Author: Avshalom Elitzur
What is the measurement problem anyway?
Introductory reflections on quantum puzzles (2005) Introduction to
What’s the Measurement
Problem with you Anyway?
introductory reflections on Quantum puzzles
Avshalom C. Elitzur
“Can quantum-mechanical description of physical reality be considered complete?” It is perhaps no coincidence that this question, which titled Einstein’s famous onslaught on quantum mechanics [], was echoed verbatim in the title of Bohr’s reply []. Although Bohr opted for a “Yes,” today, even his ardent followers (see Wheeler below) believe that quantum mechanics is not the last word.
This brainchild of the Center for Frontier Sciences at
With awe to the great minds that took part in this enterprise, I take the liberty of offering some introductory thoughts about what makes quantum mechanics so wonderful, intriguing – yet probably incomplete.
Someday, we all believe, a new theory will revolutionize physics, just as relativity and quantum mechanics did at the dawn of the 20th Century. It will include its two parent revolutions as special cases, just as classical mechanics has been comfortably embedded within relativity theory and, less comfortably, within quantum mechanics. What will this theory tell us about the nature of reality is anybody’s guess, but John Wheeler [] has vividly captured its most immediate feature:
Surely someday, we can believe, we will grasp the central idea of it all as so simple, so beautiful, so compelling that we will say to each other, “Oh, how could it have been otherwise! How could we have been so blind so long!” (p. 28)
Greenberger [], however, has much more sobering reflections:
Most physicists believe that had they been around at the birth of relativity, they would have been able to instantly appreciate its radical elements. But my own experience indicates that if Einstein were to send his paper to Physical Review today it would have almost no chance at all of being published. “Highly speculative!” would be the referee report, a death shell to any paper. He would have to append it to an article on string theory, or some other fad, and hope it wasn’t noticed (p. 558).
We can only hope that Wheeler is correct and Greenberger is exaggerating, and that the new theory is not already laid down in some yellowing manuscript concealed in some embittered author’s drawer. Let us also hope that the discovery of the theory will occur within our lifetime.
How would the puzzles of quantum mechanics fare in that revolution? Before indulging in some guesses, which are naturally bound to reflect personal biases, let us recall the puzzles themselves. They are mainly three []:
I. The Wave-Particle Duality. Subject any particle to an experiment set to measure waves and it will manifest unmistakably undulatory properties. Perform on it an experiment designed to measure corpuscular properties and you will end up with a particle. Both results are unequivocal – and mutually exclusive. As Feynman [] aptly remarked, the double-slit experiment (where this dual nature becomes most visible through the interference pattern) contains the core of quantum mechanics’ mystery. The uncertainty principle is the general formulation of this duality, allowing only one out of a pair of physical values to be measured with arbitrary accuracy.
II. The Quantum-Classical Limit. The extraordinary predictions of quantum mechanics, such as the above interference effects, perfectly hold for particles, but flatly fail for macroscopic objects, even though the latter are made of the former. In other words, superposition is observed in particles but never in cats. Where does quantum mechanics’ jurisdiction end? Atoms also exhibit interference, and so do large molecules, although the experiments become difficult with the interfering object’s size. Does classical mechanics simply take over at some scale [] or is it only technological limitations that do not yet allow demonstrating quantum behavior of larger objects []? This is the “measurement problem,” arising every time the properties of a particle are amplified to macroscopic extent.
III. Non-Locality. The wavelike behavior of a single particle entails that,
in order to obey conservation laws, distant parts of the wave function must
instantaneously affect one another upon measurement. And indeed the violations of
It is such puzzles that herald a scientific revolution, yet despite repeating proclamations made by superstring and other theories, no such revolution is here yet. Still, although we cannot know the theory itself, Wheeler’s poetic sentiments about how we would feel upon encountering it reflect sound scientific intuition: The theory will probably appeal to us as true. We therefore can – in fact, we should – lay down our expectations. It may prove to be a constructive exercise. So, based on science’s past experience, our long-longed-for theory should demonstrate the following qualities:
- Beauty. Every scientist is familiar with the aesthetic pleasure one experiences upon understanding a profound theory. An entire realm of facts becomes more organically integrated, and, at the same time, simpler. Seemingly-accidental effects, which the earlier theory regarded as “just-like-that,” turn out to be meaningful, even imperative. Hence, the theory that we yearn for should likewise render the quantum peculiarities just as natural as the effects known from classical physics. A consequence of this expectation for elegance is –
- Unity. Frankly, it would be quite disappointing if the new theory explains, say, only the wave-particle duality while non-locality is merely assumed and the measurement problem is relegated to yet another revolution. Rather, one resolution should naturally entail the others.
