All i see is vector tempertature or diffusion

Eqs, which i dont imagine a need for yet

Juan Weisz Pretty much all of modern physics rests upon Maxwell's equations, an - as we now know - incomplete and inconsistent first order model. Be sure to read ChatGPT's "Comparison of New Model with Maxwell" (currently) at the bottom of the page (screenshot attached):

https://bit.ly/AetherPhysics

"By preserving this distinction, the new model avoids the inconsistencies in Maxwell’s equations, where the electric field is described as a superposition of scalar and vector potentials. This second-order formulation provides a clearer, more consistent physical description of the electromagnetic field, ensuring that linear and angular dynamics are treated as separate entities."

So, the difference between Maxwell and the new model really is that "firm foundation" Einstein was talking about:

"All my attempts to adapt the theoretical foundation of physics to this new type of knowledge (Quantum Theory) failed completely. It was as if the ground had been pulled out from under one, with no firm foundation to be seen anywhere, upon which one could have built." (P. A Schlipp, Albert Einstein: Philosopher – Scientist, On Quantum Theory, 1949)

While it may do something for maxwell,

Already reformulTed in many ways,

Nothing to do with joining cm with qm

Juan Weisz Probabilistic QM is fundamentally flawed, because considering Nature to be fundamentally probabilistic implies one can have an action without a cause, which is also what Einstein complained about:

"You believe in the God who plays dice, and I in complete law and order in a world which objectively exists, and which I, in a wildly speculative way, am trying to capture. I hope that someone will discover a more realistic way, or rather a more tangible basis than it has been my lot to find. Even the great initial success of the Quantum Theory does not make me believe in the fundamental dice-game, although I am well aware that our younger colleagues interpret this as a consequence of senility. No doubt the day will come when we will see whose instinctive attitude was the correct one." (Albert Einstein to Max Born, Sept 1944, 'The Born-Einstein Letters')

According to this paper, just the the assumption of simultaneous measurements alone already invalidates "all proofs of Bell's theorem" aka “spooky action at a distance”:

Article Bell's Theorem: A Critique

So rather than joining QM with our new foundation, we let the bottom drop from underneath it, because in the new model we have uniquely defined potential fields, thus eliminating so called “gauge freedom” on top of which the so called “gauge theories” including the standard model are built:

https://en.wikipedia.org/wiki/Gauge_theory

“The Standard Model is a non-abelian gauge theory with the symmetry group U(1) × SU(2)× SU(3)and has a total of twelve gauge bosons: the photon, three weak bosonsand eight gluons.“

Fortunately, we no longer need all that quantum mumbo jumbo anymore, because the solutions to our new wave equation are the spherical harmonics as well (see attached screenshot from my notebook).

Thus, to quote Steve Jobs:

Simplicity is the ultimate sophistication.

So what is a vector on the RHS?

Juan Weisz Quite frankly, the solutions of the wave equation are over my head. I've used ChatGPT for validation and explanations. Those sections are marked by "ChatGPT:" and the equations are not numbered. However, what it said about these solutions is:

"By maintaining dimensional consistency, we derived a wave equation that reflects the fundamental interplay between spatial and angular components. This solution approach using separation of variables in spherical coordinates is standard for solving such partial differential equations."

And it is that fundamental interplay between linear and angular components and the fact that this is a second order model that makes it a new fundamental foundation for physics that's radically different from anything I've seen out there, as also reflected by ChatGPT's comparison of the new model with Maxwell's:

"In summary, while Maxwell’s equations provide a mathematically valid formulation, the new model offers a more physically consistent framework by rigorously separating linear and angular components, avoiding the blending of different types of behavior and ensuring adherence to fundamental principles of vector calculus."

And all that is accomplished by writing out that single equation describing the fundamental relation between space and time for the velocity, acceleration (and jerk) fields:

d[F]/dt = - k Delta [F]

Note that this new theory is testable and can be implemented in a fdtd simulator. I've forked an existing python simulator and worked on that. I've implemented the essentials, but it's quite a challenge to get it all right and also implement sources, boundaries, etc.

