A hypothesis on the nature of light

December 11, 2007 by jarnold

Abstract

It is proposed that light is at absolute rest, its apparent motion being the reflection of the motion of mass in time. The hypothesis resolves the paradox of the apparent wave/particle duality of light, accounts for its speed being invariant and a physical limit, and explains other peculiarities of its behavior.

Introduction

Light is regarded as in some ways wavelike, in some ways particle-like, invariant in speed, the limit of speed, and as having various strange non-local effects. Einstein's suggestion (1905) that light be accepted as both wavelike and particulate pending an intelligible resolution of the evidence has become an abiding commitment to paradox as quantum theory has expanded the range of the counter-intuitive, or irrational, to encompass much of physics. Nonetheless, the value of the fundamental scientific preference for simplicity of description, explanatory power, and logical coherence remain as desirable as ever. However much science is now accommodated to the paradoxical features of light, a theory that would preclude the need for concession is always to be preferred by scientific standards. The idea that light might be at absolute rest is no doubt a strange and unlikely remedy at first impression, but I hope to justify it here by an appeal to the explanatory power by which it may be judged superior to conventional theories.

A Heuristic Graphic

A simple spacetime diagram (figure 1) conforming to Special Relativity and the Lorentz transformations(1), and drawn according to the relativistic perspective of a single observer, provides a heuristic representation by which the present hypothesis may be most readily considered.

figure 1

The x-axis represents space, while its perpendicular, the t-axis, represents time - both according to observer A who is considered to be at rest and moving in time(2) along the t-axis. Vector B represents a body in motion relative to A.

A travels 5 sec(3), in time in the scope of the diagram while “at rest” in space. Body B, which as a matter of convenience is located initially at O, moves from the vicinity of A at a velocity, according to A, which takes it 4 ls in 5 sec. The coordinates of B (4,3) can be derived from the Lorentz transformations, or geometrically by means of the gradations in the diagram. By locating B at 3 seconds in time it is represented that the clock of B has moved 3 sec in the reference frame of A.

The spacetime interval given by s2 = t2 - x2 (with t proportional to c) is expressed here by

s2 = 52 - 42
s2 = 9

Thus s, the interval, is represented in the diagram as the proper time of body B.

A significant implication of the diagram is that there are actually two invariants involved in a relativistic relationship: the interval of the proper time of B, and in addition, the interval of the world-line of A. The latter is not commonly recognized as being identical to the interval of the world-line of a body being observed. But in the relationship shown in figure 1 between an observer and a body in relative motion (where t2 = s2 + x2), the spacetime interval of the observer is necessarily equivalent to any world-line in relative motion, as the latter would form the hypotenuse of the Euclidean triangle described by the observer’s measure of a body’s distance traveled in space and the time elapsed on the moving body’s clock.

It is important to note that both the Lorentz Transformations and the equation for the invariant interval indicate a Euclidean relationship between space and time, and between bodies in relative motion. Although the relationship between clocks in relative motion given by t' = (t2 -x2).5 is indeed parabolic, as is generally recognized, the fact that a hypotenuse relates to the sides of a Euclidean triangle by a parabolic function presupposes the right-angle. And as figure 1 shows, the temporal component of any body’s motion in spacetime (including the observer’s) is at a right-angle to the observer’s space axis. The parabolic relationship between different reference frames should therefore be understood as derivative of the Euclidean relationship.

The motion of light is especially noteworthy in terms of figure 1. It should first be kept in mind that whereas the motion of light is commonly expressed as (approximately) 300,000 km per second, to fully describe its observed motion relativistically is to report that it travels 1 ls in space relative to an observer’s spatial reference, and zero seconds in time relative to an observer’s temporal reference, as is given both by the Lorentz transformations and the spacetime interval. A world-line representing a ray of light in figure 1 would therefore have a spacetime interval of 5, but a proper time of zero, and would lie directly along the x-axis. (The spacetime interval in this case would be s2 = 52 - 52.)

