The Map Is Not The Territory

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 2

Chapter 5 Section 2: The Map Is Not The Territory

In physics, as elsewhere, the map is not the territory. Michael Faraday was a scientific pathfinder who led the way into unexplored terra incognita by following his instinctive understanding of first principles. Others boldly followed, each in his or her own way. Nonetheless, maps representing unknown territory in physics and the other physical sciences have often proved theoretically unrealistic or less than adequate in the real world despite the remarkable progress from Newton to the present day in scientific knowledge.

Some contemporary Earth science maps, for example, are diligently revised and updated daily through the use of satellite imaging and other remote sensing techniques. Contemporary maps of untested scientific territory also require diligent periodic revision and updating despite the unquestioned authority attributed to the pathways or maps created by eminent scientists and theoreticians of the past. Indeed, absent the comprehensive understanding provided by the universal principle of energy recently discovered by this author, some maps used in some areas by the scientific community may prove to be little better than the 16th and 17th century maps that were purported to represent the New World discovered by Christopher Columbus in 1492.

Gravity:

Isaac Newton (1643-1727) created a new, enlarged map of 17th century scientific territory by quantifying his concept of the forces acting on material bodies. Deriving the equation F = ma in the process, where F is force, m is mass and a is acceleration, Newton published his De Philosophiæ Naturalis Principia Mathematica in 1687.

Newton then generalized his concept by describing the effect of the gravitational force acting between all material bodies in a closed or isolated system and asserted that every material particle in the universe attracts every other material particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The equation thus derived for universal gravitation is F = Gm₁m₂ / r², where F is force, G is the gravitational constant, m₁ and m₂ are the masses under consideration, and r is the distance between their centers.

Careful scientist that he was, Newton declined to offer a hypothesis concerning the physical nature or source of gravity.

It turns out that while gravity has a theoretically infinite range, it is the weakest of the four known fundamental forces or interactions with a strength of only 6 × 10^-39 compared to the strong force (with an assigned value of 1.0) that holds the atomic nucleus together. Gravity is a property of physical mass, and its effect is cumulative. Nonetheless, the source of the gravitational force remains unknown to the present day.

Interestingly, in principle Michael Faraday's early 19th century experiments in diamagnetism demonstrate that the diamagnetic repulsion of a material object by a strong magnetic field can not only counterbalance but also completely overcome the force of gravity between two material bodies. Section 4 of this chapter describes planetary diamagnetism.

Electric charge and magnetism:

Working with static electricity in the last decade of the 18th century CE, Charles-Augustin de Coulomb investigated the electric force between two charged particles and formulated the mathematics of the Coulomb force as it applies to electrostatics and magnetostatics. Coulomb's law is expressed as F = kq₁q₂ / r², where F is force, k is the proportionality factor, q₁ and q₂ are the charges under consideration, and r is the distance between their centers.

The magnetostatic forces described by Coulomb's law were classical approximations based upon their presumed similarity to discrete, isolated electric charges. Curiously, unlike the discrete, isolated negative charge of an electron (e^-, charge -1) or the discrete, isolated positive charge of the positron (e⁺, charge +1), magnetic energy per se is a nonmaterial subatomic phenomenon generated as an inseparable dipole. From the subatomic to the macroscopic scale, energetic, nonmaterial magnetic properties are dipolar (i.e., always paired, never separate).

Intensive experimental investigations in the 19th and 20th centuries discovered no physically isolated magnetic monopole. Thus, a magnet – indeed, each atom of the magnet – has an inherent dipolar magnetic property which manifests as an inseparably paired North and South pole. If an iron bar magnet is broken into smaller pieces not only will individual iron atoms continue to manifest a magnetic North and South pole, but also each small piece of the magnet will exhibit the characteristic magnetic properties of attraction and repulsion. Section 3 of this chapter describes the subatomic generation of magnetic energy.

Despite the fact that the physical nature and source of magnetic energy were unknown to Coulomb, much like the physical nature and source of the gravitational force were unknown to Newton, the magnetostatic force is accurately described by Coulomb's law.

Mass-energy equivalence:

Albert Einstein (1879-1955), the versatile pathfinder of early 20th century science, was the beneficiary of many qualitative and quantitative maps created by the scientific discoverers and investigators who preceded him. His paper, or map, Does the Inertia of a Body Depend Upon Its Energy Content?, published 21 November 1905, not only described the derivation of the virtual or apparent equivalence of the so-called relativistic mass and rest energy, m = ^E/_c², but also followed his special relativity paper On the Electrodynamics of Moving Bodies, published 26 September 1905, by only two months.

These two, a third paper, On a Heuristic Point of View Concerning the Production and Transformation of Light, published 9 June 1905, a fourth paper on Brownian motion, and his Ph.D. dissertation on molecular dimensions firmly established Einstein as a new member of a close-knit group of theoretical physicists during his so-called miracle year or annus mirabilis of 1905.

