We may begin with some accepted truths in physics.

• Radiation is quantized (as photons) and matter is quantized (as atoms, electrons, etc.).

• The entities of physics move in space and time (Newton) or in spacetime (Einstein/Minkowski).

That both radiation and matter are quantized seems indisputable, but the idea that physical entities are characterized by movement through space and time may be open to question. Photons progress through space at the speed of light but they are stationary in time since time does not advance for a photon. Hence a radiation quantum, according to its own measure, only progresses through space and not through time.

Similarly, material quanta not subject to external forces are inertial in nature and inertial objects/observers cannot detect their motion in space and so consider themselves to be at rest. Hence an inertial mass quantum, according to its own measure, only progresses through time and not space.

One may conclude that time progression is not an intrinsic property of light quanta since light quanta by their own measure are "frozen" in time. And space progression is not an intrinsic property of inertial mass quanta since all inertial observers are justified in regarding themselves at-rest. But motion through space is an intrinsic property of light since ALL observers agree on its velocity and light cannot be present without possessing a velocity of c. It is equally hard to imagine mass quanta where time does not advance.

• Quanta in some circumstances only progress in a single dimension: space for radiation quanta and time for inertial mass quanta.

Quanta that by their own measure progress in one dimension while not advancing in the other dimension will have both location and extension in the dimension in which they do not move. For example, an inertial mass quantum will have a relative location within that inertial system and it will also extend (occupy space) within that same system. Similarly, a time-stationary photon will have a temporal location relative to other photons and it will extend over a time interval.

• Quanta that progress in a single dimension also have an orthogonal extension dimension.

All quanta have a kinetic (patent, evident) identity which is energy for a photon and mass for a material quantum. But quanta will also store their opposite number. Photons store potential mass as a consequence of E = mc² and mass quanta store potential energy, perhaps as electron orbital displacement energy within an atom, or the energy a radioactive atom possesses before emitting ionizing radiation.

• Quanta therefore: 1) have a dual identity, kinetic and potential, and 2) they are motionless in one dimension and progress in the other.

If quanta progress in a dimension then we may reasonably assume they progress over paths in that dimension. That a photon progresses over all available paths was a famous conclusion of Feynman’s path integral formulation of quantum mechanics. Of course these Feynman paths are in three dimensional space and one may justifiably ask if there are anal­o­gous paths in time which have but a single (linear) dimension. This book argues that there are linear paths in time which overlap but begin at a common origin and terminate at separate endpoints. Accepting that argument confirms the conjugal parallel nature between quanta; rejecting it does not impair the arguments that follow.

• All quanta follow paths in space or in time.

Path endpoints in space or in time are dependent upon quantum storage release. When a photon is created it thereby has stored (rel­a­tivistic) mass and this potential mass stays with the photon until it is released via photon termination (photons may terminate completely, or they may be transformed into a new photon with different energy which terminates the original photon). So are paths physically real?

Quanta paths are not "real" aside from the physical entities that traverse them and give them significance. So what are the entities that traverse quanta paths? To answer that question we have to look at the two identities of a quantum. The kinetic identity of a quantum has an interval (in time for the photon) or a volume (in space for the mass particle) and both of these are present in the extension dimension. These extension measures (and identities) remain unaffected by quantum progression: photon kinetic energy remains un­chang­ed across galaxies and an atom's kinetic mass may remain constant over in­def­i­nite time measures. It is the po­ten­tial identities of quanta that are present in the progression di­men­sion: the potential mass of photons traverse paths in space and the po­ten­tial energy of mass quanta traverse paths in time.

• Paths are simply the routes taken by potential mass or potential energy in space or time respectively.

Because time is linear the potential energy that mass quanta store is unaffected by progression in time. What is stored at an initial point in time by a mass quantum progresses along time paths and is simply released at a subsequent point in time. But things are a bit more com­plicated for photon potential mass as it spreads/progresses over space.

