On Space, Time and the Fabric of Nature

By Arend Lammertink, MScEE, September 2016.

Introduction

To date, our basic understanding of space, time and the fabric of Nature rests on the theories of Quantum Mechanics and Einstein's Relativity Theory. These two useful theories are pretty much being taken for granted as unalterable givens. Einstein himself gravely warned us this might happen and that "scientific progress is often made impossible" because of it.

The state of current science is, if anything, the result of a lack of well founded scepticism. We should not be afraid of well founded scepticism, we should embrace it and take it seriously. Without serious consideration of well founded sceptic arguments, we cannot correct the errors we have made. And that is what has led to a process whereby science went onto a diverging path whereby it enhanced the errors made in the past, instead of using new information to correct them.

In this work, we shall investigate the history of our current scientific theories and formulate a Physical, Unified theory based on fundamental ideas to integrate the currently diverging theories at the origin of their divergence: the Maxwell equations. We shall see that, actually, all currently known areas of Physics' theories converge naturally into one Unified Theory of Everything once we make one fundamental change to Maxwell's aether model, which is to replace his incompressible aether with a compressible one.

Compressibility and Albert Einstein's intuition

Since our objective is to form a physical theory based on fundamental ideas, it is of the most importance that we clearly define our ideas and concepts and make sure that we keep the concepts we use consistent troughout the whole of our theory. As we shall see, for the concepts of space and time, their place within our current theoretic body has not been kept consistent, which is the main reason of the divergence from a "real" space time concept into a "curved" space time concept within Einstein's Relativity Theory, which was a/o heavily criticized by Nikola Tesla .

Yet, Einstein's theory did predict a number of phenomena theretofore unknown, some of which have been verfied by experiments, which, ironically, has led to the concept of curved space-time achieving exactly this "excessive authorithy" over us Einstein warned about:

"Concepts that have proven useful in ordering things easily achieve such authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they might come to be stamped as "necessities of thought," "a priori givens," etc. The path of scientific progress is often made impassable for a long time by such errors. Therefore it is by no means an idle game if we become practiced in analysing long-held commonplace concepts and showing the circumstances on which their justification and usefulness depend, and how they have grown up, individually, out of the givens of experience. Thus their excessive authority will be broken. They will be removed if they cannot be properly legitimated, corrected if their correlation with given things be far too superfluous, or replaced if a new system can be established that we prefer for whatever reason." Obituary for physicist and philosopher Ernst Mach (Nachruf auf Ernst Mach), Physikalische Zeitschrift 17 (1916), p. 101

"I fully agree with you about the significance and educational value of methodology as well as history and philosophy of science. So many people today — and even professional scientists — seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is — in my opinion — the mark of distinction between a mere artisan or specialist and a real seeker after truth." Letter to Robert A. Thorton, Physics Professor at University of Puerto Rico (7 December 1944) [EA-674, Einstein Archive, Hebrew University, Jerusalem].

At some point, he also realized perfectly well that science was disgarding all the intuitive signs something was going terribly wrong and lost any connection to a firm foundation which could be built upon:

"All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken." (Albert Einstein, 'The Born-Einstein Letters' Max Born, translated by Irene Born, Macmillan 1971)

"The quanta really are a hopeless mess." (Albert Einstein, On doing Quantum Theory calculations with Pauli, 'The Born-Einstein Letters' Max Born, translated by Irene Born, Macmillan 1971)

He also challenged us, to find "a more tangible basis" for adapting "the theoretical foundation of physics" to new knowledge, whereby he clearly rejected the fundamental idea of randomness which had made it's way into theoretical physics:

"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)

"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')

As we shall see, this day has finally come. Let us take Einstein's advice and see if we can use "knowledge of the historic and philosophical background" and the analysis of "long-held commonplace concepts" to free ourselves from the shackles of "prejuidice" and "excessive authority" in order to be able to make some "scientific progress" and become "real seekers after truth".

Let us start in 1920, with Einstein's lecture in Leiden, wherein he stated that "space without aether is unthinkable":

"Since according to our present conceptions the elementary particles of matter are also, in their essence, nothing else than condensations of the electromagnetic field, our present view of the universe presents two realities which are completely separated from each other conceptually, although connected causally, namely, gravitational ether and electromagnetic field, or as they might also be called space and matter.

Of course it would be a great advance if we could succeed in comprehending the gravitational field and the electromagnetic field together as one unified conformation. Then for the first time the epoch of theoretical physics founded by Faraday and Maxwell would reach a satisfactory conclusion. The contrast between ether and matter would fade away, and, through the general theory of relativity, the whole of physics would become a complete system of thought, like geometry, kinematics, and the theory of gravitation. An exceedingly ingenious attempt in this direction has been made by the mathematician H. Weyl; but I do not believe that his theory will hold its ground in relation to reality. Further, in contemplating the immediate future of theoretical physics we ought not unconditionally to reject the possibility that the facts comprised in the quantum theory may set bounds to the field theory beyond which it cannot pass.

Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether 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 ether 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."

Let us first note that Einstein connected the "electromagnetic field" to "space" and "gravitational ether" to "matter", while at the same time he referred to matter as "condensations of the electromagnetic field".

However, perhaps the most essential to note is the following: "space is endowed with physical qualities; in this sense, therefore, there exists an ether".

In a Letter to Max Born (March 1948) (published in Albert Einstein-Hedwig und Max Born (1969) "Briefwechsel 1916-55") titled "What must be an essential feature of any future fundamental physics?" Einstein wrote:

"I just want to explain what I mean when I say that we should try to hold on to physical reality.

We are … all aware of the situation regarding what will turn out to be the basic foundational concepts in physics: the point-mass or the particle is surely not among them; the field, in the Faraday-Maxwell sense, might be, but not with certainty. But that which we conceive as existing ("real") should somehow be localized in time and space. That is, the real in one part of space, A, should (in theory) somehow "exist" independently of that which is thought of as real in another part of space, B. If a physical system stretches over A and B, then what is present in B should somehow have an existence independent of what is present in A. What is actually present in B should thus not depend the type of measurement carried out in the part of space A; it should also be independent of whether or not a measurement is made in A.

If one adheres to this program, then one can hardly view the quantum-theoretical description as a complete representation of the physically real. If one attempts, nevertheless, so to view it, then one must assume that the physically real in B undergoes a sudden change because of a measurement in A. My physical instincts bristle at that suggestion.

However, if one renounces the assumption that what is present in different parts of space has an independent, real existence, then I don't see at all what physics is supposed to be describing. For what is thought to be a "system" is after all, just conventional, and I do not see how one is supposed to divide up the world objectively so that one can make statements about parts."

Now let us go back to "space is endowed with physical qualities; in this sense, therefore, there exists an ether". Since our objective is to form a physical theory based on fundamental ideas, it is of the most importance that we clearly define our ideas and concepts and make sure that we keep the concepts we use consistent within our theory.

When considering the concepts of "space", "physical qualities" and "aether", we must therefore clearly define what is what. And besides these three concepts, we will need another one, which is "location", which we need in order to describe what is where.

The concept of location is logically closely related to the concept of space, it is an aspect of "space". In order to describe this aspect of space, we use coordinate systems, which are also called "reference frames". Simply put, reference frames describe what is where within what we call "space" from a certain point of view called an "observer".

However, once we have a way to describe what is where, we do not yet have a way to describe "what is what", which would be these "physical qualities" which surround us, that which we normally consider to be "in" space. So, "physical qualities", that which is "in" space, is logically not an aspect of space and therefore we should define a separate concept to describe that which is "in" space, which we shall call "the aether" from now on.

This way, we have a clear and fundamental distinction between the concepts of "space" and that which is "in" space. With these fundamental definitions, "space" cannot have "physical qualities" because these are fundamentally described by the "aether", that which is "in" space. And therefore, "space" cannot enact forces upon the aether, because forces fundamentally describe physical interactions between two or more "things" like "waves", "particles" and "bodies", which are "in" space along Newton's third law of "every action is accompanied by an equivalent reaction".

Based on these fundamental ideas, we can formulate a strong sceptic argument against Einstein's relativity theory, as has been done by Nikola Tesla:

"It might be inferred that I am alluding to the curvature of space supposed to exist according to the teachings of relativity, but nothing could be further from my mind. I hold that space cannot be curved, for the simple reason that it can have no properties. It might as well be said that God has properties. He has not, but only attributes and these are of our own making. Of properties we can only speak when dealing with matter filling the space. To say that in the presence of large bodies space becomes curved, is equivalent to stating that something can act upon nothing. I, for one, refuse to subscribe to such a view."

And:

"During the succeeding two years of intense concentration I was fortunate enough to make two far-reaching discoveries. The first was a dynamic theory of gravity, which I have worked out in all details and hope to give to the world very soon. It explains the causes of this force and the motions of heavenly bodies under its influence so satisfactorily that it will put an end to idle speculations and false conceptions, as that of curved space.

According to the relativists, space has a tendency to curvature owing to an inherent property or presence of celestial bodies. Granting a semblance of reality to this fantastic idea, it is still self-contradictory. Every action is accompanied by an equivalent reaction and the effects of the latter are directly opposite to those of the former. Supposing that the bodies act upon the surrounding space causing curvature of the same, it appears to my simple mind that the curved spaces must react on the bodies and, producing the opposite effects, straighten out the curves. Since action and reaction are coexistent, it follows that the supposed curvature of space is entirely impossible.

But even if it existed it would not explain the motions of the bodies as observed. Only the existence of a field of force can account for them and its assumption dispenses with space curvature. All literature on this subject is futile and destined to oblivion. So are also all attempts to explain the workings of the universe without recognizing the existence of the ether and the indispensable function it plays in the phenomena."

