1.6 The Plan & Purpose of this Book

In a way, Fields & Energy is an adventure story describing the long conflict between two opposing views of reality: atoms versus continua or particles versus waves. There’s also a conflict between two opposing methods of figuring things out: an Aristotelian approach in which new laws of nature are induced from observation, and a Platonic approach in which the consequences and implications of those laws are deduced from first principles.

The next chapter begins a brief history of physics. We will see how the accepted model of how the world works has oscillated from Democritus’ atomism to the continuous plenum of Aristotle and Descartes, to the purely atomistic perspective of Newton’s successors, to the all-pervasive fields of Faraday and Maxwell, and finally to the unholy synthesis of wave and particle theory proposed by quantum mechanics that characterizes contemporary thought.

We’ll look at the origins of relativity and quantum theory. We will discover that philosophic preconceptions drove the physical theories instead of the other way around. In contemporary thought, electromagnetism is the collection of physical effects that arise from the behavior of a single entity, a force-carrying particle called a “photon.” Sometimes a photon behaves like a particle. Sometimes it behaves like a wave. Sometimes it behaves like both at the same time in a confusing, contradictory fashion that defies comprehension. No wonder many physicists believe reality is inherently contradictory and unknowable. They bake in the contradiction from first premises.

In the new approach of this book, electromagnetism follows from two entities: from the interplay of both fields AND energy. Fields are non-local, distributed, wavelike phenomena. They may start tied to particular charges and currents, but they sometimes end up decoupling from their sources and propagating away at the speed of light. The behavior of the superposition of fields at any given point guides the local flow of energy. Fields behave like waves. In the atomic or quantum limit, energy behaves like discrete particles.

We will see how a physical parameter often ignored by physicists, the “field impedance,” or the ratio of electric to magnetic field intensity, relates to the speed at which energy flows.

For isolated electromagnetic waves in free space there is a balance, equal amounts of electric and magnetic energy. The field impedance has the special value: Z = 376.7 ohms, and the energy moves together with the fields at the speed of light. Wave interactions upset the balance and change the impedance. We have an excess or deficit of electric or magnetic energy. Energy slows down. Fields exchange energy with each other. Fields continue on their way at the speed of light. Energy slows down, changes direction, and goes another way with a different field.

Fields go one way, energy goes another way. They cannot be aspects of a single entity as conventional wisdom assumes. They must instead be two different, distinct phenomena.

We’ll consider the conflict between wave and particle theories of light and see how fields or waves guiding energy provides a clear interpretation of how light works in such diverse phenomena as two-slit interference and the mysterious spot of Arago.

The spot of Arago in cross-section [[i]].

An examination of how electromagnetic radiation works lends further evidence to this model. The traditional model of radiation as a bend or kink in a field line is simply wrong because it neglects the role of the fields that cause that radiation in the first place. We’ll see how accelerating and decelerating charges absorb energy and how the energy they appear to radiate comes from sources other than the charges themselves. We’ll look at the complex interactions of fields and energy around small antennas. The simple model of point charges emitting point photons will be shown to be completely inadequate for describing many of the most fundamental processes in electromagnetic physics. Instead, we have to look to the overall system of charges. We will see how fields and energy are two distinct phenomena that collaborate to yield the observed behavior of reality. Fields guide energy. Fields go one way; energy goes another way.

Finally, we will consider the fascinating implications of this new concept. We will see how an often ignored or neglected interpretation of quantum mechanics – the pilot-wave interpretation – follows naturally from taking classical ideas of electromagnetic fields and energy flow into the quantum realm. We will discover that photons – far from being non-interacting particles propagating at the speed of light, as is conventionally assumed – often have a relatively short mean-free path and a relatively slow drift velocity. They may sometimes move at the speed of light, but their interactions with other photons make their time-average speed much slower. At the end of our journey, we will emerge at an alternate view of reality entirely consistent with known physical facts and experiments, yet profoundly at odds with conventional wisdom.

Before we can understand and explore this new frontier in physics, however, we need a common frame of reference on which to build a new understanding. We must travel back in time to understand the evolution of physical models.

When I was a young and hungry physics graduate student, I got a side job teaching Algebra at ITT Technical Institute to help make ends meet. On the first day of class, I put what I thought was a simple problem on the whiteboard. I wrote the answer next to it, by way of review.

I was greeted by a mix of dumbfounded looks and resolute hands in the air. “You’re skipping steps, Mr. Schantz,” my students insisted. “You’re skipping steps!”

My teaching experience taught me a valuable lesson. What has become obvious through frequent use and long exposure is not so obvious to someone starting off on the path of knowledge.

By completing this chapter, you’ve taken your first steps with me on a journey to understand a remarkable new physical theory. We’ll start in familiar territory. Soon, however, we will be traveling along a trail unappreciated and unknown until I discovered it just a few years ago. I appreciate and value the effort you’ve made. If you follow through and join me and all the others who have embarked down this path for the rest of the journey, in return, I will make you this solemn promise:

I’ll try my best not to skip steps.

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[i] Amplitude of a scalar plain wave illuminating a circular obstacle at normal incidence (Dirichlet boundary condition). Formation of the spot of Arago is visible in the shadow. Computed by superposing a plain wave with a wave radiated by 300 concentric rings of Green's function point sources across the obstacle. The amplitudes for the sources found from the condition that the total amplitude is zero at the obstacle. Wavelength equals 6 pixels (1/120 of width of the image). See: https://en.wikipedia.org/wiki/Arago_spot#/media/File:Scalar_Arago_shadow.png