The multiplicity of worlds and the problem of predetermination
Let's think about this: is the only world in which we live? Is there another world & quot ;? If our world is the only one, then why is this so? The answers to the questions posed, or rather the search for answers, depend on our understanding of the world. For a person of ancient Greece, for example, the world was limited spatially. There was a concept of Oikumene (Greek - I live, I live). Oikumena is inhabited or inhabited earth, the universe, in particular all the land known to the Greeks and predominantly populated by them. What lay outside the Oecumene existed, but as it were not considered, therefore the world, in essence, was one. Of course, there were, for example, the afterlife and the world of the gods. But other worlds were inextricably linked with this world even geographically, for example, Mount Olympus - a specific place of dwelling of the gods or Lefkada - a white rock at the entrance to the underground kingdom of Hades. To some extent, the ancient ideas were adopted by the Western Christian Middle Ages, so the discovery by the Spaniards of the New World meant a revolution in the universe.
The mechanical concept of a single and unique world as something of a limited field is in fact internally contradictory. Abroad, the only world because something also lies - maybe another world? So the world is not the only one. They united these two worlds in a single, big world (we will join the New World to the Oecumene), but abroad there is also something - and so on ad infinitum. To some extent, the expansion of our world has overcome psychological barriers (remember the fate of Giordano Bruno: his "multiple worlds in an infinite space" are, however, only parts of a single material world). The problem of the uniqueness of the world or of the multiplicity of worlds is increasingly being pushed into the metaphysical realm by the development of science. Let's try to put it that way, i.e. at the same time linking it to the currently available physical value .
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The world of modern physical knowledge is space-time. From the mathematical point of view, this four-dimensional smooth manifold satisfying certain topological constraints and equipped with a metric that allows measuring space-time intervals. World points are usually called events, but these are not exactly events in the common sense (the event is not only when? and "where?", but also "what?", the space-time point only indicates the place and time of the event, not its contents). In this picture, future events are objectively present, as if they had already taken place. It may appear that we have before us something like the Book of Destinies, i.e. the picture is completely fatalistic. This is not entirely true, given Pasha's remark about the difference in events and world points. Let's make a mental experiment. Let the universe be populated with a finite number of material (massive points), i.e. it's empty, except for the places where the dots are now. Let them not interact. Then these points will move by inertia, each emphasizing its world line, which, perhaps, will intersect, then again diverge, etc. Here, for a single material point, the event consists only in finding it there at some time, that is, is identical with the event as a space-time point. Nevertheless, space-time is not at all a Book of Judgments: our point really will not be in all conceivable events, but only lying on its world line.
What determines the fate of the particle, i.e. its world line? The physical law that determines it is a second-order differential equation (the equation of motion). If the initial position and the initial velocity of the particle are given, its motion is completely determined for the entire time forward. In this sense, general relativistic considerations are no less deterministic than Newton's mechanics. The choice of different initial data for a system of material points leads to different patterns of their motion, i.e. their lives & quot ;. The world of these particles is not the only one, although lying within the single of the encompassing world (ie, space-time). Here the plurality of worlds is reduced to the multiplicity of the initial data and is combined with the full predetermination (for fixed initial data).
Consider now the world as a whole, ie. with gravity, all kinds of fields, particles and living beings, including us with you. All parts of this world are interrelated and mutually dependent. This is a dynamic world, the motion of which is determined by Einstein's gravitational equations in conjunction with the equations of the electromagnetic field, and so on. Within yourself this world is completely deterministic, all events in it are uniquely determined. Since both Einstein's equations and others are differential equations, they have not a unique solution. It turns out that in addition to our world, completely predetermined, there are other measures, also predetermined within ourselves, but different from ours. And unlike the ancient situation, each such spatio-temporal Oykumena is closed in itself, and it is impossible to "go beyond its borders" (they simply do not exist) to get into another. Each world in itself is one and self-sufficient, and yet there are many of them!
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We come into conflict with the natural understanding of unity and uniqueness of the world. In a metaphysical sense, the world must embrace all that exists, and therefore can not be the only one. The worlds of the theory of relativity each claim to be a physical description of the only real world, therefore, it would seem that the existence of several such worlds is impossible. Moreover, unlike the worlds Giordano Bruno, these worlds can not be combined into some "larger" and a single world. Different worlds (ie, different spaces-times) of the theory of relativity are in principle not connected in any way. Where is the way out? We are clearly crossing the boundaries of physical knowledge.
We will think about the fact that we are all within the same universe, and this is what distinguishes it among others. But why are we there? One can see the manifestation of chance, fate, but not freedom in that the starting point of our world line was precisely in this universe (further mechanical determinism is even more reassuring). How to deal with other worlds? It is worth pondering why in general our science is not adapted to the study of individual objects, but only those that fit into the set or series (let us recall the discussion of the problem of the dimension of space).
There is a hypothetical way of simultaneously solving the problem of many worlds and removing the uncertainty. The world as a whole is proposed to be regarded as a quantum system. In this case, different classic worlds turn out to be different classical trajectories, or stories of the system. A quantum description involves summation over histories, or a Feynman path integral - something like averaging. Then all the worlds are united in a single picture, which allows us to make only statistical predictions about space-time. Practically, this program is very far from implementation, for there is nothing like a single quantum field theory, the first step in which should be the quantum theory of gravity, whose construction at this time has come up on exceptional difficulties, both technical and in understanding the problem.
For hypothetical quantum gravity, there is one particular difficulty that is not overcome by pure physics. This theory (as it is now supposed) is forced to deal with the world as a whole and to interpret, in terms of the quantum observables , the temporal evolution of space as a whole. It is not clear whether, let us say, an earth observer is somehow able to observe this evolution, as well as to judge the geometry and topology of the universe as a whole. If not, then our arguments become very shaky, they implicitly assumed the unknowability of which world we live in. If the difference between the worlds for a person is unknowable, then does it make any sense to talk about him at all? To some extent, this removes the acuteness of the question of the uniqueness or nonuniqueness of the world and removes us from fatalism. On the other hand, the very consideration of the world as a whole in its quantum evolution presupposes an observer who exists outside space-time and looks from eternity.
In addition, we require absolute clocks counting the time of eternity independent of the quantum-fluctuating world Without them it is pointless to talk about the evolution of the wave function of the universe. How can I not remember the famous image of the Great Watchmaker of the Universe.
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