Within our definition of "space" and that what is "in" space, Tesla is absolutely right. When we define space itself to be an empty room, while we define that what is "in" it as being the aether, then our model becomes inconsistent when we assign certain aspects of that which is defined to be "in" empty space as being aspects of empty space.

However, in principle, it is possible to describe certain aspects, certain "physical qualities", as being aspects of empty space instead of that which is "in" space, the aether. In other words: it makes no fundamental difference whether one chooses to describe certain aspects within the context of "space" or within the context of the "aether", that which is "in" space.

In some cases, this is actually being done consciously, such as the use of so called "non-intertial reference frames". If you are describing what happens to objects which are within an accelerating rocket flying trough space, for example, then it is convenient to use a reference frame, a coordinate system, which moves along with the rocket. However, in that case the objects which are present within the rocket will "fall" to the floor, so there appears to be a force akin to gravity to be present within the rocket, which arises from the acceleration of the rocket. Such an apparent force is called a "fictitious force" or "pseudo force":

"A fictitious force, also called a pseudo force, d'Alembert force or inertial force, is an apparent force that acts on all masses whose motion is described using a non-inertial frame of reference, such as a rotating reference frame.

The force F does not arise from any physical interaction between two objects, but rather from the acceleration a of the non-inertial reference frame itself.

[...]

A fictitious force on an object arises when the frame of reference used to describe the object's motion is accelerating compared to a non-accelerating frame.

As a frame can accelerate in any arbitrary way, so can fictitious forces be as arbitrary (but only in direct response to the acceleration of the frame). However, four fictitious forces are defined for frames accelerated in commonly occurring ways: one caused by any relative acceleration of the origin in a straight line (rectilinear acceleration); two involving rotation: centrifugal force and Coriolis force; and a fourth, called the Euler force, caused by a variable rate of rotation, should that occur.

Gravitational force would also be a fictitious force based upon a field model in which particles distort spacetime due to their mass."

Note that in current Physics, Gravity is also considered to be such a fictitious force.

As said, it is possible to do this and in this particular case, it enabled us to predict new phenomena, like time dilation and length contraction, which were theretofore unknown. This validated the correctness of the underlying aspects that were introduced to the model. However, the way these aspects were described within the model as being aspects of space (and time) itself, essentially describes certain "physical qualities" within a context that is not the most logical context to describe these with. Doing so distorts the conceptual relations between "space" and that which is "in" space as well as "in" time. This makes it almost impossible to extend the description of the newly introduced concepts, which were added to the model in order to describe gravity, to the current description of the Electromagnetic fields. After all, the latter have been exclusively modelled by Maxwell within the context of the "aether".

Fundamentally, the concept that has been introduced into the physics model by Einstein is the concept of compressibility. He essentially described it in terms of compressibility of space (and time) itself, but of course this concept can just as well be described within the context of the aether, that which is "in" space. This way, we can describe all known "physical qualities" within the same context, which, as we shall see, enables us to describe both the gravitational field and the electromagnetic field within one consistent, Unified model.

Doing so leads to a different understanding of "space" and especially "time", which equals our "normal", intuitive interpretation of space and time. Within Einstein's model, for example, "time dilation" is interpreted as a phenomenon influencing time itself. Within our model, "time dilation" is interpreted as a phenomenon influencing the internal hardware of our clocks, our measuring devices, basically influencing the "ticking rate" of our clocks and not time itself. Also, within our model, "influencing time" and/or "time travel" is interpreted as a phenomenon influencing the internal hardware of our bodies, our physical minds, basically influencing the "ticking rate" of our minds and thus our experience of time and not time itself.

So, essentially, our model predicts that an "Universal absolute invariant time(frame)" exists, which is not relative to the observer, while Einstein's model predicts that this is not the case.

The conclusions regarding the possibilities of time travelling by physical bodies (including our own), are practically the same. The only possibility for physical time travel is limited to slowing down (or accelerating) of our physical experience of time, which is caused by increasing (or decreasing) our internal "clocks". So, our model predicts that one cannot physically travel back trough time to the past.

However, the conclusions regarding the possibilities of travelling at speeds (vastly) exceeding the speed of light as measured normally on Earth are very different. Our model predicts that areas with different densities of the aether exist, which may or may not exist in the shape of (magnetic) filaments c.q. vortices. Within such areas, our model predicts that the oscillation frequencies of matter can be much higher than under normal circumstances, which would cause matter c.q. a physical body to shrink, because of the higher density of the compressed' aether surrounding the body. This would result in experiencing "time" to slow down, while at the same time enabling a physical body to travel at much higher speeds, because the speed of light within a compressed area of aether would be higher than what we encounter on Earth.

The Foundation of Modern Physics

"All attempts to explain the workings of the universe without recognizing the existence of the ether and the indispensable function it plays in the phenomena is futile and destined to oblivion." - Nikola Tesla (rephrased)

As we saw, Einstein was quite critical on the Quantum Mechanics theory. He clearly stated his disbelief in "the God who plays dice" and said he had no doubt his instinctive attitude will eventually turn out to be the correct one. So, let us start with considering the foundation of Quantum Mechanics, the wave-particle duality principle. As described on Wikipedia:

Wave–particle duality is the concept that every elementary particle or quantic entity may be partly described in terms not only of particles, but also of waves. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. As Albert Einstein wrote: "It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do".

