Reality in Science, Philosophy, and Theology
 
 
 
 

Faculty of Mathematics and Science, Cardinal Stefan Wyszynski University,

Dewajtis 5, 01-815 Warsaw, Poland;

Space Research Centre, Polish Academy of Sciences,

Bartycka 18 A, 00-716 Warsaw, Poland
 
 
 
 

e-mail: macek@cbk.waw.pl

http://www.cbk.waw.pl/~macek
 
 
 

Abstract. The scientific revolution in twentieth century physics and mathematics requires a new metaphysics with an ontology exceeding the classical ontological principles. Classical metaphysics would only be, in a way, an approximation of the new metaphysics, similarly as classical physics is the limiting approximation of quantum physics. This would render possible an opening of philosophy to the mathematical natural sciences, and consequently would admit a better understanding of man, and maybe also of the theology.
 
 
 
 

Presented at International Conference on Theology and Science in Conversation

Comenius University, 31 January - 2 February 2003, Bratislava, Slovakia.
 
 
 
 

1. Introduction

The natural sciences have originated from Platonic-Archimedean tradition. However, since the Middle Ages philosophy and theology have been deeply rooted in the metaphysics of Aristotle, in which the notion of Being satisfies the principles of identity, excluded middle, and noncontradiction. This dichotomy has resulted in the separation of various types of cognition [1,2]. This question has been discussed from a historical perspective in my previous paper [3]. In this talk I would like to focus on a recent history of science during the last century. I will try to convince you that the scientific revolution in twentieth century physics and mathematics requires a new metaphysics. Classical metaphysics would only be an approximation of the new metaphysics. This would render possible an opening of philosophy and possibly of theology to the mathematical natural sciences.

Certainly, in the twentieth century we have a veritable revolution in the natural sciences owing to the foundations of three great physical theories: special relativity, general relativity, and quantum mechanics. Quantum mechanics is modelling the world at very small distances (microphysics), while special and general relativity refer to large velocities (as compared with the speed of light) and strong gravitational fields, respectively. It is still not clear how relativity is related to quantum mechanics.

One should remember that the fundamental question of the interpretation of quantum mechanics, founded at the beginning of the twentieth century, is not yet understood clearly in terms of Reality. Indeed, it was necessary to abandon sensible imaginations. Roughly, we have at least two possible approaches: ontological (the Copenhagen school) and epistemological (genuine statistical) interpretations of the wave functions describing microphysical objects. This question is discussed in Section 2.

It would seem that at least classical physics, describing phenomena at large scales and at velocities small as compared with the velocity of light, remains consistent with our sensible imagination. But also in this field of science we have again a surprising revolution, which is briefly discussed in Section 3. Admittedly, it is true that the classical sensible world contains a multitude of shapes, forms, and structures. According to Aristotle, any conjecture that such a wealth of variety of forms might result from any mathematical ideas would be rather absurd. However, one should remember that the mathematics of antiquity originated in the needs of daily life and was practically limited to Euclidean geometry. From that time mathematics has developed into an immense system of various disciplines. The possibility of a new ontology is considered in Section 4 and main conclusions are given in Section 5.

2. Reality in Modern Physics

For modern physics mathematics is not only the language of these theories, serving as a powerful instrument for our knowledge and mastery of nature, but mathematics has also become the material of the ideal world of these theories. Furthermore, the mathematical structures used by physicists for modelling the world do not have any natural perceptible counterparts. For example, hydrogen atoms or elementary particles (e.g., protons, electrons, neutrinos or photons) are described by the wave functions that are in turn elements of an abstract Hilbert space. What is observed results from a mathematical procedure of the projection of these abstract elements onto certain sub-spaces. It would be difficult to find a better metaphor than Plato's metaphor of shadows seen by prisoners on the wall of the cave. Imagine the objects outside of Plato's cave, or say the statues on the balustrade that are producing shadows in the light of the fireplace. According to Carl F. von Weizsaecker, the German physicist and philosopher, co-founder of quantum mechanics, these statues should be considered as fundamental objects of nature, which are subjects of study of theoretical physics. Hence these statues are real atoms or real elementary particles. But in experiment, which is non-trivial extrapolation of our senses, we can only observe shadows of these true objects, i.e., the properties of the real atoms or the real elementary particles.

Albert Einstein, who preferred a statistical interpretation of the wave function, defended the realism of nature [4,5]. In my view, his concept of hidden parameters, which was formulated in order to save physical reality, was deeply rooted in the common conviction of a simple concept of reality. Consequently, the famous founder of two great relativistic theories and co-founder of quantum mechanics did not believe that quantum mechanics could fully describe the real world. In 1935 Albert Einstein, Boris Podolski, and Natan Rosen formulated a well-known paradox and proposed a local realistic theory of nature [4]. Their reasoning can be summarized as follows. Because no influence of any kind can propagate faster than the speed of light, and assuming that induction is a valid way of reasoning in quantum mechanics, we cannot reconcile two obvious premises: one is realism, phenomena are caused by a physical reality whose existence is independent of human observers, and second is local causality (assuming independence of well separated objects). One cannot reject any of these self-evident truths. Hence one is led to conclude that the description of reality as given by a wave function is not complete.

