Vol.2, No.3, 228245 (2010) Natural Science http://dx.doi.org/10.4236/ns.2010.23035 Copyright © 2010 SciRes. OPEN ACCESS A retrospective view on the history of natural sciences in XXXXI Vladislav Sergeyevich Olkhovsky Institute for Nuclear Research, Kiev, Ukraine; olkhovsky@mail.ru Received 1 December 2009; revised 8 January 2010; accepted 30 January 2010. ABSTRACT The presented paper is dedicated to a new ret rospective view on the history of natural sci ences in XXXXI cc, partially including the sci ence philosophy (mainly, the problems of the scientific realism, i.e. the correspondence of science to reality) and also a novel scheme for different classes of sciences with different ob jects and paradigms. There are analyzed the chosen “great” and “grand” problems of phys ics (including the comprehension of quantum mechanics, with a recently elaborated new chapter, connected with time as a quantum obs ervable and time analysis of quantum processes) and also of natural sciences as a whole. The particular attention is paid to the interpretation questions and slightly to the aspects, inevitably connected with the world views of the res earchers (which do often constitute a part of the interpretation questions). Keywords: science history; science realism; paradigm; problem of interpretation and comprehen sion of quantum mechanics; the wavefunction col lapse; the EinsteinPodolskyRosen paradox; time as a quantum observable, canonically conjugated to energy; maximal hermitian time operator; time analysis of quantum processes; relationship be tween physics and biology; problem of origin of biologic life; reductionism; cosmologic problem; Big Bang; anthropic principle 1. INTRODUCTION In the science history and in the science philosophy of ХХXXI (especially in the field of the natural sciences and most of all in physics) there has been a lot of inter esting things, which had not obtained a sufficiently complete elucidation and analysis yet. Firstly, under the influence of scientific and technological progress a great attention has been paid to the development of such di rection in the science philosophy as the scientific realism (i.e. the correspondence of the science to the reality), which has successively acquired three forms: the naïve realism, the usual realism and the critical science realism. Secondly, some new important problems of physics (es pecially the problem of the essentially probabilistic de scription of the reality of the microscopic world, the problem of the essential influence of the observer on the reality, the collapse of the wave function and the Ein steinPodolskyRosen paradox) had been revealed in the development of quantum mechanics; the continuously complicated explanation of the Universe origin and the expansion after the Big Bang; and no succeeded attempt in explaining the origin of the biological life in terms of physics and other natural sciences, all being with a vari ety of interpretation versions (often connected with the worldviews of the researchers), cause to undertake a new view of the science history. And thirdly, a clear analysis of the variety of known sciences brings to the reconsidering of the science classification and a novel scheme for different classes of natural sciences with quite different objects (including not only simple natural phenomena and processes, but also the human intelligent design and the origin of the Universe and life). Finally, a simple study of the enlargement of mathematics in prac tically all of sciences did not only indicate that mathe matics became the branch of the natural sciences (as to the opinion of some scientists, such as N.N.Bogolyubov and others) but has also in fact induced the solution of the longstanding problem of time in quantum mechan ics. 2. THE SCIENTIFIC REALISM AND ITS DIFFERENT KINDS If the science does correspond the reality? In the science philosophy the term reality defines the direction, postu lating the existence of the reality, independent from the cognitive subject. The scientific realism postulates the existence of the objective truth, the aim of the scientific theories is being declared the revelation of the real truth, the moving force of the scientific progress is declared
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 229 the approach to the truth (the truth is explained as en tirely adequate description of the reality). The scientific theories, if they ate really truthful, do describe in an adequate way the reality and the essences, which are postulated by the well tested theories, are existing really. R.Boyd [1] selected three types of the scientific real ism: The ontological realism assumes that the reality, which is described by the scientific realism, does not depend, on the whole, from our thinking and from the theoretic assumptions. The ontological realism responds to the questions like “what essences are real?”, “if the world, which is independent from the observer, does exist?” The epistemological realism assumes that the scien tific theories are confirmed as true and in fact are often approach to the reality. The epistemological realism re sponds to the question: “is the knowledge about the world possible?” The semantic realism assumes that “the theoretical terms” of the scientific theories indicate to the realistic essences, i.e. the theories have to be interpreted realisti cally. The semantic realism responds the question: “if the truth of the objective world is expressed by the scientific language?” Respectively, the scientific realism on the whole as sumes that the scientific theories tend to give the truthful description of the reality which is existing independently (“the truth” signifies here the complete correspondence between the science and the reality). If the scientific theory is really true, then the unobserved essences, which it postulates, are really existing. A.Bird [2] had formulated the short thesis of the sci entific realism. He states that the scientific theories: a) can be estimated in the terms of the truthfulness or the approach to the truthfulness; b) their reasonable aim is the truth or the approach to the truth; c) their success, confirmed by the scientific progress, testimonies their truth; d) if they are true, then the unobserved essences, which they assume, are really existing; e) if they are true, they will explain the observed phe nomena. The main argument for the realism is the conclusion on the best explanation of the reality: the scientific real ism is the only science philosophy that can explain the scientific progress. The scientific realism is exposed to the critics from the antirealism (antirealism, appeared in the second part of the XX, does represent the scientific philosophy, which is opposite to the realism). Antireal ists state that to consider the scientific theories to be true is too risky. Some previous scientific theories were false, for example, the theories of heat matter, phlogiston, the ether conception. So, modern theories can be also false. The position of the scientific realism is criticized by an tirealists, although it has a lot of supporters. In the nonuniform current of the scientific realism there are known 3 kinds: naïve, usual and critical. The naïve realism is the position of the majority of men from the point of view of the common sense. [The common sense is acquired by all normal men during the natural living process, in the overall man communications and in actions with the objects of our usual experience. It is like the assimilation of the natal language with which the common sense is therefore closely connected. In many situations the common sense is used as a matter of fact the primordial universal kind of knowledge]. Ac cording to this position, the world is such, which is rep resented by the modern (however, prequantum!) science: those essences, the existence of which are postulated by the wellsupported scientific theory, are really existing. And only objects, which are described by the scientific theories, have the authentically real ontological status, and the scientific knowledge as an epistemological base of the science does also represent the realism. The usual realism is the position of the investigators like [1,2], and also somewhat different positions of a series of other authors (for instance, such as J.Smart, R.Harre, H.Putnam etc.). Later the more “weak” realistic position appeared – the critical realism, with the more modest declarations of its supporters. The critical scientific realism had been declared by the not very equal positions of many various authors. The position of the critical realism had been rather clearly formulated by I.Niiniluotto from the Hel sinki University [3], which added some more precise definitions to the position of the critical realism. In par ticular, he recognizes the conceptual pluralism, under the influence of the uncertainty thesis of W.Quine [4]: our appeal to the world does always occur in some linguistic frame. The thesis of the pessimistic induction forces him to accept the possibility of the untrue theories: the knowledge about the reality is not very trustworthy and demands certain corrections, and even the best scientific theories can contain the mistakes, however the success ful theories approach to the reality. The thesis about “the human insertion” signifies that the reality is partially (but only partially!) constructed by the humanity. And in the whole the position of Niiniluotto conserves the real istic optimism: the scientific progress can be rationally explained. As before, the best explanation does consist in that the scientific theories approximate to reveal the truth. Concretely I.Niiniluotto had formulated such thesis of the critical realism [3]: а) At least, the part of the reality is ontologically in dependent from the human intelligence. b) The truth is the semantic relation between the lan guage and the reality. c) The conception of the truth or the falsification can de used to all linguistic derivatives of the scientific ac tivity including the reports on the observations, the laws
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 230 and the theories. In particular, the statements on the ex istence have the truthfulness significations. d) The attainment of the truth is the main aim of the science. The truth is not being found and recognized in a simple way and even the best scientific theories can be false. Nevertheless, it is possible to approach to the truth and obtain the rational conception on the cognitive process. e) The best explanation of the practical success of the science consists in the approximate truthfulness or suc cessful approaching to the revelation of the truth about the reality. And therefore the scientific progress can be rationally explained. Not always it is possible clearly distinct the usual scien tific realism and the critical scientific realism because in the scientific thinking a lot of attention is paid to the criti cal analysis of the cognition methods and the scientific knowledge with utilization of all logic cognition methods with understanding of their limitedness. But with the suf ficiently completeness of the utilization of the logic cog nition methods, the position of the critical realism is better defended against the standard arguments utilized against the realism (usual and especially naïve). If earlier the main attention in the science philosophy had been paid to the justification of the scientific method, during the last doz ens of years mainly the questions of the ontological status of objects, introduced by the scientific theories, are dis cussed. It must be noted that the problems of the quantum theory, revealed as a result of the long (during many years) discussion of N.Bohr with A.Einstein, had seriously un dermined the traditional forms of the naïve realism in the science and have strongly influenced not only on physics but also on other kinds of knowledge and on our under standing of the human knowledge at all. The quantum mechanics, in difference from the classi cal (nonquantum) physics, revealed that on the micro scopic level there is the unremovable indeterminism, represented by the uncertainty relations of Heisenberg, by the essential nonlocality of the particlewaves (still un measured, i.e. before measurements) and also by the measurements with the discrete interaction of the micro scopic objects and the measurement devices (when, for instance, there are the photons are emitted and absorbed). Then in quantum mechanics there is the problem of the interpretation of the quantum measurements and particu larly the wavefunction collapse etc, when the state of the measured system is formed by the observer [5,6]. All these problems and paradoxes had arisen as a challenge to the philosophy and even now bring to the acute discus sions [5,6]. And if the majority of the physicists agree with the Bohr Copenhagen interpretation of the quantum mechanics, a certain part of the physicists still assumes that A.Einstein was righteous in his statement that the quantum theory (in its Copenhagen interpretation) does not directly describe the reality. Still the more acute situa tion had arisen from other quantum phenomena such as the EinsteinPodolskyRosen paradox. But as to opinion to some ideologists, such conclusions are justified only in the frame of the physical description and even in such description many of these problems are open even now, so there is no the final necessity now to extrapolate them into the philosophy and theology with profound “revolution ary” philosophical and theological conclusions. 