Measurement Problem In Quantum Mechanics Research Articles

The Measurement Problem in Quantum Mechanics(In Commemoration of the 50th Anniversary of the Foundation of People's Republic of China)

The Measurement Problem in Quantum Mechanics(In Commemoration of the 50th Anniversary of the Foundation of People's Republic of China)

The measurement problem revisited

It has been realized that the measurement problem of quantum mechanics is essentially the determinate-experience problem, and in order to solve the problem, the physical state representing the measurement result is required to be also the physical state on which the mental state of an observer supervenes. This necessitates a systematic analysis of the forms of psychophysical connection in the solutions to the measurement problem. In this paper, I propose a new, mentalistic formulation of the measurement problem which lays more stress on psychophysical connection. By this new formulation, it can be seen more clearly that the three main solutions to the measurement problem, namely Everett's theory, Bohm's theory and collapse theories, correspond to three different forms of psychophysical connection. I then analyze these forms of psychophysical connection. It is argued that the forms of psychophysical connection required by Everett's and Bohm's theories have potential problems, while an analysis of how the mental state of an observer supervenes on her wave function may help solve the structured tails problem of collapse theories.

Spontaneous collapse: A solution to the measurement problem and a source of the decay in mesonic systems

Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and Dynamical reduction models propose a solution to the measurement problem in quantum mechanics: the collapse of the wave function becomes a physical process. We compute the predictions to decaying and flavor--oscillating neutral mesons for the two most promising collapse models, the QMUPL (Quantum Mechanics with Universal Position Localization) model and the mass-proportional CSL (Continuous Spontaneous Localization) model. Our results are showing (i) a strong sensitivity to the very assumptions of the noise field underlying those two collapse models and (ii) under particular assumptions the CSL case allows even to recover the decay dynamics. This in turn allows to predict the effective collapse rates solely based on the measured values for the oscillation (mass differences) and the measured values of the decay constants. The four types of neutral mesons ($K$-meson, $D$-meson, $B_d$-meson, $B_s$-meson) lead surprisingly to ranges comparable to those put forward by Adler (2007) and Ghirardi-Rimini-Weber (1986). Our results show that these systems at high energies are very sensitive to possible modifications of the standard quantum theory making them a very powerful laboratory to rule out certain collapse scenarios and studying the detailed physical processes solving the measurement problem.

Is the World Local or Nonlocal? Towards an Emergent Quantum Mechanics in the 21st Century

What defines an emergent quantum mechanics (EmQM)? Can new insight be advanced into the nature of quantum nonlocality by seeking new links between quantum and emergent phenomena as described by self-organization, complexity, or emergence theory? Could the development of a future EmQM lead to a unified, relational image of the cosmos? One key motivation for adopting the concept of emergence in relation to quantum theory concerns the persistent failure in standard physics to unify the two pillars in the foundations of physics: quantum theory and general relativity theory (GRT). The total contradiction in the foundational, metaphysical assumptions that define orthodox quantum theory versus GRT might render inter-theoretic unification impossible. On the one hand, indeterminism and non-causality define orthodox quantum mechanics, and, on the other hand, GRT is governed by causality and determinism. How could these two metaphysically-contradictory theories ever be reconciled? The present work argues that metaphysical contradiction necessarily implies physical contradiction. The contradictions are essentially responsible also for the measurement problem in quantum mechanics. A common foundation may be needed for overcoming the contradictions between the two foundational theories. The concept of emergence, and the development of an EmQM, might help advance a common foundation - physical and metaphysical - as required for successfull inter-theory unification.

