|
First Steps To
Jainism (Part-2)
SANCHETI ASOO LAL
BHANDARI MANAK MAL
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
-
Determinism and Free will
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).
| 
