last updated: 05/14/2003
SUMMARY ANALYSIS
The aforementioned alternative theory proposed with respect to electromagnetic phenomena and the principle of relative velocity suggests that electromagnetic particle waves embody two distinct components of motion, that is they exhibit attributes of both linear and angular velocity. For this reason the physical characteristics of an electromagnetic wave can be analyzed from two perspectives, i.e., that of a linearly propagating wave front and/or that of an oscillating stream of particles. As a wave front, linear velocity is of paramount concern, as a stream of oscillating particles, angular velocity becomes the focus of attention. Although these distinct qualities of the wave can be considered separately, their interaction should nevertheless be understood as part and parcel of a singular motion. With this awareness in mind, an analysis of the issues is in order.
When encountering an object, the corresponding reaction of a photon wave is predicated upon the relative velocity of the object it encounters. For purposes of comparison, a standard wave is presumed to exist when zero relative velocity exists between the source of the wave and the object it encounters. When relative motion prevails between the source of the wave and the object it encounters the wave is construed to be a Doppler effected wave. Comparing the attributes of a hypothetical standard wave with those of a Doppler effected wave from the same theoretical source leads to the following conclusions.
With respect to energy, when a photon wave encounters an object in motion relative to the wave's source of emission there is a change in the kinetic energy of the photon wave. The measure of this change is a function of the velocity of the object. If the object has a positive relative velocity, i.e., the object is moving in the same direction as the wave, the wave is elongated as compared to a standard wave and its kinetic energy decreases. Conversely, if the object has a negative relative velocity, i.e., the object is moving opposite the direction of the wave, the wave is compressed compared to a standard wave and its kinetic energy increases. Kinetic energy is therefore either given up or acquired by the Doppler effected wave as compared to a standard wave dependent upon the relative direction of the object's motion.
As described by Planck's radiation equation, energy and wave frequency are related by the formula E = h f and as such both are a function of the object's relative velocity. Therefore a change in the kinetic energy of the wave should be traceable to a change in the object's relative velocity. However, with respect to linear velocity, this can not be the case because the Doppler effect linear deformation of the photon wave occurs at an offsetting rate identical to the object's relative velocity. The result is a constant linear velocity relative to the object. This phenomenon associated with electromagnetic waves occurs for all objects or observers as a consequence of their relative velocity and is the embodiment of the law of the transmission of light.
In theory, the currently accepted quantum mechanics concept of rest mass is somewhat akin to the proposed concept of a standard wave. Both concepts provide a benchmark from which to measure changes in the mass of a photon. Could a change in the photon's mass account for a change in the Doppler wave's kinetic energy? Referring to the hypothetical data it can be seen that the linearly calculated mass of a Doppler effected photon wave also varies proportionally to the magnitude and direction k' 's relative velocity. However, from a practical standpoint such a change in mass would require an equivalent change in the material composition of the photon. The quantum nature of the photon appears to preclude such an effect.
As has been demonstrated, the angular velocity of the photon wave varies directly with the relative velocity of the object, in contrast to its linear velocity which remains constant. The greater the change in the wave's frequency the greater the change in its angular velocity and hence the greater the change in its kinetic energy. As it appears then, it is this change in the angular velocity of the wave that leads to a change in the kinetic energy of the wave. As previously indicated, the magnitude and direction of the change in the angular velocity of the Doppler effected photon wave correlates to the magnitude and direction of the relative velocity of the object.
In the opinion of this author, the photon wave's energy-frequency interrelationship as revealed by Planck's equation is most effectively explained in terms of the photon wave's angular velocity. From this author's perspective the kinetic energy of the photon wave is reasonably a function of its angular velocity, and as such a change in the kinetic energy of the Doppler effected photon wave should be accounted for solely as a change in the wave's angular velocity and not as a change in the photon's mass. This approach to the Doppler effected photon wave's mechanics affords a constant photon mass with respect to a given wave and hence avoids the somewhat troublesome concepts of rest (energy) mass.