Sourcing semiclassical gravity from spontaneously localized quantum matter

The possibility that a classical space-time and quantum matter cohabit at the deepest level, i.e. the possibility of having a fundamental and not phenomenological semiclassical gravity, is often disregarded for lack of a good candidate theory. The standard semiclassical theory suffers from fundamental inconsistencies (e.g.: Schr\"odinger cat sources, faster-than-light communication and violation of the Born rule) which can only be ignored in simple typical situations. We harness the power of spontaneous localization models, historically constructed to solve the measurement problem in quantum mechanics, to build a consistent theory of (stochastic) semiclassical gravity in the Newtonian limit. Our model makes quantitative and potentially testable predictions: we recover the Newtonian pair potential up to a short distance cut-off (hence we predict no 1 particle self-interaction) and uncover an additional gravitational decoherence term which depends on the specifics of the underlying spontaneous localization model considered. We hint at a possible program to go past the Newtonian limit, towards a consistent general relativistic semiclassical gravity.

Response to Stuart Kauffman: The Measurement Problem in Quantum Mechanics

ABSTRACTRichard Feynman, a 1965 Nobel Prize winner in physics, quoting an unknown philosopher, said: “It is necessary for the very existence of science that the same conditions always produce the same results.” And Feynman's reply: “Well, they don't.” Double-slit experiments with both slits open and the wave interference pattern created by electrons falling on a screen behind the slits speak volumes to those two statements and the interpretive problem created by the non-deterministic behavior of microscopic matter. Quantum mechanics (QM) with its successes over the last 85 years has created the information age, and with insights into nature has given humans an economy concentrated with products based on quantum technology. All this even with questions about the fundamental aspects of measurement in the quantum world still being debated! Discussing the measurement aspect of QM does not require a physics background where physics scholars join other scholarly disciplines engaged in gaining knowledge about the reality of the one world of human experience. The necessary tools for discussion are imagination, speculation, and curiosity. But for a new credible interpretation of the measurement problem, quantum training or a quantum theoretician is required.

Structures of Confinements as an Empirical Property of Consciousness and a Fundamental Property in Physics

Our consciousness is confined to experience our own thoughts. By subjectively investigating associations between conscious experiences from different senses, it can be shown how confinement must be an existing property relating to smaller parts of our conscious experiences as well. In this article, it is investigated how entities confining other entities may serve as fundamental building blocks of physics and consciousness. The model evolves by changing the structure of confinements. It turns out that classical mechanics, relativity, quantum mechanics, non-locality, and a solution to the measurement problem in quantum mechanics follow from the definition of this model. The model also clarifies how different conscious experiences can be determined by different physical states, which is related to the hard problem of consciousness.

Measurement Problem: A Prediction Problem in Quantum Mechanics and Classical Physics

Quantum mechanics is based on Schrodinger’s wave function with linear superposition of vectors in a Hilbert space. Due to superposition, multiple physical states are considered simultaneously for the same time point, but when the corresponding quantum mechanical experiments are realized, there is only one outcome and not a superposition of pointer positions. This observation characterizes the quantum mechanical measurement problem, which for about a century found multiple interpretations, which can be classified as potentiality, as proposed by Heisenberg, or as real physical entities, for instance fields. Potentialities are yet inexistent in reality and unobservable in the present, since they represent a possible future. Thus, they can only be an intra-mental representation of a future process and not a physical extra-mental process ongoing in the present. There is coexistence of a physical object observable in reality and a mental prediction by an observer concerning the future behavior of this object. The characterization of quantum mechanical formalism by some physicists corresponds to a prediction and therefore to a mental representation of the future behavior of elementary particles and not to a description of an ongoing extra-mental process. Prediction in life and science has some characteristics, which resemble the measurement problem, since it undergoes a “multiple to one” reduction of mental potentialities to only one observable real outcome. Besides quantum mechanics, such reductions can also be found with many kinds of predictions, in classical physics for regular and irregular dynamical processes and in humans for programming future actions. Superposition in classical physics only concerns variable effects, but in quantum mechanics includes variable effects and non-localizable causes. Quantum mechanics, interpreted as prediction of future outcomes with multiple potentialities but only one realization, would resemble the general prediction problem in life and science and thereby loos its weird aspects.

