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DoT: The Duality of Time Postulate

And Its Consequences on General Relativity and Quantum Mechanics

Mohamed Haj Yousef

9. Appendix: Deducing from :

 

Starting from equation 8 above:

 

                                                                                                    (26)

 

and we can find  by differentiating , with respect to :

 

                                                                                  (27)

 

From this equation we find: , and by replacing in equation 26 we get:

 

                                                      (28)

 

This method, however, can not be considered a mathematical validation of the mass-energy equivalence relation , because the starting equation  is not derived by any other fundamental method from current Relativity, other than being analogous to the equations of time dilation and length contraction: , .

Using the same equation  with ; thus: , we can also derive the relativistic energy-momentum relation, by squaring and applying some modifications:

 

                                                                     (29)

 

From this equation we get: , thus , or:

 

                                                  (30)

 

Again, since this derivation relies originally on the equation: , it can not be considered a mathematical validation of the mass-energy equivalence relation.

 

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