Adam: Well, do you remember where we left off?

Max: Not exactly, so I was hoping maybe you could summarize what we covered.

Adam: Let me try in terms of results, rather than in terms of topics covered. We agreed the waveform characterized both the photon gas collectively and the photons individually, while the field form characterized both the molecular gas collectively and the molecules individually. But we saw that wave and field form are independent of the quanta that give them reality and, regardless of their quanta, existing entities have a field form, just as occurring entities have a waveform. We found that material field entities exist and store energy, while radiation wave entities occur and store mass. We also found that any field of any quanta must have the properties of kinetic mass and potential energy, while any wave of any quanta must have the properties of kinetic energy and potential mass.

Max: You are taking some liberties with the extent of our agreement. Aside from that, you make all of this sound simple but I don’t find it so.

Adam: Ontology can appear complex, yet I believe that many parts of it are simple. It seems complex because it is unfamiliar and does not conform to our commonsense and rather naive perceptions of what exists and what occurs. But it is simple in that its fundamental principles are few and are valid regardless of quanta. But our analysis has just begun.

Max: So, what do we cover today?

Adam: Velocity: I want to examine the nature of velocity for both matter and radiation quanta. However, the term "velocity' is specific to transit over space, so we need to generalize this.

Velocity is progression over space, but since ontology does not favor one dimension over another, we should say that some entities have progression over space, while others have progression over time. The common description of progression over time is "aging." A field entity, gas or solid object/particle, is an existence and, as such, progresses over time; a wave entity is an undulatory occurrence and necessarily progresses over space. While my remarks apply to the two Einstein gasses--photon gas and space-stationary molecular gas--it is convenient to also reference those gasses as individual quanta, namely, as photon and molecule/particle.

Now, a stationary particle as a field and a photon as a wave progress without limit over time and space, respectively, until their identity terminates: the particle exists and so ages over time while the photon occurs and so speeds across space. Such identity termination depends on a change in the mass/energy measure of the entity. The stationary particle changes its identity when it loses or gains stored (potential) energy; the photon changes its identity when it gives up part or all (the case for annihilation) of its stored (relativistic) mass. Think of a Feynman diagram where photons or particles are represented as straight lines and where those straight lines terminate at a vertex which represents a change of mass/energy.

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Max: You keep characterizing a field entity as stationary [aside to the reader: projectile motion is only considered in subsequent chapters], but I don’t see how that applies to radiation wave entities, which are anything but stationary.

Adam: Good point. When I describe a field-particle as stationary with respect to an observer, I mean it has zero space velocity relative to that observer. Of course, this field does have a significant velocity in time. In fact, if you think about it, a field-particle at zero space velocity is moving across time at the maximum rate: set that field-particle into space motion and special relativity tells us that its clock--its rate of time progression--slows down. This tells us that a space-stationary field has the absolute minimum (zero) space velocity and the absolute maximum time velocity, and this provides the clue for characterizing the wave side of reality. An electromagnetic wave must have the absolute maximum space velocity and the absolute minimum (zero) time velocity. Photons moving at the speed of light don’t age; their clocks come to a halt. Photons are stationary in time just as static fields (particles) are stationary in space.

A matter field that is space-motionless relative to an observer (no kinetic energy), has zero space progression and maximum time progression for that observer. A photon wave, necessarily time-motionless relative to an observer, has maximum space progression and zero time progression.

This kinematic symmetry is, of course, no accident. Perhaps we can examine it more closely next week.

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[for light] each electric or magnetic event is a quantized entity unto itself which means that "continuous" radiation is actually composed of discrete events [collapse of quantized electric field occasioning rise of quantized magnetic field, and the reverse] that are temporally adjacent. Occurrence is therefore formally the same as existence: entities that appear to extend (even without limit) over expanses of space or of time are merely aggregations of quanta that are discrete in both extension and quantity. The light beam is an aggregation of (self-perpetuating) occurring quanta over time; the meter stick is an aggregation of existing quanta [molecules] over space. Both of them give the illusion of continuity in their extension dimension whereas their real continuity is in their progression dimension: time for existing quanta, space for occurring quanta.

All entities (matter and radiation) are quantized in amount and they are also quantized (discrete, limited) in extension (length/duration). Any instance of matter "continuous" in space or radiation "continuous" in time is merely an aggregation of discrete quanta arrayed in their extension dimension. [space for matter, time for radiation]

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If you detect a photon via its crossover absorption and then pronounce the photon to be particle-like (exists) because you receive momentum and a space measure (location) from its absorption, then you might as well detect a material object (space-stationary particle) via its infrared radiation emission and pronounce the object to be wave-like (occurs) because you receive a frequency measure and a time location from its emission.

Max: Okay I can agree with that part. I am intrigued by your parallel concept that intensity of a potential entity determines crossover rate for both emission and absorption. This might unify the probability concepts that physicists use so freely. But what about probability as it relates to a speeding electron rather than to a photon?

Adam: Up to this point I have maintained that any entity with rest mass, such as an electron, be treated as a stationary field. I think I shall be ready to lift that restriction next week.

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