The quantum theory has been developed for a description of phenomena in the atomic and subatomic scale. The striking agreement of its predictions with experiment puts it among the greatest achievements of science. It seems one of the most important theories of physics. There is no doubt as to the correctness of its description of the microworld, however, its application for a description of the universe seems senseless or contradictory. Nevertheless, there are at least the following two reasons for the correctness of such an approach.

We know exact mathematical formulation allowing a precise description of such a way of existence of microobjects. This formalism has been many times verified by a variety of methods and confirmed to a very high accuracy by many physical experiments. However, it does not describe the movement of physical objects in time and space – as the classical physics does – but the time and space evolution of potential possibilities leading to this or the other behaviour of a microobject at the time of measurement. The quantum theory in general does not predict exact behaviour of elementary particles, but allows exact determination of the chance or probability of their certain behaviour at the moment of measurement. Sometimes it is said that the principle held in the microworld is the probabilistic determinism. This is the way the contemporary physics restricts the possibility of using the ideas of determinism in the microworld. The conviction that determinism seems to be valid in the macroworld is first of all a result of the law of large numbers (macroscopic bodies are composed of a huge number of micro-particles). Similarly, it is easier to predict the behaviour of a crowd than that of an individual.

The quantum theory equations describing the evolution of probabilities are linear, but the reduction of superpositions of possibilities at the moment of measurement is strongly non-linear and cannot be described by these equations. It seems that there is no objective description (in time and space) of the reduction of possibilities at the moment of measurement, which would be in agreement with the demands of the theory of relativity. However, it should be noted that the effects following from the quantum theory are not in contradiction to the theory of relativity. The quantum theory does not explain when and why the reduction happens or why we cannot observe a linear superposition of states (possibilities). This fact implies that there is an inner inconsistency in the fundaments of the most important physical theory. This is the key issue of the contemporary physics, which has not been satisfactorily solved for the last 70 years.

Moreover, despite considerable efforts of many physicists who always try to improve their theories, no subterfuge has been found which would slightly change the theory and at the same time not lead to a logical catastrophe. This fact is symptomatic as the majority of other physical theories can be easily somewhat changed. The impossibility to improve the principles of the quantum theory seems to prevent finding a solution to the problem of quantum measurement, so the reasons and mechanism of the instantaneous jumpwise reduction of the possibilities at the moment of measurement remain unknown. This fact indicates that the quantum theory seems to delimit an unsurpassable border for recognition of nature by the empirical-mathematical method.

Moreover, it should be remembered that the quantum theory was more or less reconciled with the Einstein’s theory of relativity only on the level of the linear evolution of possibilities, whereas the non-linear and instantaneous reduction of possibilities is in direct contradiction to its spirit.

Discoveries in the microworld dismayed physicists as they unavoidably implied that the commonly accepted and disseminated ideas about the structure of matter were only ideal limiting cases and not the actual reality.

The discoveries brought also essential implications to the quantum cosmology, which treats the whole closed universe as a microscopic object subjected to the laws of quantum theory. In this approach, the quantum description implies that in the time t<<10^-35 s, the spherical geometry of the universe undergoes specific fluctuations – spontaneous and unpredictable changes – resulting from the fact that geometrical quantities do not have strictly defined values but undergo a special quantum broadening. In the quantum theory no physical quantity except probability has a defined value. Moreover, this indeterminacy also holds for pair of certain quantities – determination of one of them means that the value of the other cannot be predicted. In the quantum theory this property is formulated as the Heisenberg uncertainty principle, which is related to the earlier mentioned probabilistic determinism valid in the microworld.

In the Planck epoch, t=10^-44 s, the geometry fluctuations become comparable with the values of the geometry parameters. Instead of a universe with a certain geometry, according to the quantum theory, we have a superposition of possible universes. Therefore the notions of space, in the sense of the general theory of relativity, and time, understood as a unidirectional parameter numbering the states of the universe, cease to be valid. Only after the Planck epoch, the superposition of possible universes boils down to one because the fluctuations of geometry disappear, and it becomes possible to talk about the time of one specific universe.

The question appears what is the size of the set of potentially possible universes. To answer it we have to explain a few fundamental questions of the quantum theory.

