Relativity Theory: Acceleration is Everything

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Acceleration increases the energy state of matter within an accelerated frame, resulting in higher frequency rates for affected matter. This elevated energy level leads to decreased efficiency in energy and force exchanges during dynamic processes, particularly at relativistic velocities where energy is disproportionately consumed for storage and loading rather than for acceleration. The discussion critiques the reliance on velocity as a primary factor in understanding matter dynamics, arguing that it oversimplifies the complex energy flow involved. An invariant formula is proposed to illustrate the relationship between acceleration, distance, and the speed of light, suggesting that the inner product of generalized acceleration and distance remains constant, equal to the square of the speed of light in a vacuum.
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We assume that acceleration increases the energy state of all matter in the the frame accelerated, and that for the elevated energy level, translated into higher frequency rates for all affected matter, the efficiency of material dynamic processes becomes inversely less effecient in energy and force exchanges. This includes equilibrium state processes, velocity a constant. At relativistic velocities the accelerations have been enormous. The efficiency of the energy exchange and force exchnge processes of the matter accelerated decreases grossly as observed. Lower the energy level, increase the efficiency of process dynamics of the matter undergoing the process.

What is observed in relativistic accelerations? More and more energy used for storing and loading than accelerating, inversely proportionately less for velocity increases.

The lorentz term using velocity as the key to understanding the dynamkics of matter is shortsighted. Velocity is merely a measure of the limiting parameter for that particlular process under scrutiny: how acceleration affects matter is reflected in the current limited state reflected by velocity term. What is being ignored is the dynamics of complex energy flow in all material processes.
 
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As what the title of this thread indicates "Acceleration is Everything," I came up with an invariant formula that shows the relationship of acceleration, distance and the speed of light in vacuum.

\vec{a} \cdot \vec{r} = c^2

This says that the inner product of generalized acceleration, a, and a distance, r is a constant, the square of speed of light in vacuum, c.
 
I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
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