Voigt's Conjecture of Space-time Mixing
Contradiction between Non-simultaneity and the Proportionality of Time Dilation
2017-01-31
Relativity and Gravity Publication - No. 64
Buenker
Robert J.
Prof. Dr.
Buenker, Robert J.
aut
en
<p>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.
2017-01-31T13:33:32.259Z
2017-01-31T13:34:20.354Z
published
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