Through the work of Max Planck, Einstein, Louis de Broglie, Arthur Compton, Niels Bohr and many others, current scientific theory holds that all particles also have a wave nature (and vice versa). This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules.

[...]

James Clerk Maxwell discovered that he could combine four simple equations, which had been previously discovered, along with a slight modification to describe self-propagating waves of oscillating electric and magnetic fields. When the propagation speed of these electromagnetic waves was calculated, the speed of light fell out. It quickly became apparent that visible light, ultraviolet light, and infrared light (phenomena thought previously to be unrelated) were all electromagnetic waves of differing frequency.

[...]

At the close of the 19th century, the reductionism of atomic theory began to advance into the atom itself; determining, through physics, the nature of the atom and the operation of chemical reactions. Electricity, first thought to be a fluid, was now understood to consist of particles called electrons. This was first demonstrated by J. J. Thomson in 1897 when, using a cathode ray tube, he found that an electrical charge would travel across a vacuum (which would possess infinite resistance in classical theory). Since the vacuum offered no medium for an electric fluid to travel, this discovery could only be explained via a particle carrying a negative charge and moving through the vacuum. This electron flew in the face of classical electrodynamics, which had successfully treated electricity as a fluid for many years (leading to the invention of batteries, electric motors, dynamos, and arc lamps). More importantly, the intimate relation between electric charge and electromagnetism had been well documented following the discoveries of Michael Faraday and James Clerk Maxwell. Since electromagnetism was known to be a wave generated by a changing electric or magnetic field (a continuous, wave-like entity itself) an atomic/particle description of electricity and charge was a non sequitur [Latin for: "it does not follow"].

[...]

In 1901, Max Planck published an analysis that succeeded in reproducing the observed spectrum of light emitted by a glowing object. To accomplish this, Planck had to make an ad hoc mathematical assumption of quantized energy of the oscillators (atoms of the black body) that emit radiation. It was Einstein who later proposed that it is the electromagnetic radiation itself that is quantized, and not the energy of radiating atoms.

[...]

Wave–particle duality is an ongoing conundrum in modern physics. Most physicists accept wave-particle duality as the best explanation for a broad range of observed phenomena; however, it is not without controversy. Alternative views are also presented here. These views are not generally accepted by mainstream physics, but serve as a basis for valuable discussion within the community.

[...]

At least one physicist considers the "wave-duality" as not being an incomprehensible mystery. L.E. Ballentine, Quantum Mechanics, A Modern Development, p. 4, explains:

When first discovered, particle diffraction was a source of great puzzlement. Are "particles" really "waves?" In the early experiments, the diffraction patterns were detected holistically by means of a photographic plate, which could not detect individual particles. As a result, the notion grew that particle and wave properties were mutually incompatible, or complementary, in the sense that different measurement apparatuses would be required to observe them. That idea, however, was only an unfortunate generalization from a technological limitation. Today it is possible to detect the arrival of individual electrons, and to see the diffraction pattern emerge as a statistical pattern made up of many small spots (Tonomura et al., 1989). Evidently, quantum particles are indeed particles, but whose behaviour is very different from [what] classical physics would have us to expect.

This "conundrum" leaves us with a kind of schizophrenic picture of reality, a puzzle consisting of pieces that do not match to one another and so far all efforts to complement them with additional pieces to make the picture complete have failed. So far, we have no consistent "theory of everything", most notably no theory establishing a connection between electromagnetics and gravity. Clearly, somewhere something is amiss and if it's not a matter of a missing piece, something must be amiss with the pieces we have.

Perhaps the most important piece of the puzzle we have are Maxwell's equations, which describe the electromagnetic fields. Based on these equations, we can come to one particular description of Electromagnetic radiation, namely a description of continuous transverse waves:

Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to each other and perpendicular to the direction of energy and wave propagation, forming a transverse wave.*

As we saw, electromagnetic radiation has been found to be quantized. It does not exist as continuous waves, but rather as some kind of distinguishable "packets" called photons:

Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can subsequently interact with any charged particles. EM waves carry energy, momentum and angular momentum away from their source particle and can impart those quantities to matter with which they interact. Quanta of EM waves are called photons, which are massless, but they are still affected by gravity. Electromagnetic radiation is associated with those EM waves that are free to propagate themselves ("radiate") without the continuing influence of the moving charges that produced them, because they have achieved sufficient distance from those charges. Thus, EMR is sometimes referred to as the far field. In this language, the near field refers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena.

