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arXiv:1207.6215

Is the individuality interpretation of quantum theory wrong ?

U. Klein

Published Jul 26, 2012• 2 citations
arXivHTMLPDF

Abstract

We analyze the question whether or not quantum theory should be used to describe single particles. Our final result is that a rational basis for such an 'individuality interpretation' does not exist. A critical examination of three principles, supporting the individuality interpretation, leads to the result that no one of these principles seems to be realized in nature. The well-known controversy characterized by the names of Einstein (EPR), Bohr and Bell is analyzed. EPR proved 'predictive incompleteness' of quantum theory, which implies that no individuality interpretation exists. Contrary to the common opinion, Bell's proof of 'metaphysical completeness' does not invalidate EPR's proof because two crucially different meanings of 'completeness' are involved. The failure to distinguish between these two meanings is closely related to a fundamentally deterministic world view, which dominated the thinking of the 19th century and determines our thinking even today.

DOI
10.48550/arxiv.1207.6215

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Quantum theory is a phenomenally successful cornerstone of physics. But a recent poll among quantum physicists shows that there is still little agreement on what the theory tells us about physical reality. Yet precious bits of consensus are emerging. As always, Albert Einstein was ahead of his time. Quantum theory was still in its infancy, its formalism a mere sketch, and its implications only beginning to be realized. Yet Einstein, in 1917, already spotted what would trouble him throughout his lifetime. He concluded that the nascent theory, which he had helped initiate, seemed to leave “time and direction of elementary processes,” such as the spontaneous emission of radiation from a molecule, “to chance” 1. Einstein's conclusion was visionary. It was also incredibly bold, for it suggested a radical departure from the powerful, centuries-old deterministic and causal worldview of classical physics. 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Remarkably, there has never been any serious attempt to find out what the current opinions of the community really are and how they may be correlated. We jumped on the opportunity and polled 33 participants at a 2011 conference on “Quantum Physics and the Nature of Reality” (Fig. 1) 2. (We hasten to add that our poll is to be understood as merely a snapshot and certainly cannot claim to be representative.) As soon as we had collected the questionnaires, the respondents eagerly asked to hear the results. Evidently, we had not been the only curious party. What did we find? The fundamental questions, it seems, still elicit radically different responses. Take the quantum state—represented by the wavefunction—as an illustration. The wavefunction is the central mathematical symbol of quantum mechanics. It allows us to make incredibly accurate predictions, be it in atomic, molecular, or solid-state physics. But how are we to interpret it? Is it itself a physical property, or does it merely represent our knowledge? Our poll revealed a tie between these two positions. And not only that: a third of respondents preferred a mix of both viewpoints—perhaps a sign that a more nuanced view, or even a synthesis of views, may be on the horizon. Only 3% of those polled thought that quantum states never refer to a single system but only to ensembles of systems. Perhaps this departure from the ensemble view—a view that, we suspect, remains more popular in the physics community at large—has to do with the fact that experiments with single quantum systems have become routine in today's quantum-information laboratories. Sharp disagreement was in evidence on another deep question. Abraham Pais, Einstein's biographer, recalled that “during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I look at it” 3. Putting the issue differently, are the physical properties of objects well defined before we actually measure them? Half of the respondents in our poll believed that they sometimes were, while the other half said that they never were. These two positions correspond to radically different ways of understanding the function of measurement: either as simply ascertaining—at least sometimes—of what is already there, or as an act of genuine creation. The role of measurement is also at the heart of another perennial favorite of foundational discussions, the measurement problem. The measurement problem highlights a curious fact about quantum theory: while the act of measurement assumes a fundamental role, it is not described—not without interpretive contortions, anyway—by the dynamical law of quantum theory, the Schrödinger equation. For decades, the measurement problem was seen by many as the main stumbling block for quantum theory, sparking a storm of rivaling attempts to deal with this perceived issue. Today, the waters seem to have calmed and attention shifted elsewhere, as only less than a fourth of respondents consider the measurement problem “a severe difficulty threatening quantum mechanics.” Changing attitudes are also evident when it comes to the issue of chance Einstein had brought to light in 1917. Today, the question of the randomness of quantum events no longer seems to be all that contentious. Most of our respondents accepted randomness as irreducible or a fundamental concept in nature (or both). Less than one-tenth of respondents thought that quantum randomness was merely apparent rather than fundamental, and no one believed in a hidden determinism governing quantum events. We wish we could hear Einstein's opinion today. Why have attitudes and priorities changed? It's hard to say, but we think there may be several driving forces. The rapid ascent of quantum information science has not only led to applications