- Continuity. Scientific revolutions, unlike all too many political revolutions, do not destroy the fruits of earlier theories but incorporate them within a new context. This is true not only for the empirical data which the earlier theories revealed, but also for many of their insights and principles, which find their place within the new framework. The new revolution will therefore incorporate not only present-day quantum formalism, but many features of its prevailing interpretations as well.
- Sacrifice: All the above cannot come without a price. If the solution to the quantum puzzles lingered so long, it was most likely hindered by some highly cherished assumption which no one was willing to give up. We therefore have to prepare for a serious blow that the new theory will first deliver on our world-view. Having said that, proponents of some of the existing interpretations might argue: “But we already did that! We gave up the notion of objective reality and/or locality!” Well, they did, but unfortunately did not get much in return. A genuine revolution is balanced differently: For what it has robbed us, it generously rewards us with –
- Novel Predictions. While the new theory will no doubt point out where we have been blind all along, as Wheeler so acutely put it, it will not stop there but go on to tell us what is out there that we should now see. In other words, it will make new predictions, challenging us to verify or falsify them by experiment or observation. Moreover, the theory will also yield –
- Unexpected Dividends. It is one of the most profound features of reality that parsimony and generality go hand in hand. Sometimes you drop a basic assumption or even an axiom from a theory, and, lo and behold, the edifice built on the remaining, narrower foundation turns out to wider: Additional phenomena, other than those which you sought to explain, turn out to neatly fit in within the new theory. Maxwell’s unification of electricity and magnetism, which surprisingly turned out to account for light too, is a famous example. Similarly, the new explanation of quantum phenomena is almost bound to illuminate some other conundrum, be it the origin of the universe [], the nature of consciousness [], or even something we cannot even think of yet.
Having said all that, it becomes soberingly clear why none of the prevailing interpretations of quantum mechanics has won the physical community’s general acceptance. To be sure, physics would be very dull had these interpretations not been proposed in the first place. They teased researchers’ minds and stimulated experimentation and theorizing. Yet interpretations of quantum mechanics – especially the most ingenious ones – might sometimes do a disservice to their ardent proponents. They might give the impression that quantum mechanics is the final word, and because they are not theories in themselves, offering no predictions that differ from quantum theory proper, they are unfalsifiable. This is bound to inflict barren tranquility on a too enthusiastic adherent. Popper’s [] legacy is very instrumental in this context, and can be best appreciated when considering some pseudo-sciences. Astrology, for example, which boasting enormous explanatory power and yet being unfalsifiable, is, for this reason, a conceptual ghost: It can never die, hence is not alive either. It never really forbids anything, hence never makes any other possibility more likely.
The lesson should not be lost on the quantum physicist. One should be suspicious of a framework that, instead of trying to resolve contradictions, embraces them with the aid of epistemological or methodological moves, no matter how brilliantly. Contradictions have always been the lifeblood of scientific progress, and they urge us to dare make ontological adventures. Puzzling over the popularity of some of quantum mechanics’ interpretations, one sometimes feels that they too, like the quantum itself, have become superposed. It is time for a measurement!
Anyway, “Good men must not obey laws too well” (R. W. Emerson), and neither should scientists follow too strictly any guidelines in search of a new theory. Let Nature have ample opportunities to surprise us. Einstein openly advocated some inconsistency when he said that a scientist
must appear to the systematic epistemologist as a type of unscrupulous opportunist: he appears as realist insofar as he seeks to describe a world independent of the acts of perception; as idealist insofar as he looks upon the concepts and theories as the free inventions of the human spirit (not logically derivable from what is empirically given); as positivist insofar as he considers his concepts and theories justified only to the extent to which they furnish a logical representation of relations among sensory experiences. He may even appear as Platonist or Pythagorean insofar as he considers the viewpoint of logical simplicity as an indispensable and effective tool of his research. [, p. 684].
Taking part in this enterprise has been a huge privilege. I wish to thank my friend and co-editor Shahar Dolev for his precious scientific and philosophical advice. Nancy Kolenda’s leadership and inspiration was invaluable at every stage of the work. Last but not least, heartiest thanks to the scientists and philosophers who together produced this collection. Perhaps the sentiments of all of us towards this volume’s subject can be best put in the words of Rabbi Tarfon (Ethics of the Fathers 2, 16): “It is not upon you to complete the work, neither are you free to refrain from it.”
 For this idea I am indebted to S. Dolev, whom I once observed analyzing a quantum-mechanical experiment in terms of a certain interpretation which I knew he did not like. To my inquiry he told me it’s been his habit to analyze a complex quantum process in terms of several competing interpretations, as each interpretation illuminates another facet of the situation.
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