Solving the hard problem of Bertrand's paradox

Bertrand's paradox is a famous problem of probability theory, pointing to a possible inconsistency in Laplace's principle of insufficient reason. In this article, we show that Bertrand's paradox contains two different problems: an “easy” problem and a “hard” problem. The easy problem can be solved by formulating Bertrand's question in sufficiently precise terms, so allowing for a non-ambiguous modelization of the entity subjected to the randomization. We then show that once the easy problem is settled, also the hard problem becomes solvable, provided Laplace's principle of insufficient reason is applied not to the outcomes of the experiment, but to the different possible “ways of selecting” an interaction between the entity under investigation and that producing the randomization. This consists in evaluating a huge average over all possible “ways of selecting” an interaction, which we call a universal average. Following a strategy similar to that used in the definition of the Wiener measure, we calculate such universal average and therefore solve the hard problem of Bertrand's paradox. The link between Bertrand's problem of probability theory and the measurement problem of quantum mechanics is also briefly discussed.

Insolubility from No-Signalling

This paper improves on the result in my http://philsci-archive.pitt.edu/9121/, showing that within the framework of the unitary Schroedinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The result follows directly from the no-signalling theorem applied to the entangled state of measured system and ancilla. As opposed to other 'insolubility theorems' for the measurement problem of quantum mechanics, it focuses on the impossibility of reproducing the phenomenological collapse of the state of the measured system.

A pedestrian approach to the measurement problem in quantum mechanics

The quantum theory of measurement has been a matter of debate for over eighty years. Most of the discussion has focused on theoretical issues with the consequence that other aspects (such as the operational prescriptions that are an integral part of experimental physics) have been largely ignored. This has undoubtedly exacerbated attempts to find a solution to the “measurement problem”. How the measurement problem is defined depends to some extent on how the theoretical concepts introduced by the theory are interpreted. In this paper, we fully embrace the minimalist statistical (ensemble) interpretation of quantum mechanics espoused by Einstein, Ballentine, and others. According to this interpretation, the quantum state description applies only to a statistical ensemble of similarly prepared systems rather than representing an individual system. Thus, the statistical interpretation obviates the need to entertain reduction of the state vector, one of the primary dilemmas of the measurement problem. The other major aspect of the measurement problem, the necessity of describing measurements in terms of classical concepts that lay outside of quantum theory, remains. A consistent formalism for interacting quantum and classical systems, like the one based on ensembles on configuration space that we refer to in this paper, might seem to eliminate this facet of the measurement problem; however, we argue that the ultimate interface with experiments is described by operational prescriptions and not in terms of the concepts of classical theory. There is no doubt that attempts to address the measurement problem have yielded important advances in fundamental physics; however, it is also very clear that the measurement problem is still far from being resolved. The pedestrian approach presented here suggests that this state of affairs is in part the result of searching for a theoretical/mathematical solution to what is fundamentally an experimental/observational question. It suggests also that the measurement problem is, in some sense, ill-posed and might never be resolved. This point of view is tenable so long as one is willing to view physical theories as providing models of nature rather than complete descriptions of reality. Among other things, these considerations lead us to suggest that the Copenhagen interpretation’s insistence on the classicality of the measurement apparatus should be replaced by the requirement that a measurement, which is specified operationally, should simply be of sufficient precision.