Two preliminary conclusions can be mentioned:

The speed of light as a limit: If the world-lines of bodies in relative motion are taken as having the same interval but with varying spatial and temporal components according to their spacetime trajectories, the limiting spatial velocity will be the interval of a world-line along the space axis measured in terms of the same inverval along the time axis. A vector drawn along the x-axis in figure 1 to represent a ray of light would extend as far along the x-axis as time elapses for the observer in the course of the diagram.

The speed of light as invariant: Due to the invariance of the observer’s spacetime interval, each observer will measure light as traveling the same distance in space as time elapses in that observer's reference frame, and though the measure of the spatial distance traveled by a beam of light between events will vary between reference frames, the rate will always be agreed upon. We can infer from the observation of light that distance in time is the same as distance in space - that one second in time is the same distance, but in a perpendicular direction, as 300,000 km in space.

The Hypothesis

The fact that the motion of material bodies is relative, and limited, while the motion of light is invariant, and an absolute limit, suggests a fundamental distinction. If motion in time were to be regarded as a correlate of mass, if the clock of a material body is unable to stop entirely, and if in contrast light is massless, and its clock (if it could be said to have one) is invariably motionless, then light could be construed as actually not-moving in time. And if light doesn't move in time, it may be meaningless to say it moves at all.

The question is: If light is considered to be at absolute rest, if the apparent motion of light is actually the reflection of the motion of mass in time, however absurd the idea may seem at first, what paradoxes could be resolved, what potential exists for a more comprehensive understanding of other issues and phenomena? What if material bodies exist in spacetime, but photons are embedded in space? What would be the implications if light is at absolute rest, and if the motion of mass in time - perpendicular to space and yet always in space – is the basis of all motion, real and apparent?

If uniform motion in time is regarded as perpendicular to space, such motion would arguably have two aspects: To move perpendicular to the spatial dimensions (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 or concentration, 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 one point in space, and concentrating upon another.

If the photon is regarded as a spatial (a-temporal) object, an observer who regards herself as at rest relative to light, while moving across space in time, will experience direct interactions with photons as impacts with moving particles, and she will experience indirect interactions as manifestations of waves. The apparent wave/particle duality of light would reflect the observations and interactions of bodies moving in spacetime with other bodies embedded in space.

We might 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.(4)

Let’s consider what might be explained by this hypothesis that cannot be otherwise explained, or cannot be explained as well.

Implications

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 reflection we observe with light it seems necessary to posit a trajectory that fluctuates in a cyclic manner along the surface of the radiation. If light is embedded in the four-dimensional continuum, its spatial orientation in spacetime may vary according to the energy of its emission. Depending on a photon’s spatial orientation relative to a massive body, the latter may approach the former in a more-or-less spatial, more-or-less temporal orientation, resulting in a more-or-less contracted spatial separation, and therefore a greater or lesser 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 such a 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. (Incidentally, this interpretation of wavelength suggests both an upper and lower limit, perhaps with Planck Length being the lower-limit, where spacetime orientation relative to a photon-space would approach the perpendicular.)

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 in space would remain constant. It may be significant that small variations in phase would be expected to produce wavelike phenomena like those predicted for material bodies by de Broglie (1924).

Another important aspect of light that has defied explanation is its peculiar non-local behavior. It’s been confirmed, in terms of the conventional paradigm, that a photon propagates in an expanding wave of probability that might be intercepted at any point on its wave-front, even if the wave-front is light-years in diameter. And Bell (1964) has demonstrated that a correlation between a pair of photons can be instantaneous and indifferent to distance. We could account for non-local phenomena in terms of the hypothesis by recognizing the motion of our analyzers and detectors as moving across space relative to the photons, and we could define locality at any moment in terms of the parallel radiations of the apparatus along their expanding wave-fronts. The otherwise incomprehensible simultaneities associated with light could thus be attributed to manifestations of motion in time perpendicular to space, where a point in space becomes an expanding sphere, and a contracting sphere becomes a point in space.

There is no basis in the present hypothesis for actual interference between or among photons and material bodies. (This is not especially controversial; Dirac has pointed out (1927) that “each photon only interferes with itself.”) If photons don’t actually move, and if material bodies radiate approximately in-phase, with only minor variations at the subatomic level, their apparent interference can be no more than a pattern, as on a screen, that we identify by analogy with interference found in material media. What is commonly called electromagnetic interference would be described instead as the manifestation of regularities in photon emission that makes intersection with masses moving along particular trajectories more or less likely. Similarly, light can be considered coherent when photon emission is precisely sequenced and oriented in space to be intercepted by masses along specific trajectories at regular wavelengths.