3. THE DIFFERENT CLASSES OF PARADIGMS IN THE DIFFERENT CLASSES OF NATURAL SCIENCES If the objects of natural sciences (physics, chemistry, biology, geology, astronomy etc) are limited by the only natural events and processes, the objects of some other sciences include in their objects also the artificial facts (artefacts) as creations of the human intelligent design (there are archeology, medicine, criminalistics, and, moreover, mathematics, cybernetics, informatics, and also such humanitarian sciences as history, economics and political sciences). There are also the particular sci ences where the origin and history of the Universe or the origin and history of the biological life (including genet ics) are studied and where side by side with the scientific method a metaphysical worldview approach of the in vestigators does, almost inevitably, also take place: Due to the cardinal separation of the investigators because of the incompatibility of their worldviews as to the prob lems of the origin, the dilemma of the following choice had appeared: either 1) the selforganization of the mat ter from the null or a less organized level into the much more organized level by virtue of a certain irrational chance or by virtue of unknown now synergetic processes (or phase transitions), or 2) the origin of the Universe and of the life inside it as a result of the supreme intelli gent design of a certain superhuman creative basis (or a Creator). And in these three classes of sciences with the differ ent research objects now there are coexisting for scien tific researches three different classes of paradigms (the term “paradigms” had been introduced by T. Kuhn in [7]) which exist inside the sciences of their application: the class of paradigms for research of the laws of functioning of the natural processes; the class of paradigms of intro ducing (or inserting) the human intelligent design inside the natural processes or in the human activity; and fi nally the class of paradigms of the research of the mechanisms of the origin of the Universe and the life. Moreover, the first two classes are now already ob served to be sometimes overlapped: for instance, in quan tum mechanics it is known that the state of the measured system can be in fact formed by the observer [5], i.е. the human intelligent design can actively influence on the currency of the observed natural processes! And in the third class of sciences, which deals with the origin prob
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 231 lems, for a long time there are known acute collisions of different worldviews which are sometimes expanding into the second group, including mathematics, informatics and cybernetics. Besides the confusion of the different classes of paradigms, such discussions between the supporters of the different worldviews have sometimes become more acute because of the complete incompatibility of the re searcher’s worldviews, taking the especially sharp forms between the evolutionists and creationists. Even A. Ein stein in his lastlife period had participated, at least par tially and philosophically, in these discussions (see, for instance, [8]): “Considero le dottrine evoluzionistiche di Darwin, Haeckel, Huxley, come tramontate senza sper anza” (in English: “I consider the evolutionism doctrines of Darwin, Haeckel and Huxley as being outgoing without any hope to revive ”). As to mathematics, one can note that usually the object of every mathematical discipline or theory is taken as the system of the exactly formulated axioms, and the method ology of mathematics consists in the derivations of the logical conclusions and theorems from the chosen axioms. Previously C.Gauss referred to mathematics as “the Queen of the Sciences” [9]. Later it was observed that certain scientific fields (such as theoretical physics) are mathematics with axioms that are intended to correspond to reality. In any case, mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions. And K. Popper concluded that “most mathematical theories are, like those of physics and biology, hypotheticodeductive: pure mathematics there fore turns out to be much closer to the natural sciences whose hypotheses are conjectures, than it seemed even recently”[10. Moreover, in XXXXI some mathemat icians consider that mathematics has already become practically a branch of natural sciences (theoretical physics) – see, for instance, [11]. And it is in agreement with the known statement of Galileo: “Il libro della natura è scritto in lingua matematica” (in English: “The book of nature is written by the mathematical language”) [12]. Now in the theory of quantum collisions and, in par ticular, in the theory of the dispersion relations the initial assumptions of these theories do contain, besides the physical principles, also the mathematical principle of certain analytic properties of the Smatrix in the complex plane of energies (momenta) [11, the first reference]). Finally, namely mathematics generated the solution of the longstanding problem of time as a quantum observable, canonically conjugated to energy, and selfconsistent time analysis of quantum processes. 4. AS TO “GREAT” AND “GRAND” PROBLEMS OF NATURAL SCIENCES There is an extensive introduction in the large number of open problems in many fields of physics, published by the Russian physicist V.Ginzburg in [13], which is rather interesting to study. Inside this large list of open prob lems of modern physics (and in a certain degree of mod ern natural sciences), represented by V.Ginzburg repeat edly in Russian editions, some of them are marked him “great” or “grand” problems. Between namely these problems I would like to separate three of them. a) The problem of interpretation and comprehension of quantum mechanics (even of the nonrelativistic quantum theory) remains still topical. The majority of critics of quantum mechanics are un satisfied with the probabilistic nature of its predictions. One can add here also the questions and paradoxes of the theory of quantum measurements theory, especially like the wavefunction reduction and the EinsteinPodolsky mRosen paradox. The appearance of quantum mechanics, and, in particular, the discussion of N.Bohr with A. Ein stein (lasting many years), had seriously undermined the traditional forms of the naïve realism in the philosophy of the scientific realism and had strongly influenced (and are continuating to influence) not only on physics but also on other kinds of knowledge in the sense of the dependence of the reality on the observer and, moreover, on our un derstanding of the human knowledge at all. The problem of the relativistic quantum mechanics and quantum field theory is even much more sharp because of the incom patibility of the main premises of the quantum theory and of the relativity theory. b) The relationship between physics and biology and, specifically, the problem of reductionism. The main problem, according to V.Ginzburg, is con nected with the explanation of the origin of the biologic life and the origin of the human abstract thinking (but the second one, as to me, is connected not with biology but with the origin of the human spiritual life which is far beyond natural sciences). V.Ginzburg assumes that for a possible explanation of the origin of the biologic life one can naturally imagine a certain jump which is similar to some kind of phase transition (or, may be, certain synergetic process). But there are other points of view too. c) The cosmological problem (in other words, the problem of the Universe origin). According to V.Ginzburg, it is also a grand problem, or strictly speaking, a great complex of cosmic problems many of which is also far from the solution. 5. MORE DETAILED COMMENTS ON THE PROBLEM OF COMPREHEN SION OF QUANTUM MECHANICS Various interpretations of quantum mechanics. Not only philosophers of scientific critical realism, but also up to now a certain part of physicists, beginning from A. Ein
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 232 stein, D.Bohm, Y.Aharonov and some others, did not agree with the Copenhagen interpretation of quantum mechanics and, moreover, had constructed alternative versions of interpretation (see, for instance, [1422]). Einstein never accepted quantum mechanics as a “real” and complete theory, struggling to the end of his life for an interpretation that could comply with relativity without complying with the Heisenberg uncertainty principle. As he once said: “God does not play dice”, skeptically referring to the Copenhagen interpretation of quantum mechanics which says there exists no objective physical reality other than that which is revealed through measurement and observation. In 1935 Einstein, Podolsky, and Rosen were formu lated their thought experiment, which had been called the EPR paradox (which is also referred to as the EPRB paradox after Bohm, who improved the formulation of the thought experiment). It draws attention to a phe nomenon predicted by quantum mechanics known as quantum entanglement, in which measurements on spa tially separated quantum systems can instantaneously influence one another. As a result, quantum mechanics violates a principle formulated by Einstein, known as the principle of locality or local realism, which states that changes, performed on one physical system, should have no immediate effect on another spatially separated system. The principle of locality seems to be persuasive, because, according to relativity, information can never be trans mitted faster than the speed of light, or causality would be violated. Any theory, violating causality, would be deeply unsatisfying. However, a detailed analysis of the EPR scenario shows that quantum mechanics violates locality without violating causality, because no informa tion can be transmitted using quantum entanglement. Nevertheless, the principle of locality appeals power fully to physical intuition, and Einstein, Podolsky and Rosen were unwilling to abandon it. They suggested that quantum mechanics is not a complete theory, just an (admittedly successful) statistical approximation to some yetundiscovered description of nature. Several such descriptions of quantum mechanics, known as “local hidden variable parameters”, were proposed. These de terministically assign definite values to all the physical quantities at all times, and explicitly preserve the princi ple of locality. Of the several objections to the then current interpreta tion of the quantum mechanics spearheaded by Einstein, the EPR paradox was the subtlest and most successful. The EPR paradox has not been resolved or explained, in a way, which agrees with classical intuition, up to this day. It brought a new clarity and permanent shift in thinking about ‘what is reality’ and what is a ‘state of a physical system’. The shift was caused by the EPR thought experiment, which has shown how to measure the property of a par ticle, such as a position, without disturbing it. In today’s terminology, we would say that they did the determina tion by measuring the state of a distant but entangled particle. Quantum entanglement is a property of a sys tem of two or more particles (objects) in which the quantum states of the constituting objects are linked to gether so that one object can no longer be adequately described without full mention of its counterpart  even if the individual objects are spatially separated. Accord ing to quantum mechanics, the state of the counterpart particle will instantly change even though we did not disturb it in any local way. It conflicts with our classical intuition with the relativistic principle of locality. Dif ferent views on the essence of the quantum entanglement bring to different interpretations of quantum mechanics. The very concept of quantum entanglement also con flicts with our intuition the same way. However, experiments have shown that entanglement does occur, and in fact quantum entanglement has prac tical applications in the field of quantum cryptography and quantum computation. Earlier quantum entangle ment had been utilized in experiments with quantum teleportation. Quantum teleportation is a technique used to transfer quantum information from one quantum sys tem to another. It does not transport the system itself, nor does it allow communication of information at superlu minal (faster than light) speed. Its distinguishing feature is that it can transmit the information present in a quan tum superposition, useful for quantum communication and quantum computation. In quantum cryptography, an entangled signal is sent down a communications channel making it impossible to intercept and rebroadcast that signal without leaving a trace. In quantum computation, entangled states allow simultaneous computations to occur in one step. Entanglement has many applications in quantum in formation theory [2331]. Mixed state entanglement can be viewed as a resource for quantum communication. With the aid of entanglement, otherwise impossible tasks may be achieved. Among the best known applications of entanglement there is superdense coding. In 1964 J.Bell had shown that many theories, known as hidden variable theories, are either nonlocal or known as satisfying Bell inequality [16]. Quantum mechanics pre dicts that this inequality is not satisfied. To make sure, additional experiments were made to confirm that pre dicted action at distance is indeed instant. Today most physicists agree that local hidden variable theories are untenable and that the principle of locality does not hold. Therefore, the EPR paradox would only be a paradox be cause our physical intuition does not correspond to physi cal reality. But even now the topic remains active and some people are still looking for Quantum. quantum quantumquantummechanics is neither “real” (since measurements do not state, but instead prepare proper ties of the system) nor “local” (since the state vector comprises the simultaneous probability amplitudes for all