In case anyone is interested in helping a hand, here are the most important files on my github:

https://github.com/l4m4re/fdtd/blob/master/fdtd/operators.py

https://github.com/l4m4re/fdtd/blob/master/fdtd/aethergrid.py

I thought that, nothing to do with the solution of your eq.

For a wave eq, to make more sense from

maxwell, you need a second partial derivative with respect to time on the

LHS.

Juan Weisz The fundamental breakthrough that is the subject of this discussion is that the time derivative of any given vector field F is defined by:

dF/dt = - k Delta F,

with Delta the vector LaPlacian, the unique second spatial derivative (operator) in three dimensions. And this equation is the reason we no longer need a wave equation with an explicit (partial) time derivative. We can even redefine the d' Alembert operator to get rid of that explicit time derivative, which makes the equations not only much simpler but also of higher order.

See attached picture with screenshot of ChatGPT's substitution of the second order time derivative in the d' Alembert operator.

The problem with Maxwell's equations with respect to the wave equation is that because of the entanglement of Faraday's law with the fundamental medium model, expressed by a/o curl E = -dB/dt, is that we obtain only one wave equation, while at least two distinctly different EM wave phenomena are known to exist, the so-called "near" and "far" field, of which the "far" field has that mysterious "wave particle" duality, while the "near" field is an actual non-radiating transverse surface wave.

As Elmore has shown, this non radiating near field surface wave can be guided along an unshielded conductor, is very broad band and has low losses:

Article Introduction to the Propagating Wave on a Single Conductor

And this is just about the edge of what can be done with Maxwell's equations, while Tesla's longitudinal mode cannot be described by neither Maxwell's equations nor the EM wave equation.

This in contrast to our wave equation, which has the same kind of solutions as quantum mechanics, with linear combinations of a/o the spherical harmonics, Bessel and Neumann functions and is therefore much more general than Maxwell's wave equation and capable of making the same (kind of) predictions as current quantum mechanics, but without having a need to resort to probabilities to work around the limits of a broken foundation.

Frederick David Tombe Regarding your question on the physical picture of the fluid-like aether in the context of the EM wave-carrying medium: didn't have time to properly explain, but if you wish to discuss this, let's start with what I wrote in my earlier work:

Preprint Revision and integration of Maxwell’s and Navier-Stokes’ Equ...

Page 11 and on:

When we compare this with our proposal, we end up with two fundamentally different approaches:

1 A solution that fundamentally only has viscosity and one fundamental interaction of Nature, yields harmonic solutions c.q. builds upon deterministic (spherical) harmonics and provides a basis for the observed quantization as well as a 3D generalization of the currently used under-dimensioned wave functions;

2 A solution that has both viscosity as well as elasticity, the latter of which builds upon Brownian statistical mechanics and thus requires randomness and is therefore nondeterministic.

However, with our solution so far, we have lost the description of elastic behavior and thus our model is incomplete. This again brings us to the unusual behavior of superfluids, which is currently described with a two-fluid theory43. Donnely notes a/o the following:

1. In superfluid state, liquid helium can flow without friction. A test tube lowered partly into a bath of helium II will gradually fill by means of a thin film of liquid helium that flows without friction up the tube’s outer wall.

2. There is a thermo-mechanical effect. If two containers are connected by a very thin tube that can block any viscous fluid, an increase in temperature in one container will be accompanied by a rise in pressure, as seen by a higher liquid level in that container.

3. The viscous properties of liquid helium lead to a paradox. The oscillations of a torsion pendulum in helium II will gradually decay with an apparent viscosity about one-tenth that of air, but if liquid helium is made to flow through a very fine tube, it will do so with no observable pressure drop—the apparent viscosity is not only small, it is zero!

