Collective Electrodynamics: Quantum Foundations of Electromagnetism [Paperback]

That said, I did not find that this book presented anything like a systematic presentation of electrodynamics or quantum mechanics. His main tool for connecting different results and ideas of electromagnetism is a superconducting loop, which he uses in various "thought experiments." It's interesting and novel, but not enough to really provide a foundation for a complete framework for one of the great theories of classical physics.

His criticisms of the Copenhagen school of quantum mechanics are not new, and generally seem to me to have been adequately discussed and refuted during the scientific consensus-building on quantum mechanics during the 1930's. Perhaps the strongest new piece of evidence that he brings to the table on this point, that some folks (Barut & Dowling) have recently provided a derivation of the energy levels for the hydrogen atom which is compatible with something like the original Schroedinger interpretation (of the amplitude squared as charge density) is only quoted, not described: you'll need to look up the article in Physical Review A (1990, Phys.Rev.A 41, pp. 2284-2294) to see if you can understand or believe it. This is very disappointing, since Mead's book is only 135 pages long: it seems to me that he should have made more of an effort to at least sketch what seems to be the key touchstone for his proposed approach. My impression is that he ended the book in a bit of a rush; but that's not an adequate excuse.

In summary, this book can be interesting, especially if you know some E&M and can follow the equations: there are some cute connections that may be fun to check out more carefully. But in the end, I don't think this is going to make any substantial impact on the way most physicists will think about electrodynamics or quantum mechanics.

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.