The history of the development of the Uniform Scaling Method is reviewed. It has its beginning with the Law of Causality and Newton’s First Law of Kinetics (Law of Inertia). On this basis it can be concluded that the rates of clocks do not change spontaneously, i.e. without the application of some external force. Since the ratio Q of the rates of any two such (inertial) clocks must therefore itself be a constant, it follows that whenever they are used to measure a specific time difference between two events, their respective results must always be in the same ratio: Δt’=Δt/Q. This relationship is referred to as Newtonian Simultaneity since it guarantees that if one of the clocks finds that the events occurred simultaneously (Δt’=0), the other must do so as well (Δt=0).
A useful way to interpret Q is as a conversion factor between the different units of time employed in the two rest frames. If we assume that the value of the speed of light is the same in both rest frames, it follows that they must agree on the unit of speed, i.e. the conversion factor in this case is unity (Q0). It therefore follows that the unit of distance must be exactly the same as for time, namely also Q. This claim of the Uniform Scaling Method is thus seen to be in direct contradiction to the length contraction tenet of Einstein’s theory of relativity introduced in 1905. Experiments with accelerated electrons carried out by Bucherer in 1909 indicate that their inertial mass increase in direct proportion to γ (v) = (1-v2c-2)-0.5 (v is the speed of the electrons and c = 299792458 ms-1 is the speed of light in free space), the same ratio as observed for the periods of atomic lines by
2
Ives and Stilwell in 1938. Consistency therefore requires that the conversion factor for inertial mass is the same (Q) as for time.
Since inertial mass, time and distance are the three fundamental quantities on which all other physical properties are defined (mks system), it follows that the conversion factor for any other property must be an integral multiple of Q. An analogous set of definitions can also be justified for the corresponding conversion factors in the same two rest frames caused by gravitational effects. In this case the conversion factors are always integral multiples of the quantity S, which therefore plays as analogous role as Q in kinetic scaling. Since experiments with circumnavigating atomic clocks carried out in 1971 by Hafele and Keating found that the two types of effects are completely independent of one another, it is therefore useful to define a product Z of the corresponding Q and S factors for each physical property, including those that are used to define the results of electromagnetic measurements. These total conversion factors are stored in Tables 1 and 2 of the manuscript. They are shown to guarantee that if a physical law is valid in one of the rest frames, it will also hold in the other. This relationship allows for an Addendum to Galileo’s Relativity Principle: The laws of physics are the same in all inertial rest frames, but the units in which their results are expressed can differ from one rest frame to another.