This illustrates the "non sequitur" issue we encountered above, namely that electromagnetic waves are considered to be produced by moving "charged particles", while these particles show this "wave particle duality" behaviour themselves, as does "EM radiation" on it's turn. In other words: electromagnetic radiation is essentially considered to be produced by movements of "quanta" of electromagnetic radiation, called either "photons" or "particles". Kind of a dog chasing it's own tail, or recursion as software engineers call it:

whatIsRecursion():
        if you understand Recursion:
              return
        else:
             whatIsRecursion()

We also note that, despite the Maxwell equations only describing one type of electromagnetic waves, actually at least two types of electromagnetic wave phenomena are known to exist, namely the "near" and the "far" field:

The near field and far field are regions of the electromagnetic field around an object, such as a transmitting antenna, or the result of radiation scattering off an object. Non-radiative 'near-field' behaviors of electromagnetic fields dominate close to the antenna or scattering object, while electromagnetic radiation 'far-field' behaviors dominate at greater distances.

Far-field E and B field strength decreases inversely with distance from the source, resulting in an inverse-square law for the radiated power intensity of electromagnetic radiation. By contrast, near-field E and B strength decrease more rapidly with distance (with inverse-distance squared or cubed), resulting in relative lack of near-field effects within a few wavelengths of the radiator.

[...]

The far field is the region in which the field acts as "normal" electromagnetic radiation.

[...]

In the quantum view of electromagnetic interactions, far-field effects are manifestations of real photons, whereas near-field effects are due to a mixture of real and virtual photons. Virtual photons composing near-field fluctuations and signals, have effects that are of far shorter range than those of real photons.

This quantum view suggests that the far field is well understood and described, while in order to describe the near field we need to introduce a new concept: virtual, or literally: "imaginary", photons. In the everyday practice of Electrical Engineering, however, it is the near field that can be computed with "FTDT" simulation software such as Meep:

A time-domain electromagnetic simulation simply takes Maxwell's equations and evolves them over time within some finite computational region, essentially performing a kind of numerical experiment.

Once the near field has been computed, the far field is computed afterwards, as is stated on the website of Lumerical for example:

The near to far field projections calculate the EM fields anywhere in the far field. The near field data is obtained from one of Lumerical's optical solvers, then the far field projection is calculated as a post-processing step.

These are the kind of inconsistencies we encounter all over the place in the standard model. This one, however, is found at the very foundation of Quantum Mechanics. If we can't even agree on what is actually being described by Maxwell's equations, it's no wonder we are still living in a world of an "ongoing wave-particle duality conundrum".

And this is not the only clue which suggests that we need to re-examine Maxwell's equations in order to come to a satisfactory solution to the many inconsistencies found in the standard model. C. K. Thornhill shows in his paper "Real or Imaginary Space-Time? Reality or Relativity?" that these same Maxwell equations are not only the foundation of Quantum Mechanics, but also of the concept of "imaginary" Einsteinian space-time and the relativity theory. The abstract of his article:

The real space-time of Newtonian mechanics and the ether concept is contrasted with the imaginary space-time of the non-ether concept and relativity. In real space-time (x, y, z, ct) characteristic theory shows that Maxwell’s equations and sound waves in any uniform fluid at rest have identical wave surfaces. Moreover, without charge or current, Maxwell’s equations reduce to the same standard wave equation which governs such sound waves. This is not a general and invariant equation but it becomes so by Galilean transformation to any other reference-frame. So also do Maxwell’s equations which are, likewise, not general but unique to one reference-frame. The mistake of believing that Maxwell’s equations were invariant led to the Lorentz transformation and to relativity; and to the misinterpretation of the differential equation for the wave cone through any point as the quadratic differential form of a Riemannian metric in imaginary space-time ( x, y, z, i ct). Mathematics is then required to tolerate the same equation being transformed in different ways for different applications. Otherwise, relativity is untenable and recourse must then be made to real space-time, normal Galilean transformation and an ether with Maxwellian statistics and Planck’s energy distribution.

Let us note that the "non sequitur" issue we already encountered twice so far, once again comes to the forefront, this time at the very foundation of Einstein's relativity theory. The introduction of the concept of "charge", defined as being a property of matter, is clearly problematic:

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges: positive and negative. Like charges repel and unlike attract. An object is negatively charged if it has an excess of electrons, and is otherwise positively charged or uncharged. The SI derived unit of electric charge is the coulomb (C).

It not only led to a "non sequitur" issue in Quantum Mechanics, but also to a distortion of the concepts of space and time within the relativity theory. And actually, it is quite clear why the current definition of the concept of "charge" is problematic. If the concept of "charge", which is intimately related to electromagnetism, is defined as being a physical property of matter, while particles show this "wave-particle duality", it is clear that exactly this arbitrary, explicit connection between electromagnetism and matter is the root cause for this "non sequitur" issue. So, if we can re-define our concept of "charge" in a meaningful way, we can resolve this important problem. In other words: it is clear that we need to re-examine the origin of this concept in Maxwell's work.

