Oh, okay, Biorc is a genius... So ultimately I can assert that the principle of conservation, when considered comprehensively, involves matter-energy regarded no longer as two separate realities but as a unified whole, given that one can transform into the other according to a very precise mathematical relationship. What remains constant on our little planet and in the Universe is the sum of mass and energy.
The formula expresses in any reference system the total energy of a particle at rest.
If the body is in motion, the correct (and complete) formula is:
with . For a body that starts from rest, we have v = 0 and ? = 1, and we find the particular case .
Here, mass is understood as the relativistic mass of the body, to be distinguished from the inertial mass m. The inertial mass can be considered a property of the body, since in inertial motion it remains unchanged. In inertial motion, with no variations in gravitation, velocity, direction, and the orientation of motion do not change. Conversely, a change in gravitation implies a change in the velocity vector: if the velocity of the body changes, it is its mass that modifies the external field; conversely, a significant variation in the surrounding gravitation can clearly alter the trajectory and the intensity of motion.
The concept of relativistic mass can be understood by imagining that a mass of 1 kg, falling to the ground at a speed of 100 km/h, causes the same damage as a mass of 100 kg falling from a height of just a few centimeters. The extent of the damage depends on momentum, taking into account both mass and speed factors. The concept of relativistic mass extends the concept of gravitational mass, just as Einstein's theory generalizes Newton's gravity.
With these considerations, it makes sense to define a mass that depends on speed (which would be the product of the rest mass, inertial mass, and the term ?):
m = m(v), and in particular that:
, and that:
.
In other words, relativistic mass is not an independent property of speed v, but increases with it. As speed approaches that of light, the mass of the body tends towards infinity.
To accelerate a body with a mass greater than zero from rest to the speed of light, infinite energy would be required. This would be necessary not only to exceed the speed of light but to reach it minus any small amount you desire, an infinitesimal.
A second reason why the speed of light cannot be exceeded comes from the equations that explain the contraction/dilation of space-time in special relativity.
