1 INTRODUCTION

Strange as this may seem, we do not know what is the nature ofconsciousness, especially of the very strange features of consciousness which resemble mystical phenomena. The most familiar examples of these mysterious phenomena are scientific insights (of course, we mean only "great insights" experienced by great scientists). Some people supposed that the mystery of consciousness may be puzzled out on the basis of quantum mechanics, the science which is mysterious itself.

This viewpoint has been suggested, as early as in 20th years of 20th century, by the great physicist Wolfgang Pauli in collaboration with the great psychologist Carl Gustav Jung. They supposed particularly that quantum mechanics may help to explain strange psychic phenomena observed by Jung and called "synchronisms". Jung told of a synchronism if a series of the events happened such that these events were conceptually close but their simultaneous (synchronous) emergence could not be justified causally. For example he observed causally unjustified, seemingly accidental, appearance of the image of fish six times during a single day. The work of Pauli and Jung on this topic was not properly published and was later completely forgotten, but it became popular in last decades (see about this in Enz, 2009).

The idea of connecting consciousness with quantum mechanics was suggested by some other authors, mostly without referring Pauli and Jung. In the last three decades this idea was supported by Roger Penrose (Penrose, 1991), (Penrose, 1994). He particularly remarked that people manage to solve such problems which in principle cannot be solved with the help of computers because no algorithms exist for their solving. Penrose suggested that quantum phenomena should be essential for explaining the work of brain and consciousness.

Usually attempts to explain consciousness on the base of quantum mechanics follow the line of consideration that is natural for physicists. Everything must be explained by natural sciences, may be with accounting quantum laws. Therefore, in order to explain consciousness, one has to apply quantum mechanics for analysis of the work of brain. For example, the work of brain may be explained as the work of quantum computer instead of classical one. Thus, it is usually assumed, explicitly or implicitly, that consciousness must be derived from the analysis of the processes in brain.

The approach proposed by the author in 2000 does not include this assumption. This approach is based on the analysis of the logical structure of quantum mechanics, and the phenomenon of consciousness is derived from this purely logical analysis rater than from the processes in brain. The actual origin of the concept of consciousness is, according to this approach, specific features of the concept of reality accepted in quantum mechanics (contrary to classical physics) and often called quantum reality.

Quantum reality has its adequate presentation in the so-called Everett's interpretation (EI) of quantum mechanics known also under name of many-worlds interpretation (Everett III, 1957). The approach of the author is based on the Everett's form of quantum mechanics and called Extended Everett's Concept (EEC).

Some physicists, having in mind purely classical concept of reality, consider the Everett's interpretation of quantum mechanics too complicated and "exotic". However, it is now experimentally proved that reality in our world is quantum, and the conclusions based on classical concept of reality, are not reliable. The comprehension of the concept of quantum reality was achieved after long intellectual efforts of genius scientists. Unfortunately, the ideas of Pauli and Jung were not properly estimated and timely used. The first whose thoughts about quantum reality became widely know was Einstein who, in the work with his coauthors, suggested so-called Einstein-Podolski-Rosen paradox (Einstein et al., 1935). Much later John Bell formulated now widely known Bell's theorem (Bell, 1964), (Bell, 1987) which provided an adequate tool for direct quantum-mechanical verification of the concept of quantum reality, the Bell's inequality. Less than in 20 years the group of Aspect experimentally proved (Aspect et al., 1981) that the Bell's inequality is violated in some quantum processes, and therefore reality in our world is quantum.

Most simple and convenient formulation of quantum reality was given even earlier that the Bell's works, in 1957, by the Everett's interpretation of quantum mechanics. It was enthusiastically accepted by the great physicists John Archibald Wheeler and Brice Dewitt, but was not recognized by the wide physical community until last decades of 20th century, when the corresponding intellectual base was already prepared. From this time the number of adepts of the Everett's interpretation grows permanently. Results of this difficult but very important process of conceptual clarification of quantum mechanics justify the appreciation of the Everett's interpretation as the only correct form of quantum mechanics. It is exciting that, as an additional prize, the Everett's interpretation explains the mysterious phenomenon of consciousness.

