Vol.2, No.3, 228-245 (2010) Natural Science
Copyright © 2010 SciRes. OPEN ACCESS
A retrospective view on the history of natural sciences
Vladislav Sergeyevich Olkhovsky
Institute for Nuclear Research, Kiev, Ukraine; olkhovsky@mail.ru
Received 1 December 2009; revised 8 January 2010; accepted 30 January 2010.
The presented paper is dedicated to a new ret-
rospective view on the history of natural sci-
ences in XX-XXI 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 wave-function col-
lapse; the Einstein-Podolsky-Rosen 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
In the science history and in the science philosophy of
ХХ-XXI (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-
stein-Podolsky-Rosen 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
world-views 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
re-considering 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 long-standing problem of time in quantum mechan-
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) 228-245
Copyright © 2010 SciRes. OPEN ACCESS
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-
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
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
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-
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 non-uniform 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, pre-quantum!) science:
those essences, the existence of which are postulated by
the well-supported 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) 228-245
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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
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 (non-quantum) physics, revealed that on the micro-
scopic level there is the un-removable indeterminism,
represented by the uncertainty relations of Heisenberg, by
the essential non-locality of the particle-waves (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 wave-function 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 Einstein-Podolsky-Rosen 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.
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
(arte-facts) 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 self-organization 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 super-human creative basis (or
a Creator).
And in these three classes of sciences with the differ-
ent research objects now there are co-existing 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-
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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 last-life 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,
hypothetico-deductive: 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 XX-XXI 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 S-matrix in the complex
plane of energies (momenta) [11, the first reference]).
Finally, namely mathematics generated the solution of the
long-standing problem of time as a quantum observable,
canonically conjugated to energy, and self-consistent time
analysis of quantum processes.
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 non-relativistic
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 wave-function reduction and the Einstein-Podolsky-
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.
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-
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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, [14-22]).
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
yet-undiscovered 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 [23-31]. 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 super-dense coding.
In 1964 J.Bell had shown that many theories, known as
hidden variable theories, are either non-local 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
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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 many-world
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 phd-thesis 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 [32-41].
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 in-determined 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
non-interacting 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 quantum-mechanical
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 in-deterministic for
human observers.
The MWI exhibits some kind of non-locality: “world”
is a non-local 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 de-coherence, 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
One can add here that the still inherent incompatibility
of the postulates of quantum theory as non-local theory
and relativity theory (both special and general) as local
theory is the main root of the impossibility to construct
the self-consistent relativistic quantum mechanics, qu-
antum field theory and the quantum cosmology even in
quasi-linear approximation.
Another long incompleteness of non-relativistic 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.
Introduction to the history of the problem. During almost
ninety years (see, for example, [43]) it is known that
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time cannot be represented by a self-adjoint 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, [46-82], 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 [54-60]. The second set of papers on time
as an observable in quantum physics [61-82] appeared
from the end of the eighties and chiefly in the nineties
and more recently, stimulated mainly by the need of a
self-consistent 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. [54-60]. This Naimark
theorem states [83] that the non-orthogonal 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 self-adjoint 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 [54-59] (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-
tum-mechanical observable, canonically conjugate to en-
ergy. More precisely, the time operator resulted to be
maximal hermitian, even if not self-adjoint. 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 quantum-mechanical observable, canonically conjugate
to energy, and the time operator resulted to be
quasi-self-adjoint (more precisely, it can be chosen as an
almost self-adjoint operator with practically almost any
degree of the accuracy).
We have also to note that there is known in the litera-
ture the so-called positive-operator-value-measure (POVM)
approach, often used in the second set of papers on time
in quantum physics (for instance, in [61-64, 67-77,79,80].
This approach, in general, is well-known 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 time-operator problem in the case
of the free motion already in [84]. Then, in [61-64,
67-77,79,80] (often with certain simpli- fications and
abbreviations) it was affirmed that the generalized de-
composition of unity (or POV measures) is reproduced
from any self-adjoint extension of the time operator into
the space of the extended Hilbert space (usually, with
negative values of energy E in the left semi-axis) 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 [54-57,59,60] earlier than [61-64,67-77,
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 [73-77,79,80], 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
in the (time) t-representation, (1a)
in the (energy) E-representation (1b)
which is not self-adjoint, but is hermitian , and acts on
square-integrable space-time wavepackets in representa-
tion (1a), and on their Fourier-transforms in representa-
tion (1b), once the point E=0 is eliminated (i.e. , once
one deals only with moving packets, i.e., excludes any
non-moving back tails, as well as, of course, the zero
flux cases)2. It has been shown already in [54-57,59,60].
