Einstein's Method

A scholarly inquiry...
Suppose we take a method Einstein used extensively and apply it to current problems in QM and relativity?
  » Introduction
  » Photon and the
Double Slit
  » Quantum
NonLocality
  » Elitzur-Vaidman
Experiment
  » Three Mistakes of
Quantum Theory
  » Chapter II
  » Chapter III
  » Table of Contents
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Discussion
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Chapter II of Einstein’s Method



Chapter II

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Adam: We are no longer faced with a Newtonian world where a few laws of dynamics and the law of gravitation could make sense out of reality. In quantum mechanics, the theorist confronts a long list of concepts that must be organized and reconciled: space, time, continuous, discrete, waves, fields, particles, mass, energy, radiation, and the uncertainty relation, to name just a few. The task is intimidating.

Max: But something tells me you don’t think it impossible.

Adam: I don’t think it impossible, but I do think that what’s needed is a new perspective, a different approach, a new method.

Max: And that is where the method of Einstein comes in?

Adam: Exactly! Whereas Einstein compared the photon gas and the molecular gas in terms of thermodynamic behavior, I think we can compare them in terms of the quanta they contain and how those quanta exist or occur in space and time. Are you ready to accompany me in this analysis?

Max: I am, but I’ll be following your lead.

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Adam: A beam of light is a photon gas, and this beam may consist of many photons or just a single photon. Its counterpart is a molecular gas that may contain many molecules or just a single molecule. Of course, if our two gases have but a single member, no internal interactions are possible. Otherwise, the quanta in our two gases interact with each other in a way characteristic of the type of quanta involved. Of course, I use "gas" in the extended sense so that a molecular solid or liquid also qualifies. These two gases are special because they just might include everything that exists and occurs.

Max: ...how are you proposing to analyze them differently from the way Einstein did?

Adam: Einstein compared the statistical distribution of the energy that characterizes each gas. I propose comparing the two gases not in terms of traditional physics but in terms of ontology.

Ontology, you will recall, is usually defined as the study of being, of that which exists. As a physicist, I insist upon expanding the scope of ontology to include that which occurs. Hence, an ontological analysis of our two gases is an inquiry into how each of them exists or occurs within space and time.

Max: This strikes me as more philosophy than physics.

Adam: Perhaps it is both. In fact, physicists adopt and use ontology whether they know it or not. Nineteenth-century physicists embraced the ontology of classical physics which clearly differentiated between existence and occurrence, and space, time, and causality all appeared well understood. At the turn of the century, new experimental evidence cast doubt on those assumptions, and it has been a struggle ever since to find a new understanding, a new ontology. I maintain there is an ontology for quantum mechanics although few would seem to be searching for it.

Let me restate my intentions. We know the entities of physics must either exist or occur and they must do so in space and in time. These entities are composed of both mass and energy, and they display such characteristics as storage, conversion, interaction, and discreteness or continuity. The study of these characteristics as they relate to existence and occurrence is what ontology should be for the physicist. No one that I know undertakes such an examination. It may sound a little like philosophy, but such an inquiry has some very significant consequences for the physicist.

Max: Can you give me an example of how an ontological question is relevant to physics.

Adam: Sure. Take the photon passing through a double slit and impinging on a viewing screen. During flight, the photon appears to be an occurring wave that is space continuous. Upon impact, however, the photon appears to be an existing particle that is space discrete. The apparent transformations of the photon from occurrence to existence, and from continuous to discrete are ontological problems in that they involve the ontological nature of reality. By itself, physics is not prepared to address such problems. Ontology is. The two disciplines complement each other. Ontology provides certain constructs and abstractions that physics lacks, and physics provides a rich set of quantum states and processes whose ontology can be analyzed.

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Adam: ... We first need to decide on the forms our two gases naturally assume. The photon gas is the easiest because it always displays a waveform, whether it is composed of many photons or a single photon. We can see this in diffraction experiments in which both a beam of light and a single photon diffract owing to their essential wave character or form. To have a photon with its undulatory frequency and velocity is to have a waveform. Putting aside for the moment the photon's putative "particle" characteristics, I insist that the photon is actually an energy wave and so, by extension, is the photon gas. The problem then is, what is the form for the molecular gas? ... The molecule is a mass field and so, by extension, is the molecular gas.

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In general, the field or the wave as form is independent of the quanta that constitute it. Consider the waveform: one may have sonic waves, water waves, and electromagnetic waves. The first two examples involve different types of material quanta creating a wave; the last example involves radiation quanta creating a wave. Yet all have a phase velocity and are capable of diffraction, interference, and reinforcement. A similar constituent independence holds true of the field; its quanta may be either different varieties of molecules, or radiation energy quanta of the magnetic or electric variety.

If you think about it, the waveform has become a generalized concept--for material and radiation quanta--because its undulatory and velocity characteristics are easy to spot and identify. In contrast, the field form was developed by Faraday only to explain the electric-magnetic action upon a particle at a distance. But if you can take the energy quanta of electric charge distributed over space and call it a field, you can do the same with the mass quanta of the molecular gas. Waveform and field form as I use the terms are abstractions; they are the formal characteristics of physical waves and physical fields respectively.

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Max: So you are going to take the quanta-independent abstract forms of wave and field and examine their consequences for a variety of what you call "ontological properties?"

Adam: That is correct But, remember, abstract forms become real once quanta are involved. A matter field with real quanta actually exists, and we may then call it an "ontological field" to distinguish it from an abstract, Platonic or mathematical field. Similarly, a radiation wave with real quanta actually occurs and may be called an "ontological wave." ... In effect, the ontological viewpoint separates the form of an entity [wave or field] from the quanta [matter quanta or radiation quanta] that give it reality.

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Max: Much of physics, including most of particle physics, deals with pro­jectile motion where the particle in motion has both a rest mass plus a mass deriving from its energy of motion.

Adam: Projectile motion is complicated. It’s a mixture of states (ex­is­tence, occurrence) and a mixture of forms (wave, field). We shall deal with these conditions presently. But first, I think we’d better make sure that we both share a full understanding of all those concepts we have just been discussing--existence, occurrence, field, wave, potential, kinetic, mass, energy, matter, and radiation. The best way to do that, I suggest, is to concentrate, as Einstein did, on the two special, "pure" cases: static matter field and moving photon wave. Once we understand them, projectile motion will appear a lot less confusing. For the time being, we must deal with the restricted universe of our two gases...

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