One of the interesting (to me) problems in physics is if one can admit continuous functions to the Lagrangian, and still maintain the constancy of c. In STR, the relation M_{0}=CT (for a single physical system) implies that if C is the mass creation rate, then T provides the cutoff (in mass creation time) at which M_{0}is invariant.

The same is true of VT'; if V is independent of C for all values of V, then V is orthogonal to C; V can be considered a different mass creation rate for a different time T'. However, if a final result is defined as a relation between an initial state and a final state, then the "time dilation" equation obtains, which is actually a relation between mass creation times in terms of mass creation rates:

where =

Note that a coordinate system is not referred to explicitly.

This means that CT is actually the LaGrangian (L = E_{kinetic}- E_{potential }

and can be interpreted as either a potential or a kinetic energy, but not both (since the energy defined this way is also independent of the coordinate system).

This means that the equation actually describes a change in state between two mass states M_{0}and M', where M' = M_{0}*

Further analysis results in the Relativistic Energy equation, which is also discrete for discrete mass creation times, so that the relation between E' and E_{0}is (E')^{2}=(PC)^{2}+ (E_{0})^{2}

One can then set Planck's constant H = (PC)^{2}which is again discrete, so that E_{dif}= E' - E_{0}= HF where F = 1 (since the coordinate system is still not defined as a "frequency" in space-time)

So this is the fundamental problem Einstein had with quantum mechanics, since the latter description of a change in energy is discrete and quantized, and continuous system (a Riemannian Manifold) does not apply if energy and momentum are conserved. GTR requires a continuous system which changes the "speed" of light continuously as a space-only (contra-variant) transformation that changes x_{c}= ct_{c}in flat coordinate space-time. Such a transformation destroys gauge invariance (conservation of energy), since in such a metric, t_{v}has exhausted all possible conserved mass transformations if an affine connection exists between space-time and energy-momentum domains.

If an affine connection does not exist, then the coordinate domain is that of "Ghosts", and the energy domain is that of "Machines".

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