www.jainworld.com |
First Steps To Jainism |
SANCHETI ASOO LAL |
Appendix C: Modern Physics and Syadvada (Part-2) - Dr. D.S. Kothari
This requirement about the uncertainty in momentum makes the position of the plate uncertain. It is given by the Heisenberg indeterminacy principle. But for the production of interference fringes it is necessary that Hence, it is apparent, an apparatus designed to tell us how a photon passes through the two holes cannot in the very nature of the experiment record the interference fringes. The uncertain spread in the position of the plate is far more than the separation between the fringes. The fringes are totally washed out. If the momentum change is (+hv/0), the photon came through the hole B, if the momentum change is (-hv/0), then it come through A : and if the momentum change is nearly zero, the photon came through both the holes. (In the latter case we should observe the interference fringes). What we observe is that a photon either goes through A or though B, but never through the two holes at the same time. But if we forego to determine the direction of the incoming photoms and keep the plate P fixed, interference fringes are recorded on the plate - announcing that each photon did go through the two holes at the same time. We have an extraordinary situation. A photon goes through the two holes if we forego any attempt to observe how this happens; but if we probe into it, the photon goes through only one hole or the other and no interference fringes are produced. It is because of this mutual exclusiveness of the two set-ups, (1) and (2) in the figure that the particle and the wave aspects for the photon are complementary and not contradictory. And the same holds for any ‘small object' : it holds good for any object which is not big compared to atoms.
For a 'small object' a precise measurement of its momentum invalidates any previous knowledge we had of its position. And a precise measurement of its position invalidates any earlier knowledge we had of its momentum. This occurs as we have emphasised, because of the disturbance which always accompanies an act of observation. The uncertainties in the position and in the momentum for a small object are connected by the Heisenberg relations. The existence of the Planck Constant (h) introduces an extraordinarily novel feature in that a measurement of some observable is incompatible with a measurement, at the same time, of some others. It has no parallel in everyday experience or classical physics.
There is something more to it, and much more strange, which is not always appreciated. Suppose the two holes A and B are replaced by the `box' with the two compartments we described earlier. Illuminate the (transparent) box with a beam of light. If the plate P is kept fixed and interference fringes will be observed telling us that atom is present at the same time, in both the compartments L and R. We now decide to make the plate free so that any change in its momentum in the Y-direction can be determined. Then we find that the scattered light comes either from L or from R. the atom is either in L or R, but never in both the compartments at the same time. Imagine-and this is permissible so far as the principle of the experiment goes- that the distance between the box and plate P is very large so that light takes a fairly long time (t) to travel from the box to the plate. It is up to us to choose to observe either the fringes on plate (telling us that the atom is present both in L and R), or to observe the momentum of the plate (telling us that the atom is either in L or R). A photon takes time (t) in travelling from the box to the plate. If we decide to make a choice, say, at this instant, whether to observe the interference fringes or the direction of the incoming photons, how could it influence the state of the atom a long time (t) earlier ? This looks utterly strange- totally. The lesson is that the behaviour of `small objects' is not visualisable. It is not describable in ordinary language. "There is no more remarkable feature of the quantum world (characterised by the Planck Constant) than a strange coupling it brings about between future and past...."
The disturbance we are speaking of is a direct result of the existence of the Planck Constant. In describing the motion of large objects we can ignore its existence. But this constant (h) is of paramount importance in determining the course of atomic phenomenon. Notice that experiments, and results of experiments, dealing with atom and elementary particles are described unambiguously in ordinary language (classical logic). There could be no science if this were not so. But the situation is completely, and most exasperatingly, different if we wish to understand and speak about the atomic particle themselves. How can the same atom be in two compartments L and R at the same time ? (Impossible ?). It is unimaginable. It is not describable in ordinary language. The world of atoms takes up to a `deeper layer'' or `deeper plane' of reality far removed from the world of everyday experience. The characteristic of the new plane of reality is the Planck Constant. We expect that as we probe deeper in our understanding of Nature, far deeper layers of reality are likely to be encountered (each characterised possibly by some fundamental constant of Nature).
We may denote by L0 the plane of our everyday reality, and by L1the plane of atomic reality. It is important to recognise, as repeatedly stressed here that the later reality cannot be apprehended or described in ordinary language without introducing absurdities and contradictions. To talk of L1 in the language of L0 is to talk nonsense. In terms of L0 it is inexpressible or avayakata. It is this inexpressibility or avaykata-property that provides the clue, a pointer, to the existence of L1. In describing L1 we must (as stated earlier) "either use the mathematical scheme as the only supplement to natural language or we must combine it with a language that makes use of a modified logic or of no well-defined logic at all" (Heisenberg 1958, p.160).
