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Effective theory approach to the measurement problem

William Icefield

Published May 13, 2020• 0 citations
Publisher

Abstract

One understanding of the Niels Bohr's interpretation of quantum mechanics suggests that the measurement problem arises because an observer description of reality is incomplete due to lack of complete access to an entire system of observed and observer. In general, an additional and external measuring observer is required to access the entire system. Inevitable entanglement between observers, measurement apparatus and measured objects is key to such an understanding of the measurement problem. Quantum mechanics only provides a complete `incomplete' description of reality. Nevertheless, some issues, especially providing an account of why a preferred measurement basis arises, remain. Replacing relations between observed and observer in relational quantum mechanics with those between effective (approximate) theories, one arrives at a more clear understanding of why the measurement problem arises and how a preferred measurement basis is determined. The measurement problem exists because of measurement apparatus limitations, which only allow us to formulate and verify effective theories that inevitably neglect some details of nature.

DOI
10.31219/osf.io/v3z8m

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One understanding of the Niels Bohr's interpretation of quantum mechanics suggests that the measurement problem arises because an observer description of reality is incomplete due to lack of complete access to an entire system of observed and observer. In general, an additional and external measuring observer is required to access the entire system. Inevitable entanglement between observers, measurement apparatus and measured objects is key to such an understanding of the measurement problem. Quantum mechanics only provides a complete `incomplete' description of reality. Nevertheless, some issues, especially providing an account of why a preferred measurement basis arises, remain. Replacing relations between observed and observer in relational quantum mechanics with those between effective (approximate) theories, one arrives at a more clear understanding of why the measurement problem arises and how a preferred measurement basis is determined. The measurement problem exists because of measurement apparatus limitations, which only allow us to formulate and verify effective theories that inevitably neglect some details of nature.
For over a century, scientists have been fascinated by the strange behaviour of matter at the quantum level, where particles can exist in many states at once and affect each other instantly across distances. This paper explores this realm of quantum mechanics by focusing on wave–particle duality, superposition, entanglement and the measurement problem. It shows how these concepts defy the foundations of clas-sical physics to challenge assumptions about determinism, locality, interconnection and objectivity. The paper maintains that although quantum theory works remarkably well, we lack a clear account of what kind of reality it describes, as major interpretations such as Copenhagen, Many-Worlds and objective collapse still struggle to match quantum theory’s success with a clear picture of reality. yet as its major interpretations offer com-peting and unresolved pictures of the world. Schrödinger’s cat illustrates this tension to showcase how macroscopic systems can expose the limits of observation and the line be-tween classical and quantum worlds. The paper concludes that these quantum principles are underpinned by both technical and philosophical challenges and they force us to re-think causality and the role of the observer in explaining reality.
The problem of quantum state reduction The fundamental problem of quantum mechanics, as that theory is presently understood, is to make sense of the reduction of the state vector (i.e. collapse of the wave function ), denoted here by R . This issue is usually addressed in terms of the ‘quantum measurement problem’, which is to comprehend how, upon measurement of a quantum system, this (seemingly) discontinuous R -process can come about. A measurement, after all, merely consists of the quantum state under consideration becoming entangled with a more extended part of the physical universe, e.g. with a measuring apparatus. This measuring apparatus – together with the observing physicist and their common environment – should, according to conventional understanding, all also have some quantum description. Accordingly, there should be a quantum description of this entire quantum state, involving not only the original system under consideration but also the apparatus, physicist, and remaining environment – and this entire state would be expected to evolve continuously, solely according to the Schrödinger equation (unitary evolution), here denoted by the symbol U . Numerous different attitudes to R have been expressed over many years, ever since quantum mechanics was first clearly formulated. The most influential viewpoint has been the ‘Copenhagen interpretation’ of Niels Bohr, according to which the state vector │ψ〉 is not to be taken seriously as describing a quantum-level physical reality, but is to be regarded as merely referring to our (maximal) ‘knowledge’ of a physical system, and whose ultimate role is simply to provide us with a means to calculate probabilities when a measurement is performed on the system.
The term "measurement" in quantum theory (as well as in other physical theories) is ambiguous: It is used to describe both an experience - e.g., an observation in an experiment - and an interaction with the system under scrutiny. If doing physics is regarded as a creative activity to develop a meaningful description of the world, then one has to carefully discriminate between the two notions: An observer's account of experience - consitutive to meaning - is hardly expressed exhaustively by the formal framework of an interaction within one particular theory. We develop a corresponding perspective onto central terms in quantum mechanics in general, and onto the measurement problem in particular.
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object. The complementary descriptions approach is a framework for the interpretation of quantum mechanics, more specifically, it focuses in the development of the idea of complementarity and the concept of potentiality in the orthodox quantum formulation. In PART I of this article, we analyze the ideas of Bohr and present the principle of complementary description which takes into account Einstein's ontological position. We argue, in PART II, that this development allows a better understanding of some of the paradigmatic interpretational problems in quantum mechanics, such as the measurement problem and the quantum to classical limit. We conclude that one should further develop complementarity in order to elaborate a consistent worldview.
In quantum mechanics, the measurement problem is commonly regarded as reason for deep concern. It seems that, either, the problem can be solved and there is hope for quantum mechanics, or the theory better be left behind in search of another one. We investigate the prospect of finding a solution to the measurement problem—within quantum mechanics, as well as in theoretical frameworks beyond it. As we do so, there emerges a perspective on doing physics drawing from considerations in the philosophy of language and in epistemology. Developing this perspective for further aspects in physics reveals: The notion of a system is similarly problematic. Eventually, the question arises whether these are problems of specific physical theories, or rather of specific stances towards physics. In this regard, we examine in particular the role and understanding of assumptions.
Niels Bohr introduced the concept of complementarity in order to give a general account of quantum mechanics, however he stressed that the idea of complementarity is related to the general difficulty in the formation of human ideas, inherent in the distinction between subject and object. The complementary descriptions approach is a framework for the interpretation of quantum mechanics, more specifically, it focuses in the development of the idea of complementarity and the concept of potentiality in the orthodox quantum formulation. In PART I of this article, we analyze the ideas of Bohr and present the principle of complementary description which takes into account Einstein's ontological position. We argue, in PART II, that this development allows a better understanding of some of the paradigmatic interpretational problems in quantum mechanics, such as the measurement problem and the quantum to classical limit. We conclude that one should further develop complementarity in order to elaborate a consistent worldview.