In the macroscopic world described by the laws of classical physics the energy is always conserved, i.e. it cannot be produced or destroyed. In the microworld described by the quantum theory, energy can spontaneously and unpredictably change from instant to instant, so it can fluctuate and therefore, it cannot have a certain specific value at a certain specific time. This indeterminacy of energy is very important. The shorter the time considered the greater the fluctuations can be, however, the mean value of energy is conserved – as in the classical physics. In a sense, we can say that the fluctuating microscopic system ‘borrows energy from somewhere’ but it has to give it back very quickly. According to the Heisenberg uncertainty principle, large energy loans have to be returned very quickly, while smaller can be used by the system for a longer time. Thanks to this property, such a particle as a photon can suddenly and with no reason appear but after a short while it has to disappear. Such particles exist for a very short time as they appear at the expense of borrowed energy, whose value has to be conserved. Such photons exist for such a short time that they cannot be observed, but what we usually assume to be empty space contains abundance of such instantaneous particles – not only photons but all other elementary particles as well. Such short-lived particles are known as virtual to be distinguished from the real ones. If a virtual particle gets some energy from outside so that it is able to give back the borrowed energy, it becomes a real particle and does not have to disappear in a short time.

The virtual particles cannot be directly observed but we know from experiments that they exist because they leave experimentally observable traces of their existence. The traces can be measured exactly, for instance by spectroscopic methods.

Therefore, the vacuum is not the ontological emptiness (non-existence) but the set of all possible virtual particles. This set is known as the physical or quantum vacuum.

If in the quantum cosmology the universe is treated as a microscopic system subjected to the principles of the quantum theory, it makes sense to assume the existence of virtual universes and the quantum vacuum being the set of all possible virtual universes. In contradistinction to virtual elementary particles, a virtual universe can become a real one without external energy supply if it is closed, so its total energy is zero. In such a vacuum, according to the Heisenberg uncertainty principle, open virtual universes (of planar or hyperbolic geometry) cannot exist as their energy is infinite, and the time for which infinite energy can be borrowed is exactly zero.

On the other hand, in compliance with the Heisenberg uncertainty principle for the time and energy, closed universes can exist infinitely long because at the transition from the virtual to the real state they do not have to borrow energy. Each virtual closed universe is thus a real one. Should these speculations be correct, there is an infinite set of closed universes. In this case there is no quantum vacuum understood as a set of virtual universes, because each virtual universe is real. Therefore, real universes of closed geometry are created spontaneously and causelessly out of nothing.

In quantum cosmology it is easy to create from an appropriate quantum vacuum, not only one universe but their infinite number, provided that they are closed, that is of zero total energy. Thus, the set of potentially possible universes is unlimited.

Mathematical formalism of quantum theory contains two elements: a general and unalterable set of principles and mathematical structure determining the admissible set of possibilities. This set of possibilities has a structure which in mathematics is referred to as the linear space. Therefore, instead of talking about a set of possibilities we can talk about the space of states of a given system. The space of states is determined by two factors: the so-called boundary conditions and the expression known as the operator of energy – the Hamiltonian.

Although we have no way of knowing it, we cannot exclude that different closed universes emerging from quantum vacuum have different boundary conditions and different Hamiltonians, which would mean that different laws of physics hold in different universes and each of them has a different space of states. Each of such universes can encompass a quantum vacuum comprising a set of virtual particles. It should be remembered, however, that elementary particles usually are not free and are involved in mutual interactions with forces depending on their nature. Also the virtual particles can interact, which means that there is a possibility of existence of more than one vacuum state, so a state without real particles. Different vacuum states have different energies, though they seem identical as they are empty, i.e. without real particles. The state of the lowest energy is called the real vacuum, while the others are known as false vacuum. The notion of the false vacuum appears in a natural way in all theories aiming at unification of description of elementary particles and their interactions, so also in the grand unification theories (GUT).

A false vacuum is not a permanent state, and after some time the system jumps to the state of the lowest energy, so to the real vacuum. Since this is a quantum process, it shows unavoidable indeterminism so is subjected to quantum fluctuations. This means that the process of disintegration of the false vacuum cannot be uniform in the whole space. Its occurrence involves a release of great energy. According to the GUT, the density of energy in the false vacuum can be approximately 10⁷³ that of energy density of water.

