Faster than the fundamental speed!?

It is widely believed that the theory of relativity does not allow superluminal velocities. Is it so? Can speed exist in nature, faster than the fundamental speed of light? Indeed, from the point of view of the theory of relativity there is a certain fundamental speed c, which is the greatest possible for the propagation of any force interactions. What is its physical meaning?

It is widely believed that the theory of relativity does not allow superluminal velocities. Is it so? Can speed exist in nature, faster than the fundamental speed of light?

The fact is that the value of the speed with which the same object moves with respect to different frames of reference, generally speaking, is not the same. In relation to one system, the object can rest, with respect to the other, it can move at a low speed, with respect to the third, with a large speed. In Newtonian mechanics there is such a speed, the magnitude of which is the same with respect to all frames of reference, but this is infinitely high speed. In Newtonian mechanics, the velocity of the bodies can in principle be arbitrarily large.

In the theory of relativity, there is also a case where the value of the velocity does not depend on the choice of the frame of reference. This happens when the body moves with a speed equal in magnitude to the fundamental. Thus, the fundamental speed of the theory of relativity is an analogue of Newton's infinitely large mechanics.

And yet, as it may seem strange and paradoxical, there can exist speeds exceeding the fundamental one. One example of this can be the speed of moving a light bunny along the wall. It can be made to move with any arbitrarily high speed. But this is just the speed of moving the illuminated place on the surface of the wall - no movement of matter or transfer of interaction at this speed does not occur.

Now let's try to clarify what the speed of any object is in general. This is always the speed of movement with respect to a certain frame of reference. Moreover, with respect to the point of this system through which the object is currently passing. Strictly speaking, it does not make sense to talk about the speed of the movement of an object with respect to any other point that is at a certain distance, or in relation to another object that existed in a different era.

What, then, is the speed of movement of a galaxy in relation to an earth observer? Obviously, such a concept is all the more meaningless, since we are separated both in space and in time. What speed can you speak about in this case? Only about the movement of the galaxy in relation to any particular frame of reference, encompassing both that region and the era in which we exist, and that region and the epoch in which the galaxy was located at the time of the exit of the light beam. But such a frame of reference can be constructed in various ways. Among the possible variants, we choose a system with respect to which our own velocity is zero. Then the speed of the remaining galaxies will obviously depend on whether our frame of reference deforms with time, and if deformed, how exactly. It would be natural to choose a "rigid", non-deforming reference frame. But this is impossible, since as a result of the mutual removal of galaxies, the density of the mass distribution changes, and as a result - the geometry of space.

Let's try in this case to choose a frame of reference, which does not deform at least radially from the point at which we ourselves are. In a homogeneous isotropic Universe this is possible. With respect to such a frame of reference, the velocities of galaxies are different from zero and in magnitude always less than fundamental. And they, obviously, are at the same time the rates of change of distances between retreating galaxies and the point at which we are. But in theory it is more convenient to use a deforming frame of reference that accompanies the expanding system of galaxies, that is, a reference frame in which the velocities of all galaxies are zero (if relatively small velocities of random motions are neglected). In the concomitant reference system, the distances between galaxies change not because of their displacements with respect to this system, but due to deformation (expansion) of the reference frame itself. These rates of change in the distances between galaxies can turn out to be similar to the velocity of the bunny moving along the wall, and more fundamental velocity. But they are by no means the speed of movement of any material objects. However, it seems as if a completely paradoxical situation arises. It turns out that in the first frame of reference the rate of change of distances between galaxies is always less than the fundamental, and in the second system the same velocities can be more fundamental. But this contradiction is seeming. The fact is that the distance between any two objects, and the rate of its change, are values that depend on the frame of reference.