I think there is a more simple method to proof  that,  matter (or energy ) can't  travel through the time.
It is forbidden from the law of conservation of energy (CE).  According CE a closed three dimension space contains the same total of Mass and Energy,  any time (
trace to fourth dimension).

For example, if I (or a photon) will travel when i was young in 31/12/1980, next day universe's energy will not be the same with 1980.

 

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Validakis Constintine,
NTUA Athens

045518761

validakis@gmail.com