A Summing up of the Physical Situation
To sum up:
1. We investigate the world of atom with `tools' which are unambiguously described in ordinary language. But the world of atoms with its wave-particle duality is totally beyond description in ordinary language (classical logic). "A thing cannot be a form of wave motion and composed of particles at the same time ....nevertheless, both these statements describe correctly the same situation : the equal legitimacy of both descriptions and the impossibility of eliminating either in favour of the other are inevitable consequence of Heisenberg indeterminacy relations". (M. Jammer 1974, The Philosophy of Quantum Mechanics, p. 344).
2. To describe the world of atoms we have to use the mathematical formalism of quantum mechanics. The atom in quantum mechanics has no sharply defined boundaries or size. It is described by a mathematical quantity called a wave-function- and the wave-function, strictly speaking, fills all available space. Mathematics is perhaps best defined as the discipline that deals with infinities. It therefore involves concepts which (as Godel proved in his epochal work) are inherently "incomplete" and not free of contradictions. It may seem strange that mathematics, the most precise branch of human knowledge, contains contradiction in a deep sense. But is this feature paradoxical and it may appear which gives to mathematics its surprising and unique power to deal with `layers of reality' beyond the compass of ordinary language and everyday experience.
There have been attempts specially by Birkhoff and Neumann, and Weizsacker to modify classical logic by discarding the law of the excluded middle to bring it in conformity with the demands of quantum theory. These developments are of interest for Syadvada logic, but we shall not go into that here. (See chapter VIII, Quantum Logic, Jammer 1974, p. 340-416).
1. We have already noted the distinction, on the basis of the Planck Constant, between `big objects' and `small objects'. However, to understand the small, we have to begin with the big; but big objects are made up of small ones (atoms). We therefore seem to be involved in some kind of a paradoxical or circular situation. The physico-philosophical problem of the relation between the big and the small is very difficult one. Recently, some new light has been thrown on the problem by the work of Prigogine and his associates. (I. Prigogine, Science, 1 Sept. 1978).
1. It is worth noting the special role of the observer in quantum mechanics. We have seen that to make an observation is to make a choice between two or more incompatible measurement procedures. Choice implies consciousness and a freedom to elect between alternatives. This possibly has most far-reaching consequences-but we do not quite know at present. It possibly implies a kind of some strange coupling between future and past. Every observation is a participation in genesis. J. A. Wheeler 1977, Genesis and observership, in Fundamental Problems in the Special Sciences, ed. P. Butks and J. Hintikka.
2. The physical example of the atom and the box described earlier is presented diagramatically and compared with the seven modes of Syadvada. The quantum mechanical description in the usual notation is also added in the middle column.
Seven Modes of Syadvada and the example of an ‘atom’ in a ‘box’ with two compartments.
--------------------------------------------------------------------------------------------------
Atom in Box Quantum Mechanical Syadvada Models of Representation Description
(in the usual notation)
--------------------------------------------------------------------------------------------------
1. Atom in Left System in State |L> Existence (Atom in L)
Compartment (L)
-------------
| X | |
-------------
L R
2. Atom in right System in state |R> Non-existence
Compartment ( R ) (Atom not in L)
-------------
| | X |
-------------
L R
3. Cases (1) and (2). Mixture of |L> and |R> Existence and at different times or two similar represented by boxes at the same time. | L > < L | + | R > < R |
------------- ------------
| X | | | X | |
------------- ------------
L R L R
4. Atom in both System in a state which Avayakta compartments at is superposition (Inexpressibility) the same time; of | L > and | R > : this (wave-aspect) | P > = | L > + | R > in non-visualizable
5. (4) and (1) at Mixture Avayakta and different times; | P > < P | + | L > < L | Existence or two boxes at the same time (one box for (4) and another box for (1)).
6. (4) and (2) at Mixture Avayakta and different times; | P > < P | + | R > < R | Non-existence or two boxes at the same time.
