2001 Mathematics and the 21st Century  
In a time-independent gravitational field, Emmy Noether's theorem implies that light moves upward with constant energy. The gravitational red shift is therefore to be understood as resulting from a reduction of the energy states of the emitting source. Applied to the annihilation of para-positronium, in which the entire rest mass of the positronium system is converted into gamma rays, this understanding of the red shift proves the rest masses are reduced in a gravitational field. Going back to
more » ... he emission by simple atoms, whose emission frequencies are inversely proportional to the Rydberg period, P R = h 3 /e 4 m e , it is clear that the red shift must be attributed to rest mass reduction, rather than the imagined gravitational time dilation effect, according to which, the flow of time itself is reduced. We are indebted to Niels Bohr's quantum theory of the hydrogen atom not only for the above expression for the Rydberg period, but also for the Bohr radius, a 0 = h 2 /e 2 m e . Clearly, gravitational rest mass reduction causes an increase in the size of the hydrogen atom. But Logic demands, and observation confirms, that all entities of the same dimensionality must be affected in exactly the same way. Thus all material bodies, including measuring rods, must suffer an increase in size, indicating that the presently accepted geometry of space in a gravitational field is incorrect. This paper details how gravitational rest mass reduction and the heretofore unimagined phenomenon, gravitational size dilation, play a vital role in the correct understanding of the gravitational field, quantum gravity, black hole structure, and cosmology.
doi:10.1142/9789812810243_0005 fatcat:qbmj7qmbwne7he6ew7x2wljsbi