In his book “Newton and Relativity”, Francesco Cester shows that it is possible to approach the Theory of Relativity with a more intuitive method than the traditional one.
This new procedure starts with the Equivalence Principle between Energy and Mass, which, as Einstein himself demonstrated (see: Max Born – Die Relativitätstheorie Einsteins – pages 244-247), can be obtained even without the use of relativistic considerations.
The use of the formula E = mc² together with Newton’s Second Law of Motion, coherently interpreted as the time derivative of momentum, therefore allows us to derive the relativistic mass relation, which expresses the dependence of the inertia of a physical body on its velocity.
The Lorentz factor is obtained without the use of the Lorentz transformations
Of considerable scientific interest is that, proceeding in this way, one arrives at the proof of the first formula containing the Lorentz factor without the use of the homonymous transformations that express the dependence of space and time on the velocity of the reference frame.
On the other hand, unlike length contraction and time dilation, the dependence of mass on velocity is intuitively clear if, considering the principle of equivalence, one takes into account the inertia of the mass associated with the kinetic energy of a moving body.
The formulas of Relativity are demonstrated in a transparent way
The expression of the dependence of inertia on velocity is then revealed, in the course of the treatment, to be the fundamental relationship from which it is possible to derive in a very transparent way the most important relativistic formulas using only the principles of conservation of energy and momentum.
It comes so, among other derivations, to the proof:
- of the relativistic theorem of total and kinetic energy of the physical body
- of the expression of the electromagnetic frequency at high speeds
- of the dependence of acceleration on speed
- of the relativistic velocity addition formula
And finally, as a consequence of the latter,
- of the constancy of the speed of light regardless of the motion of the emitting light source.
The latter is a natural phenomenon which, losing the character of a postulate, acquires that of a demonstrable principle through a purely theoretical way, that is, without the help of experiments, but to confirm them.