Potential energy stored by a mass quantum is continuous and unchanging in time until released at a time point, an example being the energy a radioactive atom stores before release. Similarly, potential mass stored by a photon is continuous in space until released at a space point via photon termination. This means that a photon’s potential mass will expand in­def­i­nitely in the three dimensions of space until that photon terminates upon an object. Unlike anything known to classical physics, potential mass can advance and rarify without limits to fill all available paths. Because of its wave nature, the potential mass of a single photon will pass si­mul­ta­ne­ously through more than one slit or along both paths of an interferometer. Like any wave, potential mass can be made to interfere with itself creat­ing regions of positive and negative reinforcement.

• Potential energy has the field form as it progresses in the single dimension of time. Potential mass has the wave­form as it progresses in the three dimensions of space.

Although potential mass in a photon’s progression dimension can sub­divide without limit, the photon’s potential mass, like its kinetic energy, does not cease to be a single, unitary entity. The photon’s kinetic energy and its potential mass are birthed together as one and they die together as one. The relative intensity of this potential mass, varying from point to point over a target, will determine the local probability of photon ter­mi­na­tion. But one must not confound potential mass with a probability func­tion; potential mass is physically real, just as kinetic energy is physically real.

When a photon terminates, its potential mass becomes kinetic and kinetic mass is discrete, not continuous. This conversion of mass from potential to kinetic, from continuous to discrete, is instantaneous and there are no space limitations (intergalactic is fine) regarding the "collapse" of space-smeared potential mass paths (yielding non-locality) since only a unitary potential entity is in­volv­ed. A photon’s potential (stored) mass is a wave but its conversion (release) to discrete kinetic mass at a space point on a material target fosters the illusion that it is a particle.

• Space-smeared photon potential mass becomes discrete and particle-like when it is released to become (an in­credibly small) kinetic particle mass.

The preceding is, in outline, the argument made in this book for the potential mass interpretation of quantum mechanics. This interpretation offers no new predictions for quantum behavior; instead it tries to give some rational explanation for such mysteries as wave-particle duality, quantum entanglement and non-locality. The book offers a parallel, if slightly different, argument to cover the case of the wave behavior of electrons.

One might ask the justification for explaining photon behavior on the basis of a new quantity, namely potential mass. First, entangled photons must be connected by something which is probably undetectable (until termination) and which the photons share and store in common until release; potential mass meets these requirements. Second, potential mass is not new at all; it is simply relativistic mass given a name that reflects its role as a stored quantity. Instead of viewing relativistic (potential) mass as merely a quantity the photon possesses, view it instead as we do potential energy within the atom: a quantized entity gained, stored, and eventually released that possesses a form of its own (field for potential energy, wave for potential mass) as it progresses through a dimension. And of course each terminates at a point in the dimension in which it progresses, space for the photon's potential mass, time for the atom's potential energy.

Storage of mass or energy is a fundamental part of all quanta. Atoms have potential (stored) energy in their electron shells which they release as photons which in turn have potential (stored) mass they can release back to atoms. The mass that photons store is what gives them momentum and this stored mass is necessarily released upon photon termination. It is true that some physicists now discourage the use of "relativistic mass." But that largely reflects a bias towards "invariants" that exists among General Relativity theorists. There is still a strong case to be made for the concept of relativistic mass.

Ever since 1927 when the Compton effect (photons "impacting" e­lec­trons) became known, physicists have tended to assume that photons were actual particles and their wave behavior was some hard-to-explain artifact of particle motion. This book argues instead that photons are actually waves and it is particle-like "impact" that is the artifact. Spe­cif­ical­ly, it is the photon interaction with matter that transforms a wave potential entity into a kinetic, particle-like entity that terminates at a point. Those physicists willing to reexamine their assumptions about photons may find some ideas of value in this book: ideas that focus on quantum entanglement, quantum non-locality and quantum probability.