such as secure cryptography and the promise of lightning-fast quantum computers, but has also shed new light on foundational problems and handed us new tools for addressing them. Our poll shows that these tools are considered a welcome addition, with three-fourths seeing quantum information as a breath of fresh air for foundational investigations. There is also optimism about the future technological development of quantum information, with more than 75% of respondents expecting a working and useful quantum computer to be realized within the next fifty years. Such optimism might be rooted in the astonishing experimental progress we have witnessed over the past decades, another driving force behind changing attitudes. We are now at stage where almost perfect experimental control of single quantum systems has been achieved. The 2012 Nobel Prize in physics was awarded for just such experiments. This has put at our fingertips the ability to actually carry out the thought experiments—or approximations thereof, at any rate—that the founders of quantum theory had dreamed up. Take Schrödinger's cat. In 1935, Schrödinger wanted to illustrate what seemed to him an absurd prediction of the new theory: that the strange quantum superpositions of the atomic world can be amplified to everyday objects. Schrödinger's object of choice was a cat in a specifically prepared box. Quantum theory then suggested that the state of the cat should become transformed into a bizarre quantum superposition of being simultaneously alive and dead. But what Schrödinger had intended as a “burlesque” 4 thought experiment is now approaching experimental reality. Over the last decades, researchers have become increasingly skilled in breeding small versions of Schrödinger's cat. While they don't involve actual cats, they do already involve large biological molecules. Our respondents, it seems, were inspired by such developments. A solid two-thirds majority declared that they don't expect any fundamental limit in this enterprise of observing larger and larger objects in superpositions of macroscopically distinct states. No limit, then, for quantum theory—something that Bohr had already suggested when he, in some of his early thought experiments, considered apparatuses that included macroscopic parts behaving in quantum-mechanical ways. There are other new trends. Why do people seem to be much more at ease with relativity theory than with quantum theory? For one, both special and general relativity theory are grounded in a few simple physical principles. By contrast, quantum theory is lacking such a foundation and is instead based on a rather abstract mathematical body. Today, several researchers are out to change this situation, trying to derive quantum theory from a small set of physical or information-theoretic principles. They hope that in this way, we will understand why we have this peculiar theory to begin with. A majority in our poll regarded such “reconstructions” of quantum theory as giving useful insights, indicating once more that any new tool that promises fresh insights is embraced with an open mind. To be sure, many (albeit not all) of the questions we asked in the poll are interpretive questions. This means that unless we should find out some day that quantum theory is in fact not always valid—in which case we would have to rethink the whole game—experiments arguably can't play the role of the arbiter. Some physicists will conclude from this that we need not bother with such questions, and relegate them to philosophy. We think this is too quick. Many ideas in physics didn't come out of thin air, but came about when someone started looking at a problem with a certain philosophical disposition. In this sense, we may think of the plurality of views in quantum mechanics as productive. Every interpretation highlights some aspect of quantum theory, is particularly suited for explaining particular phenomena, and may inspire new technologies—such as the quantum computer—or even new physics. What, then, does the future hold? Half of the respondents in our poll believe that in fifty years from now, we will probably still be coming together for conferences on the fundamental questions of quantum theory. But what kinds of questions will be on the agenda? Will we still be worrying about the same problems as today? Or will these problems have been solved—or found to be less relevant—and our focus shifted to new questions once again? Who knows. But the location of the conference where we conducted the poll may tell a story. It was the place of a monastery, and a central position in the battle between Catholics and Protestants during the seventeenth century. Many of the questions that were hotly debated back then are no longer of interest to many people today, and other, new questions have since taken center stage in our society. Maybe some of the battles over the interpretation of quantum theory will meet a similar fate.

Annalen der Physik•Apr 1, 2013•11 citations
We analyze the question whether or not quantum theory should be used to describe single particles. Our final result is that a rational basis for such an 'individuality interpretation' does not exist. A critical examination of three principles, supporting the individuality interpretation, leads to the result that no one of these principles seems to be realized in nature. The well-known controversy characterized by the names of Einstein (EPR), Bohr and Bell is analyzed. EPR proved 'predictive incompleteness' of quantum theory, which implies that no individuality interpretation exists. Contrary to the common opinion, Bell's proof of 'metaphysical completeness' does not invalidate EPR's proof because two crucially different meanings of 'completeness' are involved. The failure to distinguish between these two meanings is closely related to a fundamentally deterministic world view, which dominated the thinking of the 19th century and determines our thinking even today.
