Simple Derivations of E=mc2

© Copyright 1993-2004; Anthony Mathew Medland Taylor 18/07/1973 ant@odetoenergy.com
Permission is given to reproduce this document, whole, including this copyright notice.

#Given:
E=Fd # Energy(Work) equals Force times distance
F=ma # Force equals mass times acceleration
a=v2/d # Centripetal acceleration equals velocity squared over distance to the centre, i.e. radius


Imagine Energy at the speed of light moving circlularly; The centripetal acceleration would be c2/d levels
F=ma=mc2/d
Fd=mc2
E=mc2 # Energy equals mass times the speed of light squared


Interpretations:

Energy following a curved path implies centripetal acceleration, Mass and Force toward the centre.

Energy works all the time, mass accelerating space, forcing distance, moving at the maximum speed.

Energies movement implies, distance, time, acceleration, mass and force.

Imagine everything at the most fundamental level moving at the maximum speed, and some of those things moving circularly.

The different amounts of energy moving in the small circular orbits correspond to the various fundamental particles of mass.

Each particle moves relatively to other particles at less than the maximum speed, c.

Internally the energy of the electron for instance is travelling at the speed of light.

The electron itself travels at less than the speed of light relative to any proton it may be orbiting, itself made up of no less than 3 quarks, each a spinning energy moving at the speed of light, with force, mass, and acceleration .

Alternatively, given the units:
c=d/t # Speed equals distance over time
#c is the maximum constant speed, therefore any other speed is a fraction of it.
a=c/t=d/t2=c2/d # acceleration equals speed over time
Therefore:
E=Fd=mad=m(c/t)d=mc(d/t)=mc2

This alternative derivation only shows that it is possible given the units of speed, acceleration and the newtonian equations. While the first derivation gives a physical argument, that of energy travelling at the speed of light in a circular fashion implies acceleration of c2/d, mass and force, thus the first method can be said to prove that it is true, as far as proof can go.

i.e If we accept the newtonian equations and the mathematical methods then we have to accept the derivation.

You could spin the argument around and given E=mc2 and the newtonian equations, deduce that mass implies energy moving at the speed of light in a circular manner. (at least not in a straight line) Emperically, energy(eg. light) does not follow a straight line, it will always have a centripetal acceleration, mass and force toward the centre associated with it, however small it may be if the distance to the centre is large. When the radius of curvature is small, the centripetal acceleration, mass and force will be large.

Simple Derivations of E=mc2

© Copyright 1993-2004; Anthony Mathew Medland Taylor 18/07/1973 ant@odetoenergy.com
Permission is given to reproduce this document, whole, including this copyright notice.