Archives For November 30, 1999

Can de Broglie’s pilot- waves be constructed from GR?

March 22, 2014 — Leave a comment

“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….

In general relativity, pilot waves

QM from waves – pilot waves.

March 9, 2014 — 1 Comment

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.

See also (pointed out by Warren Huelsnitz) :

“Why bouncing droplets are a pretty good model of quantum mechanics“

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)

https://www.youtube.com/watch?v=KByhu3HKy5s

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

Is Quantum Mechanics Tried, True, wildly Successful, and Wrong?

Quantum Theory at the Crossroads
Reconsidering the 1927 Solvay Conference

A relaxing read:

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

Antony Valentini, Beyond the Quantum

In Front Page, general relativity, physics, pilot waves, quantum mechanics

4D Spacetime as a media for the Hilbert Space of QM

February 24, 2014 — Leave a comment

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

In general relativity, physics, quantum mechanics

How to make Dark Matter

October 20, 2013 — 2 Comments

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/cm³

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)

In general relativity, physics, The state of Physics dark matter, electron model, general relativity, particle physics, physics

Constructing a Geometrical Dipole

June 3, 2013 — Leave a comment

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.

In Front Page, general relativity, Particle Structure, physics electromagnetism, general relativity, particle physics, physics

Rotating Rings and Quadrupole Waves

February 25, 2013 — Leave a comment

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

In general relativity, Particle Structure, pilot waves

What is Quantum Mechanics

July 2, 2012 — 2 Comments

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.

In electromagnetism, Front Page, general relativity, physics, quantum mechanics, The state of Physics, Uncategorized general relativity, gravity, measurement, quantum, theory, weinberg

Lessons from the Woodward effect

July 2, 2012 — Leave a comment

Re: http://en.wikipedia.org/wiki/Woodward_effect

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.

In electromagnetism, Front Page, general relativity, physics electromagnetism, general relativity, gravity, varying mass, woodward

An Experiment with Monopole Gravitational Waves

October 16, 2011 — 4 Comments

Thought experiment, that is…

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

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

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

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

So that’s 1/2M_tV² = GM_sM_t/r

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

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

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

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

M_s – disappears.
M_t has a KE boost of the escape velocity.
So M_t is getting a KE boost of the escape velocity at each cycle.

In fact, repeat the whole process at about 10⁶⁵ hz. (see this post for a calculation of this frequency) (2014 edit – Perhaps this frequency is way off… see May 2014).

Then you have the capability to produce an acceleration of 10⁴² TIMES the normal classical gravitational acceleration on an object. Take M_s and M_t to both be the mass of the lightest charged particle, the electron. In the example above, I guess one of the particles is a positron since there is a net attraction. Attraction vs repulsion is a phase thing here. If both particles disappear and re-appear at the same time (well with speed of light taken into account between them), then you would have repulsion.

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

Obviously not a complete model at this point!

Here are some nice things about this:

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

Maxwell Equations

We now have a coulomb strength field with repulsion and attraction (caused by different phase locking). This is set in a covariant GR framework. Maxwells equations can be determined from Coulomb’s law and Special Relativity : see for example this paper by Richard E Haskell.

Questions:

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

Hints to answers:

Perhaps phase lock is the wrong way to think about the interaction, and something more like QED provides a better way to think about repulsion vs attraction, etc.
QED is modeled with the exchange of precisely timed phase clocks – the physical model of this may be the pulse exchanges outlined above.
General Relativity does not tell us how space is connected. It may not be simply connected.
The gyromagnetic ratio of the electron can be found to be 2 from several papers on gravitational models of the electron – those papers assume a classical model for charge, but still may hold. The extremely high frequency of this effect means that on a scale of even femtoseconds we have 10²⁸ oscillations – likely can ignore many effects, and again treat the electon as if it has a classical charge.
Nuclear forces may be a result of real, actual, particles interacting at distances close enough that non – linear effects and the full theory of General Relativity need to be taken into account. Perhaps get numerical relativists to work on this.
Quantum mechanics may be a phenomenon of a multiply connected GR universe, with all the fast clocks and wormhole like behaviour providing enough room to create a (now extant) hidden variables theory of QM.
Perhaps the Proton participates in this dance with a much more complicated set of machinery – and is – say not multiply connected, or has a different structure, etc.

Obviously a big pill to swallow. But it does head down the road to integrating the forces of nature.

Tom Andersen

Meaford, On Canada

October 16, 2011 (with personal notes from 1995 – 2011)

In general relativity, Particle Structure, physics, pilot waves einstein, general relativity, monopole, particle physics, quantum, waves

The gravitational electron

December 4, 2010 — Leave a comment

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.

In Front Page, general relativity, physics, pilot waves electron, electron model, general relativity, gravity, particle physics

So what are electrons, really?

July 30, 2008 — Leave a comment

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.

In electromagnetism, Front Page, general relativity, Particle Structure, physics, pilot waves electron, general relativity, gr, physics, substructure

General Relativity