### Archives For general relativity

and try to find your friend at the other end.” — Leonard Susskind

In this talk Leonard Susskind gives a convincing argument as to why he th inks that ER == EPR , where ER denotes an Einstein – Rosen Bridge (aka wormhole) and EPR is the Einstein Podolsky Rosen paper (essentially entanglement).

Leonard draws three entangled pairs of particles on the chalkboard, (image its not merely 3 by 3e40) and then collapse the left and right down to black holes, then the entaglement must continue, and thus ER == EPR

Take a ring of rotating matter.

No matter what frequency it rotates at, there is no General Relativistic waves emanating from it.

Now assume that the matter starts to clump up into two balls. NOW we have GR radiation.

Now run the camera in reverse.

What we have is an object that aggressively reflects (exchanges) GR radiation with other similar objects at the same frequency.

The rings I am talking about are the mass of an electron and very very small.

Take a run of the mill graviton detector: (Not yet built, nor would they be easy to build!).

Put it on a table top, on this planet. Say its detecting 1,000 gravitons per second. Now pull the table out – quickly but smoothly. How may gravitons will it see on its 0.5 second trip to the floor?

According to the equivalence principle: When it drops off the shelf, it is supposed to stop seeing gravitons.

According to QFT – the device is still in a gravitational field, so it will see about 500 gravitons on its half second journey. Note that the speed of the detector has not changed appreciably when it first starts to fall. “All experimental quantities are unchanged”.

This simple thought experiment lies at the

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). 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 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.”.

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.

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 and Hadley’s 4-geons. 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 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.

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 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.

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.. 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: 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 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.   Robert Brady. The irrotational motion of a compressible inviscid fluid. page 8, jan 2013.
2.   Robert Brady and Ross Anderson. Why bouncing droplets are a pretty good model of quantummechanics. jan 2014.
3.   Richard Brito, Vitor Cardoso, and Paolo Pani. Superradiance, volume 906 of Lecture Notes in Physics.Springer International Publishing, Cham, jan 2015.
4.   Mark P. Davidson. Stochastic Models of Quantum Mechanics A Perspective. In AIP ConferenceProceedings, volume 889, pages 106–119. AIP, oct 2007.
5.   L. de la Pena and A. M. Cetto. Contribution from stochastic electrodynamics to the understanding ofquantum mechanics. page 34, jan 2005.
6.   William E. East, Fethi M. Ramazanolu, and Frans Pretorius. Black hole superradiance in dynamicalspacetime. Physical Review D, 89(6):061503, mar 2014.
7.   G. Gr ̈ossing, S. Fussy, J. Mesa Pascasio, and H. Schwabl. Implications of a deeper level explanation ofthe deBroglieBohm version of quantum mechanics. Quantum Studies: Mathematics and Foundations,2(1):133–140, feb 2015.
8.   Mark J. Hadley. A gravitational explanation for quantum theory non-time-orientable manifolds. InAIP Conference Proceedings, volume 905, pages 146–152. AIP, mar 2007.
9.   M. Kutschera. Monopole gravitational waves from relativistic fireballs driving gamma-ray bursts.Monthly Notices of the Royal Astronomical Society, 345(1):L1–L5, oct 2003.
10.   J. Maldacena and L. Susskind. Cool horizons for entangled black holes. Fortschritte der Physik,61(9):781–811, sep 2013.
11.   CharlesWMisnerandJohnAWheeler.Classicalphysicsasgeometry.AnnalsofPhysics,2(6):525–603,dec 1957.
12.   TheoM.NieuwenhuizenandMatthewT.P.Liska.SimulationofthehydrogengroundstateinStochasticElectrodynamics. page 20, feb 2015.
13.   WILLIAM H. PRESS and SAUL A. TEUKOLSKY. Floating Orbits, Superradiant Scattering and theBlack-hole Bomb. Nature, 238(5361):211–212, jul 1972.

