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Title: Light-speed Invariance
Author: David J Larkin
Abstract: The apparent invariance of photon (radiation) propagation-speed is a consequence of particle–photon absorption–emission processes that modulate the energy characteristics of incident radiation. The 'characteristic propensity of emission', which constrains photon emission-speed to an upper-limit, is invariant. Consequently, photon emission-speed, as distinct from photon traversal-speed, is limited and invariant. Because emission-speed is limited and invariant, absorption–emission processes—which take place in the earth's atmosphere, in radiation-detection instruments, or in general, in any medium capable of 'transmitting' radiation—modulate (or filter) the resultant radiation propagation-speed, consequently giving rise to the 'appearance' of an invariant and limited traversal-speed. Therefore, the instant at which you attempt to measure the speed of light (radiation) is the instant at which you modulate that radiation and render its speed 'invariant and limited'.
Keywords: Light-speed Invariance, Lightspeed Invariance, Special Relativity
Created: 2001
Last Updated: November, 2002

•The issue addressed in this essay is extracted from a broader body of work on composite-particle theory (Larkin, 2000)—a work that deals extensively with radiation phenomena (such as dispersion, refraction, and diffraction) and the ramifications that (that) composite-particle theory has for special relativity and quantum mechanics. However, this essay (in the context of light-speed invariance) will only examine two radiation characteristics, which are independent of any particular particle-theory, namely: photon distortion (division of energy), and photon absorption–emission processes (energy modulation).

In order to facilitate this examination it will be necessary to draw the distinction between photon emission-speed and photon traversal-speed. It will suffice, without loss of generality, to (simply) define photon emission-speed as the speed a photon 'possesses' relative to the 'point' of emission or energy exchange—a point independent of any displacement or recession experienced by a recoiling emission-source. Conversely, photon traversal-speed may be 'defined' relative to any (arbitrary) frame-of-reference. It will be argued in this essay that while emission-speed may be 'limited and invariant', traversal-speed (relative to an appropriate frame-of-reference) may be neither limited nor invariant.

•If we idealise photons as rigid 'point-entities' without mass then we may indeed need to resort to ad hoc postulates or bizarre theories in order to explain the apparent upper-limit to light-speed. However, if we accept that under increasing applied force, such as 'high-energy' interaction, that light-photons become increasingly more susceptible to 'structural' distortion then we can readily explain why light-speed appears to be restricted to an upper-limit.

When exposed to an extraneous application of energy, any entity (composite particle or otherwise) that is susceptible to structural distortion will exhibit a constrained if not limited rate of change (if present) in any consequentially induced 'relative-speed'. In the case of high-energy (non-destructive) particle impacts or emissions, any imparted energy will be proportionately distributed between that energy retained (or absorbed) within the particle and that energy exhibited by any increase in the particle's propagation-speed. Susceptibility to distortion is an important determinant of how applied energy is distributed (or transformed) and consequently, how changes in speed and trajectory are affected. (A graphic analogy would be to consider the differing dynamics of a billiard ball, an egg, and a sealed balloon filled with water. It is simply not the case that the harder something is struck, the faster it is propelled.) Clearly, if applicable, susceptibility to distortion would also be an important determinant of photon emission-speed.

It is not difficult to imagine that, short of destruction, any increase in imparted energy may only result in a change to a particle's structural (or absorbed) energy—that is, above a certain level of imparted energy any additional energy may be absorbed or retained within the structure. Consequently, photon emission-speed would be limited. (If we make the correlation between mass and potential (absorbed) energy, we can begin to appreciate why the observed phenomenon of 'increased mass with increased speed' occurs; and indeed, comprehend the utility of Einstein's famous equation: E=mc2. It is also contended, though not argued here, that variation in absorbed energy is the principle difference between the various 'categories' of radiation photons: through the spectrum from radio-'wave' emission up to the more energetic and destructive x-ray and gamma-ray radiation.)

Emission-speed (or interaction-speed) relates to the speed imparted to a radiation particle or photon as a consequence of a direct or indirect interaction. An example of a direct interaction would be the collision of two (or more) particles in which an exchange of energy resulted in a change to the relative-speed of one or more of the respective particles. Conversely, an indirect interaction refers to a direct interaction between two (or more) particles from which a 'new' particle is emitted. While photon emission-speed may be constrained to an upper-limit, is the emission-speed, of necessity, invariant? For reasons that will become obvious, we will focus our attention upon indirect interactions.

