Global Positioning System Confirmation of a Contradiction between Einstein’s Predictions of Time Dilation and Remote Non-Simultaneity: Failure of the Lorentz Transformation

Time dilation and remote non-simultaneity are two of the most famous predictions derived from the Lorentz transformation. As a simple example, consider two lightning strikes which occur at different positions in space. According to Einstein’s special theory, the time differences Δt and Δtꞌ measured by two observers between the two strikes must satisfy a strict proportionality relation (time dilation): Δtꞌ=XΔt. However, it is also claimed, by virtue of the corresponding prediction of remote non-simultaneity, that the two events can occur simultaneously for one of them (Δt=0) without doing so for the other (Δtꞌ≠0). It is pointed out that it is impossible to satisfy both of the above conditions because that would mean having to violate the algebraic axiom which states that multiplication of any finite number, in this case X, by zero (Δt) must have a product (Δtꞌ) of zero as well. Only by violating this axiom is it possible to avoid a direct contradiction of the prediction of remote non-simultaneity. As a result, the Lorentz transformation itself is shown to be invalid since it is responsible for both of the above predictions. A different space-time transformation is therefore presented which also satisfies both of Einstein’s postulates of relativity without requiring that space and time be mixed. The Hafele-Keating experiments with atomic clocks carried onboard circumnavigating airplanes confirm that time dilation is a real effect, but they also show that the prediction of Einstein’s theory that observers can disagree in principle which of two clocks runs slower is not correct. The Global Positioning System makes use of the observed proportionality relationship between elapsed times to adjust the rates of atomic clocks carried onboard its satellites so that they run at the same rate as identical clocks located on the earth’s surface. This practice also serves as a confirmation that remote non-simultaneity has no basis in fact. Otherwise, it would make no sense to have the two clocks running at the same rate in order to measure elapsed times for laser beams to travel between the satellite and the ground position.