\begin{elementlit}
{Andrey A. Grib}
{\autor[*\dagger]{\hspace{-1ex}Andrey A. \kapit{Grib}}
\afiliacja[*]{Herzen Russian State Pedagogical University, St. Petersburg}
\aafiliacja[\dagger]{Copernicus Center for Interdisciplinary Studies, Cracow}
}
{Modern Cosmology}
{Modern Cosmology and the Problem of the Beginning of the Universe}
{Współczesna kosmologia i problem początku wszechświata}
\index{Grib, A.A.}
\oDef{\oGellMann}{Gell-Mann}{Gell-Mann, M.} % Murray, amerykański fizyk teoretyk, laureat nagrody Nobla w dziedzinie fizyki z 1969 roku
\oDef{\oEverett}{Everett}{Everett, H.} % Hugh Everett (1930-1982), amerykański fizyk, który opracował kwantową teorię wielu światów
\oDef{\oCoulomb}{Coulomb}{Coulomb de, C.A.} % Charles Augustin de (1736-1806), francuski fizyk, od którego nazwiska pochodzi prawo Coulomba i jednostka ładunku elektrycznego
\oDef{\oLandau}{Landau}{Landau, L.D.} % Lev Davidovich [Ле́в Дави́дович Ланда́у] (1908-1968), fizyk rosyjski, laureat nagrody Nobla z fizyki za teorie materii skondensowanej
\oDef{\oLifshitz}{Lifshitz}{Lifshitz, E.M.} % Evgeny Mikhailovich [Евгений Михайлович Лифшиц] (1915-1985), fizyk rosyjski
\oDef{\oKhalatnikov}{Khalatnikov}{Khalatnikov, I.M.} % Isaak Markovich [Исаак Маркович Халатников], fizyk rosyjski
\oDef{\oPoe}{Poe}{Poe, E. A.} % Edgar Allan (1809-1849)
\oDef{\oOlbers}{Olbers}{Olbers, H.W.M.} % Heinrich Wilhelm Matthäus (1758-1840), niemiecki astronom, lekarz i fizyk
\oDef{\oBorde}{Borde}{Borde, A.} % Arvind, kosmolog
\oDef{\oGuth}{Guth}{Guth, A.} % Alan Harvey, amerykański fizyk i kosmolog, twórca teorii inflacji kosmologicznej
\oDef{\oVilenkin}{Vilenkin}{Vilenkin, A.} % Alexander [Алекса́ндр Виле́нкин], fizyk, dyrektor Institute of Cosmology at Tufts University
\oDef{\oTolman}{Tolman}{Tolman, R.C.} % Richard C. (1881-1948), amerykański fizyk, chemik fizyczny i kosmolog
\oDef{\oGeroch}{Geroch}{Geroch, R.} % Robert, fizyk teoretyczny z University of Chicago
\oDef{\oTipler}{Tipler}{Tipler, F.J.} % Frank Jennings, amerykański matematyk, fizyk
\oDef{\oEllis}{Ellis}{Ellis, J.R.} % Jonathan Richard, brytyjski fizyk teoretyczny
\oDef{\oHausdorff}{Hausdorff}{Hausdorff, F.} % Felix, (1868-1942), niemiecki matematyk, jeden z twórców topologii
\oDef{\oBell}{Bell}{Bell, J.S.} % John Stewart, (1928-1990), północno irlandzki fizyk
\oDef{\oEddington}{Eddington}{Eddington, A.S.} % Arthur Stanley, (1882-1944), brytyjski astrofizyk
\oDef{\oBelinsky}{Belinsky}{Belinsky, V.A.} % Vladimir Alekseyevich [Владимир Алексеевич Белинский], rosyjski fizyk teoretyczny, kosmolog
\oDef{\oGodel}{Gödel}{Gödel, K.} % Kurt Friedrich (1906-1978), austriacki logik i matematyk
\oDef{\oTorrance}{Torrance}{Torrance, T.F.} % Thomas Forsyth (1913-2007), szkocki teolog protestancki
\oDef{\oDruskin}{Druskin}{Druskin, Y.S} % Yakov S. [Я́ков Семёнович Дру́скин] (1901-1980), rosyjski filozof i teolog
\oDef{\oZhichinskiy}{Zhichinskiy}{Zhichinskiy, Y. = Życiński, J.} % = Józej Życiński
\oDef{\oFriedmann}{Friedmann}{Friedmann, A.A.} % Aleksandr Aleksandrowicz
\oDef{\oHubble}{Hubble}{Hubble, E.P.} % Edwin Powell (1889-1953)
\oDef{\oLemaitre}{Lemaître}{Lemaître, G.} % Georges Henri Joseph Édouard (1894-1966)
\ooDef{\ooPiusXII}{Pius}{XII}{Pius XII} % Papież w latach 1939-1958
\oDef{\oPenzias}{Penzias}{Penzias, A.} % Arno Allan
\oDef{\oWilson}{Wilson}{Wilson, R.W.} % Robert Woodrow
\oDef{\oEuclid}{Euclid}{Euklides z Aleksandrii}
In this paper we shall discuss the views of modern cosmology regarding
the beginning of the Universe, together with some theological ideas
arising in connection with this. We shall mainly concentrate on those
theories that are based on some physical observations and axioms that
may be said to be more or less established within the scientific
community. One needs of these presupposed theories is \oEinstein[’s] general
relativity, along with the standard \oFriedmann{} model of an expanding
Universe that follows from it.
