Dear Dr. Tombe

The problem of describing the aether as vortices or whirlpools is generated by the fact that they are objects which “live” in a Euclidean 3-D absolute space.

Vortices correspond to the rotation motion of internal particles where the motion is invariant under the group of rotations SO(3). The three parameters of the group can be associated to the three Euler angles and the number between parenthesis correspond to the 3 spatial dimensions. Here, time does not play any role in the structure and that means than you cannot define a light cone like in Special Relativity, where events out of the cone are “forbidden” so the principle of causality cannot be violated.

So, rather than a classical object like a vortex it would be better, in my opinion, to describe the aether like something relativistic and with a quantum nature that could be described by Quantum Field Theory. Something like a gas of bosons or Einstein-Bose condensate. We could call “aetheron” to the quanta of the aether.

I agree with you about the "aetheron" internal structure that you propose in the article. My model also presents an electron-positron pair. The proposed idea is that the interaction between “aetherons” would live invariant the Lorentz group SO(3,1) and that would explain why the aether cannot be detected: it is made itself of internal electromagnetic fields, which mask the aether because you can only see the EM waves. The advantage of this model is evident: it is compatible with Special Relativity and, at the same time, it allows the existence of a medium for electromagnetic waves.

However, my model is more complex than yours because it contains additional elements that would account for quantum gravity.

In my opinion, the theory of gravitation that has to be quantized is not General Relativity as everyone that belongs to the academic world may suppose, but rather the theory to quantize is what is called in the literature as “GravitoMagnetism”, which is an exact analogy with the electrodynamic equations.

I have described this idea in my book “Theory of Gyroscopic Fields”, page 50. From my point of view, General Relativity is an emergent theory of gravitation where the metric field and the Ricci tensor only make sense for huge massive objects like planets and beyond and, hence GR is not valid for smaller objects. For example, for a model of self-gravity of an object like an apple, the equations to be applied to obtain the gravity field produced by the apple on its surroundings would be the Newton equations with a tiny “gravitomagnetic” field similar in structure to the magnetic field. This is a good point to start with, if we want the quantization of gravity because we know that is not possible to quantize General Relativity due to the emergence of infinites, whereas we already know the methodology for the quantization of EM.

In other words, GR is not the framework for arbitrary accelerated reference frames, but only of those corresponding to very massive objects like a planet or a star and beyond, where the observer can only measure the gravitational field produced by the object, not including the relation between external torques exerted on it and its angular momentum (Euler equations for rotations). As a consequence, we have to define a weaker Equivalence Principle for GR since inertial forces are not equivalent to a gravitational field but they are fundamental forces on their own, as described in my book.

Finally, the point then is to add in the “aetheron” something similar, but not equal, to the electron-positron pair.

Best Regards

Arthur Palenz

Arturo Rodriguez Palenzuela , The point is though that Tesla wasn't describing the aether as vortices or whirlpools. He was identifying the aether with a primary substance without any form. He was saying that mankind knew long ago that perceptible matter only arises when the aether is rendered into whirlpools. The whirlpools themselves would therefore be the essence of particulate matter.

It's not the case that the stuff of these whirlpools would be comprised of particles. It's a case of particles being whirlpools in the primary substance.

From my point of view, any object representing a physical phenomenon, like a whirlpool, has to be made of a system of internal particles where the relations between them define the variables of the system. It is not possible to think in an object with rotational motion without having an internal structure.

Also the aether should be composed by particles. In my opinion, the only things in Physics that have real existence (ontology) are particles. Then, space would be only a convenient mathematical construct needed to stablish an order relation that accounts for the distance between the particles by means of a coordinate system.

Basically, “space = 3-D coordinates” and “space-time = 4-D space-time coordinates” but they are not a substance. The substance with ontological existence is the aether which is made of particles that could be called “aetherons” and space-time is only the mathematical artifact necessary to define a mesh where the “aetherons” can be situated for calculation of their trajectories.

Arturo Rodriguez Palenzuela , OK then, imagine that the luminiferous medium is a dense sea of electrons and positrons. What is it that exists between these particles to account for the electrostatic force? There must be an even finer medium that obeys the rules of hydrodynamics.

Frederick David Tombe , The answer is easy to explain: what exists between these particle is a photon that travels in cycles from the positron to the electron and then goes back to the positron, or vice versa. This photon could be identified with what is called a VIRTUAL photon in Quantum Mechanics, where it is postulated to consist in a quantum fluctuation of the vacuum. Mathematically, this virtual photon can be represented with a vector potential A where its variation respect to time gives the Electrical Field E and its curl would give the Induction Field B in the “aetheron” and also the current displacement D and the Magnetic Field H along the aether.

Another question that I would like to comment is the stellar aberration problem where, for its analysis, what applies is the Galilean vector addition to the velocity of light, according to your description at https://wiki.naturalphilosophy.org/index.php?title=David_Tombe

This could be explained if we assume that the photon does not vanish, as QM postulates, after being absorbed by the atom in the measurement device or in the eye. Instead, the photon could be moving very slowly in a circular orbit around the absorbing electron. Hence, the velocity c would change to a very small value and then the Lorentz transformation approximates to the Galilean one, producing the aberration. But during the propagation of the photon Special Relativity could be still correct.