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 233 positions), and the properties of entanglement are some of the many reasons why the Copenhagen Interpretation is no longer considered standard by a large proportion of the scientific community. So, the discussion of N.Bohr with A.Einstein had originated so many interesting fun damental results, experimental applications and other (already second or derived) discussions, which have endless continuation up to now, that it was unique in the history of physics. And now, let us speak some words on the manyworld interpretation (MWI) in quantum mechanics (and in quantum cosmology). In this interpretation one assumes the existence of the parallel universes, in every of which the same nature laws and physical constants are acting, but all of them are found in different states. MWI refuses an indeterminate collapse of the wave function which is connected with the measurement in the Copenhagen interpretation. The ideas of MWI had been originated in the phdthesis of H.Everett bat the term MWI had been proposed by B.S.M. de Witt who had developed that idea, and then the various authors had participated in the fur ther development of that topic [3241]. In various versions of MWI there two main points: The first one consists in the existence of the wave function for the total Universe, described by the Schroedinger equation, but without any indetermined collapse. The second one consists in that such state of the Universes is the quantum superposition of several (and may be, of the infinite num ber of) states of the equal parallel universes which are noninteracting among themselves. According to the modern criteria of the scientific theories, MWI is not experimentally verificable and not falsified, and therefore is not scientific! However, any other interpretation of quantum mechanics, including the Copenhagen one, is also not scientific but philosophical and therefore the usefulness of the quantummechanical interpretation is determined by its pragmatism. And, although the analysis of some problems in the MWI brings to the same results as in any other interpretation, but these results are more simple logically, so they had been resulted to some physicists to be more popular in quantum mechanics (and quantum cosmology). May be, it seems that the majority of the opponents of the MWI reject it because, for them, introducing a very large number of worlds that we do not see is an extreme violation of Ockham’s principle: “Entities are not to be multiplied beyond necessity”. However, in judging physical theories one could reasonably argue that one should not multiply physical laws beyond necessity either (such a verion of Ockham’s Razor has been applied in the past), and in this respect the MWI is the most economical theory. Indeed, it has all the laws of the standard quantum theory, but without the collapse postulate, the most problematic of physical laws. The reason for adopting the MWI is that it avoids the collapse of the quantum wave. And there is no ex perimental evidence in favor of collapse and against the MWI. We need not assume that Nature plays dice. The MWI is a deterministic theory for a physical Universe and it explains why a world appears to be indeterministic for human observers. The MWI exhibits some kind of nonlocality: “world” is a nonlocal concept, but it avoids action at a distance and, therefore, it is not in conflict with the relativistic quantum mechanics . The MWI is not the most accepted interpretation of quantum theory among physicists, but it is becoming increasingly popular . The strongest proponents of the MWI can be found in the communities of quantum cosmology and quantum computing. In quantum cosmology it makes it possible to discuss the whole Universe avoiding the difficulty of the standard interpretation which requires an external observer. In quantum computing, the key issue is the parallel processing performed on the same computer; this is very similar to the basic picture of the MWI. However, the advantage of the MWI is that it allows us to view quantum mechanics as a complete and consistent physical theory which agrees with all experimental results obtained to date. And also, the elegant conception of the decoherence, proposed in 1970 by Dieter Zeh, explains that the various branches of the single wave function, which describe these worlds, are oscillating in time with the different phases and so as if do not exist each for other [42]. As a whole, the problem of the final interpretation of quantum mechanics and of quantum theory of measure ments is far from the total consensus and still remains open for both physicists and philosophers (in the science philosophy). One can add here that the still inherent incompatibility of the postulates of quantum theory as nonlocal theory and relativity theory (both special and general) as local theory is the main root of the impossibility to construct the selfconsistent relativistic quantum mechanics, qu antum field theory and the quantum cosmology even in quasilinear approximation. Another long incompleteness of nonrelativistic qu antum mechanics (even in the Copenhagen interpretation) is connected with the problem of time as a quantum ob servable, which is, moreover, canonically conjugated to energy. It has been known from the beginning of twenti eth of XX (see [43] and later also the discussion of Y.Aharonov and D.Bohm with Fock [44,45]) till the last years, when it has in fact been resolved practically by using the mathematical means. 6. TIME IS REALLY A QUANTUM OBSERVABLE, CANONICALLY CONJUGATED TO ENERGY Introduction to the history of the problem. During almost ninety years (see, for example, [43]) it is known that
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 234 time cannot be represented by a selfadjoint operator, with the possible exception of special abstract systems (such as an electrically charged particle in an infinite uniform electric field1 and a system with the limited from both below and above energy spectrum (to see later)). This fact results to be in contrast with the known circumstance that time, as well as space, in some cases plays the role just of a parameter, while in some other cases is a physical observable which ought to be repre sented by an operator. The list of papers devoted to the problem of time in quantum mechanics is extremely large (see, for instance, [4682], and references therein). The same situation had to be faced also in quantum elec trodynamics and, more in general, in relativistic quan tum field theory (see, for instance, [53,81,82]). As to quantum mechanics, the first set of known and cited articles is [5460]. The second set of papers on time as an observable in quantum physics [6182] appeared from the end of the eighties and chiefly in the nineties and more recently, stimulated mainly by the need of a selfconsistent definition for collision duration and tun nelling time. It is noticeable that many of this second set of papers appeared however to ignore the Naimark theo rem from [83], which had previously constituted an im portant basis for the results in refs. [5460]. This Naimark theorem states [83] that the nonorthogonal spectral de composition E ( ) of a hermitian operator H is of the Carleman type (which is unique for the maximal hermi tian operator), i.e. it can be approximated by a succession of the selfadjoint operators, the spectral functions of which do weakly converge to the spectral function E ( ) of the operator H . Namely, by exploiting that Naimark theorem, it has been shown in [5459] (more details having been added in [60,65,66,78,81,82]) that, for systems with continuous energy spectra, time can be introduced as a quan tummechanical observable, canonically conjugate to en ergy. More precisely, the time operator resulted to be maximal hermitian, even if not selfadjoint. Then, in [59 (1),66(3),81,82] it was clarified that time can be intro duced also for the systems with energy discrete spectra as a quantummechanical observable, canonically conjugate to energy, and the time operator resulted to be quasiselfadjoint (more precisely, it can be chosen as an almost selfadjoint operator with practically almost any degree of the accuracy). We have also to note that there is known in the litera ture the socalled positiveoperatorvaluemeasure (POVM) approach, often used in the second set of papers on time in quantum physics (for instance, in [6164, 6777,79,80]. This approach, in general, is wellknown in the various approaches to the quantum theory of measurements ap proximately from the sixties and had been applied in the simplest form for the timeoperator problem in the case of the free motion already in [84]. Then, in [6164, 6777,79,80] (often with certain simpli fications and abbreviations) it was affirmed that the generalized de composition of unity (or POV measures) is reproduced from any selfadjoint extension of the time operator into the space of the extended Hilbert space (usually, with negative values of energy E in the left semiaxis) citing the Naimark’s dilation theorem from [85]. As to our ap proach, it is based on another Naimark’s theorem (from [83]), cited above, and without any extension of the physical Hilbert space of usual wave functions (wave packets) with the subsequent return projection to the pre vious space of wave functions; and, moreover, it had been published in [5457,59,60] earlier than [6164,6777, 79,80]. Being based on the earlier published remarkable Naimark theorem [83], it is much more direct, simple and general, and at the same time mathematically not less rigorous than POVM approach! From the simple analysis of the articles [57,78,81,82], based on the remarkable Naimark theorem [83], one can see that the appearance of these articles, does demonstrate that the problem of time as an observable in quantum mechanics is factually and practically resolved for the systems with continuous spectra, and the alternative ap proach presented in the articles [7377,79,80], based on the another Naimark theorem [85], which does not con tradict this conclusion, in fact does partially support it. Time as a quantum observable in quantum mechanics for systems with continuous spectra. For systems with continuous energy spectra, the following simple operator, canonically conjugate to energy, can be introduced for time: in the (time) trepresentation, (1a) i t t ˆ in the (energy) Erepresentation (1b) which is not selfadjoint, but is hermitian , and acts on squareintegrable spacetime wavepackets in representa tion (1a), and on their Fouriertransforms in representa tion (1b), once the point E=0 is eliminated (i.e. , once one deals only with moving packets, i.e., excludes any nonmoving back tails, as well as, of course, the zero flux cases)2. It has been shown already in [5457,59,60]. The elimination of the point E=0 is not restrictive since the “rest” states with the zero velocity, the wavepackets with non moving rear tails, and the wavepackets with zero flux are unobservable. Operator (1b) is defined as acting on the space P of the continuous, differentiable, squareintegrable func tions f (E) that satisfy the conditions 1Namely that fact that time cannot be represented by a selfadjoint operator is known to follow from the semiboundedness of the con tinuous energy spectra, which are bounded from below (usually by the value zero). Only for an electrically charged particle in an infinite uni form electric field, and for other very rare special systems, the con tinuous energy spectrum is not bounded and extends over the whole energy axis from – to .
