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In Newtonian terms F = ma. Even kinetic energy requires time to define it. Rest energy does not.

Edit: Since F has an implicit change in position within its definition then this must require a rate of change in time if we agree with time dilation.

The units of gravitational potential are J kg^{-1} where energy in Joules also has an implicit time component. For equations of motion time is also implicit in the action. It is everywhere. To remove it would be counter productive.

One thing I have been considering is a coordinate value for the Planck constant that can be tied to the dynamics of spacetime. Would this allow the elimination of time from quantum mechanics?