He also describes “second sound”, fluctuations of temperature, which according to him “has turned out to be an incredibly valuable tool in the study of quantum turbulence” and provides a condensed summary:

“After one of his discussions with London and inspired by the recently discovered effects, Tisza had the idea that the Bose-condensed fraction of helium II formed a superfluid that could pass through narrow tubes and thin films without dissipation. The uncondensed atoms, in contrast, constituted a normal fluid that was responsible for phenomena such as the damping of pendulums immersed in the fluid. That revolutionary idea demanded a “two-fluid” set of equations of motion and, among other things, predicted not only the existence of ordinary sound—that is, fluctuations in the density of the fluid—but also fluctuations in entropy or temperature, which were given the designation “second sound” by Russian physicist Lev Landau. By 1938 Tisza’s and London’s papers had at least qualitatively explained all the experimental observations available at the time: the viscosity paradox, frictionless film flow, and the thermo-mechanical effect.”

This leads to the question of whether or not the effects described by the current “two-fluid” theory can also be described by the (spatial derivatives) of the two related fields we have defined, our primary field [C] and the intensity field [I], since we already noted that the intensity field [I] does appear to describe elastic behavior (eq (26)), apart from a per second difference in units of measurement, and that when dealing with harmonic functions of time, such as those describing elemental particles, it is all too easy to get these time derivatives mixed up, because there is only a phase differential between the [C] and [I] fields and their respective spatial derivative fields.

Further, since electric current can be associated with both the curl of the magnetic field as well as with electric resistance and thus dissipation, it seems clear that rather than associating the absence of dissipation/resistance with the absence of viscosity, this absence should be associated with the absence of vorticity or turbulence.

This brings us to the idea of the “vortex sponge”44, devised by John Bernoulli in 1736, although in the shape of vortex tubes rather than ring vortices, which gives rise to elastic behavior of the medium because of momentum transfer effects arising from the fine-grained vorticity. This idea matches seamlessly to a vortex theory of atoms45, which was developed after around 1855 a new type of vortex theory emerged, the so-called ‘vortex sponge theory’. Instead of viewing atoms as consisting out of small, separate vortices, this type of theory supposed that the ether was completely filled with tiny vortices. These tiny, close-packed vortices made up large sponge-like structures, which gave this category of models its name. When we consider the basic idea that particles consist of a number (quantized) vortex rings, we would then consider these to form such a vortex sponge, especially in the case of crystalline materials such as silicon. Therefore, we would associate a material substance to such a dynamic vortex sponge rather than considering the aether itself to be universally filled with tiny vortices. And since in this view there are no stiff, point-like particles that bounce onto one another in a random manner, we would also do away with Brownian statistics and consider the interactions between the vortices to occur along harmonic functions of time.

The question then becomes whether or not the static forces we consider at the macroscopic level really are forces along Newton’s third:

F=ma , (33)

or are actually time derivatives thereof, yank, along:

Y =m j , (34)

with j the jerk, the time derivative of acceleration. The derivative of force with respect to time does not have a standard term in physics, but the term “yank” has recently been proposed in biomechanics46 .

This would also offer further insight into what inertia, resistance to "change", actually is, because the dynamic viscous forces we have described thus far are proportional to a rate of deformation and describe something dynamic, whereby there is a continuous flow of mass along quantized irrotational vortices. In a way, this can be seen as the opposite of resistance to “chance” and could perhaps rather be thought of as conductance of “change”.

Let's illustrate that along the rotating superfluid wherein quantum vortexes are formed. Once a certain angular speed has been established with the rotating container, a certain number of quantum vortices have formed and the system is in equilibrium. In that situation, the vortices are irrotational and therefore no vorticity nor turbulence and thus no resistance nor dissipation. In other words: there is a steady-state situation, which could easily be confused with a "static" situation, were it not that these the vortex lines are visible.

When we wish to increase the rotation speed of the rotating container, we must exert a "force" and thus we introduce turbulence until a new equilibrium is established. This way, we convert the energy we provide into the rotating superfluid, whereby the steady state situation becomes disturbed and turbulence is introduced, which results in more quantum vortices forming until eventually the turbulence dies out and a new equilibrium is established. Thus, from the outside it appears as though the rotating mass in the container resists change, but in reality it sort of stores "change" by forming additional vortices until there is no more turbulence.