Quantum mechanics in the Everett's form implies coexisting "parallel worlds", or parallel classical realities. This clearly expresses the difference of quantum reality from the common classical reality. According to the author's Extended Everett's Concept (Menskii, 2000), consciousness is the ability to perceive the Everett's parallel worlds separately, independently from each other. An immediate consequence of this assumption is that the state of being unconscious makes all parallel realities available without the separation. This leads to irrational insights and other "mystical" phenomena. This is the central point of the theory making it plausible. Indeed, it is well known (from all spiritual schools and from deep psychological researches) that the strange abilities of consciousness arise just in the states of mind that are close to being unconsciousness (sleeping, trance or meditation).

2 PARALLEL WORLDS

According to the Everett's "many-worlds" interpretation of quantum mechanics, quantum mechanics implies coexistence of "parallel classical worlds", or alternative classical realities. This follows from the arguments (see details below) including the following points:

Let us now give some details of these arguments. What does it mean that the states of a quantum system are vectors? If vpi are states of some quantum system, then ψ = ψ₁ + ψ₂ + • • • is also a state of the same system, called a superposition of the states ψ_i (counterparts of the superposition).

This feature is experimentally proved for microscopic systems (such as elementary particles or atoms), but it has to be valid also for macroscopic systems. This follows from the analysis of measurements with microscopic measured systems and macroscopic measuring devices.

The conclusion following from this analysis is that, even for a macroscopic system, its state ψ may be a superposition of other states of this system, which have evident classical interpretation (are close to some classical states of the system) while the state ψ has no such an interpretation:

It is important that the states ψ here may be macroscopically distinct, therefore, from classical point of view incompatible, alternative to each other, presenting alternative classical realities. Nevertheless, it follows from quantum theory that even such macroscopically distinct states ψ_i may be in superposition, i.e. may coexist. Let us formulate the above situation a little bit more precisely. The quantum system is in the state denoted by the state vector and only this state objectively exists (however, taken as a whole, has no classical interpretation). The counterparts ^ of the superposition are in fact classical projections of the objectively existing quantum state ψ. These classical projections describe images of the quantum system which arise in consciousness of an observer (therefore, they concern the subjective aspect of quantum reality). This status of the classical projections will be made more transparent below.

In the following we shall use ψ for the state of our (quantum) world as a whole. The components ψ_i of the superposition will be alternative classical states of this world (more precisely, quasiclassical, i.e. the states as close to classical as is possible for the quantum world).

In the Everett's interpretation of quantum mechanics the states ψ are called Everett's worlds. We shall use also the terms "parallel worlds", "alternative classical realities", "classical alternatives" or simply "alternatives". In case if such alternatives are superposed (as in Eq. (1)), we shall say that they "coexist". Of course this word is nothing else than a convenient slang, meaning in fact "to form a superposition" or "to be in superposition". The status of the "coexistence" is connected with the consciousness and subjective perception of the world, which will be explained below.

3 EXTENDED EVERETT'S CONCEPT (EEC)

We see that the alternative classical realities in our quantum world may coexist (as components of a superposition presenting the state of the quantum world). Subjectively however each observer perceives only a single "classical alternative". These two assertions seem to contradict to each other. Are they in fact compatible? We shall show how this seeming contradiction is resolved in the Everett's interpretation (EI) and how it may be taken as a basis for the theory of consciousness and the unconscious if the EI is properly extended.

3.1 Everett's "Many-Worlds" Interpretation One may naively think that the picture of the world arising in his consciousness (the picture of a single classical alternative) is just what objectively exists. However, EI of quantum mechanics (unavoidably following from the logics of quantum mechanics applied to the phenomenon of quantum measurements) claims that it is only the superposition of all alternatives (as in Eq. (1)) that objectively exists.

The seemingly strange and counter-intuitive presentation of objective reality (in the Everett's form of quantum mechanics) as the set of many objectively coexisting classical realities adequately expresses quantum character of reality in our (quantum) world.

The single alternatives (components of the superposition) present various subjective perceptions of this quantum reality in an observer's consciousness. The natural question arises how the multiplicity of the "classical pictures" that may arise in our consciousness may be compatible with the subjective sensory evidence of only a single such picture.

This is the most difficult point of the EI and the reason why this interpretation has not been readily accepted by the physicists. This point may be made more transparent if it is presented in the terms of "Everett's worlds" as it has been suggested by Brice DeWitt.

Thus, all of the separate components of the superposition (classical alternatives, or Everett's worlds) are declared by Everett to be "equally real". No single alternative may be considered to be the only real, while the others being potentially possible but not actualized variants of reality (this might be accepted in classical physics, but not in quantum mechanics, because of the special character of quantum reality).

