In this book Carver Mead offers a radically new approach to the standard problems of electromagnetic theory. Motivated by the belief that the goal of scientific research should be the simplification and unification of knowledge, he describes a new way of doing electrodynamics--collective electrodynamics--that does not rely on Maxwell's equations, but rather uses the quantum nature of matter as its sole basis. Collective electrodynamics is a way of looking at how electrons interact, based on experiments that tell us about the electrons directly. (As Mead points out, Maxwell had no access to these experiments.)

The results Mead derives for standard electromagnetic problems are identical to those found in any text. Collective electrodynamics reveals, however, that quantities that we usually think of as being very different are, in fact, the same--that electromagnetic phenomena are simple and direct manifestations of quantum phenomena. Mead views his approach as a first step toward reformulating quantum concepts in a clear and comprehensible manner.

The book is divided into five sections: magnetic interaction of steady currents, propagating waves, electromagnetic energy, radiation in free space, and electromagnetic interaction of atoms. In an engaging preface, Mead tells how his approach to electromagnetic theory was inspired by his interaction with Richard Feynman.

Review:

"Not even wrong"

This is an unusual book and not an easy one to review.
Perhaps the best starting place is the publisher's summary:

[BEGIN PUBLISHER'S SUMMARY (from the book's back cover)]

"In this book Carver Mead offers a radically new approach to the standard problems of electromagnetic theory. Motivated by the belief that the goal of scientific research should be the simplification and unification of knowledge, he describes a new way of doing electrodynamics---collective electrodynamics---that does not rely on Maxwell's equations, but rather uses the quantum nature of matter as its sole basis. Collective electrodynamics is a way of looking at how electrons interact, based on experiments that tell us about the electron directly. (As Mead points out, Maxwell had no access to these experiments.)"

"The results Mead derives for standard electromagnetic problems are identical to those found in any text. Collective electrodynamics reveals, however,that quantities that we usually think of as being very different are, in fact, the same---that electromagnetic phenomena are direct manifestations of quantum phenomena. Mead views this as a first step toward reformulating quantum concepts in a clear and comprehensive manner.''

[END PUBLISHER's SUMMARY]

It was this summary that persuaded me to order, sight unseen, this small (132 pages) but relatively inexpensive book to read on vacation. I didn't expect a lot from it, but I hoped that it might furnish some new insights. I was very disappointed that I learned nothing of substance from it.

Indeed, I think that the above summary borders on false advertising. The book does not convincingly obtain classical electrodynamics from accepted quantum mechanical principles nor from experiments to which "Maxwell had no access". Its motivation is presented in such a vague and sloppy way that I regard it as yet one more of the endless accumulation of dreary papers which Pauli, in a famous remark, characterized as "not even wrong", i.e., too vague to be meaningful.

The book only sketchily describes the "experiments that tell us about the electron directly". These are experiments with superconducting coils, which reveal not the behavior of individual electrons, but behavior of a system of a large number of electrons coupled in poorly understood ways (hence the collective" in the book's title). Most of the book's development is based on just one experimental fact---that the magnetic flux of a superconducting loop is quantized, i.e., the flux can take on only values which are a constant multiple of integers. The book views such a system as a primitive system "having only one degree of freedom".

Before proceeding to sketch the book's main argument, I have to make some mathematical remarks. It is well known that classical electrodynamics can be plausibly developed starting with just one mathematical object---the four-potential A, which is a 1-form on four-dimensional Minkowski space. The electromagnetic field tensor F, a 2-form, is the differential of the potential 1-form: F = dA. It would be too difficult to give precise definitions here, but they can be found in my book *Relativistic Electrodynamics and Differential Geometry* and many other places. The 4-current J is then defined as (or, from a more physical point of view, assumed to be) the codifferential (covariant divergence) of the field tensor. This mathematical structure is equivalent to Maxwell's equations.

In summary, from any physical situation in which a 1-form
on Minkowski space appears naturally, one can plausibly recover much of the mathematical structure of classical electrodynamics. For example, if within the logical structure of thermodynamics there were a naturally occurring 1-form on Minkowski space, one might claim to "derive" electrodynamics from thermodynamics by identifying this "natural" thermodynamic 1-form with the electromagnetic potential A.