The elimination of the point E=0 is not restrictive since
the “rest” states with the zero velocity, the wave-packets
with non -moving rear tails, and the wave-packets with
zero flux are unobservable.
Operator (1b) is defined as acting on the space P of
the continuous, differentiable, square-integrable func-
tions f (E) that satisfy the conditions
1Namely that fact that time cannot be represented by a self-adjoint
operator is known to follow from the semi-boundedness 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
V. S. Olkhovsky / Natural Science 2 (2010) 228-245
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0| ()|2 d fE E
0()fE EdE
 
0| ()|2 2 d fE E E
(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 semi-axis 0E< .
Obviously, the operator (1a,b) is hermitian, i.e. the
relation (f1, t
ˆf2) = ((t
ˆf1), f2) holds, only if all
square-integrable 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)) =
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
self-adjoint 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 semi-axis (0 x < ) bounded
by a rigid wall located at x = 0. Consequently, the
operator for the momentum x- component of the particle,
which reads
is defined as acting on the space of the continuous,
differentiable, square-integrable functions f (x) that
satisfy the conditions
|f (x)|2dx < , 0
|f (x) / x|2dx < ,
|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 semi-axis
0x<. Therefore, operator ˆx
has the same
mathematical properties as operator t
ˆ (1a,b) and con-
sequently it is not a self-adjoint 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
(0 < r < ).
By the way, one can easily demonstrate (see, for
instance, [47]) that in the case of (hypotetical)
quantum-mechanical systems with the continuous energy
spectra bounded from below and from above
(Emin<E<Emax) the time operator (1a,b) becomes a really
self-adjoint 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 self-consistent way, the measure (or
weight) of averaging over time. In the simple
one-dimensional (1D) and one-directional motion such
measure (weight) can be obtained by the simple quan-
W(x,t)dt = (,)d
, (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 x-direction..
Such a measure had not been postulated, but is just a
direct consequence of the well-known probabilistic (spa-
tial) interpretation of
(x, t) and of the continuity rela-
(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-
ity-density j(x,t) are related with the wave function
(x,t) by the usual definitions
(x,t)|2 and j(x,t) =
Re [
*(x,t) (
(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 time-intervals 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 [53-57,59,60,78,81,82],
according to Akhiezer & Glazman’s terminology.
V. S. Olkhovsky / Natural Science 2 (2010) 228-245
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negative flux-direction values (i.e., flux signs):
W(x,t)dt= (,)d
xt t
xt t
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 = jas follows:
 ),(),(
 ),(),(
(the equalities (6) do formally serve also as a definitions
of ),( 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 x-direction) , and
< t (x) > of the time t at which a particle passes through
position x, when travelling in the positive or negative
direction, respectively :
ExGtExvGExvGtExGdE (7a)
where G (x,E) is the Fourier-transform of the moving
one-dimensional (1D) wave packet
(x,t) =
) dE
)dE (8)
when going on from the time representation to the en-
ergy one,
<t (x)> =
, (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
, 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 three-dimensional 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,
in the time (t-) representation
satisfy the typical commutation relation
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 self-adjoint
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 by-passed by introducing t
ˆwith the help of
the single-valued Fourier(Laplace)-transformation from
the t-axis (– < t < ) to the E-semi-axis (0 < E < ) and
by utilizing the peculiar mathematical properties of
maximal hermitian operators.
Actually, from Eq.10 the uncertainty relation
/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 t-representation or an aver-
age over E similar to the right-hand-part of (7a) and (8)
in the E-representation) was derived by the simple gen-
eralizing of the similar procedures which are standard in
the case of self-adjoint 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 wave-packet
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
(n>1) guarantees (although such an expansion is not
V. S. Olkhovsky / Natural Science 2 (2010) 228-245
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orthogonal) the equivalence of the mean values of any
analytic functions of time, evaluated either in the t- or in
the E-representations. 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 self-adjoint 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) =
0 )t/
] (12)
n(x) are orthogonal and normalized wave func-
tions of system bound states which satisfy equation
n(x) =
being the system Hamiltonian;
|gn|2 = 1; here we factually omitted a non-significant
phase factor exp(–i
0 t/
) as being general for all terms
of the sum
) 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
In the t-representation the relevant energy operator
is a self-adjoint 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
(see, for
instance, [90,91]). Utilizing the example and result from
[92], let us choose, instead of t, a periodical function
ˆ= t –
/2) (13)
which is the so-called saw-function 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 self-adjoint energy
and time operators acquires in this case (discrete ener-
gies and periodical functions) the form:
ˆ] = i
)}. (14)
Let us recall (see, e.g. [92]) that a generalized form of
uncertainty relation holds
A)2 (
2[ <N> ]2 (15)
for two self-adjoint operators
ˆ and
ˆ, canonically
conjugate each to other by the commutator
ˆ, (16)
ˆ being a third self-adjoint operator. One can easily
E)2 (
2 [1 –2
|(/2 )|
] , (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
nn’) the right part of (17) tends to zero since |
tends to a constant. In this case the distribution of time
instants of wavepacket passing through point x in the
Figure 1. The periodical saw-tooth function for time
operator in the case of (13).