The November 1905 paper, Does the Inertia of a Body Depend Upon Its Energy Content?, describes a decrease in the so-called relativistic mass of a material body in the rest frame of a closed or isolated (conservative) material system as a consequence of the idealized emission of radiation (energy) in the visible region of the electromagnetic spectrum from that body. Einstein wrote:

    If a body releases the energy L in the form of radiation, its mass decreases by ^L/_V². Since obviously here it is inessential that the energy withdrawn from the body happens to turn into energy of radiation rather than into some other kind of energy, we are led to the more general conclusion:
    The mass of a body is a measure of its energy content; if the energy changes by L, the mass changes in the same sense by ^L/_{9 · 10²⁰}, if the energy is measured in ergs and the mass in grams.
    If the theory agrees with the facts, then radiation transmits inertia between emitting and absorbing bodies. [Emphasis added] 20

Einstein preferred to write in his native Swabian German language, thus er schrieb auf Deutsch:

    Gibt ein Körper die Energie L in Form von Strahlung ab, so verkleinert sich seine Masse um ^L/_V². Hierbei ist es offenbar unwesentlich, daß die dem Körper entzogene Energie gerade in Energie der Strahlung übergeht, so daß wir zu der allegemeineren Folgerung geführt werden:
    Die Masse eines Körpers ist ein Maß für dessen Energieinhalt; ändert sich die Energie um L, so ändert sich die Masse in demselben Sinne um ^L/_{9 · 10²⁰}, wenn die Energie in Erg und die Masse in Grammen gemmessen wird.
    Wenn die Theorie den Tatsachen entspricht, so überträgt die Strahlung Trägheit zwischen den emittierenden und absorbierenden Körpern. [Emphasis added] 21

In the notation Einstein used in his 1905 paper, L is the idealized electromagnetic radiation energy of visible light emitted by the body under consideration and V is the speed of light. In modern notation, L becomes E and V becomes c, where E is the energy of the radiation emitted, and c is the speed of light. Einstein's derivation of the decrease in mass m can now be seen as m = ^E/_c² = ^E/_{9 × 10²⁰}.

Transposed, the result is the more familiar equation E = mc². It should be noted that Einstein's idealized thought experiment of 1905 derived the virtual or apparent so-called relativistic mass of a particle at rest in a closed or isolated (conservative) material system. Thus, contrary to modern practice, momentum is not a factor in his derivation of the equation.

The m = ^E/_c² derivation controversy:

First articulated by Herbert Ives in 1952,22 Einstein's 1905 derivation was subsequently critiqued by Max Jammer, Henri Arzeliès, and Arthur Miller, among others. In a paragraph preceding Jammer's analysis of Ives' claim in his book, Concepts of Mass in Classical and Modern Physics, Jammer wrote:

It is a curious incident in the history of scientific thought that Einstein's own derivation of the formula E = mc², as published in his article in the Annalen der Physik, was basically fallacious. In fact, what for the layman is known as "the most famous mathematical formula ever projected" in science 23 was but the result of a petitio principii, the conclusion of begging the question.24

In their article, Einstein's First Derivation of Mass-Energy Equivalence, John Stachel and Robert Torretti present a detailed argument intended to refute the persistent criticism, following Ives, et al., that Einstein made a logical error in his derivation of mass equivalence in a closed or isolated (conservative) system.25

Curiously, acknowledging the argument of Stachel and Torretti, Jammer revisits the controversy in Chapter 3 of his second book on the concepts of mass, written forty years after his first book, and inexplicably changes the parameters of his original conclusion:

The really important issue here is not so much the historical question of whether Einstein's first derivation was a petitio principii or not but rather the question of principle as to whether the derivation is – or can be supplemented in such a way that it will be – rigorously valid.26

In his most recent analysis Jammer also notes that Einstein himself continued to seek new proofs of his mass-energy concept throughout his life and was not "satisfied with his 1905 derivation or, for that matter, with any other of his various derivations of the mass-energy relation."27

Aware of the fundamental importance of this relation, he regarded it as unsatisfactory that in spite of many strenuous efforts he did not succeed in establishing a general proof of the relation, that is, a proof without premises that are valid only in special cases.28

Energy-mass interconvertibility:

Experimenters on the cutting edge of theory and technology in contemporary high-energy particle physics make extensive use of Einstein's m = ^E/_c² equation. Einstein's original derivation has been changed, of course, to meet the needs of high-energy particle physics. Mass, for example, has been redefined to make it velocity independent. And the electronvolt (eV) is used as the energy unit of measure in determining the mass of the high-energy particles produced in supercollider and linear accelerator collision experiments.

