Introduction

The method of inquiry employed in this book owes much to Einstein, specifically to the formal comparison of the photon gas with the molecular gas he makes in various papers written between 1905 and 1924. Einstein found a deep, formal analogy between radiation quanta (photons) and rest-mass quanta (molecules, electrons). This book devotes a chapter to Einstein’s use of this analogy/method (details » Here ). A fine example of it is found in his "Heuristic Viewpoint" paper of March 1905 wherein he compares the entropy decrease when molecules (of an ideal gas) or photons (of a photon gas) are squeezed into a smaller volume.

Einstein generally uses his method to draw conclusions within the realm of thermodynamics. These pages attempt to extend his method into areas he did not cover to see if doing so provides a new way of approaching various interpretative problems, including wave/particle duality. Einstein’s method suggests that matter and radiation are formally analogous in terms of what exists and what occurs (ontology). Whereas one entity (stationary matter) exists, has the field form and progresses in time, the other entity (radiation) occurs, has the waveform and progresses in space. Non-stationary matter (projectile) is a breed apart and will be treated separately since it combines aspects of radiation (de Broglie waves) and aspects of matter (rest mass).

Matter and radiation are characterized by mass and energy respectively. Providing it is stationary in space relative to an observer, matter has kinetic (rest) mass but no kinetic energy (for that observer). In contrast, radiation has kinetic energy but no kinetic (rest) mass. The following formal conditions then prevail.

Mass-as-stationary-matter exists, is quantized, has the field form, and progresses (ages) over time. On the other hand, energy as radiation occurs, is quantized, has the waveform, and progresses over space. Kinetic mass has the field form because it exists as it extends over space and progresses in time; kinetic energy has the waveform because it occurs as it oscillates over time and progresses in space. Both quanta have an intensity level (density for one, frequency for the other), and this intensity, multiplied by quantum extension (in space or in time) yields its quantitative measure.

The progression of quanta in a dimension reveals another aspect of the formal equality of mass and energy. Quanta progress in one dimension and are located in the opposite dimension. For example, the space-stationary particle (mass) progresses in time and is located in space relative to an arbitrary reference. This reference is simply another mass object that observers find convenient to use as an origin when measuring space intervals. Photon progression is similar but with the dimensions reversed: the photon is stationary in time (special relativity tells us photon clocks don’t advance) and it progresses in space. As with mass quanta, radiation quanta can also be given a relative location in their dimension by an observer. In theory we could select a specific photon as a standard whose origin would then serve as a reference for the temporal displacement of all other photons.

Space-stationary mass quanta and time-stationary energy quanta (radiation) progress at the maximum possible rate in opposite dimensions. Photons proceed through space at the speed of light which cannot be exceeded for any observer. Space-stationary mass quanta proceed through time at the maximum rate since once they start moving through space relative to some observer their time progression (clocks) slow down for that observer.

In short, the space-stationary mass (particle) and the time-stationary photon are ontological opposites, and their contrast extends beyond that of existence versus occurrence. The ontologist characterizes this opposition as field-existence versus wave-occurrence. The physicist describes particle and photon simply as matter versus radiation.

Mass and energy do not always remain kinetic. Both may become potential and be stored by their opposites: kinetic (rest) mass stores potential energy and kinetic (photon) energy stores potential mass. Examples of potential energy stored by kinetic mass include the stored energy of a watch spring, the thermal motion of a molecular gas, the electrostatic potential of a charged particle, or the energy locked within mass itself by virtue of E = mc² . On the other hand, potential mass stored by kinetic energy is the relativistic mass of a photon or the relativistic mass increment of a projectile as a consequence of E = mc² . Potential mass is stored by kinetic (radiation) energy and potential energy is stored by kinetic (rest) mass.

At some point, whatever is stored by a quantum (mass or energy) is released to the opposite realm. Thermal energy, stored by whole molecules that oscillate within an existing field, will be released as infrared radiation. Atoms will emit ultra-violet radiation when one of their electrons moves to a lower orbit. The release of such stored, field-bound energy to a non-stored waveform is known as "emission." The opposite of emission is absorption: the release of stored (relativistic) mass by a photon when the latter impinges upon matter. Each of these processes constitute crossover, and they are formally identical: mass or energy stored in one form, field or wave, is released as kinetic in the opposite form, wave or field. Quanta have both a kinetic (unstored) identity and a (stored) potential identity; it is crossover that reveals the potential identity to us. An example will clarify this process.

Assume you are blindfolded and handed a round brass paperweight that has been warmed by being in the sun. As you accept this unknown object, your arm muscles sense its weight and your fingers its shape. From its weight, you know it has rest mass, and from its shape you know it has spatial extension. Obviously, this entity/object exists because existing entities have rest mass and extend in space, whereas occurring (radiation) entities are the reverse. You then set the object down and hold your hands close to it. Your fingers sense the thermal radiation which the object gives off and you attribute this to the energy stored by the object and subsequently released via crossover. Although radiation occurs (it has no rest mass and progresses, not extends, in space) and seems inseparable from the object, you do not revise your earlier judgment that you are dealing with something that exists. Instead, you conclude that when crossover is involved, the kinetic and the potential identities of quanta will reveal themselves differently: one as field (particle) and the other as wave (radiation).

Continuing the experiment, you remove your blindfold and then attempt to measure a stream of photons coming from the sun. You arrange for the photons to pass through a narrow slit and notice that the radiation fans out, creating a spectrum of colors. You attribute this to wave interference and conclude that photons have the waveform, unlike particles, which have the field form. But if you reduce the number of photons passing through the slit and record their termination photographically, you notice that photons "impact" the film discretely, suggesting that they are particles. Just as with the brass paperweight, you now have two contradictory measurements of an entity, one suggesting wave and one suggesting particle (field). Two ways of dealing with this conundrum come immediately to mind.

The first and least demanding approach is the Copenhagen interpretation of radiation, which asserts that photons are unknowable to us and, depending upon how we measure them, will appear either as particles or as waves. The second approach is to take the radical equality of mass and energy seriously and look for a formal parallel in how we categorize information we receive from the paperweight as matter and from the photons as radiation.

This book, obviously, chooses the second approach on the assumption that mass and energy are truly ontologically equal. As will be described more fully, photons impinging on any material barrier such as a photographic film are undergoing crossover, which is to say that a radiation wave entity (photon) is giving up its potential mass to its ontological opposite, a matter field entity. In the process, the relativistic mass of the photon converts from potential energy to kinetic energy and from space-smeared (wave) to space-discrete (particle/field). This is exactly analogous to the situation of the warm paperweight giving off infrared radiation. That is, the paperweight’s potential (thermal) energy which is space-discrete and field-like converts to become space-smeared (continuous) and wave-like. If we regard the paperweight as matter/field despite its associated crossover wave identity, then it seems that we should regard the photon as radiation/wave despite its associated crossover field/particle identity. This formal equivalence suggests that photons are pure occurrence with the waveform; they are not particles and they do not exist. The reader, of course, is free to discount all of this and embrace the "classical" quantum theory that emerged in the late 1920s. This theory essentially regards large material quanta (objects) as so well-known that their radiation emission never raises questions about their existence or about their intrinsic particle (field) nature. This theory regards radiation quanta as so mysterious that their essential nature (occurring, wave) is confounded by their crossover nature (particle).

Fortunately, an increasing number of philosophers and physicists have grown dissatisfied with the classical (Copenhagen) interpretation of quantum mechanics. Others resist the very human tendency to cling to familiar and accepted ideas at the expense of considering new ideas. I hope you will read on if you belong to either of these groups.