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First, Cosmic Limit: It is logical to find that c = maximum velocity, but what is the maximum possible acceleration? No form of non asymptotic acceleration function a(t) can exist in this world because that would suggest that for some time interval [0,q]

[itex]\int[/itex][itex]^{Q}_{0}[/itex] a(t) dt ≥ C which is simply not possible...

So does that mean that one can generalize the lorentz transformation to acceleration the way it is also used for velocity? What about for the next derivative, Jerk, and so on and so forth... If there does exist a lorentz transform for each of this then that means that one could potentially find a limit as to how high these numbers get, which could build the framework for an extention of SR to study notions such as the acceleration/deceleration of time for observers etc...

Second, Energy to Mass Equivalence: As of right now the most conclusive relationship for energy I have found is as follows:

E

^{2}= (M

_{0}C

^{2}/((1-v

^{2}/c

^{2})

^{1/2}))

^{2}+ (M

_{0}VC/((1-v

^{2}/c

^{2})

^{1/2}))

^{2}

Where:

E = total energy

M

_{0}= Rest Mass

v = Velocity

C, c = speed of light

(The equation was too complicated for Latex to load)

Why is this equation once again limited to only velocity? Why is acceleration not a measure of energy, suppose two objects are of equal mass, equal velocity, but of different accelerations at that exact moment... they clearly have different energies and therefore (now extending to GR) will have a different gravitational pulls as well (and the consequences keep going from there on)