To make understanding of the EI easier, Brice DeWitt proposed (De-Witt & Graham, 1973) to think that each observer is present in each of the Everett's worlds. To make this even more transparent, one may think that a sort of twins ("clones") of each observer are present in all Everett's worlds. Subjective perception is the perception of a single twin. Objectively the twins of the given observer exist in all Everett's worlds, each of them perceiving corresponding alternative pictures.

Each of us subjectively perceives around him a single classical reality. However, objectively the twins, or clones, of each of us perceive all the rest realities. It is important that all twins of the given observer are equally real. It is incorrect to say that there is "I" and there are my twins, which are not "I". All twins embody me as an observer, each of them can be called "I".

Thus, the concept of "Everett's world" allows to make the Everett's presentation of quantum reality more transparent. We prefer to verbalize the same situation in another way (Menskii, 2000). We shall say that all alternative classical projections of the quantum world's state objectively exist, but these projections are separated in consciousness. Subjective perception of the quantum world by human's consciousness embraces all these classical pictures, but each picture is perceived independently of the rest.

Regardless of the way of wording, the Everett's assumption of objectively coexisting classical alternatives implies that all these alternatives may be accessible for an observer in some way or another. Yet it is not clear how the access to "other alternatives" (different from one subjectively perceived) may be achieved for the given observer. It is usually claimed that the EI does not allow observing "other alternatives". This makes the interpretation non-falsifiable and thus decreases its value.

It turns out however that the EI may be improved in such a way that that the question "How one can access to other alternatives?" is answered in a very simple and natural way. This improvement is realized in the author's Extended Everett's Concept. The (improved) EI becomes then falsifiable, although in a special sense of the word (see below Sect. 3.2).

3.2 Extension of the Everett's Interpretation Starting with the above mentioned formulation (that classical alternatives are separated in consciousness), the present author proposed (Menskii, 2000) to accept a stronger statement: consciousness is nothing else than separation of the alternatives.

This seemingly very small step resulted in important consequences. Finally the so-called Extended Everett's Concept (EEC) has been developed (Menskii, 2005), (Menskii, 2007), (Mensky, 2007), (Mensky, 2005), (Mensky, 2010).

The first advantage of EEC is that the logical structure of the quantum theory is simplified as compared with the EI.

The point is that the formulation "alternatives are separated in consciousness" (accepted in one of the possible formulations of EI) includes two primary (not definable) concepts, "consciousness" and "alternative separation". These concepts have no good definitions. One may object that many different definitions have been proposed for the notion "consciousness". This is right, but all these definitions concern in fact mental and sensual processes in brain rather than "consciousness as such", while the latter (more fundamental) notion has no good definition.

After the notions "consciousness" (more precisely, "consciousness as such") and "separation of alternatives" are identified (as it is suggested in EEC), only one of these concepts remains in the theory. Therefore, EEC includes only one primary concept instead of two such concepts in the EI. The logical structure of the theory is simplified after its extension.

Much more important is that EEC gives a transparent indication as to how an observer may obtain access to "other alternatives" (different from the alternative subjectively perceived by him). This very important question remains unanswered (or answered negatively) in the original form of the EI. This is seen from the following argument.

If consciousness = separation (of the alternatives from each other), then absence of consciousness = absence of separation.

Therefore, turning off consciousness (in sleeping, trance or meditation) opens access to all classical alternatives put together, without separation between them. Of course, the access is realized then not in the form of visual, acoustic or other conscious images or thoughts. Nothing at all can be said about the form of this access. However, if we accept EEC, then we may definitely conclude that the access is possible in the unconscious state of mind.

This of course has very important consequences. The access to the enormous "data base" consisting of all alternative classical realities enables one to acquire valuable information, or rather knowledge. This information is unique in the sense that it is unavailable in the conscious state when only a single alternative is subjectively accessible. One may suppose that a part of this unique information may be kept on returning to the usual conscious state of mind and recognized in the form of usual conscious images and thoughts.

Thus, when going over to the unconscious state, one obtains the information, or knowledge, which is in principle unavailable in the usual conscious state.

This information is unique first of all because it is taken from "other" classical alternatives (different from one subjectively observed). There is however something more that makes this information unique and highly valuable. All alternatives together form a representation of the quantum state of the world (vector ^ in Eq. (1)). Time evolution of this state vector, according to quantum laws, is reversible. This means that, given at some time moment, this vector is known also at all other times. Therefore, information about "all alternatives together" (i.e. about the state vector of the world) includes information from any time moments in future and past. This information may be thought of as being obtained with the help of a "virtual time machine".