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. 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

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

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

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

#### Crazy thought:

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

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

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

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

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

Wikipedia

the large potential energy of the inflaton field decays into particles and fills the Universe with Standard Model particles

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

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

Wikipedia

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

The basic process of inflation consists of three steps:
1. Prior to the expansion period, the inflaton field was at a higher-energy state.
2. Random quantum fluctuations triggered a phase transition whereby the inflaton field released its potential energy as matter and radiation as it settled to its lowest-energy state.
3. This action generated a repulsive force that drove the portion of the Universe that is observable to us today to expand from approximately 10−50 metres in radius at 10−35 seconds to almost 1 metre in radius at 10−34 seconds.

## The Aether

#### Einstein:

We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an aether. According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it. 

Brady, in the paper “The irrotational motion of a compressible inviscid fluid” hypothesizes something different – that the universe is made of a non – relativistic compressible fluid, and that this fluid generates General Relativity.

Einstein’s inertial medium behaves as a nonrelativistic barotropically compressible inviscid fluid.

Although my model of the electron and quantum effects is very similar to Brady’s, I diverge with him on the essence of the aether. I hypothesize that Brady and Einstein’s ether are the same thing, so that instead of Brady’s concept of generating GR from aether, we instead start with Classical General Relativity (with ‘no matter’, so the stress tensor T = 0), and then  create Sonons as solutions of GR. The aether is that of Einstein’s GR.

## Einstein’s Aether in Fluid Dynamics terms

Einstein’s aether is inviscid – which means it has no viscosity (rocks travelling through empty space experience no drag…). Is it compressible? Certainly – this is what constructs such as black holes are. Is it irrotational? – that is a not a property that we need to determine, since without viscosity, an irrotational flow will stay that way.

#### Truly Inviscid?

No. GR is non-linear, which makes the inviscid property only an approximation – it’s a good approximation, though! Waves generated on an ocean or an oil puddle in a lab travel a limited distance, while the waves of GR can easily travel the universe. But they don’t travel ‘forever’.

Consider now the construction of a Brady like sonon out of pure GR. We follow Brady’s paper until section 1.1, where he states:

When an ordinary vortex is curved into a smoke ring, this force is balanced by Magnus forces (like the lift of an aircraft wing) as the structure moves forward through the fluid . However a sonon cannot experience Magnus forces because it is irrotational, and consequently its radius will shrink, causing the amplitude A in (5) to grow due to the conservation of fluid energy. Nonlinear effects will halt the shrinking before A reaches about 1 since the density cannot become negative.

Intriguing. Look now at a completely classical general relativistic object – a spinning  Kerr solution. We have a tightly spinning GR object that can shrink no further.  Since we are trying to model an electron here, we use the standard black hole values (for an electron model this is a ‘naked’ a > m Kerr solution )

Brady’s sonons interact with the surrounding aether – how would that work in GR? We are after all taught that all GR objects like black holes have no hair. But of course they can have hair, its just that it will not last long. That’s the point here. Sonons can and will stop interacting if the background incoming waves die down below a certain point. But above a certain point black holes become perturbed, and things like ‘superradiance’  as Teukolsky and others discovered come into play.

Indeed, as long as there are incoming waves, it seems that objects made of GR are highly reactive, and not boring at all.

So pure GR has at least the ability to interact in interesting ways, but are the numbers there? What frequencies do we need for Brady like Sonons constructed from GR (I’ll call them geons from now on) to get to the point where there are electromagnetic strength interactions are taking place?

Bradys interactions occur with mass transfer – the compressible fluid carries away mass to and from each Sonon in a repeating manner. Not a problem for any GR ‘blob – geon’.  If they interact, then energy must be flowing in and out – that’s the definition of interaction.

#### An Electron Model

A previous post here – An Electron Model from Gravitational Pilot Waves  outlines the process.

We take a small region of space (e.g.  containing a Kerr solution) and assume that this region of space is exchanging gravitational energy with its surroundings.  Call it an geon-electron.

