The cosmological principle 10

The dimensions of the universe; the space of the universe; the cosmological principle and the principle of conservation of angular momentum.

Let us return to our hypothesis that the speed of cosmological objects is proportional to the distance. Along with this, the speed of expansion cannot be greater than c - hence, regardless of proportionality, it follows that the size of the universe is limited.

Based on this finding, is it possible to determine the supposed size of the universe? Well, you can, due to the existence of the upper limit of velocity (c), which is the speed of expansion. It will be very easy if it turns out that the radial velocity is indeed proportional to the distance - that was our priority hypothesis. However, this proportionality must first be detected observationally. We have already written this proportionality in post 7: v / r = const. The size of the universe (R) would correspond to the speed of light (c). To compute these dimensions, all you have to do is ... find the value of the proportionality coefficient ("const"). One should refer to observation. This is a very important finding. One could say that this concept is falsifiable.

And now the question: Why should more distant objects they moves away faster? This is an essential question, but it causes confusing. Who asked about it? Only children, I guess. Now, the fact of expanding means that once, in the distant past, the whole universe was relatively small. Supposedly at some point there was chaos. In it, the speed of individual elements of this whole was varied. Due to inertia (yes, just inertia), their motion is preserved. The faster ones are farther away today, and the fastest ones, almost where only light can reach. I guess I answered that question. This approach is also justified by the flatness of the Universe's space (Euclidean space). Why flatness? Therefore, because it is about the real (and inertial) movement of objects. So it is not about some kind of pushing, or about the result of some primordial pressure from nothingness of singularity. By whom? Ask theologians.

Will the model adopted today and in force answer the question that opens this reflection with the same ease?

So what defines the space of the Universe? Is it the state of its curvature, or is it just the relative inertial motion of objects, causing the universe to take up more and more space? I am inclined to view matters in such a way. And what is beyond the material everything? I guess some indefinability, or just (we should be consequent) space outside the Universe does not exist. The space of the Universe increases with the increase of distance between any specific objects (having cosmological significance). The space is created by their movement. Outside of the material universe, space does not exist. Let me even say that given the observation the Universe is everything, it is the full and only being. Have I exaggerated (judging by current perceptions)? I do not think so.

And where is the center of the universe, that is, the place of the Explosion? There is no problem with this if the observable universe is and has always been everything, both material and spatial. All points, all today's positions of bodies together constitute this point of the Explosion, because "we were all together once".

You can also look at it differently. If the universe were an object embedded in a larger (infinite?) Space, it would have a surface (like the surface of a sphere). So it would be possible to determine of the center. In addition, the points belonging to this surface would be highlighted points, and this would be contrary to the cosmological principle.

Here we come across the issue of the topology of the universe. Also this will be discussed. As a reward for your patience.

One hundred years ago, the proposition that the speed of light is invariant, was a revolutionary heuristics and the basis of special relativity. [It doesn't matter whether Einstein knew about the Michelson-Morley experiment or not.] After all, the cosmological principle could not provide the context for research in the field of electromagnetism. Today, after a hundred years, the invariance of c is a conclusion from the cosmological principle (provided that the concept proposed in this paper is applied). The very existence of the upper limit of the (relative) velocity results from the essence of electromagnetism. [Note that all particles (except for neutrinos) participate in the electromagnetic force, so their local speed is not greater than the speed of light. We will deal with neutrinos in an essay devoted to them, solving the problem of their "otherness".]

I have noticed this in my book on the special theory of relativity (An elementary introduction to the Special Theory of Relativity, a bit ... differently). And what does this cosmology have to do with the electromagnetic force (after all, it is about the speed of light)? Apparently, this interaction appeared just as the speed of the universe's expansion had stabilized. It is therefore a secondary thing. The "speed of light" is a relic of this special moment in the history of the universe. Summing up, it can be said that this speed is a relic of the time when the electromagnetic interaction appeared, as well as the moment when the expansion of the universe with today's features started. In this context, it may be justified to suppose that the velocity of the electromagnetic wave may be locally differentiated (even in a vacuum) due to inhomogeneous distribution of matter on a large scale. Is this a reasonable supposition? Is it right? This topic will be discussed in other articles.

And one more thing. According to Noether's theorem, the invariance of the fundamental laws of motion is related to the fulfillment of certain conservation laws. In particular, the invariance of the choice of direction in space is related to the conservation of angular momentum. The principle of conservation of angular momentum is universal, as experiment has shown. So there is complete symmetry with respect to the direction. What does this remind us? Of course, the cosmological principle. As you can see, the cosmological principle is not only a requirement of our cognitive intuition, not only a common-sense imperative. This is a direct conclusion from undoubtedly right and universal findings regarding the course of physical phenomena, findings based on an experiment and confirmed in all phenomena without exception. You can also the opposite. Well, the fulfillment of all these fundamental rights means the rightness of the cosmological principle, its confirmation. These rights are derived from it. This is saying something.