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 235 0 ()2 d fE E , 2 0()fE EdE , 0 ()2 2 d fE E E (2) (the notation < in (2) denotes the finite value of the integrals from the left) and the condition f(0) = 0 (3) which is a space P dense in the Hilbert space of L2 functions defined (only) over the semiaxis 0≤E< ∞. Obviously, the operator (1a,b) is hermitian, i.e. the relation (f1, t ˆf2) = ((t ˆf1), f2) holds, only if all squareintegrable functions f(E) in the space on which it is defined vanish for E=0. And also the operator t ˆ2 is hermitian, i.e. the relation (f1, t ˆ2f2) = ((t ˆf1), ((t ˆf2)) = (t ˆ2f1, f2) holds under the same conditions. Operator t ˆ has no hermitian extension because oth erwise one could find at least one function f0 (E) which satisfies the condition f0(0) 0 but that is inconsistent with the propriety of being hermitian. So, according to [86], t ˆ is a maximal hermitian operator. Essentially because of these reasons, earlier Pauli (see, for instance, [45]) rejected the use of a time operator: and this had the result of practically stopping studies on this subject for about forty years. However, as far back as in [87] von Neumann had claimed that considering in quantum mechanics only selfadjoint operators could be too restrictive. To clarify this issue, let us quote an explanatory example set forth by von Neumann himself [87]: Let us consider a particle, free to move in a spatial semiaxis (0 ≤ x < ∞) bounded by a rigid wall located at x = 0. Consequently, the operator for the momentum x component of the particle, which reads ˆx pi , is defined as acting on the space of the continuous, differentiable, squareintegrable functions f (x) that satisfy the conditions 0 f (x)2dx < ∞, 0 ∂f (x) / ∂x2dx < ∞, 0 f (x)2 x2 dx < ∞ (here the notation < denotes the finite value of the integrals from the left) and the condition f (0) = 0 which is a space Q dense in the Hilbert space of L2 functions defined (only) over the spatial semiaxis 0≤x<∞. Therefore, operator ˆx pi has the same mathematical properties as operator t ˆ (1a,b) and con sequently it is not a selfadjoint operator but it is only a maximal hermitian operator. Nevertheless, it is an observable with an obvious physical meaning. And the same properties has also the radial momentum operator 1 ˆr pi rr (0 < r < ). By the way, one can easily demonstrate (see, for instance, [47]) that in the case of (hypotetical) quantummechanical systems with the continuous energy spectra bounded from below and from above (Emin<E<Emax) the time operator (1a,b) becomes a really selfadjoint operator and has a discrete time spestrum, with the “the time quantum” = / d , where d = Emax – Emin . In order to consider time as an observable in quantum mechanics and to define the observable mean times and durations, one needs to introduce not only the time op erator, but also, in a selfconsistent way, the measure (or weight) of averaging over time. In the simple onedimensional (1D) and onedirectional motion such measure (weight) can be obtained by the simple quan tity: W(x,t)dt = (,)d (,)d jxtt jxtt , (4) where the probabilistic interpretation of j(x,t) (namely in time) corresponds to the flux probability density of a particle passing through point x at time t (more pre cisely, passing through x during a unit time interval, centered at t), when travelling in the positive xdirection.. Such a measure had not been postulated, but is just a direct consequence of the wellknown probabilistic (spa tial) interpretation of (x, t) and of the continuity rela tion (x,t)/t + divj(x,t) = 0 (5) for particle motion in the field of any hamiltonian in the description of the 1D Schroedinger equation. Quantity (x,t) is the probability of finding a moving particle in side a unit space interval, centered at point x, at time t. The probability density (x,t) and the flux probabil itydensity j(x,t) are related with the wave function (x,t) by the usual definitions (x,t)= (x,t)2 and j(x,t) = Re [ *(x,t) ( /i ) (x,t)/x]. The measure (4) was firstly investigated in [57,59,60,65,66]. When the flux density j(x,t) changes its sign, the quantity W(x,t)dt is no longer positive definite and it acquires a physical meaning of a probability density only during those partial timeintervals in which the flux den sity j(x,t) does keep its sign. Therefore, let us introduce the two measures, by separating the positive and the 2Such a condition is enough for operator (1a,b) to be a “maximal hermi tian” (or “maximal symmetric”) operator [5357,59,60,78,81,82], according to Akhiezer & Glazman’s terminology.
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 236 negative fluxdirection values (i.e., flux signs): W(x,t)dt= (,)d (,)d xt t xt t (4a) with j(x,t)=j(x,t)(j) where (z) is the Heaviside step function. It had been made firstly in [60,65,66]. Actually, one can rewrite the continuity relation (5) for those time intervals, for which j = j+ or j = j– as follows: txj tx ),(),( and txj tx ),(),( (6) (the equalities (6) do formally serve also as a definitions of ),( tx and),(tx ), respectively. Then, one can eventually define the mean value < t(x) > of the time t at which a particle passes through position x (when travelling in only one positive xdirection) , and < t (x) > of the time t at which a particle passes through position x, when travelling in the positive or negative direction, respectively : <t(x)>= dttxj dttxtj ),( ),( = 2 0 0 ),( )],( ˆ ),(),( ˆ ),([ 2 1 ExGdEv ExGtExvGExvGtExGdE (7a) where G (x,E) is the Fouriertransform of the moving onedimensional (1D) wave packet (x,t) = 0 G(x,E)exp(–iEt/ ) dE = 0 g(E) (x,E)exp(–iEt/ )dE (8) when going on from the time representation to the en ergy one, <t (x)> = (,) (,) tjxtdt jxtdt , (7b) and also the mean durations of particle 1D transmission from xi to xf > xi and 1D particle reflection from the region (xi , ) into xf xi : < T (xi , xf)> = <t+ (xf)> – <t+ (xi)> and < R (xi , xf)> = <t– (xf)> – <t+ (xi)> , (7c) respectively. Of course, it is possible to pass in Eq.7b also to integrals 0 ...dE , similarly to (7a) and (8) by using the unique Fourier (Laplace)  transformations and the energy expansion of j(x,t)=j(x,t)( j), but it is evi dent that they result to be rather bulky. The generalization for the threedimensional motions is given in [82]. Now, one can see that two canonically conjugate op erators, the time operator (1) and the energy operator in the energy (E) representation, ˆ E Eit in the time (t) representation (9) satisfy the typical commutation relation [E ˆ,t ˆ]= i . (10) Although up to now according to the Stone and von Neumann theorem [88] the relation (10) has been inter preted as holding only for the pair of the selfadjoint canonically conjugate operators, in both representations, and it was not directly generalized for maximal hermitian operators, the difficulty of such direct generalization has in fact been bypassed by introducing t ˆwith the help of the singlevalued Fourier(Laplace)transformation from the taxis (– < t < ) to the Esemiaxis (0 < E < ) and by utilizing the peculiar mathematical properties of maximal hermitian operators. Actually, from Eq.10 the uncertainty relation E t /2 (11) (where the standard deviations are a = Da, quantity Da being the variance Da=<a2> – <a>2; and a=E, t , while <...> denotes an average over t by the measures W(x,t)dt or W (x,t)dt in the trepresentation or an aver age over E similar to the righthandpart of (7a) and (8) in the Erepresentation) was derived by the simple gen eralizing of the similar procedures which are standard in the case of selfadjoint canonically conjugate quantities. Moreover, relation (10) satisfies the Dirac “correspon dence principle”, since the classical Poisson brackets {q0 , p0}, with q0=t and p0= –E , are equal to unity [89]. In [57] (see also [59]) it was also shown that the differ ences between the mean times at which a wavepacket passes through a pair of points obey the Ehrenfest cor respondence principle; in other words, in [57,59] the Ehrenfest theorem was suitably generalized. After what precedes, one can state that, for systems with continuous energy spectra, the mathematical prop erties of the maximal hermitian operators (described, in particular, in [57,59]), like t ˆ in Eq.1, are sufficient for considering them as quantum observables: Namely, the uniqueness of the “spectral decomposition” (also called spectral function) for operators t ˆ, as well as for t ˆn (n>1) guarantees (although such an expansion is not
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 237 orthogonal) the equivalence of the mean values of any analytic functions of time, evaluated either in the t or in the Erepresentations. In other words, the existence of this expansion is equivalent to a completeness relation for the (formal) eigen functions of t ˆn (n1), corre sponding with any accuracy to real eigen values of the continuous spectrum; such eigen functions belonging to the space of the square integrable functions of the energy E with the boundary conditions like (2)(3) (see details in [81,82]). From this point of view, there is no practical differ ence between selfadjoint and maximal hermitian op erators for systems with continuous energy spectra. Time as a quantum observable in quantum mechanics for systems with discrete spectra. For systems with dis crete energy spectra it is natural (following [59,81,82]) to introduce wave packets of the form (x,t) = ... 0n gn n(x)exp[–i( n – 0 )t/ ] (12) (where n(x) are orthogonal and normalized wave func tions of system bound states which satisfy equation n(x) = n n(x), being the system Hamiltonian; ... 0n gn2 = 1; here we factually omitted a nonsignificant phase factor exp(–i 0 t/ ) as being general for all terms of the sum ... 0n ) for describing the evolution of systems in the regions of the purely discrete spectrum. Without limiting the generality, we choose moment t = 0 as an initial time instant. Firstly, we shall consider those systems, whose energy levels are spaced with distances for which the maximal common divisor is factually existing. Examples of such systems are harmonic oscillator, particle in a rigid box and spherical spinning top. For these systems the wave packet (12) is a periodic function of time with the period (Poincaré cycle time) T = 2 /D, D being the maximal common divisor of distances between system energy level. In the trepresentation the relevant energy operator is a selfadjoint operator acting in the space of periodical functions whereas the function t (t) does not belong to the same space. In the space of periodical functions the time operator t ˆ, even in the eigen representation, has to be also a periodical function of time t. This situation is quite similar to the case of azimuth momentum , ca nonically conjugated to angular momentum L (see, for instance, [90,91]). Utilizing the example and result from [92], let us choose, instead of t, a periodical function t ˆ= t – no (t–[2n+1] /2) + no (–t–[2n+1] /2) (13) which is the socalled sawfunction of t (see Figure 1). This choice is convenient because the periodical func tion of time operator (13) is linear function (one direc tional) within each Poincaré interval, i.e. time conserves its flowing and its usual meaning of an order parameter for the system evolution. The commutation relation of the selfadjoint energy and time operators acquires in this case (discrete ener gies and periodical functions) the form: [E ˆ,t ˆ] = i {1– 0n (t–[2n+1] )}. (14) Let us recall (see, e.g. [92]) that a generalized form of uncertainty relation holds ( A)2 ( B)2 2[ <N> ]2 (15) for two selfadjoint operators ˆ and ˆ, canonically conjugate each to other by the commutator [ ˆ,B ˆ]=i N ˆ, (16) N ˆ being a third selfadjoint operator. One can easily obtain ( E)2 ( t)2 2 [1 –2 /2 2 /2 (/2 ) ()tdt ] , (17) where the parameter (with an arbitrary value between – /2 and + /2 ) is introduced for the univocality of cal culating the integral on right part of (17) over dt in the limits from – /2 to + /2, just similarly to the procedure introduced in [90] (see also [92]). From (17) it follows that when E0 (i.e. when gn nn’) the right part of (17) tends to zero since  (t)2 tends to a constant. In this case the distribution of time instants of wavepacket passing through point x in the Figure 1. The periodical sawtooth function for time operator in the case of (13).
