Note that A is always in space, hence the x-axis actually follows the motion of A in time and is depicted both at the origin and the end of the duration represented in the diagram.
A further deduction
If motion in time is regarded as perpendicular to the spatial dimensions, such motion would arguably have two aspects: To move perpendicular to the spatial (directly away from or toward any three-dimensional point) could be described as a concentric, wavelike motion relative to each point in space - because only a concentric radiation (away from) or concentration (toward), in the spatial aspect of a four-dimensional motion in spacetime could be considered perpendicular to a point in three dimensions at once. But since four-dimensional motion in the spacetime continuum would always remain in space as it moves across space, the motion would also involve a trajectory across definite spatial points. Therefore, a body moving in time could be described as continuously radiating from a series of points in space, and concentrating upon those it approaches.
If the photon is regarded as a spatial (a-temporal) object embedded in space, an observer who regards herself as at rest, and light as moving, while actually moving across space in time, will experience direct interactions with photons as impacts with moving particles, and will experience indirect interactions as the manifestations of waves. The apparent wave/particle duality of light would reflect the observations and interactions of bodies moving in spacetime with other bodies (photons) embedded in space.
We could therefore describe motion in time as a motion literally across space, a continuous radiation from one point in space and a concentration upon another. The apparent motion of light would in this hypothesis be the reflection of an observer's motion in time and across space.
Let's consider what else might be explained by this hypothesis that cannot be otherwise explained, or cannot be explained as well.
Implications
As already stated, the most significant implication of the present hypothesis is that the definition of light as being a-temporal and at absolute rest permits the resolution of the wave/particle paradox, a problem that has long eluded satisfactory explanation. If a body that exists in time is said to be moving perpendicular to space and yet to occupy a definite position in space at each moment, wave/particle duality can be attributed to our experience of the interaction between mass and light under different conditions - the wavelike radiation from, or relative to, one point, and the point-like intersection with another.
Given the hypothesis that mass, by moving in time, moves across space in a manner that places it always in space while also moving perpendicular to the spatial dimensions, in order to account for the variable wavelike behavior we observe with light it seems necessary to posit the four-dimensional motion of mass as a trajectory that fluctuates in a cyclic manner along the surface of its radiation. (For the sake of simplicity, the motion of mass relative to space will be treated in what follows as just a correlative radiating and revolving trajectory, without further specification. The precise characteristics of such motion is a question for experimentation and mathematical treatment.)
As Special Relativity suggests, and as the foregoing diagrams express, space and time are evidently co-metric. A body in relative motion moves relatively less in time the more it moves in space. Therefore, if light is three-dimensional, and embedded within a four-dimensional continuum, its spatial orientation within spacetime may vary according to the circumstances of its emission. Depending on a photon's spatial orientation relative to a massive body, the latter may approach the former in a relatively more-or-less spatial, more-or-less temporal orientation, resulting in a more-or-less contracted spatial separation, and therefore, a greater or lesser wavelength and frequency. The wavelength and frequency we associate with light might thus be attributed to the relative interval between cycles of the radial trajectory of mass. We might envision a four-dimensional radial motion as a spiraling in which each "wavelength" represents a cyclic return to a particular three-dimensional trajectory, and we might attribute the apparent polarity of light to a reflection of the spiraling of mass across space along two dimensions of its wave-front.
An obvious question raised by the hypothesis is how to characterize the relationships among material bodies as they move in time and across space. It seems most plausible and consistent with our experience that material bodies, if at rest relative to each other, would move in a more or less synchronous radiation along parallel trajectories, so that the spatial aspect of their motion in time would be imperceptible, and relative locations of mass in space would remain constant. It may be significant that small variations in phase would be expected to produce wavelike phenomena like those originally predicted for material bodies by de Broglie (1924).
Perhaps the most vexing difficulty in comprehending the present hypothesis is imagining the relationship between various masses, and light, when the light-source is envisioned in their midst. Consider a room with a light-source in the center and a number of observers arranged against the four walls. In this situation we would describe the light-source as depositing a series of photons in space while the source, the observers, and every mass in the room is radiating across space, all in parallel with each other, because each is at a relative state of "rest." For each photon deposited, there will eventually be an intersection with a mass (an atom) according to which of the spatial trajectories of the masses in the room is oriented toward the photon as its temporal wavefront crosses the photon's location.
The strangeness of the relationship between light and mass can be illustrated by means of Young's classic experiment with light (1803), which uses slits or pinholes in screens to produce seemingly inexplicable manifestations of simultaneity, non-locality, and interference. As is well-known, photons have been found to behave differently when passing through a slit in a screen depending on whether there is another slit some distance away.
Young's experiment is depicted in the conventional manner in figure 2, treating light as moving and mass at rest:
Point p represents a light-source, a1 and a2 are slits in screen s1, and s2 is a second screen where the light from p that "passes through" the slits is absorbed.