Assuming that the exchange takes place in a periodic fashion, the mass of this geon-electron (energy contained inside of the small region of space) is given as

me(t) = me*((1 – f) + f*sin(vt))

where v is some frequency, and f is the proportion of mass that is varying, so f is from 0 –> 1.

This varying mass will give rise to changes in the gravitational potential outside the region.  But gravitational effects do not depend on the potential, rather they depend on the rate of change of the potential over spacetime intervals.   So it’s not the potential from this tiny mass that is relevant, it is the time derivative of the potential that matters.

Potential = -G*me(t)/r

Look at the time derivative of the potential

dP/dt = -G*me*f*v*cos(vt)/r

This gradient is what one can think of as the force of gravity. This force rises linearly with the frequency of the mass oscillation.

The EM force is some 10^40 times that of gravity, so we just need to use this factor to figure out an order of magnitude estimate of the frequency of this geon mass exchange rate.

This is detailed in the ‘Coulomb Attraction’ section of an earlier post.

Using de Broglie’s frequency – he considered the Compton value of 1.2356×1020 Hz as the rest frequency of the internal clock of the electron, one arrives at an electron model with these properties:

• Entirely constructed from classical General Relativity
• Frequency of mass exchange is the Compton frequency
• Electromagnetic effects are a result of GR phenomenology
• Quantum effects such as orbitals and energy levels are a natural result of these geons interacting with their own waves, so QM emerges as a phenomenon too.

#### Einstein’s Vision:

“I published the paper on the relativistic dynamics of the singular point indeed a long time ago. But the dynamical case still has not been taken care of correctly. I have now come to the point where I believe that results emerge here that deviate from the classical laws of motion. The method has also become clear and certain. If only I would calculate better! . . . It would be wonderful if the accustomed differential equations would lead to quantum mechanics; and I do not regard it as being at all out of the question” (Ref: Miller, 62 years of uncertainty)

The State of Physics today ————————– Obviously a sea change in fundamental physics would be needed to allow for anything like these ideas to be considered. In fact its not that the ideas here might be correct – but rather that Brady and others who toil on actual progress in physics are sidelined by the current ‘complexity is king’ clique that is the physics community today. The physics community is more than it ever has been in the past, a tightly knit clique. This may be the fault of the internet and the lock in group think that instant communication can provide. This clique gives rise to ideas like ‘quantum mechanics is right‘ and other absurdities, such as the millions of hours spent on String Theory, when it’s ‘not even wrong‘.

#### Tests and Simulations

Given the entrenched frown on the subject of alternative bases for the underpinnings of our physical world, we need to look for experimental evidence to support these kinds of theories.

The work of Yves Couder and his lab in one kind of essential experiment. They have shown conclusively that quantum like behaviour can emerge from classical systems.

Another path – one that in my opinion has been somewhat neglected in this field is that of numerical techniques.

Here I outline some steps that might be taken to construct a GR based model of an electron. Excuse the more colloquial manner, I am making notes for a future project here!

#### Numerical Plans

There are only about 22 Compton wavelengths within the Bohr radius. So if one goes to a 100 Compton wavelength simulation zone, with 1000 grid points on a side, thats 1e9 grid points, and each point needs only four 8 byte doubles, so 32 bytes, so 32 GB.

The equations to solve on this simple grid are those of fluid dynamics: Compressible Isothermal Inviscid  Euler equations.  : As from I do like CFD. With a 32GB data set, 1e9 data points, and about 1000 computer FLOPs per visit, we have 1e12 FLOPs per time step, and an algorithm that gets 10GFlops, I get about a minute per time step.  Each time step needs to cover about 1/100th of the Compton time, or about 1e-22 secs, and we need to let light cross the atom (3e-19 secs) hundred times to get things to converge, or about 3e-17secs, so 300,000 time steps. (Better speed up the algorithm! Should be easy to get 20GFlops over 8 processors, and perhaps cut Flops/grid point down, which could mean a day or so on a 8 core Intel).

