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volantis · Quote #22 (**permalink**) 06-25-2005, 04:09 PM

Quote:

Originally Posted by AntonioLao

the invariance of fundamental acceleration and length is given by

$\mathbf{a} \cdot \mathbf{r}=c^2$

c is the speed of light.

The invariance of acceleration in the above equation can only work for actual objects that travel at the specified velocity of c. The only thing that travels at c is the photon, whether in the form of EM or a gamma ray.

All matter travels at speeds less than c, and so for ordinary matter the equation becomes

a * r = v^2

How do you intend to use the equation?

Quote:

the square of energy is given by

$E^2=\phi_1\times\psi_1\cdot\phi_2\times\psi_2$

Before I would consider such an equation I would take the time to understand what the unit of E^2 pertains to. When you change the dimensions of a unit, it is no longer that unit, but some other unit.

For example, velocity is one unit, but velocity squared is not velocity at all. In fact, I show that velocity squared is actually the unit of temperature. So

m * v^2 = E

or mass times temperature is equal to energy.

The unit of v^2 works out to be a quantification of the distance between molecules based upon the velocity of their collisions and the total mass of each molecule. The more energy put into a substance, the higher the velocity of individual molecules and thus the greater the temperature becomes.

It follows that if the same quantity of energy is put into a cubic centimeter of lead and a cubic centimeter of aluminum, the aluminum will heat to a higher temperature than will the lead because it has less mass.

What is your suggestion for the unit of E^2 and how would you use it?