Quandary in Quantum Mechanics

Quantum mechanics began in a cloud of doubts and hesitation and these doubts still remain with us; they have further deepened, if anything, with the passage of time. Max Planck, the reluctant father of quantum mechanics stated (6), “Either the (quantum of) action was a fictitious quantity in which case all the deductions from the radiation theory were illusory and were nothing more than mathematical juggling. Or the radiation theory is founded on actual physical ideas, and then the quantum of action must play a fundamental role in physics, and proclaim itself as something quite new and hitherto unheard of, forcing us to recast our physical ideas, which since the foundation of infinitesimal calculus by Leibniz and Newton, were built on the assumption of continuity of all causal relations. Experience has decided for the second alternative.” The idea of discrete energy was so abhorrent to Planck that he had hesitated to publish his work postulating the concept of quantum. However, once the cat was out of the bag, it created havoc in the prevalent classical worldview of Physics. Strange things were inferred and observed to happen in the microcosmic world of the subatomic particles. A subatomic particle was both a particle of matter and a wave. The very act of taking a measurement changed the state of the quantum event. Heisenberg’s Principle of Uncertainty prescribed a limit on the knowledge of the properties of the subatomic particles that was accessible to man. The uncertainty was not due to any deficiency in the method or instrumentation of measurement; it was inherent. It was a fact of life. The old cause and effect paradigm simply did not work in the microcosmic world. A particle was here, there, and every where at a given moment of time. All that the theory could predict and predict very accurately, was the probability of a particle being at a certain specified place at a given time. Likewise it could predict its momentum but not both position and momentum with equal precision. The old deterministic worldview that was so dear to Einstein and the other classical physicists was threatened. According to Murray Gell-Mann, a Nobel Prize winner for Physics and the Predictor of quarks, “All of modern physics is governed by that magnificent and thoroughly confusing discipline called quantum mechanics… It has survived all tests and there is no reason to believe that there is any flaw in it… We all know how to use it and how to apply it to problems; and so we have learned to live with the fact that nobody can understand it,” (5).

Replacement of the deterministic approach in the subatomic world by the probabilistic approach also punched a hole in the classical logic. In classical logic, if something is not true then it is necessarily false. Not so in quantum physics. According to John Barrow (1), “In practice, the intutionists did not regard all mathematical statements as either true or false. They stipulated a third category: undecidable. This three-fold logic is reminiscent of Scottish courts of law, where the verdict of not-proven may be returned, whereas English courts require a verdict of either guilty or non-guilty.” He also stated, “An alternative approach to the resolution of the quantum measurement puzzle was the adoption of three-valued logic of the intutionists… In this context, it is referred to as quantum logic. Thus, it is no longer necessary to conclude that the neutron went through one slit or the other, Schrodinger’s Cat is not necessarily dead if it is not alive…. There now exists a further intermediate logical state. The adoption of this quantum logic can provide an explanation of sorts for the world of quantum strangeness, but only at the expense of giving up the logic that applies to every thing else. Most physicists regard this as an acceptable schizophrenia. After all, one has to use ordinary logic to argue for the application of quantum logic.”

Duality of Matter and Wave

Even before the inception of quantum physics, it was known that “under some conditions light seemed to behave as if it consisted of very small particles of matter (now called photons). Under other conditions, however, light showed clear signs of being a wave of energy, a disturbance of a medium, the intensity of which could be measured,” (5). According to Pine (5), “A particle is a piece of matter, like a baseball, that at any given time has a definite size, speed and location. It can only be at one place at a time…. A wave, on the other hand, is a very different kind of thing… The wave spreads; it does not stay in one place, but it can be in many places at the same time.” Drop a pebble in a pool of water. A wave is formed that spreads out. The same wave can be at several different places at the same time. Although a particle and a wave are so different from each other in their characteristics, light however possesses both of these characteristics.

This dichotomy of light was explained and accommodated by Bohr’s concept of Complementarity. “Complementarity is the realization that particle and wave behavior are mutually exclusive, yet that both are necessary for a complete description of all phenomena,” (9). According to Sokal (9), Heisenberg noted that “the different intuitive pictures which we use to describe atomic systems, although fully adequate for given experiments, are nevertheless mutually exclusive. Thus, for instance, the Bohr atom can be described as a small-scale planetary system, having a central atomic nucleus about which the external electrons revolve, however, it might be more convenient to imagine that the atomic nucleus is surrounded by a system of stationary waves whose frequency is characteristic of the radiation emanating from the atom… Each picture is legitimate when used in the right place, but the different pictures are contradictory and therefore we call them mutually complementary.”