The EPR paper and Bohr's reply to it brought to an end the public debate between Einstein and Bohr. In the aftermath, Bohr's construal of quantum mechanics established itself as the basis of the orthodox interpretation – the ‘Copenhagen interpretation’ as it came to be called. The vast majority of physicists regarded Einstein's criticism as reactionary, and dismissed it with disdain. One of the main causes of this disdainful attitude was the general opinion that Einstein's criticism committed him to the existence of hidden states, and the existence of these, it was thought, had been conclusively ruled out by the work of von Neumann and others. What light does the subsequent work on the question of hidden states, and in particular the work of Bell, throw on the Bohr–Einstein dispute? Completeness and hidden states There are three distinct questions concerning hidden states. First, might there be such states, unbeknown to quantum mechanics? Second, can quantum mechanics, as it stands, take account of such states? Third, could some theory containing descriptions of such states reduplicate the predictions of quantum mechanics? Concerning the first of these questions, Einstein's view was that it is very likely that such states exist, and since quantum mechanics takes no account of them, it is incomplete and best regarded as a statistical theory analogous in some respects to classical statistical mechanics.
The support of Copenhagen quantum mechanics in the discussion concerning EPR experiments has been based fundamentally on two mistakes. First, quantum mechanics as well as hidden-variable theory give the same predictions; the statement of Belinfante from 1973 about the significant difference must be denoted as mistake. Secondly, the experimental violation of Bell's inequalities has been erroneously interpreted as excluding the hidden-variable alternative, while they have been based on assumption corresponding to classical physics. The EPR experiments cannot bring, therefore, any decision in the controversy between Einstein and Bohr. However, the view of Einstein is strongly supported by experimental results concerning the light transmission through three polarizers.
The immense difference between Einstein locality and EPR locality is discussed. The latter provides a basis for establishing the nonlocal character of quantum theory, whereas the former does not. A model representing Heisenberg's idea of physical reality is introduced. It is nondeterministic and holistic: the objects, measuring devices, and their environment are treated as an inseparable entity, with, however, macroscopically localizable attributes. The EPR principle that no disturbance can propagate faster than light is imposed without assuming any structure incompatible with orthodox quantum thinking. This locality requirement renders the model incompatible with rudimentary predictions of quantum theory. A more general proof not depending on any model is also given. A recent argument that purports to show that quantum theory is compatible with EPR locality is examined. It illustrates the importance of the crucial one-world assumption. The significance for science of the failure of EPR locality is discussed.
Ignited by Einstein and Bohr a century ago, the philosophical struggle about Reality is yet unfinished, with no signs of a swift resolution. Despite vast technological progress fueled by the iconic Einstein/Podolsky/Rosen paper (EPR) [1][2][3], the intricate link between ontic and epistemic aspects of Quantum Theory (QT) has greatly hindered our grip on Reality and further progress in physical theory. Fallacies concealed by tortuous logical negations made EPR comprehension much harder than it could have been had Einstein written it himself in German. EPR is plagued with preconceptions about what a physical property is, the 'Uncertainty Principle', and the Principle of Locality. Numerous interpretations of QT vis à vis Reality exist and are keenly disputed [4][5][6][7][8][9][10][11]. This is the first of a series of articles arguing for a novel physical interpretation I call ‘The Ontic Probability Interpretation’ (TOPI). A gradual explanation of TOPI is given intertwined with a meticulous logico-philosophical scrutiny of EPR, with Part I focusing on the meaning of Einstein’s ‘incompleteness’ claim for QT: a conceptual confusion, a preconception about Reality, and a flawed dichotomy are shown to be severe obstacles for the EPR argument to succeed. Part II completes the analysis, proving EPR claim of ‘incompleteness’ for QT is fallacious [12]. Part III further develops TOPI, while scrutinizing the mythical ‘Schrödinger’s Cat’, as well as the ‘Basis’ and ‘Measurement’ pseudo-problems [13]. Part IV introduces QR/TOPI: a new theory that solves the century-old problem of integrating Special Relativity with Quantum Theory [14].
