James Clerk Maxwell

Physics - Famous Scientists - James Clerk MaxwellThe Wave Structure of Matter explains James Clerk Maxwell's Equations (1876) and the Finite Velocity of Light Waves

In speaking of the Energy of the field, however, I wish to be understood literally. All energy is the same as mechanical energy, whether it exists in the form of motion or in that of elasticity, or in any other form. The energy in electromagnetic phenomena is mechanical energy. (James Clerk Maxwell)

The precise formulation of the time space laws of those fields was the work of Maxwell (1870s). Imagine his feelings when the differential equations he had formulated proved to him that the electromagnetic fields spread in the form of polarized waves and with the speed of light! To few men in the world has such an experience been vouchsafed.
Only after Hertz (1888) had demonstrated experimentally the existence of Maxwell's electromagnetic waves did resistance to the new theory break down. And what was true for electrical action could not be denied for gravitation. Everywhere Newton's (instant) actions-at-a-distance gave way to fields spreading with finite velocity.
At that thrilling moment he surely never guessed that the riddling nature of light, apparently so completely solved, would continue to baffle succeeding generations. (Albert Einstein, 1954)

Introduction

As Maxwell's Equations are founded on the ideas of Michael Faraday I shall begin this introduction with a brief summary of Faraday's conception of the Electric and Magnetic fields. I have great respect for Michael Faraday, thus it is unfortunate that history will show his ideas of the electric and magnetic force fields (in 1831) have led modern physics down a path that ultimately led to a dead end of paradox and confusion. The error arose because of the prior conception of matter existing as discrete particles, thus causing the problem of how discrete matter 'particles' acted at-a-distance on other 'particles' in Space.

To solve this problem Faraday developed the mathematical concept of the 'electric and magnetic force fields' as a way of mathematically describing action-at-a-distance for charged particles (i.e. electrons and protons). This is a continuous mathematical 'plot' of the effects (forces and thus accelerated motions) that particles have on other particles in the Space around them, thus it is a description of effects (inductive / a posteriori / observation) rather than causes (deductive / a priori / reason).
And as we shall explain, the ultimate Principles of Physics must be a priori, not a posteriori (i.e. founded on the real world of Causes, not the naive real world of Effects that we observe). Thus there was never an explanation of how the 'particles' generated these 'Electric and Magnetic Forces', and how these forces acted on other particles. And given consideration you begin to realise that Faraday's Force Fields were only ever mathematical constructions, and ultimately they must have a cause.

To Faraday's and Maxwell's credit though, at least they realised that the Space between the particles must exist to carry this force, something that modern physicists seem to conveniently ignore (as their mathematics does not require the necessary connection of Space, though it is obvious that reality does!)
When Maxwell (1876) used Faraday's field theory to assume that light was an Electromagnetic Wave, and then correctly deduced the finite velocity of light, it was a powerful logical argument for the existence of the electromagnetic force field, and that light was a continuous wave like change in the field (electromagnetic radiation) that propagated with the velocity of light c through the ether. But as Einstein noted, by 1900, when it was discovered that light energy was emitted and absorbed in discrete amounts and thus 'particle' like (photons) the assumption that light was a continuous electromagnetic wave failed.

Only now, with the knowledge of the Spherical Standing Wave Structure of Matter in Space, can we finally understand what causes these 'particles and 'forces', and why light is only ever emitted and absorbed in discrete quantities. And as you read the article below I hope you will find the solution as obvious as I do, for it is obvious that Standing Wave Interactions can only occur at discrete frequencies, which correspond to the discrete energy states of both light and matter (and explain why Quantum Theory is founded on Wave Equations).
On the left side of this page you will find links to the main articles which explain and solve many of the problems of postmodern Metaphysics, Physics and Philosophy from the new foundation of the Metaphysics of Space and the Wave Structure of Matter (WSM). We hope you find it interesting.

Sincerely,
Geoff Haselhurst

James Clerk Maxwell

Though this page is on James Clerk Maxwell, it is necessary to begin with the ideas of Michael Faraday, as it was Faraday's conception of the Electric and Magnetic Fields that provided the foundation for Maxwell's Equations.