Several of the strange aspects of light can be mentioned here in association with the various adaptations of Young’s classic experiment with light (1807) using slits or pinholes in screens to produce perplexing manifestations of simultaneity, non-locality, and interference. As is well-known, photons have been found to behave differently when passing through an aperture in a screen depending on whether there is another aperture some distance away. In terms of the present hypothesis, a screen can be regarded as a plane of material bodies, each of which intercept, or not, a photon depending on the distances of each material body from the light source, and the spatial trajectory of each at the moment its wave-front intersects the location of the photon. The light that “passes through” an aperture in a screen would be specifically out of phase with all the trajectories of the masses of the screen as the latter radiate across the space between the screen and light source. (Note that the light source should be envisioned as a mass moving parallel with the screen while depositing a series of photons.) When an additional aperture is opened, the photons that avoid interception to “pass through” one or both apertures and impinge on the second screen consist of those that would have “passed” the original aperture, those that “pass” the second, and those in-phase to “pass” both - the latter including those in a phase that would “pass” the original if not first intercepted by the now missing masses of the second aperture. Given the different phase relationships determining which photons avoid interception by the masses of the first screen, there will be distinct phase relationships with the masses of a second screen, producing the apparent interference pattern found in Young’s and subsequent experiments.

Other phenomenal aspects of light, such as reflection, diffraction, and its apparent retardation in various media can be explained, if the hypothesis is confirmed, in terms of the dynamics of absorption and re-emission, and needn’t concern us here.

Conclusion

A relativistic spacetime diagram demonstrates that a two-dimensional projection of the four-dimensional continuum can illustrate the peculiar characteristics of light as the ultimate and invariant speed, and suggests that it is not meaningful to regard light as moving in either space or time. The hypothesis that light is at absolute rest, and that the apparent motion of light is the reflection of an observer's own motion in time, has been shown to resolve the wave/particle paradox and to make the apparent non-local behavior of light intelligible. Although experimentation and formalization is needed to confirm and better define what has been described as the radial trajectory of mass in time across space, the necessarily dual and exotic nature of four-dimensional motion has been shown to make apparent characteristics of light such as wavelength, coherence, polarity, interference, and simultaneity more comprehensible as manifestations of mass, rather than light.

End Notes

1. The Lorentz Transformations are t' = (t-v)/(1-v2).5 and x' = (x-vt)/(1-v2).5, with t as time, x as distance, and v as velocity proportional to c.

2. It is permissible to say a body “moves” in time because spacetime has been recognized as a continuum as a consequence of Special Relativity. Duration in one coordinate system is a composite of motion in space and time according to another.

3. As a matter of convenience t is generally multiplied by c so that space and time can be expressed in distances of the same scale. I prefer instead to calibrate them by giving time in seconds (sec) and space in light-seconds (ls).

4. In terms of the diagram in figure 1, if light is at absolute rest, a more accurate representation of light would be to treat a photon emitted at O as a point, thus representing the motion in spacetime of body A, i.e., A’s spacetime interval, as the source of the photon’s apparent motion of 1 ls per sec. To represent a photon encountered by A, we would place a photon on the t-axis at the time where the world-line of A intersects with it.

References

Bell J. (1964), “On the Einstein Podolsky Rosen paradox”, Physics 1 195-200.

de Broglie L. (1924), “Recherches sur la théorie des quanta,” Annales de Physique 3, 22-128, 1925, translated in Gunther L., Wave Mechanics, Pergamon, 1968.

Dirac P. (1927), "The quantum theory of the emission and absorption of radiation", Proc. Roy. Soc. London A 114, 243.

Einstein A. (1905), In "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt" ("On a Heuristic Viewpoint Concerning the Production and Transformation of Light"), Annalen der Physik 17:132-148.

Einstein A., Podolsky B., Rosen N. (1935), “Can quantum-mechanical description of physical reality be considered complete?” Phys.Rev. 47:777-80.