Abstract If we reject the ‘spooky’ action at a distance that seems to be required in the Copenhagen interpretation of quantum theory, and which is highlighted by the EPR thought experiment, we must accept the EPR argument that the theory is somehow incomplete. In essence, this involves the rejection of the first postulate of quantum theory: the state of a quantum mechanical system is not completely described by the wave function or state vector.Einstein had hinted at a statistical interpretation. In his opinion, the squares of the wave functions or state vectors of quantum theory represented statistical probabilities obtained by averaging over a large number of real particles. The Copenhagen interpretation of the EPR experiment insists that the reality of the physical states that can be measured is defined by the nature of the interaction between two quantum particles and the nature of the experimental arrangement. A completely deterministic, locally real version of quantum theory demands that the physical states of the particles be established at the moment of their interaction and that the particles separate as individually real entities in those physical states. The physical states of the particles are prescribed by the physics of their interaction and independent of how we choose to set up the measuring instrument, and so no reference to the nature of the latter is necessary, except to define how the independently real particles interact with it. The instrument thus probes an observer-independent reality.
Quantum theory is a phenomenally successful cornerstone of physics. But a recent poll among quantum physicists shows that there is still little agreement on what the theory tells us about physical reality. Yet precious bits of consensus are emerging. As always, Albert Einstein was ahead of his time. Quantum theory was still in its infancy, its formalism a mere sketch, and its implications only beginning to be realized. Yet Einstein, in 1917, already spotted what would trouble him throughout his lifetime. He concluded that the nascent theory, which he had helped initiate, seemed to leave “time and direction of elementary processes,” such as the spontaneous emission of radiation from a molecule, “to chance” 1. Einstein's conclusion was visionary. It was also incredibly bold, for it suggested a radical departure from the powerful, centuries-old deterministic and causal worldview of classical physics. But Einstein also immediately expressed his discomfort with the idea of fundamental chance. In fact, his worries were just the seed of what would turn into one of the longest and most heated debates in the history of physics. What does quantum theory mean, and what does it tell us about the nature of reality? Some of the brightest minds in physics locked horns over these issues. Besides Einstein, there were Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Pascual Jordan, Carl Friedrich von Weizsäcker, Wolfgang Pauli, and Richard Feynman, just to name a few. Ask anyone today working on foundational questions in quantum theory and you are likely to hear that there is still no consensus on many of these questions—all the while, of course, everybody seems to be in perfect agreement on how to apply the quantum formalism when it comes to making experimental predictions. Remarkably, there has never been any serious attempt to find out what the current opinions of the community really are and how they may be correlated. We jumped on the opportunity and polled 33 participants at a 2011 conference on “Quantum Physics and the Nature of Reality” (Fig. 1) 2. (We hasten to add that our poll is to be understood as merely a snapshot and certainly cannot claim to be representative.) As soon as we had collected the questionnaires, the respondents eagerly asked to hear the results. Evidently, we had not been the only curious party. What did we find? The fundamental questions, it seems, still elicit radically different responses. Take the quantum state—represented by the wavefunction—as an illustration. The wavefunction is the central mathematical symbol of quantum mechanics. It allows us to make incredibly accurate predictions, be it in atomic, molecular, or solid-state physics. But how are we to interpret it? Is it itself a physical property, or does it merely represent our knowledge? Our poll revealed a tie between these two positions. And not only that: a third of respondents preferred a mix of both viewpoints—perhaps a sign that a more nuanced view, or even a synthesis of views, may be on the horizon. Only 3% of those polled thought that quantum states never refer to a single system but only to ensembles of systems. Perhaps this departure from the ensemble view—a view that, we suspect, remains more popular in the physics community at large—has to do with the fact that experiments with single quantum systems have become routine in today's quantum-information laboratories. Sharp disagreement was in evidence on another deep question. Abraham Pais, Einstein's biographer, recalled that “during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I look at it” 3. Putting the issue differently, are the physical properties of objects well defined before we actually measure them? Half of the respondents in our poll believed that they sometimes were, while the other half said that they never were. These two positions correspond to radically different ways of understanding the function of measurement: either as simply ascertaining—at least sometimes—of what is already there, or as an act of genuine creation. The role of measurement is also at the heart of another perennial favorite of foundational discussions, the measurement problem. The measurement problem highlights a curious fact about quantum theory: while the act of measurement assumes a fundamental role, it is not described—not without interpretive contortions, anyway—by the dynamical law of quantum theory, the Schrödinger equation. For decades, the measurement problem was seen by many