Quantum Correlations and the Measurement Problem

The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. Such correlations cannot be simulated with classical resources, which generate classical correlations represented by the points in a simplex, where the vertices of the simplex represent joint deterministic states that are the common causes of the correlations. The ‘no go’ hidden variable theorems tell us that we can’t shoe-horn phenomenal correlations outside the local polytope into a classical simplex by supposing that something has been left out of the story. The replacement of the classical simplex by the quantum convex set as the structure representing probabilistic correlations is the analogue for quantum mechanics of the replacement of Newton’s Euclidean space and time by Minkowski spacetime in special relativity. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are generic features of correlations that lie outside the classical simplex. This paper is an elaboration of these ideas, which have their source in work by Pitowsky (J. Math. Phys. 27:1556, 1986; Math. Program. 50:395, 1991; Phys. Rev. A 77:062109, 2008), Garg and Mermin (Found. Phys. 14:1–39, 1984), Barrett (Phys. Rev. A 75:032304, 2007; Phys. Rev. A 7:022101, 2005) and others, e.g., Brunner et al. ( arXiv:1303.2849 , 2013), but the literature goes back to Boole (An Investigation of the Laws of Thought, Dover, New York, 1951). The final section looks at the measurement problem of quantum mechanics in this context. A large part of the problem is removed by seeing that the inconsistency in reconciling the entangled state at the end of a quantum measurement process with the definiteness of the macroscopic pointer reading and the definiteness of the correlated value of the measured micro-observable depends on a stipulation that is not required by the structure of the quantum possibility space. Replacing this stipulation by an alternative consistent stipulation is the first step to resolving the problem.

A Flea on Schrödinger’s Cat

We propose a technical reformulation of the measurement problem of quantum mechanics, which is based on the postulate that the final state of a measurement is classical; this accords with experimental practice as well as with Bohr’s views. Unlike the usual formulation (in which the post-measurement state is a unit vector in Hilbert space), our version actually opens the possibility of admitting a purely technical solution within the confines of conventional quantum theory (as opposed to solutions that either modify this theory, or introduce unusual and controversial interpretative rules and/or ontologies).To that effect, we recall a remarkable phenomenon in the theory of Schrödinger operators (discovered in 1981 by Jona-Lasinio, Martinelli, and Scoppola), according to which the ground state of a symmetric double-well Hamiltonian (which is paradigmatically of Schrödinger’s Cat type) becomes exponentially sensitive to tiny perturbations of the potential as ħ→0. We show that this instability emerges also from the textbook wkb approximation, extend it to time-dependent perturbations, and study the dynamical transition from the ground state of the double well to the perturbed ground state (in which the cat is typically either dead or alive, depending on the details of the perturbation).Numerical simulations show that adiabatically arising perturbations may (quite literally) cause the collapse of the wave-function in the classical limit. Thus, at least in the context of a simple mathematical model, we combine the technical and conceptual virtues of decoherence (which fails to solve the measurement problem but launches the key idea that perturbations may come from the environment) with those of dynamical collapse models à la grw (which do solve the measurement problem but are ad hoc), without sharing their drawbacks: single measurement outcomes are obtained (instead of merely diagonal reduced density matrices), and no modification of quantum mechanics is needed.

Insolubility Theorems and EPR Argument

I present a very general and simple argument—based on the no-signalling theorem—showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility of reproducing the macroscopic measurement results). Although I believe this form of the argument is new, I argue it is essentially a variant of Einstein’s reasoning in the context of the EPR paradox—which is thereby illuminated from a new angle.

A realist interpretation of quantum mechanics based on undecidability due to gravity

We summarize several recent developments suggesting that solving the problem of time in quantum gravity leads to a solution of the measurement problem in quantum mechanics. This approach has been informally called "the Montevideo interpretation". In particular we discuss why definitions in this approach are not for all practical purposes (fapp) and how the problem of outcomes is resolved.

SHORTCOMINGS IN THE UNDERSTANDING OF WHY COSMOLOGICAL PERTURBATIONS LOOK CLASSICAL

There is a persistent state of confusion regarding the account of the quantum origin of the seeds of cosmological structure during inflation. The issue is the transition from the quantum uncertainties in the homogeneous and isotropic initial state, into the late-time "classical" anisotropies and inhomogeneities. There seems to be a widespread belief that decoherence addresses the issue in a satisfactory way. This view is taken, often implicitly, by most researchers working in the field. This can be seen most clearly in those accounts intended on facing the issue directly. For instance, a recent article [C. Kiefer and D. Polarski, arXiv: 0810.0087] argues just that, and presents a detailed explanation of the justifications. The explicit nature of that account will allow us to discuss the issue in detail. There are, of course, various other works that often indirectly address the issue with similar approaches (see Refs. 2–13). This type of arguments do not only implicitly assume that decoherence offers a satisfactory solution to the measurement problem in quantum mechanics, but also that, in particular, such approach is applicable to these quantum aspects of cosmology. We will review here, why do we, together with various other researchers in the field, consider that this assumption is not correct in general. Moreover as previously discussed in Refs. 22–26, we will argue that the cosmological situation is one where the measurement problem of quantum mechanics appears in a particular exacerbated form, and that, it is this, even sharper conundrum, that should be addressed when dealing with the inflationary account of the origin of the seeds of cosmic structure in the early Universe. We briefly discuss the ideas behind what we feel might be a promising approach to deal with this problem.