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 238 limits of one Poincaré cycle becomes uniform. When E>>D and  ( + )2 << T–1 /2 2 /2 ()dtt , the periodicity condition may be inessential for t << , i.e. (17) passes to uncertainty relation (11), which is just the same one as for systems with continuous spectra. One can also obtain the expression for the time op erator (13) in energy representation [59,82]. In general cases, for excited states of nuclei, atoms and molecules, level distances in discrete spectra have not strictly defined the maximal common divisor and hence they have not the strictly defined time of the Poincaré cycle. And also there is no strictly defined passage from the discrete part of the spectrum to the continuous part. Nevertheless, even for those systems one can introduce an approximate description (and with any desired degree of the accuracy within the chosen maximal limit of the level width, let us say, lim) by quasicycles with quasiperiodical evolution and for suf ficiently long intervals of time the motion inside such systems (however, less than / lim) one can consider as a periodical motion also with any desired accuracy. For them one can choose (define) a time of the Poincare’ cycle with any desired accuracy, including in one cycle as many quasicycles as it is necessary for demanded accuracy. Then, with the same accuracy the quasi selfadjoint time operator (13) can be introduced and all time characteristics can be defined. In the degenerate case when at the state (12) the sum 0n contains only one term (gn nn’), the evolution is absent and the time of the Poincare’ cycle is equal for mally to infinity. For systems with continuous and discrete regions of the energy spectrum, one uses both forms: (1) for the continuous energy spectrum and (13) for the discrete energy spectrum. As a concluding remark, it is possible to state that the mathematical properties of tand tn (n>1) are quite enough for considering time as a quan tummechanical observable (like for energy, momentum, spatial coordinates,...) without having to introduce any new physical postulates. Time analysis of quantum processes, based on time operator. Let us limit ourselves here by only some known results and perspectives: 1) Now there are certain foundations to accept [81,82] that energytime uncertainty relations (11) with (17) can help to attenuate endless debates on their interpretation, originated in [44,45]. 2) Time analysis of the motion of the nonrelativistic particles and photons revealed not only the similarity in the motion of particles and photons [9395] (see also [66(2 and 3),78,81,82]) but did also brought to the in troduction of the maximal hermitian time operator for quantum electrodynamics (at least, for the 1D photon motion [78, 81,82]). 3) There are already known two measures of averag ing on time in quantum mechanics. Earlier it was re ported on the first measure which is related with the par ticle passing through space point or interval (volume). The second measure is related with the particle accumu lation or dwelling (or sojourning) inside the limited space interval (volume) during passing through it (it is described, in particular in reviews [78,81,82]). 4) Actually, the time operator (1) has been rather fruitfully used in the case of the tunnelling times and, generally, in the time analysis of tunnelling processes. It had established that practically all earlier known par ticular tunnelling times appear to be the special cases of the mean tunnelling time or of the square root of the variance in the tunnellingtime distribution (or pass into them under some boundary conditions), defined within the general quantummechanical approach. It had been carried out in some reviews (in particular, in [78,81,82], see also [96]). Then, a lot of other interesting results concerning time behaviour of tunnelling particles and photons inside a barrier had been revealed, including the experimental revealing of the superluminal group ve locities of tunnelling photons [9799]. It is meaningful to stress also that, although any direct classical limit for particle tunnelling through potential barrier with subbarrier energies is really absent, there is the direct classical limit for the wavepacket tunnelling. Let us recall real evanescent and antievanescent waves, wellknown in classical optics and in classical acoustics (as it was, for instance, mentioned in [78 (conclusions IV and V)] and, in a more detailed manner, in [82 (con clusion 4)]). 5) An actual perspective for the nearest future is opened for generalizing the time analysis of quantum processes for more complicated particle and photon mo tions (for instance, such as along helixes and motions through twodimensional and threedimensional (in cluding nonspherical) potential barriers etc). 6) Similar derivations and conclusions with quite evi dent generalization can be carried out for time operator in relativistic quantum mechanics (the KleinGordon case and the Dirac case). It is rather perspective (but, of course, not always simple) to develop the analysis of fourposition operators for other relativistic cases, especially to analyze the localization problems. A review of the preliminary results on this topic is already appeared [100]. 7. MORE DETAILED COMMENTS ON THE COMPLEX OF PROBLEMS CONNECTED WITH THE ORIGIN OF THE BIOLOGIC LIFE Now let us analyze, in a condensed way, one of the great
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 239 natural problems marked in [13] – the problem of the reductionism of biology to physics (including, first of all, the problem of the physical and chemical explanation of the origin of the biologic life). Explanation of the origin of the biologic life in terms of physics and, in general, of natural sciences (chemistry etc., including also mathematics) there is a problem of the origin of the genetics, genetic code (or at least a small set of several codes) which is unique for all the terrestrial biosphere, and the defense mechanisms for the defense of the organism development during cell repro duction,… there is an inevitable choice (dilemma): eith er a natural event (or process) like a certain jump which is similar to some kind of phase transition (or like to syn ergetic process, or even like the irrational manyworld interpretation), or a supreme intelligent design of a su perhuman creative basis (or a Creator). Any attempt of the natural origin is failed. And not only because the selforigin of only one selfreproducing cell has not a scientifically reliable explanation in the limits of modern physics (the probability of the chance formation of the protein configuration, containing still 500 nucleotides, is extremely small, i.e. near 1/10950, аnd for the cell formation it is necessary at least 250 different proteins). There are no scientific explanations yet even for the following facts and no answers for the following problems: How a numerous quantity of the chemical reactions could take place in a very limited space volume for cre ate one protein molecule? How there were created the conditions, which were necessary for uniting some components and at the same time were unfavorable for uniting other components, and how then the successive creation of a protein (or RNA or DNA) molecule can happen? If even a principal possibility of the formation of the simplest protein components (DNA) had been shown in the known Oparin, Miller (etc ) experiments under the special laboratory conditions, all the same it is very re mote from the conditions of the primordial earth or of the unstable cosmos. So, no terrestrial or cosmic origin of cells (moreover, with the genetic structure) are im possible! And how one can explain that a) The genetic information in the DNA can be read only by the specific ferments, for the creation of which the special information is also coded in the DNA. b) The biochemical process of the protein synthesis is the most complicated process between all known bio chemical processes in the cell, and also some protein is already necessary for the protein production. Then, the genetic code is beforehand required for the information transfer from the DNA to the protein, and such code is almost universal for the whole terrestrial biosphere. c) And finally, the genetic code has the vitally neces sary control system, which is, in its turn, is coded in the DNA. It is impossible to explain all these facts in the natural way. d) And how one (or almost one) main genetic code for the whole terrestrial biosphere had been originated? Nobody could elaborate somehow working model of the origin of even one selfreproducing cell yet. The first main part of this problem of the origin con sists in the absence of the answer to the following ques tion: how had been originated the conditions, which are vitally necessary for living systems now, during that time when the life had been absent but which are created by only living systems! So, it is absolutely unclear: what had been earlier – habitat with is necessary for the life, or the living organisms in the medium which had not supported the life. The second main part of this problem consists in the mystery of the origin of the enormous quantity of the coded genetic information. Finally, there is no doubt that the whole terrestrial biosphere is a wonderfully balanced ecosystem of the irreducible complexity and integrity. The interaction of all its components (flora, fauna, microorganisms and habitat) is such that the disappearance of even if one of them will bring to the disappearance of the whole bio sphere. So, it is not surprising that during the last ten (or somewhat more) years the number of scientific papers dedicated to the critics of the natural evolutional biologic and prebiologic theories has become to increase [101104]. There some, may be, naturalists who do still hope that certain synergetic processes can initiate the selforganization of the nonliving matter into the living organisms. But now it is known (see, for instance, [105]) that all concrete macroscopic systems with known his tory of their origin, which are more highly ordered than their environment, were created not by rare occasional fluctuations, but under the direct influence of external forces or as a result of bifurcations caused by some nonlinearity and external forces in the open systems. Moreover, I.Prigogine denied that revealed by him processes of local decreasing of entropy can explain the origin of the alive from the nonalive [106]: “The point is that in a nonisolated system there exists a possibility for formation of ordered, lowentropy structures at sufficiently low temperatures. This ordering principle is responsible for the appearance of ordered structures such as crystals as well as for the phenomena of phase transitions. Unfortunately this principle cannot explain the formation of biological structures.” Returning to the direct analysis of the problem of the reductionism of biology to physics in the narrow sense (“if the biology (at least molecular biology and genetics) can be totally explained in terms of physics (and chem