There is, without doubt, a~great deal of speculation today regarding
both the notion of a~universe without a~beginning and the quantum
origins of the Universe. Some of this makes use of the idea of the wave
function of the Universe, where this is applied in order to achieve
a~quantization of gravity.\footnote{
\cite{Hawking:ABrief}; \cite{Vilenkin:ManyWorlds}.
}
Unfortunately one need only recall the words of the famous American
physicist M.~\oGellMann, uttered on another occasion, but nevertheless
also valid with respect to the status of quantum gravity, to the effect that
“this theory suffers from the disease of nonexistence!”
That is not to say that we would reject all speculation about quantum
gravity: it is quite possible that some of this will survive in future
theories. Nevertheless, it would be premature to discuss today something
not proved either by physical observation or established theory like
quantum physics with its Copenhagen interpretation confirmed by the
sheer number of its physical applications.
The existence of the wave function of the Universe is still a~very
dubious idea, because the main justification for it is found in the
\oEverett{} many-worlds interpretation of quantum physics, which itself
remains highly controversial. What remains unresolved in this
interpretation is not just the notion of probability and actual
occurrence of a~“splitting’ of one universe into many, but also, due to
the unitary character of evolution and its reversibility, that of a~“merging”
of different universes.\footnote{
\cite{Saunders:ManyWorlds}.
}
Non-commutative geometry, which resembles the generalization of the
so-called algebraic formulation of quantum physics, comes closer to the
standard formulation of quantum theory.\footnote{
\cite{Heller:Creative}.
}
The name for the process by which the Universe is thought to have
originated is the ‘Big Bang’. The Universe, as observed by telescopes on
Earth and on various satellites in space, is expanding in time, and this
expansion is observable in the form of the red shift of the spectral
lines of far off Galaxies.
The expansion of the Universe was predicted as a~consequence of
\oEinstein[’s] General Relativity by the Russian scientist Alexandre
Alexandrovich \oFriedmann{} in 1922,\footnote{
\cite{Friedmann:Uber}.
}
and experimentally confirmed in the USA by E.~\oHubble{} in 1929.
In fact, it is the expansion of the space of the Universe,
and this is why the beginning of this expansion marks the
beginning of space and time themselves.
Hence it is not a~beginning that itself occurs “in” time or “in” space.
According to modern observations, the Universe is 13.8 billion years
old. The point (or in some models, surface) of the beginning of time is
referred to as the ‘cosmological singularity’. This expression was
introduced by G.~\oLemaitre{} in 1931.\footnote{
\cite{Lemaitre:TheBeginning}.
}
Singularities resulting from the General Theory of Relativity occur
not only in cosmology, but also inside black holes.
The general property of singularities is that at a~singular point
the time line is cut. It is not that something “in time”
is finished, but rather that in General Relativity --- this being itself
the physics of time --- time itself can disappear… Today we are thus
witnessing the appearance of a~quite new science --- the physics and
mathematics of singularities.
Inside black holes one can have --- depending on their rotation ---
different kinds of singularities: these can be space-like, time-like or
light-like singular surfaces (every point of which is a singular point.)
A~great deal of attention is paid in cosmology both to the singularity
of the past --- i.e. the Big Bang, understood as the Beginning of the
Universe --- and to possible future singularities, such as the Big Crunch
and Big Rip, understood as the end of the Universe. Big Rip would mark
the end in the event of a~too-rapid expansion of the Universe, providing
a~phantom field can exist in Nature. The Big Crunch, on the other hand,
represents the collapse of the Universe.