Implementing these changes, Einstein's relativistic mass equation m = ^E/_c² first becomes m = ^eV/_c², where m is redefined as inertial or invariant mass, and eV is kinetic energy. In step two the equation becomes mc² = eV. And, since inertial mass and kinetic energy are seen as equivalent in a closed or isolated (conservative) material system, step three often drops the negligible value of c² for high-energy collision products and the equality becomes simply m = eV (inertial mass = electronvolts).

As in the original derivation, the modified equation m = eV is dependent upon Einstein's broadly generalized assumption – following the law of conservation of matter/mass implied by Newton and expressly stated independently by Lomonosov and Lavoisier – that all actions and reactions between mass and energy within our local space-time continuum take place in closed or isolated (conservative) material systems. Thus, whether on the macroscopic cosmic scale or the microscopic atomic scale, classical closed or isolated (conservative) material systems act as Einstein's de facto absolute reference frame.

On the one hand, using the electronvolt (eV) as an equivalent measure of inertial mass m for high-energy particles created in artificial collision experiments clearly assumes, following Einstein, that the point of collision between an accelerated, electrically charged particle and an electrically charged target of opposite sign – for example, between an electron (e^-) and a positron (e) – is a discrete, closed or isolated (conservative) material system.

On the other hand, by unequivocally demonstrating that the law of conservation of matter/mass is not valid on nuclear or subnuclear scales, the results of supercollider and linear accelerator collision experiments point well beyond the scope of classical physics and closed or isolated (conservative) material systems. Moreover, in contrast to the Einsteinian framework of relativistic mass and kinetic energy equivalence, the unexpected nuclear and subnuclear experimental results lead directly to the unambiguous conclusion that Einsteinian mass-energy equivalence can no longer be viewed as universally valid.

Taking note of the explicit difference between Einsteinian mass-energy equivalence and the physical interconvertibility of inertial mass and omnipresent, pervasive primordial energy per se in accordance with the universal principle of energy, the unexpected nuclear and subnuclear processes provide experimental proof that energy-mass interconvertibility and interdomain processes take place not only in closed or isolated (conservative) material systems, but also in open (nonconservative) material systems.

On The Energetic Holographic Paradigm (TEHP, pronounced "Teep") model of reality, each and every material or energetic virtual object in our local space-time continuum – including the accelerated high-energy particle, the target, and each material or energetic virtual product, such as photons, gluons, or neutrinos, created on any scale by an artificial collision experiment – are immersed in and pervaded by the fundamental, irreducible, omnipresent nonmaterial primordial energy domain.

Thus, the high-energy experimentalists are clearly in the vanguard of providing new maps for 21st century science.

Continued in Section 3: The Chicken or The Egg

Reference Notes (Click on the Note number to return to the text):

20 Einstein, Albert. "Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig?"; Annalen der Physik, 18 (1905): 639-641.
Anna Beck, translator. The Collected Papers of Albert Einstein, vol. 2, The Swiss Years: Writings, 1900-1909; English Edition, Doc. 24, p. 174. Princeton University Press, Princeton NJ, 1989. ISBN 0-691-08549-8.

21 Einstein, Albert. John Stachel, editor. The Collected Papers of Albert Einstein, vol. 2, The Swiss Years: Writings, 1900-1909; original papers in German, p. 314. Princeton University Press, Princeton NJ, 1989. ISBN 0-691-08526-9

22 Ives, H. E. "Derivation of the Mass-Energy Relation;" Journal of the Optical Society of America 42, 540-543 (1952).
(cf. Ives, Herbert E. Einstein Myth and the Ives Papers; Devin-Adair Publishing Company, Old Greenwich, CT, 1980. ISBN 0815958234)

23 Attributed to William Cahn in Max Jammer; Concepts of Mass in Classical and Modern Physics, footnote 22, p. 177. Harvard University Press, Cambridge MA, 1961; reprinted by Dover Publications, Inc., Mineola NY, 1997. ISBN 0-486-29998-8 (paperback)

24 Ref. 23, p. 177.

25 Stachel, John. Don Howard, John Stachel, editors. Einstein from 'B' to 'Z'; pp. 215-222. The Center for Einstein Studies, Boston University, Boston MA, 2002. ISBN 0-8176-4143-2

26 Jammer, Max. Concepts of Mass in Contemporary Physics and Philosophy; p. 65. Princeton University Press, Princeton NJ, 2000. ISBN 0-691-01017-X

27 Ref. 26, p. 66.

28 Ref. 26, pp. 66-67.

Back to Chapter 5, Section 1: Beyond Electromagnetic Induction

Index: Consciousness, Physics, and the Holographic Paradigm

Last Edit: June 22, 2006.

Comments and suggestions welcome.

This paper is a work in progress.
Please check for the latest update before quoting in other venues the concepts and hypotheses presented here.
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