However irregular it may be, we are couching our development in the context of Newtonian space and absolute time. We distinguish between a "classical" observation and a "relativistic" one. The first means observation of an event datum, or an algebraic expression such as momentum, by a physicist present in the originating frame of the event, and in near proximity to his clock, that is, Einstein's proper time. The relativistic one is an observation of either of those quantities in which one or more data did not originate in the observer's frame, but must be transformed to his frame from where it orignated. That action introduces a signal delay, which is the essence of distinction of a relativistic interpretation. Clearly, most of the nomenclature, restrictions, and formalism of space-time SR will not apply in our approach, and we ask you to bear with us on that. For example, we think the question of how long it takes a photon to travel from one point in space to another a defined distance Lo = vT1 away when sent, is quite reasonable.
Space-time accomodates the unique propogation properties of light, through a coordinate system based on the Lorentz transformation, the heart of SR, as shown by Einstein. We use the Lorentz transformation also, once, to determine the light transit time between specified frames and, having that, then employ an ordinary cartesian coordinate system and thus do not need the Lorentz transformation subsequently. As far as we can determine so far, our deductions from this approach give the accepted results of space-time SR, with some additional insights. One is that the gamma in the SR version of p belongs to the v. Velocity v is classically determinated by both S and S'. The quantity gamma v is the relativistic observation of velocity obtained in a momentum experiment (necessarily relativistic in nature), because now the measured v is altered by signal delay of it's time constituent.
Nothing we have obtained changes relativistic results, is not proposed as a better way of doing SR, much less trying to replace it. It is a pedagogical investigation which explains what SR is.
We would welcome comment and further discussion on the following apparent corollary in special relativity (SR). Through one-time application of the Lorentz transformation one can derive a general expression for the transit time of a photon between two inertial frames, T2-T1 = (Lo/c)*sqrt[(1+v/c)/(1-v/c)]. Here, Lo is the separation of the inertial frames at the time T1 when the photon is sent from one frame and T2 is the time when it arrives at the other frame. Each time is directly recorded by the observer situated in the corresponding frame. This equation is appropriate for calculations in various kinematic applications of SR. With it, one can determine time and space event coordinates in any communications with photons between frames. The equation of motion of light, as it were, permits rendition of activity, observed in one inertial frame by a physicist there, to another observers frame, thereby accomplishing the essential purpose of SR, namely reconciliation of physics everywhere. In application, no transformations as such of event coordinates are involved and there is no need for use of the velocity addition theorem. Everything is reduced to the simple question of correction to light transit time for signal delay, in form, a classical operation.
Prof. Eric T. Lane eric-lane@utc.edu
Physics Dept. 2352 423-265-7804
The University of Tennessee at Chattanooga 37403-2409