Right from the moment that the cosmological singularity was discovered,
a~lively discussion has ensued between physicists , philosophers and
theologians, about what it could mean.
Alexandre \oFriedmann, in his book “The world as space and time”,\footnote{
\cite{Friedmann:TheWorld}.
}
has written: “On the basis of a self-evident analogy, let us call the time
interval required for the curvature radius to grow from zero to some R
the time from the creation of the world”.
Meanwhile Pope \ooPiusXII{}{}, who was familiar with astronomy and
remained in close contact with the scientists of the Vatican observatory,
wrote in his encyclical\footnote{
\cite{PiusXII:LeProve}.
}:
“So, with all of the evidence typical of a physical proof,
modern science has confirmed that the existence of the Universe
is not necessary, where this has furnished us with conclusions about
the time when the world arose at the hands of the Creator.”
The official Soviet philosophers --- marxists, in the Soviet Union --- came
to very much the same conclusion as the Pope: a singularity of an expanding
Universe provides an apologia for both idealism and the clergy
(“popovshina”). The result was that university students in the Soviet
Union were not permitted to study relativistic cosmology! At the same
time, it was proclaimed that the Universe is, and must be, eternal in
time and infinite in space.
One must, however, mention that another discoverer of the expanding
Universe, who predicted the red shift of spectral lines as its experimental
consequence, Abbot George \oLemaitre, wrote more tentatively that
“As I~understand it, a~theory of this type stands completely apart
from any metaphysical and religious questions. It leaves the materialist
free to dismiss any transcendent Being: he can adopt the same reasoning
for the depths of space-time as for non-singular points in it. For the
believer, it removes any attempt at closer acquaintance with
God […] corresponding to the words of Isaiah about a~`Hidden God', perhaps?
Hidden, that is, even at the point of Creation itself”.\footnote{
\cite{Lemaitre:LHypothese}.
}
We shall discuss the theological differences between these two contrasting
views --- those of the Pope and of \oLemaitre{} --- in due course.
Even so, one can hardly fail to see the connection between these words
of \oLemaitre{} and his activities in the 1940s and 1950s, when he was
engaged in a search for models of an “eternal” Universe without a~beginning
or an end. And one may also recall the remark of \oEinstein, who
characterized \oLemaitre[’s] idea of a singularity as “a~tribute to his
religious views.”
Does this mean, then, that \oEinstein{} himself had the same view as the
Pope?
And how did cosmology and the discussion of its implications develop
later in the 20$^\textrm{th}$ century?
At first, the majority of physicists thought that the notion of a singularity
implies some sort of incompleteness on the part of General
Relativity --- as with, for example, the \oCoulomb{} potential in
electrodynamics. This potential goes up to infinity at the initial
point, but according to quantum theory some screening effect is supposed
to arise over small distances, which then precludes an infinite value
for the force. Is the situation with a cosmological singularity the
same?
This looked so reasonable that in an early version of the textbook on
theoretical physics of \oLandau{} and \oLifshitz{}\footnote{
\cite{Landau:Field} (1962).
}
it was claimed, on the basis of the work of E.M. \oLifshitz{} and
I.M. \oKhalatnikov{} (which was later proved by the authors to be mistaken),
that the most general anisotropic solution of \oEinstein[’s] equations
consistent with the expansion of the Universe was one that involved
no singularity at all!
However, in the UK in 1965-1967, R. Penrose and S. Hawking proved a
general theorem according to which there must be a singularity involved
in any mathematical model of the Universe that is consistent with
General Relativity that is either isotropic or anisotropic, and that
features both expansion and gravity manifesting itself as attraction!
After this, \oBelinsky[], \oLifshitz[] and \oKhalatnikov[] found a mistake in their
paper, and proved that one has a singularity even in an anisotropic
solution for an expanding Universe. Hence, in more recent editions of
the textbook of \oLandau{} and \oLifshitz{},\footnote{
\cite{Landau:Field2} (1967).
}
everything is correct.
In 1965 the American engineers \oPenzias{} and \oWilson{} discovered
by radar the primordial radiation or “first light” of the Universe, which
is thought to have existed before the originating of the stars
themselves…Today, this light is invisible, as it is in the form of radio
waves. However, in the early Universe it was visible, and the sky was
not dark, so that during the so-called recombination era the whole sky
was shining like a~sun.