Undecidability and the Problem of Outcomes in Quantum Measurements

We argue that it is fundamentally impossible to recover information about quantum superpositions when a system has interacted with a sufficiently large number of degrees of freedom of the environment. This is due to the fact that gravity imposes fundamental limitations on how accurate measurements can be. This leads to the notion of undecidability: there is no way to tell, due to fundamental limitations, if a quantum system evolved unitarily or suffered wavefunction collapse. This in turn provides a solution to the problem of outcomes in quantum measurement by providing a sharp criterion for defining when an event has taken place. We analyze in detail in examples two situations in which in principle one could recover information about quantum coherence: a) "revivals" of coherence in the interaction of a system with the environment and b) the measurement of global observables of the system plus apparatus plus environment. We show in the examples that the fundamental limitations due to gravity and quantum mechanics in measurement prevent both revivals from occurring and the measurement of global observables. It can therefore be argued that the emerging picture provides a complete resolution to the measurement problem in quantum mechanics.

Notes on von Neumann measurement scheme

A quantum measurement scheme devised by von Neumann plays a central role in all considerations relevant to the measurement problem in quantum mechanics. Despite the fact that the scheme ultimately did not reach the anticipated goal, a view is still maintained, that at least the very approach to the solution of the problem is correct and does not rise any doubts about its consistency. However, a little critical check of a validity of the key assumptions, lying in the foundations of the scheme, casts some shadow on its physically unimpeachable status. Speaking explicitly, the use of such physically bad established notions as a quantization of a purely macroscopic object and an “ideal” measurement, although embodied in the proper mathematical formalism of quantum theory, as well as the over-simplified interpretation of the theory, characterize this measurement scheme as a purely theoretical construction, which is far away from the situation occurring in the case of real measurements.

Consciousness, Situations, and the Measurement Problem of Quantum Mechanics

There are two versions of the putative connection between consciousness and the measurement problem of quantum mechanics : consciousness as the cause of state vector reduction, and state vector reduction as the physical basis of consciousness. In this article, these controversial ideas are neither accepted uncritically, nor rejected from the outset in the name of some prejudice about objective knowledge. Instead, their origin is sought in our most cherished (but disputable) beliefs about the place of mind and consciousness in the world. It is first pointed out that these common beliefs about mind and consciousness arise from reification of situated first-person experience. Then, situatedness is shown to be a constitutive part of any exhaustive treatment of quantum measurements. It turns out that the alleged connection between consciousness and the measurement problem is a symptom of (i) the ineliminability of our being situated from the end-product of science, and (ii) our difficulty to express correctly this being situated.

The Tausk Controversy on the Foundations of Quantum Mechanics: Physics, Philosophy, and Politics

In 1966 the Brazilian physicist Klaus Tausk (1927-2012) circulated a preprint from the International Centre for Theoretical Physics in Trieste, Italy, criticizing Adriana Daneri, Angelo Loinger,and Giovanni Maria Prosperi’s theory of 1962 on the measurement problem in quantum mechanics. A heated controversy ensued between two opposing camps within the orthodox interpretation of quantum theory, represented by Leon Rosenfeld and Eugene P. Wigner. The controversy went well beyond the strictly scientific issues, however, reflecting philosophical and political commitments within the context of the Cold War, the relationship between science in developed and Third World countries, the importance of social skills, and personal idiosyncrasies.