Evidently, this makes "irrational" inspirations (including scientific insights) possible. Here is a simple example. Let a scientist be confronted with a scientific problem and consider a number of hypotheses for solving this problem. Going, by means of the above mentioned virtual time machine, into future and backward, the scientist may find out what of these hypotheses will be confirmed by future experiments or proved with the help of the future theories. Then, on returning to the conscious state, he will unexpectedly and without any rational grounds get certain about which of these hypotheses has to be chosen.

Remark that it is not necessary, for making use of such a virtual time machine, to turn off consciousness completely (although it is known that some important discoveries were made in sleeping, or rather after awakening). It is enough to disconnect it from the problem under consideration. This is why solutions of hard problems are sometimes found not during the work on these problems but rather during relaxation.

Preliminary "rational" work on the problem is however necessary. The deep investigation of all data concerning the problem enables the consciousness to form a sort of query (clear formulation of the problem and its connections with all relevant areas of knowledge). Then the query will be worked out in the unconscious state (during relaxation) and will result in an unexpected insight.

It is clear that not only scientific problems can be solved in this way, but also problems of general character. Quite probable that, besides ordinary intuitive guesses, we meet in our experience examples of super-intuitive insights of the type described above. Anybody knows that many efficient solutions come in the morning just after awakening. This fact may be an indirect confirmation of the ability of super-intuition.

4 PROBABILISTIC MIRACLES

Thus, Extended Everett's Concept (EEC) leads to the conclusion that unconscious state of mind allows one to take information "from other alternatives" that reveals itself as unexpected insights, or direct vision of truth.

Another consequence is feasibility of even more weird phenomenon looking as arbitrary choice ofreality. Let us describe this ability in a special case of what can be called "probabilistic miracles".

Consider an observer who subjectively perceives one of the alternative classical realities at the present time moment t₀. Let in a certain future moment t > t₀ some event E may happen, but with a very small probability p. Call it the objective probability of the event E and suppose that this probability is small.

According to the Everett's interpretation of quantum mechanics, at time t two classes of alternative classical realities will exist so that the event E happens in each alternative of the first class and does not happen in the alternatives of the second class. The twins of our observer will be objectively present in each of the alternatives (this is the feature of Everett's worlds, see Sect. 3.1). However, subjectively our observer will feel to be in one of them. With some probability p it will turn out to be the alternative of the first class. The probability p may be called subjective probability of the event E for the given observer.

It is accepted in the Everett's interpretation that subjective and objective probabilities coincide, p = p. However, in the context of EEC we may assume that they may differ and, moreover, the observer may influence the value of subjective probability p'. Let us assume that the observer prefers the event E to happen. Then he can enlarge the subjective probability of this event, i.e. the probability to find himself subjectively at time t just in that classical reality in which this rare event actually happens.

Thus, besides the objective probability of any event, there is a subjective probability of this event for the given observer, and the observer may in principle influence the subjective probability. In the above mentioned situation, an event under consideration can happen according to usual laws of the natural sciences, but with small probability. This means that the objective probability of this event is small, it may seem even negligible. It is important that the objective probability is non-zero. One may say that among all alternatives at the moment t few of the alternatives correspond to the pictures of the world in which the event happens, and much more alternatives correspond to the pictures of the world where the event does not happen.

However, according to EEC, an observer can, simply by the force of his consciousness, make the subjective probability of this event close to unity. Then very likely he will find himself at the moment t in one of those classical realities where the event does happen.

The subjective experience of such an observer will evidence that the objectively improbable event may be realized by the effort of his will. This looks like a miracle. However, this is a miracle of a special type, which may be called "probabilistic miracle".

Probabilistic miracles essentially differ from "absolute" miracles that happen in fairy tales. The difference is that the event realized as a probabilistic miracle (i.e. "by the force of consciousness") may in principle happen in a quite natural way, although with a very small probability. This small but nonzero probability is very important. Particularly, because of fundamental character of probabilistic predictions in quantum mechanics, it is in principle impossible to prove or disprove the unnatural (miraculous) character of the happening.