Calculating on the basis of observation the density of this radiation,
one can arrive at an important feature of the Universe: the local
density of the entropy of the Universe itself. This turns out to be
finite, and is equal to the ratio of the number of photons of primordial
radiation to the number of protons. This number is equal to one billion.
The finiteness of this value excludes many otherwise quite rationally
intelligible models of a~temporally infinite, “eternal” universe,
because in these one is required to have an infinite “memory” of an
infinite past, equal to the local entropy, which itself must also be
infinite!
Hence it makes more rational sense to think of the Universe as
temporally finite. One may recall here the words of G. \oLemaitre,
that “the Universe is reasonable because it is finite! In a universe
that is infinite in space and time one has the “nightmare” of infinity.
It is impossible to explain anything in it, because for any cause one will
have to look beyond, for a~preceding one, and so on… to infinity”.\footnote{
\cite{Lemaitre:LHypothese}.
}
As it happens, one of the first men to speak about the finiteness of the
Universe was not a~scientist, but the American poet Edgar A.~\oPoe,
who said that “the Universe must have had a beginning in the past,
because the sky at night is dark!”
This is a~popular version of the \oOlbers{} paradox,\footnote{
\cite{Grib:Basic}.
}
which uses only such simple notions as the finiteness of the velocity
of light, of the number of sources, and of the time of its propagation
from source to observer.
The experiments known as COBE, WMAP recently PLANCK, conducted at the end of
the 20$^\textrm{th}$ and beginning of the 21$^\textrm{st}$ centuries, have made
it possible to measure the age of the Universe more precisely: it is close
to 13.8 billion years old. Hence \oFriedmann[’s] expanding universe model
is today simply known as the “standard model”. But what is the situation
today as regards the problem of singularity?
Certain paradoxical implications of the \oFriedmann{} model for the very
early phase of the Universe’s existence --- such as the paradox of
causality (Why do disconnected parts of the Universe have the same
temperature?) and the paradox of flatness (Why is space in the early
Universe so close to \oEuclid[ean] flat space?) --- have led many scientists
to conclude that there must have been another era prior to that of
\oFriedmann{} expansion itself. This is known as the ‘inflation era’, and is
dominated not by matter or light but by so-called ‘dark energy’,
involving a~special inflation field.
During this era gravitation is supposed to have manifested itself not as
attraction but as repulsion. This dark energy is observable even in the
modern era of the \oFriedmann{} Universe itself, over large distances,
but in the inflation era it was far stronger.
So it seems that given the overturning of the attractional character of
gravitation, the \oPenrose-\oHawking{} theorem will not be valid for this
case, and a~path to the embracing of “eternal” universes with inflation
is opened up.
Yet it has also transpired that this is wrong. The American physicists
A.~\oBorde, A.H.~\oGuth{} and A.~\oVilenkin{}\footnote{
\cite{Borde:Inflationary}.
}
have proved a~more general theorem than that of \oPenrose{}
and \oHawking{} to be valid for gravitation as repulsion.
According to this, for any (on average) expanding Universe
with positive energy of matter (weak energy condition), there
must have been a~singularity in the past.
The consequences of this theory are as follows:
1. Cyclic (or oscillating) universes will have to be excluded. The
example of such a~universe first discussed by A.~\oFriedmann{}\footnote{
\cite{Friedmann:TheWorld}.
}
is that which is popular in Indian mythology: before the onset of our expanding
universe there existed some other universe which, after its expansion,
collapsed down to a~small volume --- this then being the beginning of our
universe. One could imagine an infinite number of such universes
following one after another. In order for this to be free of infinite
entropy (memory) one could follow the idea of \oTolman. In spite of the
existence of the collapsing era, in any subsequent universe the
expansion would have to be larger, so that the “average” for cycles’
expansion is not zero. If one takes into account the sequence of cycles,
then one must suppose that the volume of each subsequent universe
increases in time in such a~manner that even though overall entropy
grows, the local entropy obtained by dividing the whole entropy by the
volume always remains finite!
Even so, the theorem cited prohibits an infinite number of such
universes: there must still be a~beginning.
2. Eternal inflation. According to this conception, when inside some
inflationary expanding universe one has a bubble consisting of a~false
vacuum, giving birth to another inflationary universe, so that it then
becomes possible to speculate about the existence of an infinite number
of such universes in the past. The entropy paradox is to be solved,
then, by means of \oTolman-style reasoning. This scenario will also now
be forbidden.\footnote{
\cite{Borde:Inflationary}.