as the main stumbling block for quantum theory, sparking a storm of rivaling attempts to deal with this perceived issue. Today, the waters seem to have calmed and attention shifted elsewhere, as only less than a fourth of respondents consider the measurement problem “a severe difficulty threatening quantum mechanics.” Changing attitudes are also evident when it comes to the issue of chance Einstein had brought to light in 1917. Today, the question of the randomness of quantum events no longer seems to be all that contentious. Most of our respondents accepted randomness as irreducible or a fundamental concept in nature (or both). Less than one-tenth of respondents thought that quantum randomness was merely apparent rather than fundamental, and no one believed in a hidden determinism governing quantum events. We wish we could hear Einstein's opinion today. Why have attitudes and priorities changed? It's hard to say, but we think there may be several driving forces. The rapid ascent of quantum information science has not only led to applications such as secure cryptography and the promise of lightning-fast quantum computers, but has also shed new light on foundational problems and handed us new tools for addressing them. Our poll shows that these tools are considered a welcome addition, with three-fourths seeing quantum information as a breath of fresh air for foundational investigations. There is also optimism about the future technological development of quantum information, with more than 75% of respondents expecting a working and useful quantum computer to be realized within the next fifty years. Such optimism might be rooted in the astonishing experimental progress we have witnessed over the past decades, another driving force behind changing attitudes. We are now at stage where almost perfect experimental control of single quantum systems has been achieved. The 2012 Nobel Prize in physics was awarded for just such experiments. This has put at our fingertips the ability to actually carry out the thought experiments—or approximations thereof, at any rate—that the founders of quantum theory had dreamed up. Take Schrödinger's cat. In 1935, Schrödinger wanted to illustrate what seemed to him an absurd prediction of the new theory: that the strange quantum superpositions of the atomic world can be amplified to everyday objects. Schrödinger's object of choice was a cat in a specifically prepared box. Quantum theory then suggested that the state of the cat should become transformed into a bizarre quantum superposition of being simultaneously alive and dead. But what Schrödinger had intended as a “burlesque” 4 thought experiment is now approaching experimental reality. Over the last decades, researchers have become increasingly skilled in breeding small versions of Schrödinger's cat. While they don't involve actual cats, they do already involve large biological molecules. Our respondents, it seems, were inspired by such developments. A solid two-thirds majority declared that they don't expect any fundamental limit in this enterprise of observing larger and larger objects in superpositions of macroscopically distinct states. No limit, then, for quantum theory—something that Bohr had already suggested when he, in some of his early thought experiments, considered apparatuses that included macroscopic parts behaving in quantum-mechanical ways. There are other new trends. Why do people seem to be much more at ease with relativity theory than with quantum theory? For one, both special and general relativity theory are grounded in a few simple physical principles. By contrast, quantum theory is lacking such a foundation and is instead based on a rather abstract mathematical body. Today, several researchers are out to change this situation, trying to derive quantum theory from a small set of physical or information-theoretic principles. They hope that in this way, we will understand why we have this peculiar theory to begin with. A majority in our poll regarded such “reconstructions” of quantum theory as giving useful insights, indicating once more that any new tool that promises fresh insights is embraced with an open mind. To be sure, many (albeit not all) of the questions we asked in the poll are interpretive questions. This means that unless we should find out some day that quantum theory is in fact not always valid—in which case we would have to rethink the whole game—experiments arguably can't play the role of the arbiter. Some physicists will conclude from this that we need not bother with such questions, and relegate them to philosophy. We think this is too quick. Many ideas in physics didn't come out of thin air, but came about when someone started looking at a problem with a certain philosophical disposition. In this sense, we may think of the plurality of views in quantum mechanics as productive. Every interpretation highlights some aspect of quantum theory, is particularly suited for explaining particular phenomena, and may inspire new technologies—such as the quantum computer—or even new physics. What, then, does the future hold? Half of the respondents in our poll believe that in fifty years from now, we will probably still be coming together for conferences on the fundamental questions of quantum theory. But what kinds of questions will be on the agenda? Will we still be worrying about the same problems as today? Or will these problems have been solved—or found to be less relevant—and our focus shifted to new questions once again? Who knows. But the location of the conference where we conducted the poll may tell a story. It was the place of a monastery, and a central position in the battle between Catholics and Protestants during the seventeenth century. Many of the questions that were hotly debated back then are no longer of interest to many people today, and other, new questions have since taken center stage in our society. Maybe some of the battles over the interpretation of quantum theory will meet a similar fate.