1. The Particle/Field Duality of Faraday's Electromagnetic Force Field (1832)

(Faraday's Continuous Electromagnetic Force Field is a Mathematical Approximation of Many Discrete Standing Wave Interactions)

The greatest change in the axiomatic basis of physics - in other words, of our conception of the structure of reality - since Newton laid the foundation of theoretical physics was brought about by Faraday's and Maxwell's work on electromagnetic field phenomena. (Albert Einstein, 1931)

Faraday (1832) developed the mathematical concept of the 'electro-magnetic force field' as a way of mathematically describing action-at-a-distance for charged particles (i.e. electrons and protons). This is a continuous mathematical 'plotting' of the effects (forces and thus accelerated motions) that matter has on other matter in the Space around it, thus it is a description of effects rather than causes (Inductive / a posteriori rather than deductive / a priori. And this becomes important when you read Hume and Kant, for they explain that the ultimate Principles of Physics must be a priori, not a posteriori!).

This field concept replaced Newton's instant action-at-a-distance between discrete particles. Importantly, the electromagnetic (e-m) field is a vector (directional) quantity that defines force and direction of acceleration of many charged particles upon one another. It is continuous in the sense that the distance and force between particles can vary by infinitely small amounts.
For example, electrons near one another in Space experience a mutual force of repulsion and this behaviour can be mathematically described using Faraday's e-m field which quantifies this force and describes how it varies with distance and direction. As Albert Einstein explains;

Faraday must have grasped with unerring instinct the artificial nature of all attempts to refer electromagnetic phenomena to actions-at-a-distance between electric particles reacting on each other. How was each single iron filing among a lot scattered on a piece of paper to know of the single electric particles running round in a nearby conductor? All these electric particles together seemed to create in the surrounding space a condition which in turn produced a certain order in the filings.
These spatial states, today called fields, would, he was convinced, furnish the clue to the mysterious electromagnetic interactions. He conceived these fields as states of mechanical stress in an elastically distended body (ether/space). For at that time this was the only way one could conceive of states that were apparently continuously distributed in space. The peculiar type of mechanical interpretation of these fields remained in the background - a sort of placation of the scientific conscience in view of the mechanical (Newtonian) tradition of Faraday's time. (Albert Einstein, 1940)

It seems that the 'electromagnetic force field' is a poorly understood concept which causes considerable confusion. It is quite basic though, as it is nothing more than a mathematical description of how matter affects and moves other matter in the Space around it.
This mathematical 'force field' is a very powerful tool for mathematical physicists (as is the particle) and as a consequence many physicists (including Faraday, Maxwell, and Lorentz) imagined this 'field' to be real and therefore assumed that an 'Aether' (made up of many smaller particles!) must exist in Space as the medium for this 'field'.

Born describes the ether as follows;

The undulatory, or wave theory, on the other hand, sets up an analogy between the propagation of light and the motion of waves on the surface of water or sound waves in air. For this purpose it has to assume the existence of an elastic medium that permeates all transparent bodies; this is the luminiferous ether. The individual particles of this substance merely oscillate about their positions of equilibrium. That which moves on as the light wave is the state of motion of the particles and not the particles themselves. (Born, 1924)

In fact there is no 'ether' simply because there are no 'force fields'. Both are mathematical constructions (rather clumsy and confusing ones at that) to try to explain how matter 'particles' interacted with other 'particles' in the space around them. Once we understand the Spherical Wave Structure of Matter in Space though, then we no longer need these mathematical ideas, instead we realise that Space itself is a continuous wave medium (which necessarily connects all things) and there are no such things as discrete particles.

2. On Maxwell's Equations and the Finite Velocity of Light Waves (1876)

When Maxwell (1876) used this field theory to assume that light was an Electromagnetic Wave, and then correctly deduced the finite velocity of light, it was a powerful logical argument for the existence of the electromagnetic force field, and that light was a wave like change in the field (electromagnetic radiation) that propagated with the velocity of light c through the ether.
In fact Maxwell was simply confirming that all Wave-Center to Wave-Center (particle) interactions are not instantaneous as Newton assumed, but are limited by the velocity of the In-Waves which is the Velocity of Light c.
So while Maxwell misunderstood the true nature of the waves (which are physical waves in Space rather than mathematical vector e-m waves), he is largely correct. This new knowledge was significant as it established the importance of the finite velocity of light c and further enhanced the field theory, thus rejecting Newton's theory of particles and instant action-at-a-distance.