We must remember that QM positivist philosophy does not allow for conjectures that we cannot measure, but it does not mean that a logical hypothesis could be “forbidden” when trying to explain some phenomena.

Arturo Rodriguez Palenzuela , OK, so you have something moving between the positron of one aetheron and travelling over to the electron of the neighbouring aetheron. And you identify this with the vector field A.

Well, is that stuff not the primary substance that Tesla was referring to? Using words like "photon" tell is nothing. Something travels between two aetherons when EM radiation is passing through. That something cannot be particulate. It's the stuff in which sinks and sources constitute particles.

If you read Section III in this article, you might see your photons in the context of the hydrodynamics of the primary substance,

Article Tesla on the Aether and the Implications

Arturo Rodriguez Palenzuela , I think you are on the right tracks. But the momentum vector, A, which flows between two of your neighbouring aetherons, accounting for EM radiation, is Maxwell's displacement current, although Maxwell himself never seemed to have overtly grasped this fact.

A is what gives photons their momentum and their ballistic nature when the radiation is emitted discretely from, say a quantum jump in the case of black body radiation. But A is not a photon itself. An exception might be the two gamma photons that are emitted when an electron and a positron combine in the case of so-called electron-positron pair annihilation, although no annihilation actually takes place. It's just a fusion reaction. In this case, those two photons could each be identified with a single pulse of A flowing between individual aetherons.

A is a momentum density in the primary substance that Tesla mentions in that quote from his 1907 article, "Man's Greatest Achievement".

But the electrons and positrons that fill all of space, are portals in the primary substance, leading into the realm where the vital force that controls the universe, operates from. That vital force is God.

Frederick David Tombe, Then, basically we agree in the model of the aether, although my interpretation of vortices is a bit different: I see them as a discrete system of particles in, probably, a rotation state, rather than a set of vortices in a continuum media.

Best Regards

Arturo Rodriguez Palenzuela , On one level I can see the aetherons as discrete rotating electron-positron dipoles, with the two particles in mutual circular orbit. And originally that was my theory. But later I added in that the electrons and the positrons, were in turn, sinks and sources in a more fundamental primary electric fluid, the stuff of electric current.

Arturo Rodriguez Palenzuela , On the other issue about gyroscopic fields, it's my opinion that we can have a centrifugal force field. And in the case of a spinning rigid body, this will take the form of a very weak magnetic field, as per the 1915 Barnett effect.

If a spinning body is forced to precess, the ensuing interaction with the already existing centrifugal force field will induce a torque at right angles to the applied torque. This is the gyroscopic force. But I can see no gyroscopic force field. Only a centrifugal force field.

Article Aether Friction in the Planetary Orbits

Frederick David Tombe , In the literature of the accepted and orthodox Rigid Body Dynamics the "gyroscopic effect", that we all have experienced when riding a bicycle, is not associated with a force but with a moment called “Gyroscopic momentum”, with module I w Ω, where I stands for the moment of inertia, w is the angular velocity of intrinsic rotation and Ω is the angular velocity of precession.

In my approach, the gyroscopic field is not exactly a force either, though its definition is very close to the inertial force, but more complicated and with different dimensional description: [M][L]3[T]-2. I will explain the details of the theory in future messages.

Here, I am going to describe the arguments needed to justify a Theory of Gyroscopic Fields and the existence of new fundamental forces of nature:

1. The orthodox Rigid Body Dynamics theory is based in a mathematical model that implicitly allows for the presence of an inadmissible “action at a distance”, due to the fact that the angular momentum L appearing in the equations is a vector that is supposed to be common to all the constituent particles of the body. Then, according to the wrong classical description, when a torque is exerted at a point of the body from rest, all these particles start to rotate with the same L, no matter how far away was each particle from the point of the body where the torque was applied. This is obviously an incorrect description of the motion: there should be a transitory description to account for the behavior of the particles when we study the problem from rest to a stable and permanent regime of rotation with L as a good approximation for the angular momentum of all the particles.

2. If we want to remove this “spooky action at a distance”, we should need a different mathematical model which should provide an easy way to obtain a mechanism of propagation of the angular momentum L from an arbitrary particle to their neighbors. The best example of a model like that can be found in the theory of Electromagnetism with the Maxwell equations as the mathematical model where, taking the curl to one of the vector equations and substituting in the other, gives automatically a wave equation for the propagation of a certain field.

3. Then, the idea is to express the Rigid Body Dynamics equation:

dL/dt = ∑ r x F,

in a relativistic framework, where “action at a distance” is not possible to occur. A framework similar to that of Maxwell equation: The Minkowski space-time.

