# Newton's Law of Inertia and Clock-rate Proportionality: Einstein's Historic Mistake

A straightforward extension of Newton’s First Law leads to the conclusion that the properties of objects in pure translation should remain constant for an infinite period of time. The Principle of Causality demands this because of the absence of unbalanced forces which might otherwise affect their values. Consequently, one expects that the rates of two proper clocks in different inertial systems should remain strictly proportional to one another. It is shown that this conclusion is inconsistent with the Lorentz transformation (LT) of Einstein’s Special Theory of
Relativity (STR), which holds that two clocks in relative uniform motion must each be running slower than the other (Einstein’s Symmetry Principle). Instead, time dilation is expected to be asymmetric, i.e. it is always possible in principle to know which of two clocks is running slower (Universal Time-Dilation Law). Transverse Doppler measurements that have been carried out with high-speed rotors, as well as the study of the rates of circumnavigating atomic clocks carried out by Hafele and Keating in 1971, are in quantitative agreement with clock-rate proportionality in different rest frames. The same relationship is assumed in the operation of the
Global Positioning System (GPS) between elapsed times for a given event that are measured on satellites and corresponding values obtained with atomic clocks located on the earth’s surface. It is shown that there is an alternative version of the Lorentz transformation, designated the GPSLT, which incorporates the proportionality of clock rates and elapsed times. It nonetheless satisfies both of Einstein’s postulates of relativity and is also consistent with the relativistic
velocity transformation (RVT) derived in his original work. The GPS-LT differs from the original LT in that it eschews space-time mixing and is consistent with the absolute simultaneity of remote events enunciated by Newton and his contemporaries. It is also characterized by a different relationship between space and time coordinates than the well-known LT condition of Lorentz invariance. An amended version of the Relativity Principle (RP) is proposed on this basis which assumes that the units in which the laws of physics are expressed differ from one
inertial system to another. The GPS-LT is therefore consistent with the uniform scaling of corresponding physical properties in different rest frames. Finally, it predicts that isotropic length expansion accompanies time dilation in a given rest frame, not the familiar type of anisotropic length contraction posited by STR. Experimental evidence supporting this conclusion is obtained from the Ives-Stilwell transverse Doppler experiment and studies of the range of decay of meta-stable particles.

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