E = m c². How to Get to This?

Let’s show, how about spying?

Obviously, this equation was originally developed by the famous German theoretical physicist Albert Einstein and published by him in his scientific article (paper) in 1905.

It is said that in his initial perception Einstein attributed the equation to a mathematical consequence. However, this equation gained notoriety and became a great catalyst for new technologies. How does this compact equation arise? This is what we will answer here through a possible deduction.

We will postulate that the result of the operations we present will be relativistic kinetic energy.

Considering the Work-Energy Theorem, the kinetic energy K varies as a consequence of work being done. Since work is an analytically defined physical quantity, we will necessarily make deductions based on integral calculus.

Considering a particle initially at rest, then the work-energy theorem says that the kinetic energy K will be such that

Let’s assume the force (F) and displacement (r) vectors are collinear and arbitrate such a direction as the X axis, so we can, without prejudice, use only the modules of the vectors, so that

Our component Fₓ is given according to the relativistic expression

where γ is the Lorentz factor given by

See that we have come this far to the following point:

Acceleration, on the other hand, will be subject to manipulation to obtain a transformation of variables, which is a usual method of integral calculation. So we have

So by changing the limits of integration, we have changed the variable:

This expression has an analytical solution by conventional methods, which, when done, results in

or

and the first term on the right-hand side, which is usually symbolized by E, is defined as the total relativistic energy,

Additional comments

Given the final form of our deduction, having relativistic kinetic energy as the quantity to be determined, suggests, in due course, our risky conceptual interpretation.

Note that the usual approach to physics is description through mechanical models. What currently prevails, which takes the physical description of nature further, is an apparent particle-wave duality

However, we transformed this diagram to suggest our supervening interpretation

We mean that relativistic kinetic energy appears in the diagram as an agent that injects a flow of inertia and momentum into the particle as it moves toward E. On the other hand, it can instead degenerate or colapse as an environment of probabilities, so we have wave behavior.