Wave-Particle Duality -- Executive Summary:

One does not have to invoke the particle concept to explain photon termination. Furthermore, it is counter-productive to do so.

How can we explain what happens to light when it encounters a half-silvered mirror? The path each photon takes is random/indeterminate and yet there is an ordering of the photon paths in the aggregate: half are deflected and half are not.

This is really the traditional wave-particle duality problem. Photons appear to interact with the mirror as a wave which may split into two paths with the intensity of each path determining its relative photon distribution. But individual photons appear to interact with the targets as particles that only took one unpredictable path.

The Copenhagen interpretation says that wave-particle duality is characteristic of radiation and is beyond our understanding. The evidence of the wave nature of photons is pretty clear: photons do not impact with each other as particles do but instead exhibit interference and reinforcement effects.

The evidence of the particle nature of photons seems less clear but the argument for it goes something like this. The photoelectric effect suggests that photons behave like particles.¹ Individual photon terminations can be photographically recorded on film which suggests that photons have space location, at least when interacting with material instruments. A photon also has momentum, is quantized and originates at a distant source. On this basis physicists then borrow the concept of par­ti­cle/pro­jectile from classical physics and attempt to apply it to the photon: the photon becomes a particle ejected by the source which then travels through space to impact at a point in space on the target. Between photon creation and photon termination you have wave behavior and so, voilà, wave-particle duality.

But a classical particle acting as projectile has rest mass and a definable trajectory whereas the photon has neither. In addition, a particle displays impact and rebound when colliding with one of its brethren while the photon does not. Therefore, one may properly question the validity of applying a classical concept (projectile motion) to a patently non-classical realm, namely radiation. The description of the photon as a "massless particle" seems too glib and implies an intellectual laziness. Suppose we set out to design a photon that could avoid some of the current contradictions and yet still account for "photon behavior" and wave-particle duality.

Our ideal photon is an entity of pure occurrence without even a whiff of existence. Physically it is quantized kinetic energy based upon al­ter­nating, self-generating electric and magnetic fields. It has the waveform and so displays the usual effects of that form, reinforcement and inter­ference. As a wave our photon will spread over space along all available paths and as these paths diverge the wave's kinetic energy will spread over ever-increasing space thus reducing local wave intensity. By virtue of its kinetic energy and E = mc² our photon has some relativistic mass asso­ciated with it, but we have to be very careful in characterizing this mass.

If rest mass is kinetic mass (i.e., matter), then our photon's relativistic mass must be potential (stored) mass and we can assume the latter will have some special properties. One thing unusual about this mass is that it occurs rather than exists just as potential energy (e.g. tension in a spring) exists/persists rather than occurs. As a pure occurrence, devoid of matter or any aspect of existence, the photon has an extension (interval) in time but it does not extend in space (you cannot spatially subdivide a pure occurrence). What the photon does in space is to progress there, specifically the photon's potential mass progresses along all possible space paths.

At some point a photon will terminate upon a material barrier and we might ask what happens to its kinetic energy and its potential mass? This "death" of the photon is something of a mystery, but we might gain insights from the more familiar "birth" of the photon. Suppose you have an atom, or molecule, or nucleus in an excited state which then transitions to a ground state and emits a photon in the process. The space-located atom stores potential energy in its excited state and this energy releases to become kinetic at a point in time as the photon. Therefore the birth of the photon proceeds from matter to radiation and is: 1) marked by the transition of energy from potential to kinetic, and 2) located at a point in space and in time.

Now does the birth and death of a photon constitute another one of those symmetries so pre­valent in quantum physics (e.g., Hamilton's analogy, de Broglie's particle wave thesis, Einstein's thermo­dynamic analogies in his 1905 "Heuristic" paper)? If so, the birth of the photon can teach us something about the death of the photon. Perhaps the death of the photon is: 1.) marked by the transition of mass from potential to kinetic, and 2.) located at a point in space and in time.

Consider an atom in an excited state about to transition to the ground state. The potential energy of this atom extends (progresses) over time but can only release at one (indeterminate) point in time. Similarly, the potential mass of a photon extends (progresses) over space but can only release at one (indeterminate) point in space. In both cases the releases are individually random yet in aggregate may be non-random. In sum, the birth-or-death ("crossover") of a photon is an event involving the intersection of matter and radiation wherein stored, quantized energy on one side, or stored, quantized mass on the other, is released and made kinetic at a point in space and time. Matter having potential energy (excited state) re­leases/con­verts that energy to a kinetic radiation entity (photon); radiation having (photon) potential mass re­leases/con­verts that mass to a kinetic mass entity. All of this suggests that we do not have to invoke the concepts of particle or projectile when describing either photon emission or photon absorption. The photon-as-particle concept was (naively) brought in to explain how a wave front could terminate at a space point. What actually explains photon termination at a space point is the point conversion of photon potential mass to kinetic (released) mass. This is the essential concept for an understanding of the wave-particle duality mystery.

Photons therefore are pure occurrence: no stored energy, no dependence upon matter, and stored mass due to E = mc². Their kinetic energy as wave travels all paths even though their termination upon matter will be at a single point. Photons do not have a "particle" nature, they are not projectiles, they do not follow a single path and they do not "impact" upon matter. Instead, the photon wave terminates as a whole, befitting an occurrence, and this termination releases potential mass at a space point rendering it kinetic and allowing for momentum transfer.

In the case of the half-silvered mirror the kinetic, waveform energy of the photon travels both paths, deflected and not deflected, even though termination will only occur upon one path. The aggre­gate distribution of photon terminations will reflect the relative energy intensity of the two paths.

Although the photon as a wave of kinetic energy splits into two separate paths, the photon remains a single occurring entity which can terminate in an instant regardless of how widely separated the wave's space paths become. Entangled photons exhibit the same behavior: ter­mi­na­tion/meas­urement of one will affect its distant twin immediately because together they participate in a shared, single, pure occurrence spread over space-separated paths. The radiation energy that entangled photons share "wraps up" the pair's common properties so that forcing one photon to choose a spin mode (up or down) immediately determines the spin mode of the unmeasured photon. Superluminal signaling from one photon to the other does not occur; rather a single, shared occurrence has been altered as a whole. This behavior is rooted in a deep ontological truth:

Occurrence (radiation) extends (progresses) over space and remains a single entity with one identity and one time measure (frequency) just as existence (matter) extends (progresses) over time and remains a single entity with one identity and one space measure (extent). (Chapter III)

Bottom line: If we jettison the (facile, simplistic) idea of the photon as a projectile, then photon entanglement may still be a bit strange but it makes sense ontologically and this eliminates one of the biggest ob­jections against realism in Q.M. Giving up the idea of the photon as a projectile also is the route to a full understanding of wave-particle duality.

Can electrons become entangled? Yes they can providing they are "joined" by a shared kinetic energy just as entangled photons constitute shared kinetic energy. (Chapter V.)
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¹ This evidence for this not entirely clear-cut. See Photoelectric Effect.