Criticism of the Lorentz Transformation
The Wikipedia section which asserts the viability of the Lorentz transformation (LT) is incomplete and therefore faulty. It ignores a contradiction between two of its most famous predictions, namely proportional time dilation (TD) and remote non-simultaneity (RNS). This conclusion is justified upon consideration of the following four statements, which should be answered with either YES or NO with regard to their correctness:
1) Multiplying a finite number with zero always results in a value of zero;
2)Accordingly, it is impossible for two time differences ΔT and ΔT' to always be proportional to one another (ΔT'=XΔT), where X is finite, and yet have ΔT'≠0 (non-simultaneous observation) while ΔT=0 (simultaneous observation);
3)A proportionality relationship (ΔT'=XΔT) between time differences measured for the same events by two different observers in relative motion to one another is the consequence of the phenomenon of time dilation (TD) in Einstein's Special Theory of Relativity (STR), while the other (ΔT=0 and ΔT'≠0), referred to as remote non-simultaneity (RNS), is also predicted by the same theory;
4)The fact that both TD and RNS are predicted by the LT to occur in experiment and yet are shown above to be mutually exclusive is incontrovertible proof that this relationship between space and time is not valid.
Since the only correct position on all four of the above questions is YES, it follows that a key aspect of Einstein's STR is false. In particular, it shows that the LT needs to be replaced in the theory by a different space-time transformation that a) satisfies both of Einstein's postulates of relativity, namely Galileo's Relativity Principle and the constancy of the speed of light in free space, but b) does not suffer from the above conflict inherent in the LT.