Indeed, if the objectively rare event happens, the person who has strongly desired for it to happen is inclined to consider the happening as a result of his will. Yet any skeptic may insist in this situation that the event occurred in a quite natural way: what happened, was only a rare coincidence. The secret is in the nature of the concept of probability: if the probability of some stochastic event is equal p, then in a long series consisting of N tests the event will happen pN times (very rarely for small p). But it is in principle impossible to predict in which of these tests the event will happen. Particularly, it may happen even in the very first test from the long series of them.

The latter is a very interesting and general feature of the phenomena "in the area of consciousness" as they are treated in EEC. These phenomena in principle cannot be unambiguously assigned to the sphere of natural events (obeying the laws of natural sciences) or to the sphere of spiritual or psychic phenomena (which are treated by the humanities and spiritual doctrines). Impossibility to do this may be called relativity of objectiveness.

Synchronisms studied by Jung may be considered to be probabilistic miracles. One who observes a subject or event which somehow attracts his special attention, involuntarily thinks about it (often even not clearly fixing his thoughts). According to the above said, he may increase the subjective probability of immediately observing something similar or logically connected.

Some Biblical miracles can also be explained as probabilistic miracles. An example is the miracle at the Sea of Galilee where Jesus calmed the raging storm (Matthew 8:23-27). This was completely natural event. Wonderful was only the fact that the storm ceased precisely at that moment when this was necessary for Jesus and his disciples. The probability of "timely" occurring this natural event was of course very small. The miracle was probabilistic.

5 CONCLUDING REMARKS

We shortly followed in this paper the main ideas of Extended Everett's Concept (EEC) about nature of consciousness. Let us briefly comment on the further development of this theory.

All that has been discussed above, makes sense for humans (possessing consciousness) and may be partly for higher animals. However, the theory may be generalized to give the quantum concept of life in a more general aspect. Thus modified theory is meaningful not only for humans, but for all living beings (belonging to the type of life characteristic for Earth). The idea of the generalization is follows (see (Mensky, 2010) for details).

The main point of EEC is the identification of the "separation of classical alternatives" with the human's consciousness. Now we have to identify this quantum concept with the ability of the living beings to "perceive the quantum world classically". This is an evident generalization of consciousness but for all living beings. Instead of "consciousness" in EEC we have now "classical perceiving of quantum reality" which means that the alternative classical realities (forming the state of the quantum world) are perceived separately from each other.

Similarly to what we told about consciousness (in case of humans), this ability of living beings to "classically perceive the quantum world" is necessary for the very phenomenon of life (of local type). The reason is the same: elaborating efficient strategy of surviving is possible only in a classical world which is "locally predictable". Existing objectively in the quantum world, any creature is living in each of the classical realities separately from all the rest classical realities. Life is developing parallely in the Everett's parallel worlds.

Remark by the way that from this point of view "existing" and "living" are different concepts. Important difference is that existing (evolution in time) of the inanimate matter is determined by reasons while living of the living beings is partly determined also by goals (first of all the goal of survival). Let us make some other remarks concerning philosophical or rather meta-scientific aspects of EEC.

This theory shows that a conceptual bridge between the material (described by natural sciences) and the ideal (treated by the humanities and spiritual doctrines) does exist.

This bridge is determined in EEC in a concrete way, but the idea of such a bridge is not novel (see Fig. 1). The creators of quantum mechanics from the very beginning needed the notion of the "observer's consciousness" to analyze conceptual problems of this theory (the "problem of measurement"). In fact, the difficulties in solving these problems were caused by the insistent desire to construct quantum mechanics as a purely objective theory. Nowadays it becomes clear that there is no purely objective quantum theory. Objectiveness is relative (see Sect. 4).

There is a very interesting technical point in relations between the material and the ideal. We see from the preceding consideration that the description of the ideal, or psychic (consciousness and the unconscious), arises in the interior of quantum mechanics when we consider the whole world as a quantum system. This provides the absolute quantum coherence which is necessary for the conclusions that are derived from EEC. Usually only restricted systems are considered in quantum mechanics. The resulting theory is purely material. Ideal (psychic) elements arise as the specific aspects of the whole world. The unrestricted character of the world as a quantum system is essential for this (cf. the notion of microcosm).

All these issues demonstrate the specific features of the present stage of quantum theory. Including theory of consciousness (and the unconscious) in the realm of quantum mechanics (starting by Pauli and Jung and now close to being accomplished) marks a qualitatively new level of understanding quantum mechanics itself. The present stage of this theory can be estimated as the second quantum revolution. When being completed, it will accomplish the intellectual and philosophical revolution that accompanied creating quantum mechanics in the first third of 20th century.