•Photon emission is precipitated by an exchange of energy; and emission only occurs at or above an energy-threshold, that is, below this threshold there is insufficient 'energisation' necessary to precipitate emission. Emission-speed is dependent upon the photon's susceptibility to distortion (as discussed), and the amount of energy being exchanged. It will suffice to describe the photon emission-speed that occurs at the 'threshold-level' of energy exchange as the threshold-emission-speed. If we allow that the emission of a radiation photon occurs at a level of energisation 'sufficiently high' such that, due to susceptibility-to-distortion, no further increase above the threshold-emission-speed is possible, that is, any excess imparted-energy is absorbed within the photon structure, then emission-speed would indeed be invariant. Or to rephrase it, the level of energisation required to precipitate photon emission, the energy-threshold, is so large that at any level of energy-exchange at or above this threshold, due to 'excessive' structural distortion within the photon, no further increase or variation in emission-speed is possible.

However, in the context of distortable particles, while it may seem plausible that emission-speed could be limited and invariant, the apparent upper-limit and apparent invariance of traversal-speed is bewildering if not problematic.

By way of analogy, for the purpose of explication, consider the following hypothetical scenario. A cannon, capable of propelling rubber-balls, is attached to a movable platform. The platform (hence cannon) can be moved toward or away from a fixed (target) measuring-device or speed-gun located within the path of the projected balls. Whether stationary or in motion, a 'muzzle-speed' sensor, attached to the platform, indicates that the cannon propels the balls consistently (within acceptable limits) at 100 kph: the emission-speed.

As the platform is moved toward the target speed-gun at 10 kph—the approach phase—and upon reaching the 'firing point', balls are fired from the cannon toward the target. Relative to the sensor attached to the platform, the emission-speed remains invariant at 100 kph. However, relative to the target, the target speed-gun registers a speed of 110 kph: the traversal-speed of a ball (during approach) relative to this fixed frame-of-reference. That is, the traversal-speed is equal to the emission-speed plus the speed of approach.

Finally, during a recession phase, balls are fired at the target speed-gun while the platform is moved away from the target at 10 kph. Similarly, relative to the sensor attached to the platform, the emission-speed remains invariant at 100 kph. However, relative to the target, the target speed-gun registers a speed of 90 kph: the traversal-speed of a ball (during recession) relative to this fixed frame-of-reference. Therefore, the traversal-speed is equal to the emission-speed minus the speed of recession.

While the emission-speed remains invariant (with respect to the stated frame-of-reference) the traversal-speed reflects the changes in the speed of approach or recession and is, therefore, not invariant (relative to the stated frame-of-reference). Why is this outcome problematic? This outcome, per se, is not problematic. But, for example, when solar-radiation emission, incident upon the Earth during phases of approach and recession, is examined no variation in radiation traversal-speed can be detected—(despite speeds of approach and recession of the order of 30,000 m/s). Radiation traversal-speed, it would appear, is invariant; and this unexpected result is problematic.

Before proceeding to the explanation, consider the following additions to our hypothetical scenario. A second cannon is fitted with a sensor to measure the emission-speed of balls fired from its muzzle. Attached to the back of this cannon is a target and collection hopper into which balls striking this target fall. This hopper provides a reservoir of balls for subsequent firing. This (second) cannon, which is set to fire balls at 100 kph, is placed between the first cannon and the target speed-gun. In order to simplify proceedings the first-cannon emission-speed is varied from 90, to 100, to 110 kph in order to simulate phases of recession, rest, and approach respectively. The first cannon is set to fire balls at the target of the second cannon. When the target on the second cannon is struck, this cannon fires a ball from its reservoir at the target speed-gun.

Now assume that the second cannon is obscured from view, that the trajectories of both cannons are sufficiently flat, and that any emanating sound is adequately screened with background noise. A casual observer would note that despite the emission-speed of the ball the target speed-gun invariantly displayed a reading of 100 kph. That is, when the (first) cannon fired at 90 kph, simulating recession, the speed-gun surprisingly, displayed a reading of '100'. However, when the cannon fired at 100 kph, simulating rest, the speed-gun displayed, reassuringly, a reading of '100'. Finally, when the cannon fired at 110 kph, simulating approach, the speed-gun continued to display a reading of '100'. Now a number of conclusions could be drawn in order to explain this outcome. But for the purpose of this analysis it will suffice simply to parallel the striking of the second cannon and associated ball-collection as a process of absorption, and to parallel the subsequent firing by this, the second cannon, as a process of emission. It will also be instructive to identify the striking and subsequent firing of the second cannon with the process of particle energisation and subsequent de-energisation.

A process of moderated energy-exchange—referred to as modulation—provides the basis for the resolution (indeed explanation) of this problematic issue—without resort to ad hoc postulates such as those advanced by Einstein in his theory of special relativity; postulates which lead inextricably to notions of space-time warps.

