### Archives For Front Page

Posts that can go on the front page.

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

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

I maintain a list on Research Gate of my publications.

##### Mar 2016 · Journal of Physics Conference Series
Jul 2009 · Physical review D: Particles and fields
Jan 2009
##### Article:Determination of the νe and total 8B solar neutrino fluxes using the Sudbury Neutrino Observatory Phase I data set
Apr 2007 · Physical Review C
##### Article:Measurement of the nue and Total 8B Solar Neutrino Fluxes with theSudbury Neutrino Observatory Phase I Data Set
Feb 2007 · Physical Review C
##### Article:A radium assay technique using hydrous titanium oxide adsorbent for the Sudbury Neutrino Observatory
Apr 2003 · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment
##### Article:Measurement of radium concentration in water with Mn-coated beads at the Sudbury Neutrino Observatory
Apr 2003 · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment
##### Article:Measurement of day and night neutrino energy spectra at SNO and constraints on neutrino mixing parameters
Full-text Article · Aug 2002 · Physical Review Letters
##### Article:Direct evidence for neutrino flavor transformation from neutral-current interactions in the Sudbury Neutrino Observatory
Aug 2002 · Physical Review Letters
##### Article:Measurement of Day and Night Neutrino Energy Spectra at SNO and Constraints on Neutrino Mixing Parameters
May 2002 · Physical Review Letters
##### Article:Direct Evidence for Neutrino Flavor Transformation from Neutral-Current Interactions in the Sudbury Neutrino Observatory
Apr 2002 · Physical Review Letters
##### Article:Measurement of the rate of nu(e) + d –> p + p + e(-) interactions produced by (8)B solar neutrinos at the Sudbury Neutrino Observatory.
Sep 2001 · Physical Review Letters
##### Article:Measurement of the Rate of {nu}{sub e} + d {yields} p + p + e{sup -} Interactions Produced by B
Aug 2001 · Physical Review Letters
##### Article:First neutrino observations from the Sudbury Neutrino Observatory
Jan 2001 · Nuclear Physics B – Proceedings Supplements
##### Article:Measurement of the Rate of nue + d –> p + p + e Interactions Produced by 8B Solar Neutrinos at the Sudbury Neutrino Observatory
Jan 2001 · Physical Review Letters
##### Article:The Sudbury Neutrino Observatory
Nov 1999 · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment
Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment
Jan 1997
##### Article:Direct evidence for neutrino flavor transformation from neutral-current interactions in SNO
SNO Collaboration · AB McDonald · QR Ahmad · […] · M Yeh

#### The Speed of Light

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

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

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

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

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

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

#### Lorentz Transformation

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

#### Consequences

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

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

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

#### Conclusion

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

My take: Its all GR.

–Tom Andersen, July 1 2015

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

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

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

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

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

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

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

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

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

What causes the emission? The wave function has presence inside and outside of the barrier, so it can ‘feel’ that there is a lower energy state out there waiting for it. In a real pilot wave sense the pilot wave extends into the region beyond the barrier. We have a series of waves inside a femto metre sphere or so, and they bounce around for a few years (or 1024) years, or 10-6 seconds.

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

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

Unpredictable Tunneling of a Classical Wave-Particle Association

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

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

## The Aether

#### Einstein:

We may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an aether. According to the general theory of relativity space without aether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this aether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it. [1]

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

Einstein’s inertial medium behaves as a nonrelativistic barotropically compressible inviscid fluid.[2]

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

## Einstein’s Aether in Fluid Dynamics terms

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

#### Truly Inviscid?

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

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

When an ordinary vortex is curved into a smoke ring, this force is balanced by Magnus forces (like the lift of an aircraft wing) as the structure moves forward through the fluid [10]. However a sonon cannot experience Magnus forces because it is irrotational, and consequently its radius will shrink, causing the amplitude A in (5) to grow due to the conservation of fluid energy. Nonlinear effects will halt the shrinking before A reaches about 1 since the density cannot become negative.[3]

Intriguing. Look now at a completely classical general relativistic object – a spinning  Kerr solution. We have a tightly spinning GR object that can shrink no further.  Since we are trying to model an electron here, we use the standard black hole values (for an electron model this is a ‘naked’ a > m Kerr solution [6])