}
This theorem certainly does not exclude temporally finite universes that
are without any singularity, but which involve some version of the idea
of spontaneous quantum origination of the universe in question from
nothing.
This would include the proposals of S.~\oHawking{} and A.~\oVilenkin.
However, as we said earlier, if one is to take these proposals seriously
one must subscribe to the idea of the wave function of the Universe,
along with the \oEverett{} many-universes interpretation of quantum
physics, which is still very far from being confirmed.
What this means, then, is that one must take singularities seriously! It
means that instead of trying to avoid them, one must construe them as
novel features of space-time itself. In conventional space-time, objects
such as tables, trees, etc., are allowed to have “edges”, so why should
we rule out the possibility of some world-lines or regions of space-time
itself “terminating” at certain points or surfaces?
Thanks to the activities of scientists such as \oGeroch, \oTipler, \oHawking,
\oEllis{} and \oPenrose, we can formulate certain conceptions pertaining to
the science of singularities in General Relativity.
A singular point is a point where the curvature tensor (more exactly the
invariant formed from it) is infinite. But such a point cannot be
contained in space-time. Therefore everything in the Universe will have
its beginning in the point of cosmological singularity, but it (i.e. the
singularity itself) will not belong to it! Moreover, this point
corresponding to the Big Bang can be defined mathematically as the set
of all time-like geodesic lines that converge together as one passes
further into the past --- a~set that may be considered to constitute one
object!
Indeed, there is one particularly salient property of this point --- one
that has made it a~topic of discussion amongst both physicists and
theologians. This is the property known as “\oHausdorff{}
non-isolatedness”.\footnote{
\cite{Tipler:ThePhysics}.
}
What this amounts to is that in spite of the fact
that it counts “for us” as located very far in the past --- some 13.8
billions years ago --- “the distance from it to us” is in fact zero!
The point describes a~global property of a~universe containing
a~beginning within itself.
In his popular book \oHawking{}\footnote{
\cite{Hawking:ABrief}.
}
compares the beginning of time with the North Pole.
If somebody asks what lies north of Paris, one can answer
‘London’, if they ask what lies north of London one can say ‘Edinburgh’,
etc. But what lies north of the North Pole? Everything lies to the south
of it. The notion of something being north of the North Pole makes no
sense… Likewise, the notion of “earlier” makes no sense when one is
speaking about the beginning of time itself.
Is that a~complete answer? Within such reflections one thing not taken
into account is the important property of time known as ‘Becoming’.
In both Special and General Relativity there is no Becoming in time;
instead, there is a so-called ‘block universe’ in which time and space
are treated along the same lines. Becoming certainly figures in quantum
physics, though, and, as has been proved by the breaking of the
so-called \oBell[’s] inequalities, it occurs due to measurement.
So the beginning of time, as the beginning of Becoming too, must be
some sort of act!
Can quantum gravity provide some sort of solution to this problem?
To complete our overview of how things stand in modern physics with
respect to the beginning of the Universe, let us offer some additional
remarks about singularities.
It is sometimes said that if the Universe, in the past, was very small,
then it could have had, for example, the size of a~human finger.
But how can one imagine all one hundred billion galaxies, with the same
number of stars as now, compressed into such a~small volume?
Is the density of matter in a~singularity also infinite --- and what could
the physics of all that be like? We have given an answer to this question
in the papers summarized in our book.\footnote{
\cite{Grib:Nonlocality}.
}
There was no infinite density of particles close to the beginning,
because there was no matter in the form of particles at that time.
Particles and galaxies were created from a vacuum later,
by the gravitation of the expanding Universe. There was
an period of particles being created prior to that of the first nuclei
being created, and so on. Today, gravitation is small, and particles are
not created. They will also not be created if the gravitation of the
expanding Universe is very strong, approaching a singularity. But there
is some period during which, from its outset, time has the order of
Compton time, defined by the mass that the particle has once the process
is underway. An observable number of visible particles (the \oEddington{}
number) will be obtained, if super-heavy particles with a~mass of the
order of the Grand Unification scale are created, and these then decay
on visible particles. However, one may also suppose that there was an
inflationary period prior to the era of particle creation, with either
an inflation field or dark energy playing the role of matter. Yet, as
has been shown by V.~\oBelinsky, E.~\oLifshitz{} and
I.~\oKhalatnikov{},\footnote{
\cite{Landau:Field2} (1967).
}
in the general case of anisotropic space-time one can safely ignore the
matter component in \oEinstein[’s] equations, so that a~singularity can even
exist in a~vacuum.
