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 | |  Lorentz's Theory of the Electron (1900) | |
[size=35]Lorentz's Theory of the Electron (1900)[/size]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 / wave 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 this 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 the Article onQuantum 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).
We shall consider this in more detail shortly, but first let us proceed with the further discoveries of Lorentz.
The Lorentz Transformations & How the Electron Changes Ellipsoidal Shape With MotionOn How a Change in Velocity of the In-Wave (Vel. of Light c) Causes a Change in Ellipsoidal Shape of the In-Wave, and also Causes a Change in the Future Position and Thus the Apparent Motion (Acceleration) of the Wave-Center.Thus far we have largely considered a SSW stationary in Space, so let us now consider a SSW where the Wave-Center appears to be moving through Space, as this then leads to the Lorentz Transformations and the foundations of Special Relativity.
As the particle does not exist, and instead we are considering the behaviour of the Wave-Center of a SSW, we realize that the motion of the particle through Space is actually the apparent motion of successive Wave-Centers which are determined by where each successive spherical (in reality ellipsoidal) In-Wave meets at its respective Wave-Center.Fig:1.6.1 The Ellipsoidal Shape of a Moving Wave-Center: If the In-Waves on the right are slowed down as they travel in through Space of higher mass-energy density of space (Principle II) then they are stretched back into an ellipsoidal shape (rather than being exactly spherical) and have a shorter Wavelength. It is this change in ellipsoidal shape and Wavelength of the In-Wave which causes the apparent motion of the Wave-Center and thus the Lorentz Transformations.If a Wave-Center is to move through Space then it is clear that we must change the velocity of the In-Waves from one side relative to the other such that they no longer meet in the same place. Thus by changing the velocity of the In-Waves we cause the Wave-Center to change its position in Space. This is the cause of acceleration (and in fact of all forces, as per Newton's Law of Inertia F=m.a).This also explains the foundation of the Lorentz transformations and how this was used by Albert Einstein to develop his special and general relativity.To begin, if we slow down the In-Wave on one side of the Wave-Center then these In-Waves will meet more in the direction of the slower In-Waves. Further, the spherical shape of the In-Waves will become ellipsoidal and this change in shape will directly relate to the apparent motion of the Wave-Center (particle). A convenient analogy is to imagine the point (particle) where the In-Wave meets at its Wave-Center as a footstep, and the motion of the particle through Space can be imagined as a sequence of discrete steps corresponding to where each successive In-Wave meets at its Wave-Center.The Lorentz Transformations provide formulas for the change of ellipsoidal shape of matter (as a spatially extended e-m field) with motion of the Wave-Center (particle) and how this affects Mass, Time and Length/Dimension. The motion (and change in ellipsoidal shape) is simply relative between the source and observer, it makes no difference as to who is moving. (This formula for change of mass and dimension has been amply verified in particle accelerators and TV tubes.)As Born confirms;Lorentz assumed that every moving electron contracts in the direction of motion, so that from a sphere it becomes a flattened spheroid of revolution, the amount of flattening depending in a definite way on the velocity. This hypothesis seems at first sight strange. It certainly gives a simpler formula for the way electromagnetic mass depends on velocity than does Abraham's theory, but this in itself does not justify it. (Born, 1924)As the dimension of matter as Spherical Wave Motions is determined by BOTH the wavelength and shape of the ellipsoidal standing waves about the Wave-Centre of the electron (matter), which relates to the motion of the centre, thus the moving electron's spatial dimensions must be distorted into an ellipsoidal shape. This explains the true foundations of the Lorentz Transformations and the 'null result' of the Michelson-Morley experiment. And Lorentz was very close to the truth in explaining this, he writes;In order to explain this absence of any effect of the Earth's translation (in the Michelson/Morley experiment), I have ventured the hypothesis, that the dimensions of a solid body undergo slight change, of the order of v2/c2, when it moves through the ether.
From this point of view it is natural to suppose that, just like the electromagnetic forces, the molecular attractions and repulsions are somewhat modified by a translation imparted to the body, and this may very well result in a change of dimensions. ... The electrons themselves become flattened ellipsoids. (Lorentz, 1906) Fig: 1.6.2 The Michelson-Morley experiment with the center of an ellipsoidal wave system as the observer. Due to our dimension being determined by wavelength, we shall always measure arm 1 of an interferometer, to be the same length as that of arm 2, irrespective of which direction we may rotate the interferometer. The arms are both 7 wavelengths long. From this we can conclude that it will take the same time for the ellipsoidal In-Waves to propagate in to the center along arm 1 as it does along arm 2. (This must be true, as the electron 'particle is caused by the Wave-Center of the ellipsoidal wave system, and this is where the ellipsoidal wave meets, obviously at the same time. As there is no time difference for the two paths, no interference is observed.)
NOTE: This diagram is not exactly accurate, but it gives you the general idea!The Michelson Morley experiment confirms that this is true, and that the light takes the same time to travel each path. This is a general principle, and is the cause of Albert Einstein's principle of special relativity.
This enables Albert Einstein to postulate that the velocity of light is always measured to be the same, as this is true. Albert Einstein writes;The so called special or restricted relativity theory is based on the fact that Maxwell's equations (and thus the law of propagation of light in empty space) are converted into equations of the same form, when they undergo a Lorentz transformation. (Albert Einstein, 1954)So now let us briefly explain Albert Einstein's Relativity, which has had such a profound, and yet ultimately confusing, impact on modern physics.
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