The simplest hypothetical scenario of the origin of our universe implied by the quantum cosmology principles, could be as follows. A closed universe emerges from the quantum vacuum in a causeless, random and spontaneous way as a quantum fluctuation. The existence of this universe in time can be talked about only after the Planck epoch, so later than 10^-44 s. The universe has a definite number of states, implied by the form of its hamiltonian and the boundary conditions which are the result of the quantum fluctuation. Therefore, it exits as a superposition of all possible universes from its space of states.

In t>10^-44 s the quantum fluctuations of geometry disappear and the universe starts to expand, in compliance with the Einstein’s classical theory of gravity. However, the universe does not expand in an existing space – its expansion unceasingly created time and space. Space and time have just started. Matter existed as non-differentiated superdense energy, since the real separate particles had not emerged yet. In quantum cosmology time is not a direct quantity but is a product of the material contents of the universe and the matter distribution.

At t 10^-35 s, a state of false vacuum appeared, characterised by a constant energy density despite the universe expansion, and this energy brought a dominant contribution to the total energy density. Therefore the energy density in the universe remained constant. According to the laws of the general theory of relativity this caused enormous acceleration of the universe expansion, so initiated the process of inflation. The expanding universe doubled its size every 10^-34 s. Every ten doublings the universe size increased 1024 times. The tremendous inflation of the universe caused a decrease of its temperature almost to the absolute zero. After disintegration of the false vacuum, at t 10^-30 s, the process of inflation stopped, the energy density started decreasing and the expansion of the universe continued at a decreasing rate. At the expense of the gigantic energy held in the false vacuum, the virtual particles became real. The released energy of the false vacuum partly transformed into the kinetic energy of elementary particles, which after the process of thermalisation was revealed as heat. The heat liberated after inflation caused an increase in the universe temperature up to about 10²⁸ K and this huge heat survived as the relic or background radiation.

According to this simplest scenario following from the quantum cosmology, the basic features of the universe structure have been determined by the physical processes which ended already at 10^-30 s after the universe emergence. After inflation, elementary particles have undergone many transformations, but eventually they were the building blocks of the matter, as we know it, stars, planets and people. If not for the process of inflation, appearing as a small fluctuation of the quantum vacuum, the universe would be a phenomenon occurring in a small space and lasting in a short time – it would be a very fast disappearing fluctuation.

Quantum cosmology can explain the mechanism of the universe creation and the inflation process, which have led to a Big Bang of our universe. Of course this scenario is highly speculative and drastically simplified. However, the important fact is that the quantum cosmology allows a construction of a scientific explanation of the origin of the universe in compliance with observations and laws of physics as well as its global structure. Probably in future more precise scenarios based on the future full quantum theory of gravitation will be proposed. However, even this primitive scenario contains ‘a grain of truth’, because it has been to a certain degree confirmed by observations of fluctuations of the background radiation recorded by the COBE satellite in the beginning of the 90s. Inhomogeneous quantum fluctuations inevitable in the early universe have stretched to gigantic size in the process of inflation. Therefore, we should observe at present fluctuations of all size – from small to huge, and the area of the sky occupied by them should not depend on their amplitude. In other words, the spectrum of the fluctuations should not depend on the scale of observation. The fluctuations are reflected in the distribution of the background radiation. The distribution of the fluctuations observed by COBE did not depend on the scale and the amplitude of the fluctuations in relative units is 10^-5. Such a distribution of the fluctuations could lead to the presently observed cosmic structures. Thus, it confirms the correctness of the scenario of Big Bang proposed within the quantum theory and the hypothesis of inflation.

To sum up, quantum cosmology gives the following scenario of the origin of the universe.

Quantum cosmology allows construction of scenarios of the universe emergence from nothingness, its inflation and heating up to enormously high temperatures. Therefore, it reduces the question of the universe emergence to that of the origin of the quantum theory. According to this theory the appearance of the universe is causeless and spontaneous, so senseless. If the existence of the universe nevertheless has a sense it can be hidden only in the structure of the quantum theory principles.

Despite a huge success, quantum cosmology cannot answer the two fundamental questions:

1. Why did the laws of quantum theory hold at the moment of the universe emergence, and
2. How did the universe, which is a set of potentially existing universes, realise in the form of the universe we live in?

To answer these questions we have to go beyond physical cosmology and pass to transcosmology.

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