Solution to the Quantum Measurement Problem via Entanglement-STT-Theory with Ontological Objectivity Regarding the Wave-Function and the Collapse

Solution to the Quantum Measurement Problem via Entanglement-STT-Theory with Ontological Objectivity Regarding the Wave-Function and the Collapse It seems that entanglement should be the key to solving the measurement problem because one of the essential differences between the quantum world and the classical world is the presence or absence of entanglement. If we wish to establish a theory such that collapse occurs when some physical threshold is reached, it is reasonable to expect that such a threshold should be an entanglement-related quantity. Entanglement itself is not an appropriate choice for the threshold for the following reason. If collapse occurs when entanglement reaches a high threshold, even the classical world should exhibit entanglement-related phenomena because highly entangled systems that have not yet reached the threshold would exist in the classical world. This supposition is contradictory to everyday observations. As a suitable threshold that overcomes this difficulty, we choose the entangling speed, i.e., the time derivative of the von Neumann entropy of a system. The entangling speed can be large even when entanglement itself is small, and, in particular, it can be enormous when a system is simultaneously interacting with a large number of environmental particles. Simultaneous interaction with a myriad of particles is a common feature of macroscopic classical objects. Hence, if we postulate that collapse occurs when the entangling speed reaches a certain threshold, then macroscopic objects should be able to reach that threshold easily. After collapse, the entangling speed of the object can increase again very rapidly, resulting in multiple consecutive collapses within a short period of time. We will see that this nearly continuous collapse causes macroscopic object to behave classically. In this respect, we expect the entangling-speed-threshold theory to suitably explain the quantum-to-classical transition. According to the orthodox interpretation of quantum mechanics, there are two different types of processes in the universe: deterministic unitary processes and indeterministic collapse processes that occur at measurement. This dualism has made many physicists uncomfortable. Because, even at measurement, one can define a closed system that contains both the measured system and the measuring apparatus, whether the collapse actually occurs has remained controversial. Moreover, even if one accepts the collapse postulate, the question of what conditions are required to achieve measurement has remained problematic. In addition, the question of why classical objects are observed in a certain preferred basis among infinitely many legitimate bases has also been intensively discussed. These problems are collectively known as the quantum measurement problem and have been a subject of debate since the birth of quantum mechanics. Many theories and interpretations have been proposed to address the quantum measurement problem. Some of them explicitly or at least tacitly accept the collapse postulate, whereas others reject the notion of collapse. On the collapse side, examples include the Copenhagen interpretation, the von Neumann-Wigner interpretation [1], and objective collapse theories such as the Ghirardi-Rimini-Weber theory [2] and the Penrose theory [3]. On the no-collapse side, examples include the de Broglie-Bohm theory [4], the many-worlds interpretation [5], the many-minds interpretation [6], the consistent histories interpretation [7], and many others. Despite the variety of these endeavors, there has been no broad consensus that the problem was clearly solved. The theory proposed in this paper is an objective collapse theory in which both the wavefunction and the process of collapse are regarded as ontologically objective. We accept the dualism that states that there are fundamentally two different types of processes in the universe: unitary processes and collapse processes. Because current quantum theory is satisfactory for unitary processes, we intend to establish a theory about collapse processes. The key postulate of the theory is that the state of a system collapses when the entangling speed of that system reaches a threshold. We call this theory the entangling-speed-threshold theory. Using this theory, we provide plausible answers to the questions of where and when collapse occurs, what determines the collapse basis, how subsystems should be defined given a large system, and what determines the observables (or, more generally, the measurement. operators). We also explain how deterministic classical dynamics emerges from indeterministic quantum collapse, where nearly continuous collapse plays a crucial role in explaining the quantum-to-classical transition. In addition, we show that before and after collapse, energy is accurately conserved when the environment consists of many degrees of freedom. To convince ourselves that the theory is consistent with everyday observations of classical phenomena, we apply the theory to a macroscopic flying body such as a bullet in the air, and show that the collapse basis of the bullet derived by the theory has both a highly localized position and a well-defined momentum. The success achieved in deriving the classical states of a macroscopic body can be considered as evidence that the theory is well suited for explaining the quantum-to-classical transition. Finally, we suggest an experiment that can verify the theory. To resolve the quantum measurement problem, we propose an objective collapse theory in which both the wavefunction and the process of collapse are regarded as ontologically objective. The theory, which we call the entangling-speed-threshold theory, postulates that collapse occurs when the entangling speed of a system reaches a threshold, and the collapse basis is determined so as to eliminate the entangling speed and to minimize its increasing rate. Using this theory, we provide answers to the questions of where and when collapse occurs, how the collapse basis is determined, what systems are (in other words, what the actual tensor product structure is), and what determines the observables. We also explain how deterministic classical dynamics emerges from indeterministic quantum collapse, explaining the quantum-to-classical transition. In addition, we show that the theory guarantees energy conservation to a high accuracy. We apply the theory to a macroscopic flying body such as a bullet in the air, and derive a satisfactory collapse basis that is highly localized in both position and momentum, consistent with our everyday observation. Finally, we suggest an experiment that can verify the theory.