In 1935 Erwin Schroedinger proposed a famous 'gedanken' experiment, with a metaphor of a cat, which is known as Schroedinger's cat in academic literature. We can think about a photon, i.e., a fundamental unit of light that can behave like either a particle or a wave. According to quantum mechanics the photon can exist in an ambiguous state until a measurement is made. If a particle's property is measured, the photon behaves like a particle, and if a wavelike property is measured, the photon behaves like a wave. In our experiment the photon impinges on a half-silvered mirror. The photon has a probability of, say, one-half of passing through the mirror and a probability of one-half of being reflected. If the photon is reflected we observe its wavelike property (e.g., an interference pattern) and nothing dramatic happens. On the contrary, if the photon passes through the mirror, it is detected by the photodetector in a box. The detection actuates a device that brakes a bottle of cyanide, which in turn kills the cat in the box. Remarkably, due to a certain switch, the photon could not have been informed whether to behave like a particle or like a wave until it is registered. Hence, it cannot be determined whether the cat is dead or alive until the box is opened.

There would be nothing paradoxical in the outcome of this experiment, if the passage of the photon through the mirror were objectively definite but merely unknown prior to observation. However, according to quantum mechanics, the passage of the photon is objectively indefinite, and so is the aliveness of the cat. One may say that the cat is suspended between life and death until it is observed. The conclusion is paradoxical, but still it concerns only the results of a thought experiment. But truly this is not pure speculation. In fact, something similar to Schroedinger's thought experiment has been achieved by a number of groups of investigators in scientific laboratories [6].

3. Reality in Modern Mathematics

I would like to give also just one example from only one of modern mathematical disciplines, topology. In 1883 Georg Cantor, the German mathematician, invented a curious mathematical structure. One can schematically shows how to construct Cantor's set. We start with the closed interval, say of unit length. We divide this interval into three equal parts and remove its open middle third, i.e., we delete the interval (1/3, 2/3) and necessarily leave the endpoints behind. This produces the pair of closed intervals, each of length one-third. Then we remove the open middle thirds of those two remaining intervals to produce four closed intervals, each of length one-ninth, and so on; we repeat this procedure an infinite number of times.

The limiting set is the Cantor set, called also the Cantor dust [7]. It is difficult to visualize, but one can notice that this dust consists of an infinite number of infinitesimal pieces, separated by gaps of various sizes. The total length of all intervals removed is equal to the length of the initial interval. Thus, the remaining length must be zero. Therefore, in the Cantor set the number of points is obviously infinite but its total length is zero. Even more paradoxically, one can demonstrate that elements of the Cantor set may be placed in a one-to-one correspondence with the elements of the initial interval of length one (real numbers). It can be proved that the number of elements of the Cantor dust (of length zero) is exactly the same as the number of elements of the full interval (of length one). One may say that 'nothing is full of everything'. Therefore, this mathematical structure is so curious that it has even been considered pathological. Extension of the above to the two-dimensional case of a square (or triangle) was done by the Polish mathematician Waclaw Sierpinski, in 1916, and his construction is known as the Sierpinski carpet (or gasket).

Recently, owing to the works of Benoit B. Mandelbrot, we know that such mathematical curiosities, abstract as they seem, have now found a place in the study of dynamic systems. Mandelbrot coined the name fractal from the Latin adjective fractus (means fragmented, divided into irregular fragments) [8]. He has also codified and popularized fractals. Naturally, the Cantor set is an example of a fractal. The fractals are very useful to describe the complicated structure of objects in the real world such as clouds, mountains, coastlines, and the bark of trees. In 1971 David Ruelle and Floris Takens proposed a new theory for the onset of turbulence in fluids, based on abstract considerations about so-called strange attractors. Due to the development of nonlinear dynamics, we are now convinced that the strange attractors that have fractal structure can be applied to a description of various complex phenomena in nature, such as convection in the atmosphere (weather prediction), earthquake prediction, chemical reactions, electronic circuits, fluctuations of the populations of animals in biology, ecosystems, mechanical and biological nonlinear oscillations, especially circadian (roughly 24-hour) rhythms, heart rhythms and fibrillations, and even epilepsy [7]. Finally, it is worth noting that complexity is derived from simple mathematical rules, and not from a variety of causes; fractals are convenient measures of complex reality.

Incidentally, scientists are now commonly convinced that there is One simple law at the base of all complex phenomena in nature; all the Universe is subject to this unique law. Hence the multiplicity and complexity of laws are illusionary. The new physics is continuously searching for such a fundamental principle from which the other laws should be derived. In a way, in contemporary physics the aesthetic criterion becomes an epistemological criterion of truth. The only problem is that we can never be sure as to whether there exists a mathematical structure which is even more beautiful than those that have already been found.

