Consciousness, Physics, and the Holographic Paradigm
Essays by A.T. Williams
Part I: Sneaking Up On Einstein
In physics, as elsewhere, the map is not the territory.
- A.T. Williams
Section 6: Turning Points
(excerpted from On the Generalized Theory of Gravitation, by Albert Einstein)
In Newtonian physics the elementary theoretical concept on which the theoretical description of material bodies is based is the material point, or particle. Thus matter is considered a priori to be discontinuous. This makes it necessary to consider the action of material points on one another as "action at a distance." Since the latter concept seems quite contrary to everyday experience, it is only natural that the contemporaries of Newton – and indeed Newton himself – found it difficult to accept. Owing to the almost miraculous success of the Newtonian system, however, the succeeding generations of physicists became used to the idea of action at a distance. Any doubt was buried for a long time to come.
But when, in the second half of the nineteenth century, the laws of electrodynamics became known, it turned out that these laws could not be satisfactorily incorporated into the Newtonian system. It is fascinating to muse: Would Faraday have discovered the law of electromagnetic induction if he had received a regular college education? Unencumbered by the traditional way of thinking, he felt that the introduction of the "field" as an independent element of reality helped him to coordinate the experimental facts. It was Maxwell who fully comprehended the significance of the field concept: he made the fundamental discovery that the laws of electrodynamics found their natural expression in the differential equations for the electric and magnetic fields. These equations implied the existence of waves, whose properties corresponded to those of light as far as they were known at that time.
This incorporation of optics into the theory of electromagnetism represents one of the greatest triumphs in striving toward unification of the foundations of physics; Maxwell achieved this unification by purely theoretical arguments, long before it was corroborated by Hertz's experimental work. The new insight made it possible to dispense with the hypothesis of action at a distance, at least in the realm of electromagnetic phenomena; the intermediary field now appeared as the only carrier of electromagnetic interaction between bodies, and the field's behavior was completely determined by contiguous processes, expressed by differential equations.
Now a question arose: Since the field exists even in a vacuum, should one conceive of the field as a state of a "carrier," or should it rather be endowed with an independent existence not reducible to anything else? In other words, is there an "ether" which carries the field; the ether being considered in the undulatory state, for example, when it carries light waves?
The question has a natural answer: Because one cannot dispense with the field concept, it is preferable not to introduce in addition a carrier with hypothetical properties. However, the pathfinders who first recognized the indispensability of the field concept were still too strongly imbued with the mechanistic tradition of thought to accept unhesitatingly this simple point of view. But in the course of the following decades this view imperceptibly took hold.
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 behavior of electrically charged particles in their interaction with one another, does not provide a theory of the particles themselves. They must therefore be treated as mass points on the basis of the old theory. The combination of the idea of a continuous field with that of material points discontinuous in space appears inconsistent. A consistent field theory requires continuity of all elements of the theory, not only in time but also in space, and in all points of space. 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.
Maxwell's equations for empty space remain unchanged if the spacial coordinates and the time are subjected to a particular kind of linear tranformations – the Lorentz transformations ("covariance" with respect to Lorentz transformations). Covariance also holds, of course, for a transformation which is composed of two or more such transformations; this is called the "group" property of Lorentz transformations.
Maxwell's equations imply the "Lorentz group," but the Lorentz group does not imply Maxwell's equations. The Lorentz group may indeed be defined independently of Maxwell's equations as a group of linear transformations which leave a particular value of the velocity – the velocity of light – invariant. These transformations hold for the transition from one "inertial system" to another which is in uniform motion relative to the first. The most conspicuous novel property of this transformation group is that it does away with the absolute character of the concept of simultaneity of events distant from each other in space. On this account it is to be expected that all equations of physics are covariant with respect to Lorentz transformations (special theory of relativity). Thus it came about that Maxwell's equations led to a heuristic principle valid far beyond the range of the applicability or even validity of the equations themselves.
Special relativity has this in common with Newtonian mechanics: The laws of both theories are supposed to hold only with respect to certain coordinate systems: those known as "inertial systems." An inertial system is a system in a state of motion such that "force-free" material points within it are not accelerated with respect to the coordinate system. However, this definition is empty if there is no independent means for recognizing the absence of forces. But such a means of recognition does not exist if gravitation is considered as a "field."
Let A be a system uniformly accelerated with respect to an "inertial system" I. Material points, not accelerated with respect to I, are accelerated with respect to A, the acceleration of all the points being equal in magnitude and direction. They behave as if a gravitational field exists with respect to A, for it is a characteristic property of the gravitational field that the acceleration is independent of the particular nature of the body. There is no reason to exclude the possibility of interpreting this behavior as the effect of a "true" gravitational field (principle of equivalence). This interpretation implies that A is an "inertial system," even though it is accelerated with respect to another inertial system. (It is essential for this argument that the introduction of independent gravitational fields is considered justified even though no masses generating the field are defined. Therefore, to Newton such an argument would not have appeared convincing.) Thus the concepts of inertial system, the law of inertia and the law of motion are deprived of their concrete meaning – not only in classical mechanics but also in special relativity. (The parenthetical remarks are Einstein's)1
In general, and in addition to describing a serious limitation of closed or isolated (conservative) material systems, Einstein's example also describes the expected behavior of an open (nonconservative) material system in which – according to the universal principle of energy – not only electromagnetic and gravitational fields, but also independent large and small nonconservative inertial systems like galaxies and the energetic atom are essentially discrete states of energy within the fundamental, irreducible, nonmaterial primordial energy domain.
Continued in Chapter 6, Section 1: Cosmology
Reference Notes (Click on the Note number to return to the text):
1 Excerpted from Scientific American, Vol. 182, No. 4, April 1950, pp. 13-17. Reprinted in Ideas and Opinions, pp. 341-356. Wings Books, New york, NY, 1954. ISBN 0-517-00393-7
Back to Chapter 5, Section 5: The Energetic Atom, Inertia, and Nonmaterial Interfaces
Index: Consciousness, Physics, and the Holographic Paradigm
Last Edit: October 27, 2006.
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Copyright © 2006-2008 by Alan T. Williams. All rights reserved.