Modulation, as stated, is a process of moderated energy-exchange. An energised particle (visualise our second cannon), such as an electron, can de-energise (that is, stabilise) by emitting a radiation photon. The energy that the emitted photon possesses is a measure of the excess energy of the unstable electron (the energised cannon) and the propensity of that electron to pass-on energy to the photon subsequently emitted. In addition, the emission-speed (as discussed) is limited or constrained by the photon's susceptibility to distortion. These factors (in particular, the propensity to pass-on energy, and susceptibility to distortion) or the 'characteristic propensity of emission', which constrains photon emission-speed to an upper-limit, is invariant. Consequently, (as previously discussed) photon emission-speed is limited and invariant.

Because emission-speed is limited and invariant, absorption–emission processes—which take place in the earth's atmosphere, in radiation-detection instruments, or in general, in any medium capable of 'transmitting' radiation—modulate (or filter) the resultant radiation propagation-speed of any (subsequently) emitted photon. The important issue is that the (subsequent) emission of the photon is an outcome of an absorption–emission process. The particle, in this case the electron, is energised by a process of absorption, that is, the absorption of an incident-photon whose traversal-speed may not be limited, and de-energised by a process of emission. In essence, the absorption–emission process modulates or filters the traversal-speed of an incident-photon. Regardless of the speed possessed by the incident-photon (visualise the output of the first cannon), the speed of the emitted-photon (or the output of the second cannon) remains limited and invariant. The apparent invariance of the traversal-speed of the incident or absorbed photon is merely a chimera; what is actually being measured is the invariance of the emission-speed of a (subsequently) emitted photon in a sequence of absorption–emission processes.

During either the approach or recession phases of the Earth's orbit around the Sun, the traversal-speed of any incident solar-radiation would be modulated by the interaction of that radiation with atmospheric particles.

•Because the characteristic-propensity-of-emission of absorption–emission processes is invariant (in the sense described) any medium, atmospheric particles or the components of a radiation-detection instrument, which is capable of transmitting (or passing-on) radiation, will modulate that radiation. To-date, traversal-speed experiments have only measured the (subsequent) photon emission-speed of absorption–emission (or modulated) processes. Therefore, there is no evidence to support the conclusion that traversal-speed is invariant; nor (indeed) that traversal-speed is limited to c. The instant that we attempt to measure the speed of light (radiation) is the instant that we interfere with or modulate that radiation and render its speed 'invariant and limited'. To speak analogously, we effectively insert a second cannon into our evaluation.


•In the context of modulation, Einstein's ad hoc special-relativity postulates would appear exposed and his famous theory rendered redundant. One practical application of special relativity, heralded as irrefutable empirical-evidence for Einstein's theory, relates to global positioning systems (GPS). It is asserted that, without special relativity factored into the calculation of an entity's global-position, the consequent inaccuracy of such calculations would render such systems useless. On the contrary, it is not special relativity that is critical to accurate positioning; it is the set of formulae referred to individually and collectively as a Lorentz-transformation. The Lorentz-transformation is a mathematical model of electromagnetic-radiation behaviour; the transformation is quantitatively useful but qualitatively useless. Einstein based his theoretical position upon a qualitative interpretation of the Lorentz-transformation. Lorentz regarded the inherent 'time anomaly' as a matter to be subsequently resolved rather than reconciled. Einstein, however, enshrined a reconciliation of this anomaly by advancing the notion of 'time dilation'.

The rejection of special relativity is a consequence of a different qualitative interpretation of the physical evidence. The acceptance of the Lorentz-transformation is simply a matter of pragmatism. Its acceptance, like the acceptance of any mathematical model, is a measure of its utility in yielding quantitative results that are in good agreement with those observed. Mathematics, it is contended (and is yet to be refuted, if indeed it can be), can model any scenario regardless of whether that scenario has a 'physical-reality' or not. Or to put it succinctly, mathematics can model both the thesis and the antithesis. Therefore, mathematical models cannot provide evidentiary support (or input) to claims of 'verification' for theoretical-dispositions. Additional compounding-factors are that mathematical models are neither (necessarily) definitively descriptive, thus compromising their qualitative usefulness, nor descriptively unique.

When we examine the claims of experimental verification for special relativity (muon-decay, GPS, atomic-clock disparity, and so on) in the context of particle structures that facilitate modulation, the claims are rendered tenuous. It is not that the arguments of special relativity theory are invalid. A valid argument is simply one in which the conclusion follows from the premises (or assumptions). The problem with special relativity is that the arguments are unsound because the premises are false.
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