The law of inertia leads to the derivation of the multiplicity of inertial frames of reference. Not one but many frames of reference exclude “causeless” motions.

If one such frame of reference is found, we can immediately find another, moving (without rotation) uniformly and rectilinearly with respect to the first. Moreover, one inertial frame of reference is not the least bit better than the others, does not in any way differ from the others. It is in no way possible to find a best frame of reference among the multitude of inertial frames of reference. The laws of motion of bodies are identical in all inertial frames of reference: a body is brought into motion only under the action of forces, is slowed down by forces, and in the absence of any forces acting on it either remains at rest or moves uniformly and rectilinearly.

The impossibility of distinguishing some particular inertial frame of reference with respect to the others by means of any experiments whatsoever constitutes the essence of the Galilean principle of relativity—one of the most important laws of physics.

But even though the points of view of observers studying phenomena in two inertial frames of reference are fully equivalent, their judgements about one and the same fact will differ. For example, one of the observers will say that the seat on which he is sitting in a moving train is located at the same place in space all the time, but another observer standing on the platform will assert that this seat is moving from one place to another. Or one observer firing a rifle will say that the bullet flew out with a speed of \(500~\mathrm{m/s}\), while another observer, if he is in a frame of reference which is moving in the same direction with a speed of \(200~\mathrm{m/s}\), will say that the bullet is flying considerably slower, with a speed of \(300~\mathrm{m/s}\).

Who of the two is right? Both. For the principle of the relativity of motion does not allow a preference to be given to any single inertial frame of reference.

It turns out that no unconditionally true (as is said, absolute) statements can be made about a region of space or the velocity of motion. The concepts of a region of space and the velocity of motion are relative. In speaking about such relative concepts, it is necessary to indicate which inertial frame of reference one has in mind.

Therefore, the absence of a single unique “correct” point of view on motion leads us to recognize the relativity of space. Space could have been called absolute only if we were able to find a body at rest in it-at rest from the point of view of all observers. But this is precisely what is impossible to do.

The relativity of space means that space may not be pictured as something into which bodies have been immersed.

The relativity of space was not recognized immediately by science. Even such a brilliant scientist as Newton regarded space as absolute, although he also understood that it would be impossible to prove this. This false point of view was widespread among a considerable number of physicists up to the end of the 19th century. The reasons for this are apparently of a psychological nature: we are simply very much accustomed to see the immovable “same places in space” around us.

We must now figure out what absolute judgements can he made about the character of motion.

If bodies move with respect to one frame of reference with velocities \(\mathbf{v_{1}}\) and \(\mathbf{v_{2}}\) then their difference (vector, of course) \(\mathbf{v_{1}} - \mathbf{v_{2}}\) will be identical for any inertial observer, since both of the velocities \(\mathbf{v_{1}}\) and \(\mathbf{v_{2}}\) undergo the same change when the frame of reference is changed.

Thus, the vector difference between the velocities of two bodies is absolute. If so, the vector increment in the velocity of one and the same body for a definite interval of time is also absolute, i.e. its value is identical for all inertial observers.