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

Indeed, as long as there are incoming waves, it seems that objects made of GR are highly reactive, and not boring at all.[4][5]

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

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

#### An Electron Model

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

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

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

me(t) = me*((1 – f) + f*sin(vt))

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

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

Potential = -G*me(t)/r

Look at the time derivative of the potential

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

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

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

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

Using de Broglie’s frequency – he considered the Compton value of 1.2356×1020 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

#### Abstract

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

#### Electron model:

An electron is modelled as a small region of space which has a varying mass. The origin of this varying mass will not be discussed here. The mass of the electron is given as

me(t) = me*((1 – f) + f*sin(vt))

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

This varying mass will give rise to very large changes in gravitational potential – essentially the time derivative of the mass will be a potential that has a slope proportional to the frequency. Assume that this frequency is very high, and you can see potential for some huge effects to come into play, as compared with the tiny gravitational field of a normal mass the size of an electron.

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

I said that the mechanism for this time – varying mass will not be discussed, but here are two possibilities. One possibility is that electrons are some sort of wormhole, with some portion of their mass disappearing into and out  of this wormhole, like some mass bouncing between two open throats. The other more simple way this could happen is if the electron was simply losing mass off to infinity – and getting it back – in a periodic fashion.

#### Coulomb Attraction

So how would two of these time varying mass electrons interact?

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

Please open up that paper and have a look:

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

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

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

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

me == rest mass of electron,

and

ν = frequncy (greek nu).

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

dp/dt = f*me*ν/(4πr^2)*Q

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

dp/dt = f*me*ν*(4πre^2*c)/(4πr^2)

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

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

f*me*ν*(re^2*c)/(r^2) = ke*q*q/r^2

f*me*ν*(re^2*c) = ke*q*q

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

ν = 1.5×10^25 Hz

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

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

f*me*ν*(re^2*c)

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

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

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

#### Quantum Mechanical Behaviour

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

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

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

#### Conclusion

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

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

From the Brady and Anderson conclusion:

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

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

#### Appendix

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

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

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

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

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

Oza, Harris, Rosales & Bush (2014)Pilot-wave dynamics in a rotating frame
MIT site: John W.M. Bush
Is quantum mechanics just a special case of classical mechanics?
Monopole GR waves
Other posts on this site as well..

–Tom Andersen

May 17,  2014

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

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

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

So can one construct a machine that behaves like a dipole?

Take a canonical dipole. Two radio antennas, both vertical, one transmitting, the other receiving. The question then is, can we make a mass (or more likely a Rube Goldberg system of masses) bob up and down by the action of another mass-system moving at some distance away? if we can, then we have constructed a ‘spin one’ field from gravity, in much the same way that one can build something that is more than its parts.

The underlying field would of course be spin 2, but the field interpreted from the motions of our mass systems would look like a covariant, fully geometric compliant spin 1 field. It would in fact be a spin 1 covariant field.

Contraptions and questions come to mind right away. How do normal gravitational waves radiate as the eccentricity of an orbit approaches 1? What about a similar structure but with say a small particle orbiting a slender rod along the long axis. Not looking for stable orbits here at all. Just a mechanism to transfer a dipole motion across empty space to another construction of masses.

It seems more than possible that such an arrangement exists.

I read this paper today like a breath of air.

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

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

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

Have a look at the image on the right. We see a ‘strong’ force holding these particles apart.

Could this be an actual model for real particles? I don’t think that the author of the paper intends for this model to be taken literally, but it certainly has some obviously interesting properties. Intrinsic Charges and the Strong Force.

# How is that even a question?

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

Here are some thoughts:

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

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

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

Some sort of varying field that supplies ‘randomness’:

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

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

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

Quantum field theory:

• This monopole field is calculable and finite, unlike the quantum field theories of today, which are off by a factor of 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.

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.

$\Phi(r,t)=2\frac{m_eG}{r}sin(\omega t)$

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:

$\frac{\partial}{\partial t}\Phi(r,t)=2\omega\frac{m_eG}{r}cos(\omega t)$

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.