As if this was not strange enough, “(Louis) De Broglie argued that just as Einstein showed waves of light to have particle properties, so particles of matter might also have wave properties,” (3). According to Herbert (3), “Here was a delicate situation. Prince De Broglie was serious about his proposal but his conclusion was patently absurd. His thesis professor decided to send a copy to Einstein. Einstein enthusiastically backed de Broglie’s idea and the prince got his degree. Six years latter de Broglie received the Nobel Prize for his crazy idea. In the mean time, the de Broglie wave length of a piece of matter – the electron – had been measured at Bell Labs by Americans Davisson and Germer.”

Herbert stated further, “By dissolving the matter/field distinction, quantum physicists realized a dream of the ancient Greeks who speculated that beneath its varied appearances the world was ultimately composed of a single substance. Some philosophers said it was All Fire; some All Water. We now believe the world to be all Quantumstuff.”

An Electron is Not a Thing until We Observe It

“If an electron is not a thing until it is observed by some instrument, does this imply that reality depends on our observations and hence, ultimately, the thoughts we use to frame the world? Metaphysical idealism is an old and widespread belief stating that the physical world as we experience it is basically an illusion; the perception of a world of material things separated in space is said to be only an appearance,” (5). This is reminiscent of the Cartesian adage: I think therefore I am. Later, George Berkeley (1685-1753) comprehensively dwelt upon and developed the Cartesian duality of Mind and Matter. He “maintained that material objects only exist through being perceived. To the objection that, in that case, a tree, for instance, would cease to exist if no one was looking at it, he replied that God always perceives every thing," (7), see the note at the end of the essay also. Heretofore this was a philosophical curiosity only; in quantum mechanics it seems to have acquired a trait, which is not intelligently describable in the ordinary language, which we use in our daily life. Many physicists including the founding fathers (Bohr, Heisenberg, etc.) have indeed mystified it in endeavoring to explain it in our day-to-day language. Such attempts have opened up vistas, which lead directly into the metaphysical world of the mystics.

Discussing the Copenhagen Interpretation (formulated by Bohr), Herbert (3), remarked, “For Bohr and Heisenberg the world is forever divided into two types of reality: quantum reality, which we can never experience, and classical reality, which is all that we can ever experience. Quantum theory is not a representation, much less a description of quantum reality, but a representation of the relationship between our familiar reality and the quoin’s utterly inhuman realm.” Quon is a term coined by Herbert who defined it as “any entity, no matter how immense, that exhibits both wave and particle aspects in the peculiar quantum manner.”

Einstein could never reconcile himself with the probabilistic aspect of quantum mechanics. He argued with Bohr incessantly developing new lines of argument in order to find holes in Bohr’s interpretation but did not succeed. So far, there is no evidence to support the relevance of cause and effect paradigm in the subatomic world; determinism simply does not govern the quantum mechanical behavior.

God Does Not Play Dice With the World

Trying to refute the statistical aspect of quantum mechanics, Einstein remarked, “God does not play dice with the world.” However, in the microcosmic world, God does seem to play dice. Deliberating on this subject, Heinz Pagels (4) observed, “But is there a possibility that beyond quantum theory there exists a new deterministic physics, described by some kind of sub-quantum theory, and the all-knowing mind uses this to determine the world? According to the quantum theory, this is not possible. Even all-knowing mind must support its knowledge with experience, and once it tries to experimentally determine one physical quantity the rest of the deck of nature gets randomly shuffled again. The very act of attempting to establish determinism produces indeterminism. There is no randomness like quantum randomness. Like us, God plays dice – He, too only knows the odds… But in fact the quantum theory has closed the door on determinism.”

On the other hand, Subramanyan Chandrasekhar (10), a Nobel Prizewinner and the Originator of the black hole concept, just wryly remarked, “How does he (Einstein) know (that God does not play dice)?” Well, of course, Einstein did not give any proof of his statement, which has now become part of history of science.