Arend Lammertink Thank you. That was a very lengthy reply which seemed to be suggesting that you believe space to be densely packed with tiny aethereal vortices. Is that correct?

If the magnetic vector potential, A, is the momentum density of the aether, then the magnetic flux density, B, is the fine-grained vorticity. Is that correct?

Frederick David Tombe Yes, it was quite lengthy, but just a cut&paste from my earlier work, to provide the background information around the properties of superfluids and the "two fluid" theory with which these are currently described.

Since I consider the aether to be a superfluid, these "two fluid" aspects also play in the aether, leading to the idea that the "vortex sponge", this dense package of tiny aethereal vortices, should be related to the "normal fluid" properties that arise when temperature rises.

And since the scalar potential in the second order fields has a unit of power density, I consider that to represent temperature, probably apart from some constant.

Thus, it appears that in the new model the "superfluid" aspects should be associated with the first order fields, while the "normal fluid" arises when temperature - power density - rises above a certain threshold value and thus should be associated with the second order fields.

Another interesting detail is this:

"we already noted that the intensity field [I] does appear to describe elastic behavior (eq (26)),"

This refers to eq. 26 on page 11:

"An interesting detail is that the intensity field I can also be defined as:

I =κ v ,

(26)

with κ the modulus or elasticity in [Pa] or [kg/m-s2], which has a unit of measurement that differs by a per second [/s] from the unit of measurement for viscosity η in [Pa-s] or [kg/m-s]."

To sum this up: it appears that the classic "vortex sponge" is related to the "normal" fluid behavior that arises when temperature rises above a certain threshold.

Frederick David Tombe

In the new theory in the notebook, which is now much more readable and without comparison to Maxwell,

https://bit.ly/AetherPhysics

I defined the vector potential A differently than Maxwell's, more like a second order version of the classic definition in fluid dynamics. The angular fields are defined as in the attached screenshot.

So, I essentially reversed the relation between the torque density field and the vector potential compared to Maxwell.

In this new model, the magnetic field is defined by torque density tau times 1/e, with e elemental charge, while the vector potential has a unit of force density. Of course this could also be multiplied by 1/e to obtain a vector potential within the context of the electromagnetic fields, but that one would not be the same as Maxwell's.

So, within the new framework, the more fundamental angular fields have a clear meaning with corresponding units of measurement, while linked to the magnetic field by multiplication by 1/e.

Thanks to feedback from Arne Kjellman I realized my notebook read like code full of commented out sections that serve no purpose and are only distracting, so yesterday I spent a couple of hours "cutting the crap" and updating the article:

https://bit.ly/AetherPhysics

In the introduction, I added a remark about the currently popular quantum mechanics theory:

"You believe in the God who plays dice, and I in complete law and order in a world which objectively exists, and which I, in a wildly speculative way, am trying to capture. I hope that someone will discover a more realistic way, or rather a more tangible basis than it has been my lot to find. Even the great initial success of the Quantum Theory does not make me believe in the fundamental dice-game, although I am well aware that our younger colleagues interpret this as a consequence of senility. No doubt the day will come when we will see whose instinctive attitude was the correct one." (Albert Einstein to Max Born, Sept 1944, 'The Born-Einstein Letters')

And while the day that quantum magicians realize that fundamental randomness implies one can have an action without a cause and become aetherists has not yet come, according to this paper by Michael Clover just the assumption of simultaneous measurements alone already invalidates "all proofs of Bell's theorem", the method by which "spooky action at a distance" is supposedly proven, while "only time-independent classical local hidden variable theories are forbidden by violations of the original Bell inequalities".

Article Bell's Theorem: A Critique

Arend Lammertink

AMO: Good move to bring out the main subject of discussions --- "practical measurements or technical ... " ... since the other two on Einstein's SR-theory seem to be more about personal relations - where may participants descend to a lower level and start throw rotten apples at each other. The way the envious part of mankind has done with Einstein since 1905 and thus personified themselves as Frankenstein's monster.