#### Computer Model:

Note on the Fine Structure Constant (useful in a numerical model)

The quantity was introduced into physics by A. Sommerfeld in 1916 and in the past has often been referred to as the Sommerfeld fine-structure constant. In order to explain the observed splitting or fine structure of the energy levels of the hydrogen atom, Sommerfeld extended the Bohr theory to include elliptical orbits and the relativistic dependence of mass on velocity. The quantity , which is equal to the ratio v1/c where v1 is the velocity of the electron in the first circular Bohr orbit and cis the speed of light in vacuum, appeared naturally in Sommerfeld’s analysis and determined the size of the splitting or fine-structure of the hydrogenic spectral lines. [*]

#### Cosmic Censorship:

Weak or strong, the cosmic censorship conjecture states that naked singularities can’t be seen, otherwise everything will break down, it would be really bad and worst of all theorists would be confused. Hawking and Ellis, in The LargeScale Structure of Space-Time (Cambridge 1973)

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

#### Cosmic Serendipity Conjecture:

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

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

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

I will let Brandon Carter speak now:

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

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

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

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

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

Kerr Geometry as Space-Time Structure of the Dirac Electron

#### Conclusion

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

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

http://physics.stackexchange.com/questions/193340/does-general-relativity-entail-singularities-if-theres-a-positive-cosmological –Tom

Koide and Compton

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

The Koide formula has been compared to Descartes theory of circles: One can see that the two relationships bear a resemblance. Jerzy Kocik, in his paper called “The Koide Lepton Mass Formula and Geometry of Circles” uses this correspondence to determine that the Koide formula looks like a generalization of Descartes Circle equation – with a characteristic angle of about 48 degrees. If one uses this formula, then the radius of the electron is actually the biggest, and tau smallest, (with a further particle having no or almost no mass…-  ν  ?). So are there any physical models that work well with the lightweight electron being large?

The Koide Lepton Mass Formula and Geometry of Circles

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

Gravity vs. Quantum theory: Is electron really pointlike?

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

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

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

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

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

Click to access 0701006.pdf

1112.0225.pdf (burininski)

Why not emergent QED?

My thesis is that electro magnetic effects along with quantum behaviour emerge from large amplitude GR monopole wave interaction in the high memory regime.

So its basically a recipe for QED.

What is the biggest problem in the accepted QED? The renormalization problem. So lets look at how to solve it with my emergent sonon like gravity system.

“De Broglie’s law of motion for particles is very simple. At any time, the momentum is perpendicular to the wave crests (or lines of constant phase), and is proportionally larger if the wave crests are closer together. Mathematically, the momentum of a particle is given by the gradient (with respect to that particle’s co-ordinates) of the phase of the total wavefunction. This is a law of motion for velocity, quite unlike Newton’s law of motion for acceleration. “ –

Antony Valentini, Beyond the Quantum

So are the GR constructs that I espouse in these posts able to naturally create such an effect?

We have monopole waves….

I start with a screen grab from the video below. Yves Couder and friends are clearly looking at hidden variable theories:  Here is a 3 minute movie with the above slide:

# The pilot-wave dynamics of walking droplets

Here is a paper about eigenstates, etc… Self-organization into quantized eigenstates of a classical wave driven particle  (Stéphane Perrard1, Matthieu Labousse, Marc Miskin, Emmanuel Fort, and Yves Couder).

Compare that with my hastily written post.

Yves Couder . Explains Wave/Particle Duality via Silicon Drop

“Couder could not believe what he was seeing”.

Here it was sort of a eureka moment at home on a Sunday afternoon.