4. Possibility of a New Ontology

One may look at the Einstein-Podolski-Rosen paradox also from the point of view of believing in the principle of noncontradiction. And this was probably the justification of the Einstein's objections, which was expressed in his celebrated letter to Max Born: You believe in a God who plays dice, and I in complete law and order. Admittedly, Einstein had not seriously taken into consideration that there are two well-justified approaches to the problem of Reality. One approach tries to defend the principle of noncontradiction. In this case quantum-mechanics cannot be fully true, or at least quantum-mechanical description of physical reality cannot be considered complete. On the other hand, there is the other possibility defended by Niels Bohr, Werner Heisenberg and many others (the Copenhagen interpretation) [5]. The basis of Bohr's criticism was that Einstein's use of induction was unwarranted. Consequently, quantum-mechanical description is true and complete [4]. One may also say that the principle of noncontradiction is not valid in microphysics. Simply because so strange is the nature of the quantum world. Paradoxically, many laboratory tests show that Einstein was altogether likely wrong; the bizarre nature of the quantum world must be accepted, in spite of a lack of nourishment for sensible imagination. Notwithstanding the variety of ways of understanding this difficult problem [6], there is no doubt that quantum mechanics requires a new philosophical concept of existence of objects in nature, and even a new dynamic concept of Being.

In the near future we can expect even more paradoxical concepts referring to the notion of existence. For example, scientists are continuously trying to unify the physical theories, including quantum physics and relativity. However, in attempts of quantisation of spacetime there arises the question of the existence of physical objects in space and time. Maybe one should rather speak about 'quanta of existence', which is not compatible with changeless Being.

It also seems to me that science and, in particular, physics are surprisingly well consistent with the dynamic Platonic-Augustinian concept of Being. Therefore, physics can help, or at least be a good adviser, in the search for a new ontology. Naturally, one should also appreciate the Aristotelian-Thomist approach. I feel that nowadays St. Thomas would not follow exactly any static philosophical vision elaborated before the actual foundations of science. After all, his intention was an opening of theology and philosophy to the knowledge of nature that was acquired during his times, in order to provide rational bases for faith. We ought to follow his attitude, though taking also into account signs of our times. Naturally, this is not possible without the opening of thought to the most important ideas and achievements of the twentieth century.

In addition, in both Augustinian and Thomist approaches faith was not at variance with intellect. This demonstrates that science, philosophy, and theology need to be neither in conflict nor in separation. However, one should not necessarily identify the concept of intellect with common sense, which could be very misleading, as it has often happened in the history of science. Under this condition this new ontology must not be irrational, notwithstanding some strangeness for our senses and inconsistency with the two-valued logic. Surely, we have already know that such a logic does not work at the level of microphysics. Therefore, we cannot expect and demand that it should be obligatory at the ontological level. I hope that the new ontology will open new horizons with the perspectives that have not been available up till now. This would render possible a better understanding of nature, man as a person with his existential problems and social relations, history of mankind, and maybe even a better intuition of Trinitarian dynamics in the theology of God.

To summarize, at present there is good evidence that the bizarre nature of reality must be accepted. Because of the wave-particle duality, it is not anymore possible to limit our thoughts to a static concept of Being, which satisfies the fundamental classical ontological principles of excluded middle and noncontradiction. In the language of philosophy we could even say that at the level of the microworld Being is dynamic: Being is and is not.

5. Conclusions

If we do not like to continue philosophical and theological studies in separation from science, then classic metaphysics should open its thought to the most important ideas and achievements of the mathematical natural sciences. In particular, twentieth century physics requires a new metaphysics with ontology exceeding the classical ontological principles. The classical metaphysics should only be a limiting approximation of the new metaphysics.

The way of the limiting implication would probably be analogical just as quantum physics and relativistic physics would be the limiting cases of the new fundamental physical theory, containing both quantum and relativistic physics. Similarly as is in the case of classical physics describing the world of the senses, which in turn is the limiting approximation of quantum physics.

I hope that this dynamic concept of Being will shed light on the nature of the Universe, with man in his existential and historical dimensions, and maybe even will render possible a better intuition of God.

References

[1] Heller M., New Physics and New Theology, Biblos, Tarnow, 1992 (in Polish).

[2] Pedersen O., Historical interaction between science and religion, in: Science and Religion:

    One World - Changing Perspectives on Reality,  ed. J. Fennema et al., Kluwer Academic Publishers,

    Dordrecht, 1990, pp. 139-160.

[3] Macek, W. M., On being and non-being in science, philosophy, and theology, in Proceedings of

    Seminar on Interpretations of Reality: a Dialogue among Theology and Sciences, 16-17 April 1999,

    Pontifical Lateran University, Quaderni Sefir, Rome, Italy, eds. P. Coda, R. Presilla, pp. 119-132.

[4] Einstein A., Podolski B., Rosen N., Can quantum-mechanical description of physical reality be

    considered complete?, Physical Review, 47, 777-780, 1935.

[5] Bohr, N., Can quantum-mechanical description of physical reality be considered complete?,

    Physical Review, 48, 696-702, 1935.

[6] Espagnat B. d', In Search of Reality, Springer-Verlag, New York - Berlin, 1983.

[7] Stewart I., Does God Play Dice?: The New Mathematics of Chaos, Penguin Books, 1990.

[8] Mandelbrot B. B., The Fractal Geometry of Nature, Freeman, San Francisco, 1982.