Voigt's Conjecture of Space-time Mixing : Contradiction between Non-simultaneity and the Proportionality of Time Dilation
The history of the development of the Lorentz transformation (LT) is reviewed, starting with the original suggestion of Voigt in 1887 for a modification of the longstanding classical (Galilean) relationship between space and time coordinates. His conjecture has led to the currently accepted view by theoretical physicists that space and time are inextricably mixed and are thus merely two components of a single entity "spacetime." The LT itself, which retains the space-time mixing characteristic, was first introduced by Larmor. He recognized that Voigt's transformation needed to be amended in order to conform to the requirements of the Relativity Principle (RP). It is pointed out that Newton's First Law indicates that clock rates must remain fixed in the absence of unbalanced external forces, which therefore implies that the ratio of two such rates in different inertial rest frames should be time-independent as well (Δt'=Δt/Q). It is critical in this discussion to note that the non-simultaneity of events demanded by space-time mixing is not consistent with the proportionality of the time-dilation prediction of the LT; it is
impossible for Δt and Δt' to be proportional to one another without both of them vanishing at the same time. This contradiction removes the LT from contention as a physically valid transformation. Lorentz showed at the end of the 19th century that there was a degree of freedom in the definition of the LT that could be explored to eliminate this inconsistency. By choosing a particular value for a normalization constant, it is possible to obtain a different transformation (GPS-LT) which eliminates space-time mixing while still satisfying both of Einstein's two postulates of relativity and remaining consistent with Newton's First Law. The asymmetric time dilation observed in many experiments and assumed in the operation of the Global Positioning System indicates that clock-rate proportionality should be an essential component of relativity theory, in agreement with the GPS-LT assumption of a strict proportionality between the rates of clocks in different inertial systems.