Here is a link to the whole show.(45 mins)

## Valentini:

Valentini (along with me) thinks that QM is wrong, in that its not the ‘final layer’. His de Broglie arguments are powerful and hit close to home for me. I have read most of David Bohm’s papers and books since discovering him as a 4th year undergrad back in the 80s. Bohm’s ideas launched mine. Note that much of physics is built on the assumption that with QM somehow ‘this time its different’ – that any future theory will need to be QM compliant or it is wrong. As if QM was somehow as certain as the (mathematical and hence solid) 2nd Law or something. This leaves no room for argument or dissent. Perfect conditions for a paradigm change!

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

EG:

This is the presentation that outlines things as he sees them. I see things that way too, although I am of the opinion that the pilot waves are GR ripples.

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

Not even wrong. Why does nobody like pilot-wave theory?

“De Broglie’s law of motion for particles is very simple. At any time, the momentum is perpendicular to the wave crests (or lines of constant phase), and is proportionally larger if the wave crests are closer together. Mathematically, the momentum of a particle is given by the gradient (with respect to that particle’s co-ordinates) of the phase of the total wavefunction. This is a law of motion for velocity, quite unlike Newton’s law of motion for acceleration. “

Antony Valentini, Beyond the Quantum

If QM runs as wiggles in GR, we have a possible way to get collapse, and have a linear QM theory that breaks down over long times or with too many signals in one place.

In other words:

Each QM state vector is represented NOT only as a vector in a Hibert Space, but are really ‘real’  arrangements of (usually small scale) GR waves.

Since GR waves behave linearly over a large range of frequencies and amplitudes, these waves do not interact, and can be represented well as they are now in QM – by a Hilbert Space.

Collapse occurs when this linearity is compromised.

Thus there is a limit to entanglement and Quantum computing. The collapse of the wave function is a physical happening independent of observers. It occurs when these waves self – interact.

Indeed – with a theory where the QM states can only interact in a linear fashion, we have absurdities such as infinite computing power combined with massive Hilbert Spaces.

This should be quantifiable. In other words the collapse can be simulated on a computer system without Bohr like handwaving or the Many World’s trillions of universes per second per cubic cm coming into existence to avoid a true collapse (ok I know its more than trillions per second…).

To estimate the conditions for collapse: Take the likely amplitude of a single quantum wave (by looking at this mass – difference theory that I have for instance) and then see how many can pile into the same place before non-linear interference occurs – which would start a collapse. So collapse occurs when a simple isolated system interferes with a system with many more moving parts – an observation.

Entanglement/EPR/Bell outside the light cone is handled by non-local topology “worm – holes” in GR.

-Tom

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

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.

Take a ring of some material (in my thinking its likely a construct of some compact gravitational solution, like a Kerr singularity with a >> m).

This ring is rotating a some huge speed, with a frequency of nu_e.

Along comes an incident regular gravitational wave, with the roughly same frequency as the rotation of the structure, nu_w ~ nu_e.

What will happen?

Look at what happens with the ring (which is assumed at least somewhat pliable and soft), is not spinning.

The gravity wave simply interacts with it causing a change in its shape from circular to an ellipse. Make the ring a spinning entity, – (so that the dots above are rotating) and what happens: The ring becomes an emitter of gravitational radiation – it scatters the incoming waves.

Why – well its easy to imagine that the ring has some properties like tension and stiffness, due to rotation. Then as the ring is turning  its shape shifting will turn with the ring, making a new gravitational emitter. In other words the ring gets deformed, rotates to a new position, and then un-deforms – radiating the gravitational energy it has stored.

With systems like this in the normal world, we know that when the frequencies of the spinning object is comparable to the frequency of the incoming radiation, we get resonant tuning – the ring will maximally scatter incoming radiation.

What are the numbers?

Looking at energy radiated, need to start over again, but

Click to access GW_Physics.pdf

10-60 watts. Is that enough for an electron?

http://www.wolframalpha.com/input/?i=%2832%2F5*G**4%2F%28c**5%29%29%2F%28planck+length%29**5*%28%28electron+mass%29**5%29

# 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.