But before we do that, let us shortly address the issue of whether or not the aether theory has been disproven by the Michelson-Morley experiment and the myth that GPS would not be possible without the relativity theory. These issues have been thoroughly addressed by William H. Cantrell, Ph.D., in his article "A Dissident View of Relativity Theory"(on-site copy), amongst others referring to the work of Ronald Hatch:

Given that the nothingness of a perfect absolute vacuum is bestowed with the physical properties of a permittivity, epsilon_0 of 8.854 pF/m, a permeability mu_0 of 4pi x 10-7 H/m, and a characteristic impedance of 377 ohms, is the concept of an aether really that outlandish?

[...]

What does one of the world’s foremost experts on GPS have to say about relativity theory and the Global Positioning System? Ronald R. Hatch is the Director of Navigation Systems at NavCom Technology and a former president of the Institute of Navigation. As he describes in his article for this issue (p. 25, IE #59), GPS simply contradicts Einstein’s theory of relativity. His Modified Lorentz Ether Gauge Theory (MLET) has been proposed as an alternative to Einstein’s relativity. It agrees at first order with relativity but corrects for certain astronomical anomalies not explained by relativity theory.

This same Ron Hatch recemtly gave a presentation about his findings:

RON HATCH: Relativity in the Light of GPS, II

Revisiting Maxwell's equations

In order to re-examine and eventually revise Maxwell's equations, we need to go all the way back to his publications in the late 1800s and follow his reasoning. Fortunately, Malcolm Longair published an article (pdf) with an overview of Maxwell's work, for the occasion to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. This gives a good historic overview and is easier to read than the originals, because it uses modern SI units. It also contains a table which shows the difference between Maxwell's notations and our modern notations. In this article, we read:

In [..] 1856, Maxwell published the first of his series of papers on electromagnetism, ‘On Faraday's lines of force’. In the preface to his Treatise on Electricity and Magnetism of 1873, he recalled:

"before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday's Experimental Researches in Electricity."

The first part of the paper enlarged upon the technique of analogy and drew particular attention to its application to incompressible fluid flow and magnetic lines of force. [...] In 1856, the partial derivatives were written out explicitly in Cartesian form. The mathematics of rotational fluid flow and the equivalents of div, grad and curl were familiar to mathematical physicists at the time. Thomson and Maxwell, for example, needed these tools to describe fluid flow in vortex ring models of atoms.

Maxwell started with the analogy between incompressible fluid flow and magnetic lines of force. The velocity u is analogous to the magnetic flux density B. If the tubes of force, or steamlines, diverge, the strength of the field decreases, as does the fluid velocity. This enabled Maxwell to write down immediately the mathematical expression for the behaviour of magnetic fields in free space,

$ div \mathbf{B} = 0 $.

The same type of reasoning applies to electric fields in free space, but they can originate on charges and so there is a source term on the right-hand side

$ div \mathbf{E} = \frac{ \rho_e }{ \varepsilon_0 } $,

where E is the electric field strength and ρe is the electric charge density.*

[...]

Maxwell developed his solution in 1861–1862 in a series of papers entitled ‘On physical lines of force’. Since his earlier work on the analogy between u and B, he had become more and more convinced that magnetism was essentially rotational in nature. His aim was to devise a model for the medium filling all space which could account for the stresses that Faraday had associated with magnetic lines of force—in other words, a mechanical model for the aether, which was assumed to be the medium through which light was propagated.

[...]

The model was based upon the analogy between a rotating vortex tube and a tube of magnetic flux. The analogy comes about as follows. If left on their own, magnetic field lines expand apart, exactly as occurs in the case of a fluid vortex tube, if the rotational centrifugal forces are not balanced.

[...]

Maxwell began with a model in which all space is filled with vortex tubes. There is, however, an immediate mechanical problem. Friction between neighbouring vortices would lead to their disruption. Maxwell adopted the practical engineering solution of inserting ‘idle wheels’, or ‘ball–bearings’, between the vortices so that they could all rotate in the same direction without friction. Maxwell's published picture of the vortices, represented by an array of rotating hexagons, is shown in figure 2.

He then identified the idle wheels with electric particles which, if they were free to move, would carry an electric current as in a conductor. In insulators, including free space, they would not be free to move through the distribution of vortex tubes and so could not carry an electric current. I have no doubt that this rather extreme example of the technique of working by analogy was a contributory cause to ‘a feeling of discomfort, and often even of mistrust,…’ to which Poincaré alluded when French mathematical physicists first encountered the works of Maxwell.

Remarkably, this mechanical model for the aether could account for all known phenomena of electromagnetism. As an example of induction, consider the effect of embedding a second wire in the magnetic field of a wire carrying a current I. If the current is steady, there is no change in the current in the second wire. If, however, the current changes, a rotational impulse is communicated through the intervening idle wheels and vortices and a reverse current is induced in the second wire.

Part III of the paper contains the flash of genius which led to the discovery of the complete set of Maxwell's equations. He now considered how insulators store electrical energy. He made the assumption that, in insulators, the idle wheels, or electric particles, can be displaced from their ‘fixed’ equilibrium positions by the action of an electric field. He then attributed the electrostatic energy in the medium to the elastic potential energy associated with the** displacement of the electric particles**. In his subsequent paper of 1865, he refers to this key innovation as electric elasticity.

