment, that is…

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

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

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

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

So that’s 1/2M_{t}V^{2} = GM_{s}M_{t}/r

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

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

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

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

- M
_{s}– disappears. - M
_{t}has a KE boost of the escape velocity. - So M
_{t}is getting a KE boost of the escape velocity at each cycle.

In fact, repeat the whole process at about 10^{65} hz. (see this post for a calculation of this frequency) (2014 edit – Perhaps this frequency is way off… see May 2014).

Then you have the capability to produce an acceleration of 10^{42} TIMES the normal classical gravitational acceleration on an object. Take M_{s} and M_{t} to both be the mass of the lightest charged particle, the electron. In the example above, I guess one of the particles is a positron since there is a net attraction. Attraction vs repulsion is a phase thing here. If both particles disappear and re-appear at the same time (well with speed of light taken into account between them), then you would have repulsion.

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

Obviously not a complete model at this point!

Here are some nice things about this:

- Obviously covariant, GR friendly (as long as you can stomach the varying mass thing).
- If correct, things like the Maxwell equations should drop out. That would be a telling feature.
- It forms a way to unify gravity with the other forces of nature.
- It does not use the well worn QFT as a starting point, which has never really amounted to much.

**Maxwell Equations**

**Questions**:

- Why the phase lock?
- What about QED and its exact predictions?
- What is the mechanism that controls the mass swings?
- What about the ‘other’ properties of the electron – the gyromagnetic ratio, etc.
- Can this model be used for nuclear forces as well?
- What about quantum effects? Can time and energy be used at these scales?

**Hints to answers**:

- Perhaps phase lock is the wrong way to think about the interaction, and something more like QED provides a better way to think about repulsion vs attraction, etc.
- QED is modeled with the exchange of precisely timed phase clocks – the physical model of this may be the pulse exchanges outlined above.
- General Relativity does not tell us how space is connected. It may not be simply connected.
- The gyromagnetic ratio of the electron can be found to be 2 from several papers on gravitational models of the electron – those papers assume a classical model for charge, but still may hold. The extremely high frequency of this effect means that on a scale of even femtoseconds we have 10
^{28}oscillations – likely can ignore many effects, and again treat the electon as if it has a classical charge. - Nuclear forces may be a result of real, actual, particles interacting at distances close enough that non – linear effects and the full theory of General Relativity need to be taken into account. Perhaps get numerical relativists to work on this.
- Quantum mechanics may be a
*phenomenon*of a multiply connected GR universe, with all the fast clocks and wormhole like behaviour providing enough room to create a (now extant) hidden variables theory of QM. - Perhaps the Proton participates in this dance with a much more complicated set of machinery – and is – say not multiply connected, or has a different structure, etc.

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.

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.