V. S. Olkhovsky / Natural Science 2 (2010) 228-245
Copyright © 2010 SciRes. OPEN ACCESS
limits of one Poincaré cycle becomes uniform. When
E>>D and |
)|2 << T–1
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
quasi-cycles with quasi-periodical 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 quasi-cycles as it is necessary for demanded
accuracy. Then, with the same accuracy the quasi-
self-adjoint time operator (13) can be introduced and all
time characteristics can be defined.
In the degenerate case when at the state (12) the sum
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
(n>1) are quite enough for considering time as a quan-
tum-mechanical 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 energy-time 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 non-relativistic
particles and photons revealed not only the similarity in
the motion of particles and photons [93-95] (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 tunnelling-time distribution (or pass into
them under some boundary conditions), defined within
the general quantum-mechanical 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 [97-99].
It is meaningful to stress also that, although any direct
classical limit for particle tunnelling through potential
barrier with sub-barrier energies is really absent, there is
the direct classical limit for the wave-packet tunnelling.
Let us recall real evanescent and anti-evanescent waves,
well-known 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 two-dimensional and three-dimensional (in-
cluding non-spherical) 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 Klein-Gordon case
and the Dirac case). It is rather perspective (but, of course,
not always simple) to develop the analysis of four-position
operators for other relativistic cases, especially to analyze
the localization problems. A review of the preliminary
results on this topic is already appeared [100].
Now let us analyze, in a condensed way, one of the great
V. S. Olkhovsky / Natural Science 2 (2010) 228-245
Copyright © 2010 SciRes. OPEN ACCESS
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-
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 many-world
interpretation), or a supreme intelligent design of a su-
per-human creative basis (or a Creator).
Any attempt of the natural origin is failed. And not
only because the self-origin of only one self-reproducing
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
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-
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
It is impossible to explain all these facts in the natural
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 self-reproducing 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 eco-system of the
irreducible complexity and integrity. The interaction of
all its components (flora, fauna, micro-organisms and
habitat) is such that the disappearance of even if one of
them will bring to the disappearance of the whole bio-
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 pre-biologic theories has become to increase
There some, may be, naturalists who do still hope that
certain synergetic processes can initiate the
self-organization of the non-living 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
non-linearity 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 non-alive [106]: “The point
is that in a non-isolated system there exists a possibility
for formation of ordered, low-entropy 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) 228-245
Copyright © 2010 SciRes. OPEN ACCESS
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 self-reproduction
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
quantum-mechanical description the process of the cell
self-reproduction cannot be explained by quantum me-
chanics. Then M.Eigen had shown that the possibility of
the cell self-reproduction can be explained by quantum
mechanics if and only if the evolution matrix (the
S-matrix 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 pre-biologic 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 supreme-Intelligence-design
writing of certain genetic programs (including the ge-
netic program of the cell reproduction) in cells of alive
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 super-condensed 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 super-condensed hot Universe state
is not known. Such initial point (or super-small 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
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 space-time 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 non-standard alternative mod-
els. Now there are many supporters of Big Bang models.
The number of papers and books on standard and
non-standard 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, [110-113] for
initial reading in cosmology of the Universe and in the
different quasi-classical and quantum approaches in
cosmology for description of the creation and the initial
expansion of the Universe). However, there is no
well-supported model describing the action prior to 1015
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, to-day 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) 228-245
Copyright © 2010 SciRes. OPEN ACCESS
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
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.
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 “meta-systems” 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 XX-XXI: 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 world-views 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 world-views.
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 XX-XXI, which in many respects define and
pre-determine the further science history.
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