While there is still not any worthwhile evidence available in support of the classical determinism in the subatomic world, David Bohm (2) did indeed construct a theory assuming there were some “hidden variables”, which had not been accounted for in the conventional theory of quantum mechanics but his theory did not attract much attention. He was able to preserve causality in his theory but no body seemed to take much notice of it.

Concluding Remarks

Einstein had heuristically suggested that the conventional theory of quantum mechanics was an incomplete theory. That was the reason, he argued, that we had to make do with the probabilistic theory. This had led to the belief that there were hidden variables, which had provided incentive for Bohm’s formulation.

There is still some optimism in that once complete unification of all the fundamental forces is accomplished (Theory of Everything), new and deeper insights might come forth which might provide better explanation of the statistical character of the existing theory. Although there is a great deal of confidence that such unification will soon be achieved via Theory of Quantum Gravity (Loop Quantum Gravity), there is no guarantee that of necessity such unification has to occur. The unification, if it occurred, would provide a bridge between the deterministic theory of gravity and the statistical theory of quantum mechanics. It should also explain how the transition between the microcosmic and the macrocosmic worlds occurs.

The theory seems to throw some new and significant light on the incidence of the so-called Big Bang. Writing in his essay, A quantum leap for cosmology, Smolin (8) reported, “Bojowald had discovered that there is never an initial singularity (i.e. a point where the curvature of space-time becomes infinite) and therefore no first moment to come… the universe continues back before the moment classical cosmology predicts that it began, to a phase where it was previously expanding. This behavior has been called a ‘bounce’; it suggests that the big bang arose from an event in a previous universe, either through the collapse of a black hole or from the collapse of the whole universe.” So there is no beginning of time. Smolin underlined the fact “..this is the first time that the replacement of the initial singularity by a bounce has been shown to be a necessary result of an exact quantum theory of gravity.”

Will it demolish the statistical character of the subatomic physics and, once again, restore the classical determinism? Nothing can be said with certainty. Whole new facts of which we do not have any idea at present might be revealed. Until then, the apparent metaphysical descriptions of the microcosmic world would continue coming forth without any satisfactory resolution of the underlying fundamental issues.

It is however only the philosophers who are so much concerned about the issues of determinism, quantum reality, or classical reality; the research physicists take them in their usual stride. As long as they continue obtaining accurate computational results from their theories, they are content with their work.

Note

A limerick by Ronald Knox, with Reply, sets forth Berkeley’s theory of material objects (7).

There was a young man who said, “God
Must think it exceedingly odd
If he finds that this tree
Continues to be
When there’s no one about in the Quad.

Reply

Dear Sir:
Your astonishment’s odd:
I am always about in the Quad,
And that’s why the tree
Will continue to be,
Since observed by
Yours faithfully,
God

References

1. Barrow, John D., “What is Mathematics?” in “The World Treasury of
Physics, Astronomy, and Mathematics,” ed. Timothy Ferris, Little,
Brown and Company, Boston, 1991, pp. 541-58.
2. Bohm, David, and Basil J. Hiley, The Undivided Universe,” Routledge,
1995.
3. Herbert, Nick, “Quantum Reality,” Anchor Books, A Division of
Random House, Inc., New York, 1987, pp. 39-40, 143.
4. Pagels, Heinz, “Uncertainty and Complementarity,” in “The World
Treasury of …. And Mathematics,” ed. Timothy Ferris, Little, Brown
and Company, Boston, 1991, p. 98.
5. Pine, Ronald C., “Quantum Physics and Reality,” http://personal.tcu.edu/
~dingram/edu/pine3.html
6. Planck , M., “A Survey of Physical Theory,” Dover Publications, Inc.,
New York, 1993, p. 109.
7. Russell, Bertrand, “A History of Western Philosophy,” A Touchstone
Book, Simons and Schuster, New York, 1972, pp. 646 - 47.
8. Smolin, Lee, “A Quantum Leap for Cosmology,” Physics Web,
http://physicsweb.org/article/world/14/11/3, November, 2001.
9. Sokal, Alan D., “Transgressing the Boundaries: Towards a
Transformative Hermeneutics of Quantum Gravity,”
httP://www.physics.nyu.edu/faculty/sokal/transgress_v2/
transgress_v2_singlefile.html
10. Tierney, John, “Quest for Order,” in “The World Treasury…and
Mathematics,” ed. Timothy Ferris, Little, Brown and Company,
Boston, 1991, p. 610.