Now it is time to turn to the theological and philosophical discussions
surrounding all of this.
The existence of a cosmological singularity in the past means that the
physical Universe is not “self sufficient”: it cannot be explained using
physical laws derived solely from itself. In a~sense, this is analogous
to \oGodel[’s] theorems in mathematics, showing that mathematics,
or at least the ideal world of mathematics construed as some sort
of formal system, is not self-sufficient.
In a~sense, this is similar to the situation with the existence of
a~person as “me”.
I~am not self-sufficient, because in order to understand myself,
I~must appeal to something external to me.
This can be construed as an apophatic definition of what is meant by the
idea of the Universe being created out of nothing by God. The claim that
“the Universe was created by God” may thus be considered equivalent to
an affirmation of the non-conformity of the Universe to the totality of
its own laws.
Here one may also recall G.~\oLemaitre, and say that a “pessimistic
atheist” could agree with all this, declaring that our Universe is,
unfortunately, not self-sufficient… In opposition to this, though, an
“Optimistic believer” might say that crushing the idol of the
self-consistent Universe leaves one free to pray to the One who is
higher than the Universe itself.
There have also been attempts to arrive at a~cataphatic (i.e. positive)
theological interpretation of the cosmological singularity.
For example, in his books F.~\oTipler{}\footnote{
\cite{Grib:Vacuum}; \cite{Tipler:ThePhysics2}.
}
goes so far as to identify the singularity with God.
Everything in the Universe, including its own laws, is taken to have
originated in the past singularity. As we said earlier, the “distance”
from the singularity to any event in the Universe is zero, even though
the distance from us to it remains large: it is very far away in the sky
(i.e. the astronomical sky) --- some 13.8 billion light years away…. There
has been some theological speculation about the meaning of such notions
as “far”, “close”, “higher”, “heaven” and even “distance” (see the Scottish
theologian T.~\oTorrance{},\footnote{
\cite{Torrance:Space}.
}
and the Russian theologian Y.~\oDruskin) when speaking about the
relation of human beings to God.
These speculations are close to those of \oTipler. One might even recall
Newton’s insistence on God’s use of absolute space in his relation with
us and with everything in the Universe. So, in spite of \oTipler[’s]
critics, there is room for fruitful discussion here.
Nevertheless, one should be careful about this sort of use of
mathematics and its applications to physics. We have already considered
the absence of any notion of “temporal becoming” in General Relativity.
To this one might also then add that singularity is defined as
a~geometrical property --- as a~set of all lines terminating in the past.
This does not mean that besides such lines, it will also contain all the
creatures that happen to be located on these lines. At any rate, this is
by no means clear.
Apart from a~past singularity, there can also be a future singularity ---
constituting the End of the Universe. Even more: one can also speak
about the possibility of a~“present” singularity.
General Relativity opens up the possibility of there being solutions to
\oEinstein[’s] equations that lead to an expanding Universe terminating at
any moment in time, thanks to a “weak singularity”: at any moment in
time, then, time itself can terminate. Such solutions are described as
“incomplete”, in contrast to the typical \oFriedmann{} solutions involving
the Big Bang and Big Crunch, which are said to be “complete”.
This means that the Universe is non-sufficient even in the sense that
it is not evident that it is guaranteed that at any immediately subsequent
moment one will see the same Universe with the same laws and that
it will exist.
Here one may perhaps be tempted to recall the theological idea of
“continuous creation”: God preserves the Universe from annihilation,
“giving being to its being”. And unlike in the English translation, in
the Slavic translation of the Credo from Greek, God is not called
“Almighty” but “Vsederjitel”, i.e. the “All-keeper”. The Universe exists
because it is kept by God.
Summing up, it is worth remembering the words of the Polish theologian
Y.~\oZhichinskiy{},\footnote{
\cite{Zhichinskiy:Nothing}.
}
who referred to theological speculations of the kind
pursued by \oTipler{} as “a mysticism of the singular point”, manifesting
a~theology of a~“God of the gaps”.\footnote{
\cite{Tipler:ThePhysics2}.
}
The apophatic interpretation of the singular point surely seems
preferable, though. Yet this need not mean that no general positive
points can be found in modern discussions of cosmology and theology. In
any case, there is here a point where both sides – physicists and
theologians – are presented with a fine opportunity to engage in
potentially fruitful discussions and disputes.
\bigskip
Acknowledgements. The author is indebted to the Templeton Foundation
for its financial support in connection with the preparation of this paper.
\end{elementlit}