The measurement problem of quantum theory (QT) is the unsolved problem of how the probabilistic predictions of QT are turned into definite measurement results. A related question is whether a measurement in QT implies a collapse of the wave function and what the collapse of the wave function exactly means. Theories proposed on these subjects have not found general agreements among physicists. This paper proposes a solution to the QT measurement problem in terms of a functional model of the measurement process. A functional model describes the process of the dynamic evolution of a physical system. The model assumes that the interactions between the measured QT object and the measurement apparatus are normal interactions which adhere to the laws of quantum field theory.
The measurement problem of quantum theory (QT) is the unsolved problem of how the probabilistic predictions of QT are turned into definite measurement results. A related question is whether a measurement in QT implies a collapse of the wave function and what the collapse of the wave function exactly means. Theories proposed on these subjects have not found general agreements among physicists. This paper proposes a solution to the QT measurement problem in terms of a functional model of the measurement process. A functional model describes the process of the dynamic evolution of a physical system. The model assumes that the interactions between the measured QT object and the measurement apparatus are normal interactions which adhere to the laws of quantum field theory.
The so-called measurement problem of quantum theory (QT) is still lacking a satisfactory, or at least widely agreed upon, solution. A number of theories, known as interpretations of quantum theory, have been proposed and found differing acceptance among physicists. Most of the proposed theories try to explain what happens during a QT measurement using a modification of the declarative equations that define the possible results of a measurement of QT observables or by making assumptions outside the scope of falsifiable physics. This paper proposes a solution to the QT measurement problem in terms of a model of the process for the evolution of two QT systems that interact in a way that represents a measurement. The model assumes that the interactions between the measured QT object and the measurement apparatus are ''normal" interactions which adhere to the laws of quantum field theory.
In this paper, a functional model of interactions in quantum theory (QT) is proposed. A functional model describes the dynamic evolution of a physical system in terms of process steps and intermediate states. That is, it describes how things function. The proposed functional model of QT interactions was developed in the context of the author's work toward a computer model of QT with the goal of supporting the largest possible scope of QT concepts. In QT, the results of interactions are computed using quantum field theory (QFT). Therefore, the proposed functional model of interactions is based on QFT. There are a number of important QT concepts, such as measurement, entanglement, and decoherence, that are related to interactions. The functional model of interactions also addresses these phenomena.
Attempting to describe the "collapse of the wave function" of the orthodox quantum theory as a physical process, a natural assumption is that the measurement apparatus is subject to the same physical laws as the measured object, leading to a theory without rules for measurement. This – together with the loss of classical-quantum correspondence for chaotic systems – enforces the inclusion of the environment. I very shortly describe the present state of the art in this field – a challenge for the quantum many body community.
The collapse postulate in quantum mechanics is problematic due to the measurement problem. The problem lies not with collapse per se, but with the appeal to measurement; a theory that could underwrite the collapse process without ineliminable reference to measurement would constitute a solution to the measurement problem. This is the strategy pursued by dynamical (or spontaneous) collapse theories. But dynamical collapse theories face a number of challenges. First, they make different empirical predictions from standard quantum mechanics, and hence are potentially empirically refutable. Second, there are difficulties reconciling the dynamical collapse mechanism with special relativity. Third, the post-collapse state is not the same as the post-measurement state of standard quantum mechanics, raising the possibility that dynamical collapse theories do not solve the measurement problem after all. Assuming that these challenges can be met, dynamical collapse theories can lay claim to being serious contenders for the correct description of the quantum world. And the description they provide has a number of interesting consequences. First, it makes indeterminism an irreducible fact about the physical world. It has been argued that this has important consequences for the foundations of statistical mechanics, for free will, and for consciousness. Second, many dynamical collapse theories can be taken to imply that the quantum wave function is fundamental, giving rise to a new kind of vagueness, since a wave can be fuzzy around the edges in a way that a particle cannot. Furthermore, the quantum wave function is defined over a high-dimensional space, not the three-dimensional space of experience, suggesting to some that three-dimensionality is an illusion.
The topic of measurement in relativistic quantum field theory is addressed in this article. Some of the long standing problems of this subject are highlighted, including the incompatibility of an instantaneous ``collapse of the wavefunction'' with relativity of simultaneity, and the difficulty of maintaining causality in the rules for measurement highlighted by ``impossible measurement'' scenarios. Thereafter, the issue is considered from the perspective of mathematical physics. To this end, quantum field theory is described in a model-independent, operator algebraic setting, on generic Lorentzian spacetime manifolds. The process of measurement is modelled by a localized dynamical coupling between a quantum field called the ``system'', and another quantum field, called the ``probe''. The result of the dynamical coupling is a scattering map, whereby measurements carried out on the probe can be interpreted as measurements of induced observables on the system. The localization of the dynamical coupling allows it to derive causal relations for the induced observables. It will be discussed how this approach leads to the concept of selective or non-selective system state updates conditioned on the result of probe measurements, which in turn allows it to obtain conditional probabilities for consecutive probe measurements consistent with relativistic causality and general covariance, without the need for a physical collapse of the wavefunction. In particular, the problem of impossible measurements is resolved. Finally, there is a brief discussion of accelerated detectors and other related work.
Abstract The problem of the wave function collapse (a problem of measurement in quantum mechanics) is considered. It is shown that it can be solved based on quantum mechanics and does not require any additional assumptions or new theories. The particle creation and annihilation processes, which are described based on quantum field theory, play a key role in the measurement processes. Superposition principle is not valid for the system of equations of quantum field theory for particles and fields, because this system is a non-linear. As a result of the creation (annihilation) of a particle, an additional uncertainty arises, which “smears” the interference pattern. The imposition of such a large number of uncertainties in the repetitive measurements leads to the classical behavior of particles. The decoherence theory also implies the creation and annihilation of particles, and this processes are the consequence of non-linearity of quantum mechanics. In this case, the term “collapse of the wave function” becomes a consequence of the other statements of quantum mechanics instead of a separate postulate of quantum mechanics.