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 240 istry)”), I can recommend to pay a particular attention to the discussion on the special problem of the principal possibility of the explanation of the cell selfreproduction in terms of quantum mechanics, initiated by E.Wigner [107], then continued by M.Eigen [18] and afterwards analyzed by M.V.Vol’kenstein [109]. Firstly, E.Wigner had simply demonstrated that really in the stochastic quantummechanical description the process of the cell selfreproduction cannot be explained by quantum me chanics. Then M.Eigen had shown that the possibility of the cell selfreproduction can be explained by quantum mechanics if and only if the evolution matrix (the Smatrix of the process) is specially instructed for this aim. Further M.V.Vol’kenstein in his analytic review [109] had expressed his expectation that M.Eigen in his future study of the prebiologic evolution can find the possibility of such special instruction. But up to now nobody had revealed such possibility! As to me, I can see only a certain similarity (of course, partial) between two kinds of processes (with are more intellectual than naturalistic, by the way): between the process of the hu man writing of certain scientific files in modern computer devices and the process of the supremeIntelligencedesign writing of certain genetic programs (including the ge netic program of the cell reproduction) in cells of alive organisms. 8. MORE DETAILED COMMENTS ON THE COMPLEX OF PROBLEMS CONNECTED WITH THE UNIVERSE ORIGIN 1) Earlier, after Enlightenment till approximately 1920, scientists in the natural sciences did usually consider the Universe as eternally existing and eternally moving. Now the most convincing arguments against the model of the eternally existing Universe are: а) the second law of thermodynamics which does in evitably bring to the heat death of the Universe, b) the observed cosmic microwave background . The most surprising conclusion of the revealed non stationary state of the Universe is the existence of the “beginning”, under which the majority of physicists un derstand the beginning of the Universe expansion. The cosmologic problem as the problem of the origin and evolution of the Universe has initiated to be ana lyzed by A.Einstein (after 1917) and now it is connected with papers of many other physicists. The first several authors had been G.Lemaître (who proposed what be came known as the Big Bang theory of the origin of the Universe, although he called it his “hypothesis of the primeval atom”), A.Friedman and G.Gamow. And what namely had been in the “beginning”? Ga mow had assumed in 1921 that the expansion had initi ated from the supercondensed hot state as a result of the Big Bang, to which he and others had ascribed the time moment t = 0, i.e. the beginning of the Universe history. The initial state in this model is postulated. However, the nature of the initial supercondensed hot Universe state is not known. Such initial point (or supersmall region), in which the temperature, pressure, energy density etc had reached the anomalous huge (almost infinite) values, can be considered as a particular point, where The “physical” processes cannot be described by physical equations and in fact are excluded from the model analysis. Strictly speaking, namely in the region of this point (from t = 0 till t0 = 10–44 sec, where t0 is the Planck time) is arising the general problem of the world origin and also the choice dilemma: the beginning of the Uni verse formation from vacuum (“nothing”) is either a result of the irrational randomness after passing from other spacetime dimensions or from other universe, caused by some unknown process, or a result of the creation of the expanding Universe (together with the laws of its functioning) by the supreme intelligent design from nigilo. The framework for the standard cosmologic model re lies on Albert Einstein’s general relativity and on sim plifying assumptions (such as homogeneity and isotropy of space). There are even nonstandard alternative mod els. Now there are many supporters of Big Bang models. The number of papers and books on standard and nonstandard versions of the cosmologic Big Bang mod els is too enormous for citing in this not very large paper (it is possible to indicate, only for instance, [110113] for initial reading in cosmology of the Universe and in the different quasiclassical and quantum approaches in cosmology for description of the creation and the initial expansion of the Universe). However, there is no wellsupported model describing the action prior to 10−15 seconds or so. Apparently a new unified theory of quantum gravitation is needed to break this barrier. Un derstanding this earliest of eras in the history of the Universe is currently one of the greatest unsolved prob lems in physics. Moreover, it is worth to underline that many physi cists consider that the second law of thermodynamics is universal for all closed systems, including also our Uni verse as a whole (which is closed in naturalistic one world view). Therefore the heat death is inevitable (see, for instance, [13] and especially [114]). Finally, today a lot of attention of researchers is dedicated to the prob lems of the hypothesis of dark mass and of dark energy. 2) From 1973 (and particularly after eighties) the term “anthropic principle”, introduced by B.Carter, has be come to acquire in the science and out of the science a certain popularity [115,116]. Carter and other authors had been noted that physical constants must have values in the very narrow interval in order the existence of the biologic life can become possible, and that the measured
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 241 values of these constants are really found in this interval. In other words, the Universe seems to be exactly such as it is necessary for the origin of the life. If physical con stants would be even slightly other, then the life could be impossible. After meeting such testimonies, a number of scientists had formulated several interpretations of anthropic prin ciple each of which brings the researchers to the world view choice in its peculiar way. We shall consider here two of them. According to the weak anthropic principle (WAP), the observed values of physical and cosmological constants caused by the necessary demand that the regions, where the organic life would be developed, ought to be possible. And in the context of WAP there is the possibility of choice between two alternatives: 1) Either someone does irrationally believe that there are possible an infinity of universes, in the past, in the present and in the future, and we exist and are sure in the existence of our Universe namely because the unique combination of its parameters and properties could per mit our origin and existence. 2) Or someone does (also irrationally) believe that our unique Universe is created by Intelligent Design of a Creator (or God) and the human being is also created by Creator in order to govern the Universe. According to the strong anthropic principle (SAP), the Universe has to have such properties which permit earlier or later the development of life. This form of the anthropic principle does not only state that the universe properties are limited by the narrow set of values, com patible with the development of the human life, but does also state that this limitation is necessary for such pur pose. So, one can interpret such tuning of the universe parameters as the testimony of the supreme intelligent design of a certain creative basis. There is also a rather unexpected interpretation of SAP, connected with the eastern philosophy, but it is not widely known. 9. CONCLUSIONS It is proposed firstly a novel division of the different classes of natural sciences (and in some degree of all sciences) with different objects and paradigms: a) the entirely natural sciences, b) the natural sciences with the essential role of the human factor, or with the human intelligent design, in their objects and c) the sciences, implicated in the origin and the subsequent history of such natural “metasystems” as the whole Universe and the whole (terrestrial) biosphere. Several reasons caused here to formulate a new retro spective view of the science history (especially in the field of natural sciences) in XXXXI: Firstly, under the influence of scientific and technological progress it has been intensified such direction of the science philosophy as the scientific realism (i.e. the correspondence of the science to the reality), which has in turn changed three forms: from the naïve realism to the usual realism and then to the critical scientific realism (the last one had been developed under the strong influence of sharp dis cussions in quantum mechanics). Secondly, some big problems of physics and natural sciences a) sharp prob lems and paradoxes revealed in the development of quantum mechanics and quantum theory of measure ments, b) a huge complex of the problems connected with the Universe origin and the expansion after the Big Bang, c) the open problem of the origin of the biological life) have been gradually concentrated the attention of the researchers, if not scientifically but at least philoso phically, to those problems as to the grand or great prob lems. And thirdly, the analysis of mathematics in differ ent sciences, beginning from physics, shows that mathematics did now become the branch of the natural sciences (namely of theoretical physics) and in fact gen erated the final solution of the old problem of time as a quantum observable. The interpretation questions in the considered here grand and great problems of natural sciences are practi cally inevitably connected with the worldviews of the researchers. Therefore, it is quite clear that the strong divergences in the various interpretations and even para digms of various researchers, especially relating to these grand and great open problems, can be caused by the incompatibility of their worldviews. Such phenomena, as 1) the enhancement of the phi losophy of the critical scientific realism, 2) the problems, the paradoxes and the variety of interpretations in quan tum theory, 3) the open problems of origin of the Uni verse and 4) the unresolved problem of the origin of the biosphere, 5) the clear extension of the role of mathe matics in physics and other sciences, 6) the competition of various interpretations and even of the worldviews of researchers in the study of the great and grand problems, are the important peculiarities of the history of natural sciences in XXXXI, which in many respects define and predetermine the further science history. REFERENCES [1] Boyd, R. (1983) On the current status of the issue of scientific realism. Erkenntnis, 4550. [2] Bird, A. (1998) Philosophy of science, UCL Press, Montreal, McGillQueen’s University Press, London, 124. [3] Niiniluotto, I. (2002) Critical scientific realism. Oxford University. Press. [4] Quine, W.V.O. (1968) Ontological Relativity. Journal of Philosophy, LXV, 7, 185212. [5] Polkinghorne, J. (1991) Reason, and Reality, The Rela