[...]

Notice that, even in a vacuum for which μ=1, ϵ=1, the speed of propagation of the waves is finite, c=(ϵ0μ0)−1/2. Maxwell used Weber and Kohlrausch's experimental values for the product ϵ0μ0 and found, to his amazement, that c was almost exactly the speed of light. In Maxwell's letters of 1861 to Michael Faraday and William Thomson, he showed that the values agreed within about 1%. In Maxwell's own words, with his own emphasis, in the third part of his series of papers in Philosophical Magazine: "The velocity of transverse modulations in our hypothetical medium, calculated from the electro–magnetic experiments of MM. Kohlrausch and Weber, agrees so exactly with the velocity of light calculated from the optical experiments of M. Fizeau that we can scarcely avoid the inference that light consists in the transverse modulations of the same medium which is the cause of electric and magnetic phenomena."

This remarkable calculation represented the unification of light with electricity and magnetism.

Maxwell was fully aware of the remarkable mechanical basis for his model of the vacuum which had provided the inspiration for his discovery. As he wrote, "The conception of a particle having its motion connected with that of a vortex by perfect rolling contact may appear somewhat awkward. I do not bring it forward as a mode of connection existing in Nature … It is however a mode of connection which is mechanically conceivable and it serves to bring out the actual mechanical connections between known electromagnetic phenomena."

No one could deny Maxwell's virtuosity in determining the speed of light from his mechanical model of electromagnetic forces.

From this historic perspective, we can note the following:

• Maxwell deduced that magnetism was essentially rotational in nature.
• Since the magnetic field was associated with "lines of force" and magnetism was rotational in nature, he modelled the magnetic field as consisting of vortex tubes and postulated that all space is filled with these vortex tubes. In other words: Maxwell modelled the magnetic field of a single permanent magnet as consisting of a number of vortex tubes and NOT as a single vortex.
• Because within this tube model, he got a problem with friction, which he solved by the inserting ‘idle wheels’, or ‘ball–bearings’, between the vortices postulated to fill all space.
• He identified the idle wheels with electric particles, which could move freely in conductors and thus carry an electric current, while they would not be free to move in an insulator, including vacuum, which could thus not carry an electric current.
• He introduced the concept of "displacement of [bound] electric particles" to which he associated a "displacement current" to come to a model describing electric elasticity, both in conductors as well as insulators including the vacuum.
• The combination of mechanical momentum modelled as multiple vortex tubes and mechanical elasticity modelled as displacement of [bound] electric particles constitutes the two basic requirements for sustaining oscillations and/or waves: momentum and elasticity.
• When he worked this further out, he noted that the transverse waves he had described this way turned out to propagate at the speed of light, which connected the phenomena of light with that of electromagnetism.

Let us first consider his magnetic model. While he realised the rotational nature of magnetism, he chose not to explicitly describe magnetism as vortexes in a fluid-like medium, but rather as the result of a (large) number of vortexes postulated to fill all space. Essentially, he abstracted the actual vorticity of magnetism away by describing magnetism as a field B, which describes the force which would act on a charged particle or magnet entering the "field" without any connection whatsoever to how these forces arise from the medium acting upon the charged particle or magnet.

As an analogy, we can think of the force enacted by a steady-state airflow (wind) on the sail of a boat. In this analogy, Maxwell description does not describe how the air flows along the sail and how this results in a force. He essentially describes it as: The force F working on a sail with surface area A at location X in the "air flow field" B is given as:

F(X) = B(X) * A.

It is this abstracting away from the underlying physical model, which shaped 20th century physics. With the description of physical phenomena in terms of mathematical field equations, all connection the the underlying models was lost and replaced by an abstract field model. Freeman Dyson expressed this as follows (as quoted by Longair):

"Maxwell's theory becomes simple and intelligible only when you give up thinking in terms of mechanical models. Instead of thinking of mechanical objects as primary and electromagnetic stresses as secondary consequences, you must think of the electromagnetic field as primary and mechanical forces as secondary. The idea that the primary constituents of the universe are fields did not come easily to the physicists of Maxwell's generation. Fields are an abstract concept, far removed from the familiar world of things and forces. The field equations of Maxwell are partial differential equations. They cannot be expressed in simple words like Newton's law of motion, force equals mass times acceleration. Maxwell's theory had to wait for the next generation of physicists, Hertz and Lorentz and Einstein, to reveal its power and clarify its concepts. The next generation grew up with Maxwell's equations and was at home in a universe built out of fields. The primacy of fields was as natural to Einstein as the primacy of mechanical structures had been to Maxwell."