The precise formulation of the time space laws of those fields was the work of Maxwell (1870s). Imagine his feelings when the differential equations he had formulated proved to him that the electromagnetic fields spread in the form of polarized waves and with the speed of light! To few men in the world has such an experience been vouchsafed.
Only after Hertz (1888) had demonstrated experimentally the existence of Maxwell's electromagnetic waves did resistance to the new theory break down. And what was true for electrical action could not be denied for gravitation. Everywhere Newton's (instant) actions-at-a-distance gave way to fields spreading with finite velocity.
At that thrilling moment he surely never guessed that the riddling nature of light, apparently so completely solved, would continue to baffle succeeding generations. (Albert Einstein, 1954)

And this is true. Because they were using a mathematical construction of a continuous e-m wave, rather than the true Spherical Standing Wave, they were in for a rather disturbing discovery not long thereafter. For standing wave interactions only occur at discrete frequencies, like notes on the string of a guitar, thus while the true Spherical Standing Wave Structure of Matter predicts that wave interactions will be discrete, the continuous e-m wave does not anticipate this.
Thus when Max Planck (1900) discovered that there are only certain allowed discrete energy states for electrons in molecules and atoms, and that light is only ever emitted and absorbed by electrons in discrete amounts or 'quanta', contrary to Maxwell's formulation that light is a continuous electromagnetic wave, then this caused a fundamental problem for the field theory that was never resolved. It is only now, with knowledge of the true foundations of physics and reality, that we can understand, and thus anticipate and correct, the errors of contemporary modern physics. (This is explained in more detail in Quantum Theory)

3. On Lorentz's Theory of the Electron (1900)

Hendrik Lorentz in The Theory of the Electron describes the electron as a spherical spatially extended electromagnetic field about a charged particle (electron) in the ether. Thus inadvertently he continued this error of assuming the 'field' to be real, and described the electron as a charged particle that somehow 'generated' a spherical spatially extended 'field' in the ether around it.
This was profound simply because Albert Einstein used Lorentz's foundations to develop his 'field' theory of matter which founds his theory of Relativity. As Albert Einstein explains;

At the turn of the century the theoretical physicists of all nations considered H.A. Lorentz as the leading mind among them, and rightly so. The physicists of our time are mostly not fully aware of the decisive part which H.A. Lorentz played in shaping the fundamental ideas in theoretical physics. The reason for this strange fact is that Lorentz's basic ideas have become so much a part of them that they are hardly able to realize quite how daring these ideas have been and to what extent they have simplified the foundations of physics.
Then came H.A. Lorentz's decisive simplification of the theory. He based his investigations with unfaltering consistency upon the following hypotheses:
The seat of the electromagnetic field is the empty space. In it there are only one electric and one magnetic field vector. This field is generated by atomistic electric charges upon which the field in turn exerts ponderomotive forces. The only connection between the electromagnetic field and ponderable matter arises from the fact that elementary electric charges are rigidly attached to atomistic particles of matter. For the latter Newton's law of motion holds.
Upon this simplified foundation Lorentz based a complete theory of all electromagnetic phenomena known at the time, including those of the electrodynamics of moving bodies. It is a work of such consistency, lucidity, and beauty as has only rarely been attained in an empirical science. (Albert Einstein, 1954)

Lorentz imagined that the ether exists throughout Space and that matter/fields existed as a state of this ether.

Indeed one of the most important of our fundamental assumptions must be that the ether not only occupies all space between molecules, atoms, or electrons, but that it pervades all these particles. We shall add the hypothesis that, though the particles may move, the ether always remains at rest.
I cannot but regard the ether, which can be the seat of an electromagnetic field with its energy and its vibrations, as endowed with a certain degree of substantiality, however different it may be from all ordinary matter. (Lorentz, The Theory of the Electron, 1906)

In fact Lorentz was very close to the truth, if he had just discarded the old notions of 'particles' and 'fields' then his concept of vibrations/motions of the ether, and the equivalence of the ether with Space would have been correct and would then have led to the correct conception of matter as the spherical wave motion of Space.
As Max Born writes;

Lorentz proclaimed the very radical thesis which had never before been asserted with such definiteness: The ether is at rest in absolute space. In principle this identifies the ether with absolute space. Absolute space is no vacuum, but something with definite properties whose state is described with the help of two directed quantities, the electrical field E and the magnetic field H, and, as such is called the ether. (Born, 1924)

Thus we now realise that Lorentz's fundamental problem was believing that the e-m field physically existed. The solution is to realize that, yes, a fundamental Space does exist, as Faraday, Maxwell, and Lorentz sensibly imagined, but it is a wave medium for real waves in a physical medium, described by their Wave Amplitude only (Scalar waves). Space does not exist as an 'ether' for mathematical e-m waves of force (vector waves that must include both force and direction of force for both Electric and Magnetic Fields).