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 242 tionship Between Science and Theology, Trinity Press Internat, Philadelphia. [6] McGrath, A.I. (2004) The science of God, TT Clark International, London, 139152. [7] Kuhn, T.S. (1962; 2nd edition, 1970; 3rd edition, 1996) The Structure of Scientific Revolutions, University of Chicago Press, Chicago, IL. [8] Einstein, A. (1944) Remarks on Russel’s theory of knowledge, Philosophy of Bertrand Russel, Schlipp, A., Muschalek, H., Ed. (1950, 2nd ed.) Dio e gli scienziati [Translation in Italian from German (Original title: Gottbekenntnisse moderner Naturforscher) by Valeria Cremona ], Alba: Paoline, , 421, 3031. [9] von Wolfgang Sartorius von Waltershausen (1856, repr. 1965) Gauss zum Gedächtniss, Sändig Reprint Verlag H. R. Wohlwend. http://www.amazon.de/GaussGedächtnisWolfgangSart oriusWaltershausen/dp/3253017028 http://en.wikipedia.org/wiki/Mathematics. von Wolfgang Sartorius von Waltershausen (Autor) [10] Popper, K.R. (1995) In Search of a Better World: Lec tures and Essays “On knowledge”, from Thirty Years. Routledge. [11] Bogolyubov, N.N., Medvedev, B.V. and Polivanov, M.K. Ed., Dispersion relations, transactions Problems of mod ern Physics, N2 [in Russian: Боголюбов Н.Н., Медведев Б.В., and Поливанов М.К. (редакторы), (1957) Дисперсионные соотношения, ст атьи в сб. Проблемы современной физики, 2 ]; Arnold V.I., What is mathe matics?, Moscow, MCNMOpress < 3 [in Russian: Арнольд В.И., Что такое математика? М., издво МЦНМО, 2008, стр.3]. [12] Galilei, G. (1623) II Saggiatore (in Italian) (Rome) [13] Ginzburg, V.L. (1999) What problems of physics and astrophysics seem now to be especially important and interesting (30 years later, already on the verge of XXI century), Physics – Uspekhi, 42, 353272; (2002) On some advances in physics and astronomy over the past 3 years, 45, 205211. [14] Einstein, A., Podolsky, B. and Rosen, N. (1935) Can QuantumMechanical Description of Physical Reality be Considered Complete? Physical Review, 47, 777780. [15] Bohm, D. (1952) A Suggested Interpretation of the Quantum Theory in Terms of “Hidden Variables” I, Physical Review, 85, 66179; (1952) A Suggested Inter pretation of the Quantum Theory in Terms of “Hidden Variables” II, Physical Review, 85, 80193; Bohm,D., Aharonov, Y. (1957) Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky, Physi cal Review, 108, 10701076; Aharonov, Y. and Bohm D., (1959) Significance of electromagnetic potentials in the quantum theory. Physical Review, 115 , 485491; Bohm, D. and Aharonov, Y. (1960) Further discussion of possi ble experimental tests for the paradox of einstein, Podol sky and Rosen, N.C. 17, 964; Aharonov, Y. and Bohm D. (1962) Remarks on the possibility of quantum electro dynamics without potentials, Physical Review, 125, 192; Aharonov, Y. and Bohm D. (1963) Further discussion of the role of electromagnetic potentials in the quantum theory. Physical Review, 130, 1625. [16] Bell, J.S. (1964) On the EinsteinPodolskyRosen paradox. Physics, 195200 [Bell, J.S. (1965)On the Ein steinPoldolskyRosen paradox, Physics 1, 195200] ,Bell, J.S, (1987) Speakable and unspeakable in quantum me chanics. Cambridge University Press. [17] Pais, A. (1979) Einstein and the quantum theory. Reviews of Modern Physics, 51, 863914. [18] Popper, K. (1982) A critical note on the greatest days of quantum theory. Foundations of Physics, 12, 971976. [19] Holland, P.R. (1993) The quantum theory of motion: an account of the de brogliebohm causal interpretation of quantum mechanics. Cambridge University Press, Cam bridge. [20] Mermin, N.D. (1993) Hidden variables and the two theorems of john bell. Reviews of Modern Physics, 65, 803815. [21] Paty, M. (1995) The nature of Einstein’s objections to the copenhagen interpretation of quantum mechanics. Found. Phys., 25, 183204. [22] Dürr, D., Goldstein, S. and Zanghì, N. (1997) Bohmian Mechanics and the Meaning of the Wave Function, in Cohen, R.S., Horne, M., and Stachel, J., Eds., Experimental Metaphysics — Quantum Mechanical Studies for Abner Shimony, 1; Boston Studies in the Philosophy of Science,193, Boston: Kluwer Academic Publishers; Dürr, D. (2001) Bohmsche mechanik als grundlage der quantenmechanik. SpringerVerlag. Berlin [23] Hardy, L. (1993) Nonlocality for 2 particles without inequalities for almost all entangled states. Physical Re view Letters, 71, 16651668; Sakurai, J.J. (1994) Modern Quantum Mechanics. AddisonWesley, USA, (see 174 187, 223232). [24] Vaidman, L. (1994) Teleportation of quantum states. Physical Review, A, 49, 14731476. [25] Brassard, G., Braunstein, S., and Cleve, R. (1998) Teleportation as a quantum computation. Physical D, 120, 4347. [26] Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Wein furter, H., and Zeilinger, A. (1997) Experimental quan tum teleportation. Nature, 390(6660), 575579. [27] Boschi, D., Branca, S., De Martini, F., Hardy, L. and Popescu, S. (1998) Experimental realization of teleporting an unknown pure quantum state via dual classical and EinsteinPodolskyRosen channels, Physical Review Letter, 80(6), 11211125. [28] Kilin, S.Y. (2001) Quanta and information, Progress in optics, 42, 190. [29] Riebe, M., Häffner, H., Roos, C. F., Hänsel, W., Ruth, M., Benhelm, J., Lancaster, G. T., Körber, T. W., Becher, C., SchmidtKaler, F., James, D.F.V., and Blatt, R., (2004) Deterministic quantum teleportation with atoms. Nature, 429, 734737. [30] Ursin, R., et al. (2004) Quantum teleportation link across the danube. Nature, 430, 849. [31] Olmschenk, S., et al. (2009) Quantum teleportation be tween distant matter qubits. Science, 323, 486. [32] Everett, H. (1957) Relative State Formulation of quantum mechanics. Review of Modern Physics, 29, 454462. [33] De Witt, B.S.M. (1970) Quantum mechanics and reality. Physics Today, 23, 3035. [34] Everett, H. (1973) The theory of the universal wave function. De Witt, B. and Graham, N. Eds., The ManyWorlds Interpretation of Quantum Mechanics, Princeton NJ: Princeton University Press.
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 243 [35] Deutsch, D. (1986) Three experimental implications of the Everett interpretation, in Penrose, R. and Isham, C.J., Ed., Quantum Concepts of Space and Time, The Clarendon Press, Oxford, 204214. [36] Tipler, D. (1986) The manyworlds interpretation of quantum mechanics in quantum cosmology. in Penrose, R. and Isham, C.J. Eds., Quantum Concepts of Space and Time, The Clarendon Press, Oxford, 204214. [37] Albert, D. and Loewer, B. (1988) Interpreting the many worlds interpretation. Synthese, 77, 195213. [38] Barvinsky, A.O. and Kamenshchik, A.Y. (1995) Preferred basis in quantum theory and the problem of class icalization of the quantum universe. Physical Review D, 52, 743757. [39] Deutsch, D. (1996) The fabric of reality, The Penguin Press, New York. [40] Lockwood, M., Brown, H.R., Butterfield, J., Deutsch, D., Loewer, B., Papineau, D. and Saunders, S. (1996) Sy mposium: The “many minds” interpretation of quantum theory. British Journal for the Philosophy of Science, 47, 159248. [41] Barrett, J.A. (1999) The quantum mechanics of minds and worlds. Oxford: University Press. [42] Zeh, H.D. (1970) On the interpretation of measurement in quantum theory. Foundations of Physics, 1, 6976; Zeh, H.D. (1973) Toward a quantum theory of observation. Foundations of Physics, 3, 109116. [43] Pauli, W. (1926) in: Handbuch der Physik, 5(1), 60, ed. by Fluegge, S. (Berlin),; see also: Pauli, W. General prin ciples of quantum theory. (Springer; Berlin, 1980). [44] Aharonov, Y. and Bohm, D. (1961) Time in the quantum theory and the uncertainty relation for time and energy, Physical Review, 122, 16491658; Aharonov, Y. and Bohm, D. (1964) Answer to fock concerning the time energy indeterminacy relation. Physical Review B, 134, 14171418. [45] Krylov, N.S. and Fock, V.A. (1947) On two main inter pretations of energytime uncertainty. Sov. J. Zhetf, 17, 9399; Fock, V.A. (1962) On the energytime uncertainty and on an attempt to refute it. Sov. J. Zhetf, 42, 11351140. [46] Paul, H. (1962) Über quantenmechanische Zeitoper atoren. Annalen der Physik, 9, 252261. [47] Engelman, F. and Fick, E. (1963) Quantentheorie der Zeitmessung. Zeitschrift für Physikalische A, 175, 271 282; (1964) Quantentheorie der ZeitmessungII. Zeits chrift für Physikalische A, 178, 551562. [48] Lippmann, B.A., (1966) Operator for time delay induced by scattering. Physical Review, 151, 10231024. [49] Razavy, M. (1969) Quantummechanical conjugate to the Hamiltonian operator. Nuovo Cimento, B, 63, 271308. [50] Gien, T.T., (1969) On the operators for time of motion and delay time induced by scattering. Can. Journal of Physics, 47, 278289; (1970) Delay time and phase of the initial state. Canadian Journal of Physics, 48, 639652. [51] Allcock, G.R. (1969) The time of arrival in quantum mechanics. Annals of Physics (N.Y.), 53, 253285. [52] Rosenbaum, D.M. (1969) Super hilbert space and the quantummechanical time operators. Journal of Mathe matical Physics, 10, 11271144. [53] Olkhovsky, V.S. and Recami, E. (1968) Spacetime shifts and cross sections in collisions between relativistic wane packets. Nuovo Cimento, A53, 610624; (1969) About collisionprocess lifetimes and causality. Nuovo Cimento A, 63, 814826; (1970) About a spacetime operator in collision descriptions. Nuovo Cimento, 4, 11651173. [54] Olkhovsky, V.S. (1973) On the problem of time operator and collision duration, Ukrainskiy Fiz. Zhurnal [in Ukrainian and Russian], 18, 19101913; Olkhovsky, V.S., Recami, E. and Gerasimchuk, A.I. (1974) Time operator in quantum mechanics – nonrelativistic case. Nuovo Cimento A, 22, 263278. [55] Recami, E. (1977) A time operator and the timeenergy uncertainty relation. in The Uncertainty Principle and Foundation of Quantum Mechanics (J.Wiley; London), 2128; “An operator for observable time”, in Proceeding of the XIII Winter School in Theor. Physics, (Wroclaw; 1976), 2, 251256. [56] Holevo, A.S. (1978) Estimation of shift parameters of a quantum state. Re Math. Phys., 13, 379399; Holevo, A.S. (1982) Probabilistic and statistical aspects of quantum theory, Amsterdam. [57] Olkhovsky, V.S. (1984) To the investigation of nuclear reactions and decays by analysis of their durations. Soviet