7. (4) and (3) at Mixture Avayakta and different times; Existence and or three boxes at Non-existence the same time. | P > < | +P | R < > R | + | L > < L |
Syadvada Reasoning
The Syadvada dialectic (Syad means "May be") was formulated by Jaina thinkers probably more than two thousand years ago. Syadvada asserts that the knowledge of reality is possible only by denying the absolutists attitude. According to the Syadvada scheme every fact of reality leads to seven ways or modes of description. These are combinations of affirmation and negation :
(1) Existence, (2) Non-existence, (3) Occurrence (successive) of Existence and Non-existence, (4) Inexpressibility or Indeterminateness, (5) Inexpressibility as qualified by Existence, (6) Inexpressibility as qualified by Non-existence and (7) Inexpressibility as qualified by both Existence and Non-existence.
The fourth mode of inexpressibility or avayakta is the key element of the Syadvada dialectic. This is especially well brought out by our discussion of waveparticle duality in modern physics. (See. also P.C. Mahalanobis, and J.B.S. Haldane. Sankhya, May 1957, Indian Statistical Institute Calcutta. Their papers deal with the significance of Syadvada for the foundations of modern statistics.)
Take any meaningful statement. Call it 'A'. It may describe a fact of experience. It could be proposition of logic or mathematics. The Syadada dialectic demands that in the very nature of things the negative statement is also correct. Denote by not-A the negative statement of 'A'. The conditions under which the two statement, A and not-A, are correct cannot, of course, be the same. (In general) the respective conditions are mutually exclusive. Given a statement 'A'. it may not be at all easy to discover the conditions or situations under which not-A holds. It may even appear at the time impossible. But faith in Syadvada should keep us not to continue the search. For example, in the geometry of Euclid, the sum of the three angles of triangle is two right angles. The negation of this theorem is a new geometry in which the sum of three angles of a triangle is not equal to two right angles. It was some two thousand years after Euclid that non-Euclidean geometry was discovered in the nineteenth century.
Einstein's theory of general relativity is based on this geometry. When we know that both 'A' and not-A are correct, we are ready to move on to a deeper layer or a plane of reality which corresponds to simultaneous existence of both A and its negation. The deeper plane cannot be described in terms of the conceptual framework which described 'A' and not-A : In this framework it is avayakta. In the conceptual framework of `A' and not-A, for any particular situation, either A is true or not-A is true. The two being mutually exclusive cannot be simultaneously true. Think of the example of an atom in a box. In the framework of classical physics, as described earlier, the atom is either in the box or it is outside the box. There is no third possibility at this level or plane of reality. We have called this plane L0. The Syadvada assertion of the simultaneous existence of `A' and not-A, in some, strange, not explicable in the plane L0, leads us on to the search for a new deeper framework, or new dimension, of reality characterised by features not explicable in L0. Call the new framework L1. An understanding of L1 will eventually lead on to a still deeper layer L2, and so on. Syadvada is a dynamic dialectic taking us ever deeper and deeper in the exploration and comprehension of reality. What is now and of the utmost significance as vividly brought out by modern physics, is the fact that Syadvada provides a valuable guide and inspiration for fundamental studies in science and mathematics. The Syadvada, indispensable for ethical and spiritual quest and for ahimsa, is also of the greatest value for the advancement of natural science. In case this seems surprising we may remind ourselves of the profound words of Erwin Schroedinger : "I consider science an integrating part of our endeavour to answer the one great philosophical question which embraces all other, the one that Plotinus expressed by his brief-who are we ? And more than that : I consider this not only one of the tasks, but the task, of science the only one that really counts".
For the quest of truth, scientific, moral and spiritual, what is most important is the Syadvada or the complementarity principle, the precise definitions and number of modes are not so important.
Appendix
Examples of Syadvada
approach to fundamental problems
Two contradictory facts :
a) One knows by direct incontrovertible experience that it is one's own self that directs the motion of one's body; and because of this freedom arises moral responsibility for one's actions.
b) The body functions as a pure mechanism according to the Laws of Nature. (See E. Schroedinger, What is Life ? Cambridge University Press, 1948).
2. Euclidean and Non-Euclidean geometry. Cantorian and Non-Cantorian sets. (P.J. Cohen and R. Hersh, Scient. Am., Dec. 1967).
3. Einstein's theory of relativity and gravitation.
(See especially, Einstein's Creative Thinking and the General Theory of Relativity, A Rothenberg, Am J. Psychiatry. January 1979).
4. a) `We can draw a straight line joining two points'.
b) `We cannot draw a straight line joining two points'. This reminds of Zeno's Paradox.
(See A New Perspective on Infinity, New Scientist, 8 June, 1978).