The only problem would be if the thermodynamic definition of A were somehow in physical conflict with the electrodynamic definition. But if A should be an unmeasurable quantity within thermodynamics, then this problem would not exist.

The essence of Mead's argument is that within quantum mechanics, there is a naturally occurring 1-form on three-dimensional space with the property that integrating it over a superconducting loop gives the phase change of the "wave function" of the loop, which must be a constant multiple of an integer. Also, integrating the space part of the four-potential 1-form A over a loop gives the magnetic flux threading the loop, which for a superconducting loop is observed to be a constant multiple of an integer. This suggests identifying the "phase change" 1-form with a constant multiple of the space part of A.
Later the full A is recovered by hand-waving analogies. In my opinion, the main problem with his argument is that his construction of the "phase change" 1-form is so vague, sloppy, and problematic that it is "not even wrong".

Another difficulty is that the electrodynamic potential 1-form
has special properties which may or may not be possessed by Mead's "phase change" 1-form, a point which Mead does not address. Since there seems no way to experimentally determine Mead's "phase change" 1-form independently of electromagnetic measurements, his identification of the "phase change" 1-form
with a constant multiple of the electrodynamic 1-form seems physically sterile.

I cannot point out the precise difficulties with his construction without using symbols which are unavailable here.
A more extensive review on my website gives the mathematical details of some of the problems with it.

Is there anything of interest in the book?
Well, some may find of interest an 11-page "Personal Preface" describing, among other things, the author's relationship with and impressions of Richard Feynman. Mead was an undergraduate student of Feynman and later his colleague at Caltech.

I have mixed feelings about these.
His reminiscences sound sincere, but also seem to me to have a
flavor of name-dropping. For example, he discusses a "sticking point" in his development of electrodynamics which held him up for years, and informs us that "it is resolved in this treatment in a way that Feynman would have liked". It seems presumptuous to claim to know what a great, deceased physicist would have thought about this work.




Review:

Coherent, Concise, and Challenging

For those of us who were fascinated by Feynman's presentation of the vector potential field A, this book is irresistable. Mead tries to build the foundations of electricity and magnetism anew, and does a fascinating job of it.

There is a lot of history and historiography mixed in with this short book, but I myself find that fascinating. If you're interested in how the currents of thought might have eddied, or where key suggestions were missed, or what from Einstein may have been underappreciated, you'll enjoy this side of the book.

All that said, this book is chewy, and does only a mild amount of hand-holding in walking through the math. This is NOT anybody's first book of mathematical physics - but if you have enjoyed reading books by (e.g.) Feynmann, Misner/Thorne/Wheeler, Herb Kroemer, Andy Grove, Morse/Feshbach, Francon, Ichimaru, Khinchin, Papoulis, Polya, Sapriel, or Wiener, you're part of the natural audience for this book. If you liked "The Elegant Universe" you may love this book (and find some common themes), but this book is more mathematically demanding. On the other hand this is no mere tome, and does not require more than undergraduate competence.

I would have liked to see more visualization aids - some of the concepts in this formulation lend themselves very well to a visual presentation. I'm going to be rereading this book, and I'm really looking forward to expository textbooks which may follow this line of presentation.

If you're in doubt, buy this - it's challenging, but very broad and brilliant, and is not only about electrodynamics.




Review:

Successor to Feyman's Red Books

From time to time I ask people if there's been anything better than Feyman's "Lectures in Physics," and the answer is generally no, that's about all there is...

Seems to me this beautiful book is at least the start of the current generation's canonical physics text set.




Review:

Pioneering Research

Carver Meade is a Pioneer. Like Einstein, he recognized that Maxwell's Equations (ME) are not correct because they are based on the assumption that the electron is a point particle. This myth was handed down from the Greek Democritus. Like Milo Wolff before him, Meade deduces that the electron is quantum wave structure, as proposed by Schroedinger. Wolff's book is also sold here at Amazon.com.
Meade uses the properties of a wave structure to provide new equations for the analysis of electronic engineering ciruits - very useful in the design of micro chips. He also shows how the collective behavior of waves is the cause of low-temperature behavior.