To aid our understanding, let us now have Albert Einstein summarize this confusing state of affairs that had arisen by the early 1900s.

It became clear that there existed in free space states which propagated themselves in waves as well as localized fields which were able to exert forces on electrical masses or magnetic poles brought to the spot. Since it would have seemed utterly absurd to the physicists of the nineteenth century to attribute physical functions or states to space itself, they invented a medium pervading the whole of space, on the model of ponderable matter (i.e. tiny particles that moved backwards and forwards as they propagated waves) the ether, which was supposed to act as a vehicle for electromagnetic phenomena, and hence for those of light as well.
The picture was, then, as follows: space is filled by the ether, in which the material corpuscles or atoms of ponderable matter swim around; the atomic structure of the latter had been securely established by the turn of the century (1900). Thus the introduction of the field as an elementary concept gave rise to an inconsistency of the theory as a whole.
Maxwell's theory, although adequately describing the behaviour of electrically charged particles in their interaction with one another, does not explain the behaviour of electrical densities, i.e., it does not provide a theory of the particles themselves. They must therefore be treated as mass points on the basis of the old Newtonian theory. The combination of the idea of a continuous field with that of material points discontinuous in space appears inconsistent. Hence the material particle has no place as a fundamental concept in a field theory. Thus even apart from the fact that gravitation is not included, Maxwell's electrodynamics cannot be considered a complete theory. (Albert Einstein, 1950)

As Albert Einstein explains though, the particle was a necessary part of the evolution of the field theory, for 'forces' must have 'particles' to act upon!

The participation of matter in electromagnetic phenomena has its origin only in the fact that the elementary particles of matter carry unalterable masses and electric charges and on this account are subject on the one hand to the actions of ponderomotive (Newtonian / Mass) forces and on the other hand possess the property of generating a field (Charge). The elementary particles obey Newton's law of motion for material points. This is the basis on which H. A. Lorentz obtained his syntheses of Newton's mechanics and Maxwell's field theory.
The weakness of this theory lies in the fact that it tried to determine the phenomena by a combination of partial differential equations (Maxwell's field equations for empty space) and total differential equations (equations of motion of point particles), which procedure was obviously unnatural. The inadequacy of this point of view manifested itself in the necessity of assuming finite dimensions for the particles in order to prevent the electromagnetic field existing at the surfaces from becoming infinitely large.
The Maxwell equations in their original form do not, however, allow such a description of particles, because their corresponding solutions contain a singularity. Theoretical physicists have tried for a long time (1936), therefore, to reach the goal by a modification of Maxwell's equations. These attempts have, however, not been crowned with success. Thus it happened that the goal of erecting a pure electromagnetic field theory of matter remained unattained for the time being, although in principle no objection could be raised against the possibility of reaching such a goal. What appears certain to me, however, is that, in the foundations of any consistent field theory the particle concept must not appear in addition to the field concept. The whole theory must by based solely on partial differential equations and their singularity-free solutions. (Albert Einstein, 1936)

(Note: A singularity is where the radius of the particle tends to zero thus the field strength tends to infinity and the mathematics to describe it fails. And this led to Feynman's problems of 'renormalisation' as explained in Quantum Theory.)

This explains why Albert Einstein tried to develop a field theory of matter (without the use/need of particles) though he never succeeded in this venture, simply because matter, as a Spherical Standing Wave Motion of Space cannot be described by continuous force fields. (i.e. Standing Wave interactions are discrete, not continuous!) Thus he writes;

Since the theory of general relativity implies the representation of physical reality by a continuous field, the concept of particles or material points cannot play a fundamental part, nor can the concept of motion. The particle can only appear as a limited region in space in which the field strength or the energy density are particularly high. (Albert Einstein, 1954)

We now realise his error of working with 'spherical force fields' rather than Spherical Wave Motions, whose changing velocities of In-Waves cause the apparent motions of the particles and thus the 'forces' between these particles! Thus he was correct to discard the concept of discrete particles, his error was to also discard the concept of motion and work with 'forces' when a careful analysis leads to the realisation that Motion is more fundamental than Force (i.e. That Force requires the measurement of Motion)

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