The relativity of the mass
There is no technology that can get an engine to generate enough force to carry a ship at speeds close to the speed of light, let alone equalize it
From the second law of Newton we can affirm that a constant force will produce a constant acceleration. Therefore, if once an object is moving, it continues to be pushed with the same force, it will continue to accelerate, going faster and faster. And, according to Newton's formula, there is no limit to the speed that can be achieved.
But this is inconsistent with the theory of relativity, which imposes a speed limit for objects in the space of c = 299,792,458 m / s, the speed of light in vacuum. So the expression of Newton's second law must be altered so that it takes this fact into account.
Einstein did this by stating that m, the inertial mass, does not remain constant but increases as speed increases, a fact that is observed experimentally, for example, in elementary particles at high speed.
If the inertial mass increases with speed that means that more and more force is required to achieve the same acceleration, and finally it would take an infinite force to try to reach the speed of light. Einstein deduced from the two postulates of the theory of invariance that the inertia of an object in motion increases with velocity, and it does so in a manner completely analogous to that used for the expansion of time. As expected, you get an expression equivalent to the one you found for time: mm = me / √ (1-v2 / c2), where mm is the mass of the object in relative motion, and I am the mass of the same object before that starts moving, static. Very often I call it mass at rest. [1]
Similar to our analysis of the expression for the time intervals, we find that, as the velocity of an object increases, the mass observed from a stationary frame of reference also increases. It will reach an infinite (or indefinite) mass if it reaches the speed of light. This is another reason why something that has mass can not be made to reach the speed of light; it would require, as we said before, apply an infinite force to accelerate it at that speed.
By the same argument, objects that do move at the speed of light, like light itself, must have a mass at zero rest. Following the result of Einstein that the mass of an object increases when it is in motion in relation to a stationary observer, the Newton equation that relates force and acceleration can be written as a more general law of the following form: F = me · A / √ (1-v2 / c2).
Let us realize that for very small speeds compared to the speed of light, like those of our ordinary world, this formula becomes continuously F = m · a. Again we see that Einstein's physics is not a break with Newton's, but a continuation of it.
Note:
[1] Here we are doing a simplification for the sake of keeping the story line simple. Actually the mass is invariant, that is, as the observers in all the inertial frames will observe the same energy and the speed of the light c is constant, they observe the same value for what we are calling "mass at rest". To explain this in detail we would have to resort to the concept of spacetime and the equivalence between mass and energy, things that we will touch but very simplified. Suffice it to say, to silence the physical readers, that we are aware that the magnitude of the invariant energy-moment quadrivector is the resting energy of the mass m.
About the author: César Tomé López is a scientific disseminator and editor of Mapping Ignorance