As we saw, however, Maxwell's equations describe only one type of electromagnetic radiation, transverse waves, while at least two types of waves are known to exist, namely the near and far fields. One of the arguments against the existence of a fluid-like aether is that transverse waves cannot propagate trough a fluid. They can only propagate along the surface of a fluid or along the boundary between two media with different densities, such as a water-air boundary. And actually, water waves are a combination of both longitudinal and transverse motions, which can be beautifully animated:

Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The animation [below] shows a water wave travelling from left to right in a region where the depth of the water is greater than the wavelength of the waves. I have identified two particles in orange to show that each particle indeed travels in a clockwise circle as the wave passes.

As we saw, in the everyday practice of electrical engineering, the near field is what can be simulated using Maxwell's equations, while a post-processing (transformation) step is required to compute the far field. And while in general the far field is considered to be a transverse wave also, this cannot be the case within a fluid-like aether model. In other words: both a fluid-like aether model as well as everyday electrical engineering practice predict that the near field is an actual transverse wave, while the far field has a thusfar unknown nature, although it propagates at speeds up to the speed of light, it possesses a magnetic component and it is quantized. So, if we can identify a type of wave that has these properties and can also propagate trough a fluid-like medium, we may be able to make a model for the far field as well.

Note that the circles in the 2D animation would be long stretched vortexes in 3D, which would correlate directly with Maxwell's vortex tubes, where it not for the ‘idle wheels’, or ‘ball–bearings’ he introduced to his model in order to avoid perceived problems with friction. Also note that the distance between the rotating particles varies with time, which requires a compressible medium. In other words: if we replace Maxwell's incompressible aether with a compressible one, we can avoid the friction problem altogether in an elegant and natural way. Doing so, would also predict a third type of waves to exist in the aether, namely longitudinal waves which would not have a magnetic component and would therefore not be electromagnetic but dielectric in nature.

Now let us consider the rotational nature of the magnetic field of a permanent magnet. This can be made visible by placing a permanent magnet under water and use it as an electrode in an electrolysis process. At YouTube, several examples of such an experiment can be found (1, 2, 3), which show that the magnetic field of a permanent magnet actually has a vortex nature:

Since these are permanent magnets connected to a DC power supply, it is hard to imagine a transverse electromagnetic wave propagating along the surface of the magnet to be responsible for inducing the vortex, because that would also generate electromagnetic radiation, which would probably have been detected by now. If we assume this to be correct, then if the nature of the magnetic field would be like in Maxwell's multi-vortex-tube model, we would not expect a vortex to appear in the water. For this reason, we must reject Maxwell's multi-vortex model filling all space.

Another reason to do so has to do with the 'idle wheels’, or ‘ball–bearings’ and especially the identification thereof with electric particles, such as we now know the electron to be. While the association of the flow of electric current with either bound or free electric particles would be pretty accurate in the case of (semi)conductors and insulators, it would be hard to imagine ‘ball–bearing’ electrons to be bound in vacuum and therefore we have to reject the ‘ball–bearing' friction resolving tubes and with it the model of associating magnetism with vortex tubes in an incompressible medium.

In other words: the only way to resolve the friction problem while maintaining the rotational nature of magnetism is to postulate the aether to be a compressible medium.

With such postulate, we have little choice but to directly associate the concept of electric elasticity with the compressibility of the aether itself, thus associating Maxwell's "displacement current" concept with currents flowing within the aether itself instead of being "carried" by electric particles. Thus, we would no longer consider the concept of "charge" to be a physical property of matter, which thus would allow us to resolve the "non sequitur" recursion problem we encountered earlier in an elegant and intuitive way.

So far, we have found ample reasons to continue our effort by considering the medium be akin to a compressible fluid, although we have not yet solved the problem of what kinds of waves could make up the far field, consisting of some kind of distinctly distinguishable entities, which sometimes propagate at the speed of light (light, electromagnetic radiation) and sometimes at slower speeds (matter, particles).

For now, we just note that:

• Vortex rings do exist and can propagate trough a fluid-like medium:

• We can conceive structures consisting of multiple vortexes to also exist (courtesy Nassim Haramein):

• Haramein's "string theory" clearly suggests rotational movements to play an important role within 3D wave propagation, etc.:

With this in mind, we also note that David LaPoint performed some fascinating experiments in the laboratory, which shows in various ways how magnetic forces play an indispensable function in the Universe, from the nano-scale all the way up to galaxies and beyond:

The link starts the video at about 19 minutes in, where it is shown and said that a plasma spins under the influence of a magnetic field, which confirms that magnetic forces are indeed rotational in nature.

End of part I. What's next?

In An exceptionally elegant "Theory of Everything" we make the mathematical case that there is a hole in Maxwell's equations which should not be there, given that we started with the same basic hypothesis as Maxwell did:

A physical, fluid-like medium called "aether" exists.

Maxwell did not explicitly use this underlying hypothesis, but abstracted it away. This leads to a mathematically inconsistent model wherein, for example, units of measurements do not match in his definition for the electric potential field. By correcting this obvious flaw in the model and extending it with a definition for the gravity field, we obtain a simple, elegant, complete and mathematically consistent "theory of everything" without "gauge freedom", the fundamental theoretical basis for Quantum Weirdness which we must therefore reject.