Review:

Collective Electrodynamics--Carver Mead's book

Despite his preface upbraiding physicists for their work of the past 50-75 years, the main text makes reasonable claims based upon well-founded experimental and theoretical results. The book endorses earlier work of Einstein, Feynmann, Reimann, Lorentz, Maxwell, Planck, and others while making computational and conceptual adjustments to accommodate modern experimental results.

Also in the text, Bohr and other die-hard quantum statisticians are continually under attack for their poo-pooing of possible phenomena, algorithms, and concepts behind the observed quantum behavior. Bohr and his clan, apparently, claimed that the statistics made up the whole baseball team of quantum physics--and that we should not, and could not, look further.

In refuting this micro-labotomic approach of Bohr, Dr. Mead makes reference to systems--macroscopic in size--that exhibit quantum behaviors. While he mentions lasers, masers, semiconductors, superconductors, and other systems in the text, the primary results of the book hinge upon experimental results from the field of superconductors. He points out that physics can be split into several areas:

Classical Mechanics explains un-coherent, uncharged systems such as cannon balls, planets, vehicles, etc.
Classical Electrodynamics explains un-coherent, charged systems such as conductors, currents, and their fields.
Thermodynamics explains how macroscopic statistics, such as temperature and entropy, guide the time evolution of systems.
Modern Quantum Mechanics tries to explain coherent, charged systems.

Here 'coherent' refers to quantum coherency, where many particles/atoms march to the same drum such as the photons in a laser, or the electrons in a superconductor, or any isolated one or two particles. Another description of coherency is that the states are quantum entangled; their time-evolution depends upon each other.

The thrust of Carver's book: QM applies to all matter--not just small systems or isolated particles--is well made. He brings up experimental data from superconductors to illustrate that the phenomenon of coherent quantum entanglement can, and does, occur at macroscopic scales; and that such behavior is very quantum. Thus he proves, quite convincingly, that quantum mechanics applies to all coherent systems.

He then closes by making some very important points. (1) He shows that quantum behavior of such systems can be expressed in quantum language (wave function), relativistic language (four-vectors), or electrodynamics (vector potential, scalar potential) in an equivalent fashion. This is important, as it proves that a superconductor is macroscopic, exhibits quantum behavior, and that these quantitative results agree with those found from the other approaches. (2) He makes the point that the quantum and relativistic equations show that electromagnetic phenomena consist of two parts: one traveling forward in time; the other backward in time. Feynmann and others have said this for a long time, and he shows how thermodynamics (or un-coherent behavior) forces what we see as only time-evolution in one direction in un-coherent systems. (3) He illustrates, modeling single atoms as tiny superconducting resonators, that two atoms that are coherently linked will start exchanging energy. This causes an exponential, positive-feedback loop that ends with each atom in a quantum eigenstate. Thus quantum collapse is neither discontinuous, nor instantaneous; and in fact makes a lot of sense. (4) He explains, using four-vectors, that all points on a light-cone are near each other in four space. This point--together with (2)--shows that there's no causality contradiction between relativity and quantum mechanics. For example, he explains that two entangled particles, such as photons light years apart, can affect each other immediately if one falls into an eigenstate, since the four-dimensional distance between them (R1 dot R2) is zero. Although separated in three space, they're neighbors in four space. Through these demonstrations and proofs, he successfully suggests that there is a way to further develop the 'behavior of charged, coherent systems' such that quantum mechanics and relativity will agree--but the conceptual changes he suggests are necessary and must be further developed. Also, he admits that a better, more appropriate mathematical and computational methods will be needed, since the complexity of coherent systems runs as n^2.

Pleasantly, then, the book makes elegant, defensible, mathematical and conceptual steps to resolve some nagging points of understanding. Also, the narrative gives the best introduction to electrodynamics and quantum mechanics that I've ever seen. Since the theoretical criticisms and experimental data are quite valid, his proposed resolutions are eye-opening and valuable. The methods he suggests greatly simply thinking about complicated quantum/classical problems. New approaches for future theoretical research are also suggested. Despite the dark tone in the preface, the book is positive, enlightening, and well anchored to accepted, modern experimental results and theoretical work.

It's a short book, about 125 pages, and well worth the read. Familiarity with classical and quantum physics, and special relativity, is required to get the most out of it. As you can tell, I enjoyed it tremendously.pass: gigapedia.org





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