To be continued…

Preprint Theory of Gyroscopic Fields

4. The presently accepted model of Rigid Body Dynamics presents two separated mathematical pieces:

On one hand, a differential equation dL/dt = ∑ r x F which is equivalent to the conservation of the angular momentum of the body in a Euclidean space,

On the other hand, a kinematic definition of the velocity of a constituent particle of the body: v = w x r.

We would like to have a compact vector structure, where the above equalities could be derived from. And this is exactly what we get when you use the structure of Maxwell’s equations for Continuum Media as an analogy necessary to describe the usual equations for rotation.

But now we obtain some new terms that are absent in the orthodox formulation. These extra-terms account for the transient regime of the motion, from rest to rotational motion.

One of them represent a field of internal torques or dynamic moments that propagate from the point where the external torque was exerted to the rest of the body particles, thus explaining the angular momentum propagating wave obtained from the analogy with electromagnetism.

To understand this analogy more vividly, we must remind that, whereas Maxwell’s equations are used for a model that represents the dynamics of a flow of electrons, our equations of Gyroscopic Fields represent the dynamics of a flow of protons which would carry the rotational velocity vr = (w x r) and a different set of Maxwell-like equations to represent the dynamics of a flow of neutrons that would carry the precesional velocity vp = (Ω x r).

Then, we have defined two independent vectors: one for the angular velocity of intrinsic rotation (w), and the other for the angular velocity of precession (Ω).

As we know, the Euler equations for rotation which are obtained when identifying the three components of angular velocity which the variation respect to time of the Euler angles that represent the dynamical variables of the rotational motion of an object in the Euclidean space with symmetry group SO(3).

We claim that this representation, being mathematically correct, does not describe the real motion because it is not compatible with the Minkowski framework where action at a distance is not possible and also it is not invariant under a Lorentz transformation with symmetry group SO(3, 1).

In other words, with the orthodox approach based on a unique vector w where the three components of w correspond to the derivatives respect to time of the intrinsic rotation angle ψ, the precession angle φ and the nutation angle θ respectively, is not possible to get an element of metric distance ds2 as the sum of the squared angular velocities plus the squared time.

However, we will see that, postulating two independent (2 dimensional) vectors, one corresponding to the angular velocity of intrinsic rotation and the other corresponding to the angular velocity of precession, it is possible to get two Minkowski-like elements of metric distance ds2.

Arturo Rodriguez Palenzuela , I only see one gyroscopic force, and it's that which occurs when a spinning object is forced to precess. And I see it as simply being an inertial force. It acts to induce a precession at right-angles to the forced precession.

It therefore accounts for gyroscopic stability, because it reacts to external perturbations.

The bigger difficulty is in trying to establish the physical explanation for this inertial force in the context. It will certainly be to do with the interaction between the luminiferous medium and the molecules of the spinning object, but it's the details which are hard to guess since we can't clearly see what is going on on the molecular scale. A suspect it will be some kind of aethereal equivalent to the Magnus force.

Here's my attempt at the rattleback,

Article The Rattleback and the Magnus Force

Frederick David Tombe ,

I have been thinking on your idea of the existence of a gyroscopic force and the conclusion is that you are right: your gyroscopic force would be the analogous of the Lorentz force in Electromagnetism (EM), where the charge now is (1/r2) in the place of the electric charge q.

The analog of the electric field E is the moment of inertia I multiplied by the inertial acceleration, and the analogous of the magnetic field would be the angular or kinetic momentum L. However, in this case there are more elements than in EM, due to the existence of the analogous of “magnetic monopoles”, which don't exist EM, but we know how the Maxwell's equations would have to be modified if they really existed.

After some calculations, we get for the Gyroscopic-Lorentz force, the exact expression of the classical inertial forces multiplied by a factor equal to the inverse of squared gamma, where gamma stands for the typicall relativistic factor 1/sqrt(1 – v2/c2).

Arturo Rodriguez Palenzuela , Yes, the F = qvxB force is the same thing as the Coriolis force (and gyroscopic force), F = 2mvxω, but the physical interaction context is different. In the electromagnetic case, the vorticity (H = 2ω) is in the background magnetic field and the force acts on charged particles, whereas in the Coriolis force, the vorticity is in the atoms or molecules that make up the gyroscope.

I think I have covered all the case scenarios in this article,

Article Aether Friction in the Planetary Orbits

Equations (4) and (5) are particularly relevant.

Frederick David Tombe. In my opinion, the absence of friction that you describe correctly in your article "Aether Friction in the Planetary Orbits" is due to an internal mechanism that takes place inside the "aetheron", which is not only composed by an electron-positron pair, but it contains, in my model, another pair of particles with electric charge, let's call them massless W+ and W- correponding to the SU(2) group without spontaneous symmetry breaking. In the electromagnetic configuration of the "aetheron" (when a photon goes through it) both pair are tranversal and the electromagnetic field is propagated. However, in the gravitational configuration (when a graviton goes through the "aetheron") both pairs are parallel and then the electric charges cancel completely, avoiding friction.