Journal Nuclear Physics, 15, 130148. [58] Jaworski, W. and Wardlaw, D.M. (1988) Time delay in tunneling: Transmission and reflection time delays. Physical Review A, 37, 28432854. [59] Olkhovsky, V.S. (1990) Nonstationary characteristics in study of nuclear reaction mechanism and kinetics and compoundnucleus properties. Nukleonika, 35, 99144; (1992) Time analysis of nuclear collisions and decays. Atti Accademia Peloritana dei Pericolanti, Sci. Mat. Nat. 70, 2140; (1998) in Mysteries, Puzzles and Paradoxes in Quantum Mechanics, Bonifacio, R. Ed., (AIP Conference Proceeding, Amer. Institute of Physics, Woodbury, NY, USA), 272276. [60] Olkhovsky, V.S. and Recami, E. (1992) Recent develop ments in the time analysis of tunnelling processes. Phys ics Reports, 214, 339356; Olkhovsky, V.S., Recami, E., Raciti, F. and Zaichenko, A.K. (1995) More about tun nelling times, the dwell time and the Hartman effect. Journal de Physique, (France) I, 5, 13511365. [61] Busch, Grabowski, M. and Lahti, J. (1994) Time observ ables in quantum theory. Physics Letters A, 191, 357361. [62] Kobe, D.H. and AguileraNavarro, V.C., (1994) Deriva tion of the energytime uncertainty relation. Physical Re view A, 50, 933938. [63] Blanchard, and Jadczyk, A. (1996) Timeof events in quantum theory. Helvetica Physica Acta, 69, 613635. [64] Grot, N., Rovelli, C. and Tate, R.S. (1996) Time of arri val in quantum mechanics. Physical Review A, 54, 46764690. [65] Olkhovsky, V.S. and Agresti, A. (1997) Developments in time analysis of particle and photon tunnelling, in pro ceeding of the adriatico research conference on tunnel ling and its implications (World Sci.; Singapore), 327355. [66] Olkhovsky, V.S. (1997) Time analysis of particles and photons. Physics of the Alive, 5, 1937; (1998) Develop ments in examining time as a quantumphysical observ able. Physics of the Alive, 6, 1729; Olkhovsky, V. S. (19981999) Recent developments on time as a quantumphysical observable, Atti dell’Academia di
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 244 Pericolanti, classe di scienze fis. mat. e natur., Universita’ di Messina, v.LXXVILXXVII, 193209. [67] Leo’n, J. (1997) Timeofarrival formalism for the relativistic particle. Journal of Physics A, 30, 47914801. [68] Giannitrapani, R. (1997) Positiveoperatorvalued time observable in quantum mechanics. International Journal of Theoretical Physics, 36, 15751584. [69] Aharonov, Y., Oppenheim, J., Popescu, S., Reznik, B. and Unruh, W. (1998) Measurement of time of arrival in quantum mechanics. Physical Review A, 57, 41304139. [70] Atmanspacher, H. and Amann, A. (1998) Positive operatorvalued measures and projectionvalued measures of noncommutative time operators. International Journal of Theoretical Physics, 37, 629660. [71] Toller, M. (1999) Localization of events in spacetime. Physical Review A, 59, 960970. [72] Kijowski, J. (1999) Comment on “arrival time in quan tum mechanics” and “time of arrival in quantum me chanics”. Physical Review A, 59, 897899. [73] Delgado, V. (1999) Quantum probability distribution of arrival times and probability current density. Physical Review A, 59, 10101020. [74] Muga, J., Papao, J. and Leavens, C. (1999) Arrival time distributions and perfect absorption in classical and quantum mechanics. Physics Letters A, 253, 2127. [75] Kochànski, and Wòdkievicz, K. (1999) Operational time of arrival in quantum phase space. Physical Review A, 60, 26892699. [76] Kobe, D.H., Iwamoto, H., Goto, M. and AguileraNavarro, V.C., (2001) Tunneling time through a barrier using the local value of a “time operator”. Physical Review A, 64, Article ID 022104, 8. [77] Muga, J., Egusquiza, I., Damborenea, J. and Delgado, V. (2002) Bounds and enhancements for negative scattering time delays. Physical Review A, 66, Article ID 042115, 8 pages. [78] Olkhovsky, V.S., Recami, E. and Jakiel, J. (2004) Unified time analysis of photon and particle tunneling. Physical Review, 398, 133178. [79] Góźdź A. and Dębicki M. (2007) Time operator and quantum projection evolution. Physics of Atomic Nucle, 70, 529536. [80] Wang, Z.Y. and Xiong, C.D. (2007) How to introduce time operator. Annals of Physics, 322, 23042314. [81] Olkhovsky, V.S. and Recami, E. (2007) Time as a quan tum observable. International Journal of Modern Physics A, 22, 50635087; Olkhovsky, V.S. and Recami, E. (2008) New developments in the study of time as a quantum observable. International Journal of Modern Physics B, 22, 18771897. [82] Olkhovsky, V.S. (2009) Time as a quantum observable, canonically conjugated to energy, and foundations of selfconsistent time analysis of quantum processes. Ad vances in Theoretical and Mathematical Physics, 2009, аrticle ID 859710, 83. [83] Naimark, M.A. (1940) Spectral functions of a symmetric operators. Izvestiya Akademii Nauk SSSR, seriya mate maticheskaya [in Russian, partially in English], 4, 277318; we stress that it is used here the Carleman type of the spectral function of (a maximal and not only maximal ) symmetrical operator, which was cited from the reference [Carleman, T. (1923) Sur les e’quations i’ntegrales a’ noyau re’el et syme’trque (Uppsala)] and was utilized as a tool of the proof, based on the approxi mation of the (maximal and not only maximal) symmet ric operator H by such succession of the bounded selfadjoint operators, the spectral functions the spectral functions of which do weakly converge to the spectral function E ( ) of the operator H (This circumstance was kindly indicated to the author by Holevo, A.S.). [84] Aharonov, Y. and Bohm, D. (1961) Time in the quantum theory and the uncertainty relation for time and energy. Physical Review, 122, 16491658. [85] Naimark, M.A. (1943) Positive definite operator func tions on a commutative group, Izvestiya Akademii Nauk SSSR. seriya matematikcheskaya, 7, 237244. [86] Akhiezer, N.I. and Glazman, I.M. (1981) The Theory of Linear Operators in Hilbert Space, Pitman; Boston, Mass. [87] Neuman, J. (1932) von, Mathematischen Grundlagen del Quantum Mechanik (Hizzel, Leipzig). [88] Stone, M.H. (1930) Proceeding Nat. Acad. Sci. USA, 16, N1. [89] ter Haar, D. (1971) Elements of hamiltonian mechanics, Oxford. [90] Judge, D. and Levis, J.L. (1963) On the commutator [L z , ].Physics Letters, 5, 190195. [91] Carruthers and Nieto, M.M. (1968) Phase and angle variables in quantum mechanics. Reviews of Modern Physics, 40, 411440. [92] Davydov, A.S. (1976) (1982) Quantum Mechanics (Per gamon, Oxford). [93] Chiao, R.Y., Kwiat, G. and Steinberg, A.M. (1991) Analogies between electron and photon tunneling: A proposed experiment to measure photon tunneling times. Physica B, 175, 257262. [94] Martin, T. and Landauer, R. (1992) Time delay of eva nescent electromagnetic waves and the analogy to parti cle tunneling. Physical Review, A45, 26112617. [95] Steinberg A.M. (1995) Conditional probabilities in quantum theory, and the tunneling time controversy. Physical Review A, 52, 3242. [96] Abolhasani, M. and Golshani, M. (2000) Tunneling times in the Copenhagen interpretation of quantum mechanics. Physical Review A, 62, 012106, 7. [97] Enders, A. and Nimtz, G. (1992) On superluminal barrier traversal, Journal of PhysicsI (France), 2, 16931698; (1993) Zerotime tunneling of evanescent mode packets. Journal of PhysicsI (France), 3, 10891092; (1993) Photonictunneling experiments. Physical Review B, 47, 96059609; (1993) Evanescentmode propagation and quantum tunneling. Physical Review E, 48, 632634; G.Nimtz, in: (1997) Tunneling and its applications. World Scientific,Singapore, 223237. [98] Steinberg, A.M., Kwiat, G. and Chiao, R.Y. (1993) Meas urement of the singlephoton tunneling time. Physical Re view Letter, 71, 708711; Chiao, R.Y., Kwiat G., and Steinberg, A.M. (1993) Faster Than Light? Scient.Am., 269, 3852; Chiao, R.Y. and Steinberg, A.M. (1997) Tunneling times and superluminality, in progress in op tics, by Wolf, E., Ed., 37, Elsevier Sci., Amsterdam, 346405. [99] Longhi, S., et al. (2002) Measurements of superluminal optical tunneling times in doublebarrier photonic band
V. S. Olkhovsky / Natural Science 2 (2010) 228245 Copyright © 2010 SciRes. OPEN ACCESS 245 gaps. Physical Review E, 65, 046610. [100] Recami, E., Olkhovsky, V.S. and Maydanyuk, S.P. (2010) On nonselfadjoint operators for observables in quantum mechanics and quantum field theory. accepted and to be published in Internat. International Journal of Modern Physics A. [101] Macnab, R. (1978) Bacterial motility and chemotaxis  molecularbiology of a behavioral system. CRC Critical Reviews in Biochemistry, 5, 291341; Moorhead, S. and Kaplan, M.M. Ed. (1967) Mathematical challenges to the neodarwinian interpretation of evolution. Wistar Insti tute Press ,Philadelphia. [102] Behe, M.J. (1996) Darwin’s Black Box. The biochemical challenge to evolution, the Free Press. [103] Junker, R. and Scherer, S. Evolution: Ein kritisches Lehrbuch, 4th ed. Giessen (Germany): Weyel Verlag, 1998; 5th ed. Giessen (Germany): Weyel Verlag, 2001; 6th ed. Giessen (Germany), Weyel Verlag, 2006. [104] Olkhovsky, V.S. (2001) Comparison of the faith postu lates in evolutionism and creationism with respect to modern scientific data. Physics of the Alive, 9, 108121. [105] Prigogine, I. and Stengers, I. (1984) Order out of chaos. man’s new dialogue with nature, Heinemann, London; Nicolis, G. and Prigogine, I. Exploring complexity, Free man, W. and Co, N.Y.,1989. [106] Prigogine, I., Nicolis, G. and Babloyants, A. (1972) Thermodynamics of evolution. Physics Today, 25, 23. [107] Symmetries and reflections, scientific essays of Eugen Wigner, Indiana University Press, Bloomington–London, 1970; essay 11 (“The possibility of existence of a self reproducing system”). [108] Eigen, M. (1971) Selforganization of matter and the evolution of biological macromolecules. Naturwiss, 58, 465523. [109] Vol’kenstein, M.V. (1973) Physics and biology. Soviet Physics Uspekhi, 16, 207216; see also: Vol’kenstein, M.V. (1988) Complementarity, physics and biology. So viet Physics Uspekhi, 31, 140150. [110] Hartle, J.B. and Hawking, S.W. (1983) Wave function of the Universe. Physical Review D, 28, 29602975. [111] Vilenkin, A. (1994) Approaches to quantum cosmology. Physical Review D, 50, 25812594. [112] Kragh, H. (1996) Cosmology and controversy, Princeton (NJ), Princeton University Press. [113] Peacock, J. (1999) Cosmological physics, Cambridge University Press. [114] Adams, F.C. and Laughlin, G. (1997) A dying universe: the longterm fate and evolution of astrophysical objects. Reviews of Modern Physics, 69, 337372. [115] Carter, B. (1974) Large number coincidences and the anthropic principle in cosmology. IAU Symposium 63: Confrontation of Cosmological Theories with Observa tional Data, Dordrecht, Reidel. [116] Barrow, J.D. and Tipler, F.J. (1986) The anthropic cos mological principle. Clarendon Press, Oxford.
