The concept of the theory of measurement and choice of quantum alternative is considered, according to which the outcome of a particular measurement is determined by the reservoir (detector) state. The way of deducing standard (probabilistic) quantum-mechanical interpretation rules is discussed, with special emphasis on the theoretical demonstration of the wave-function reduction phenomenon. The method of resolving the “Schrodinger cat” paradox is suggested. The interrelation between the mechanisms of formation of shot and flicker noises and the role of reservoir in the formation of quantum-mechanical probability is discussed.
The concept of the theory of measurement and choice of quantum alternative is considered, according to which the outcome of a particular measurement is determined by the reservoir (detector) state. The way of deducing standard (probabilistic) quantum-mechanical interpretation rules is discussed, with special emphasis on the theoretical demonstration of the wave-function reduction phenomenon. The method of resolving the “Schrodinger cat” paradox is suggested. The interrelation between the mechanisms of formation of shot and flicker noises and the role of reservoir in the formation of quantum-mechanical probability is discussed.
Although quantum mechanics is a mature theory, fundamental problems discussed during its time of foundation have remained with us to this day. These problems are centered on the problematic relation between the quantum and classical worlds. The most famous element is the measurement problem, i.e., the measurement of a quantum system by a classical apparatus, and the concomitant phenomena of wave packet reduction, the appearance of probability, and the problems related to Schrödinger cat states. A fundamental question in this context is whether quantum mechanics can bootstrap itself to the classical world: is quantum mechanics self-consistent, such that the measurement process can be understood within quantum mechanics itself, or does this process require additional elements from the realm outside of traditional quantum mechanics? Here, we point to a problematic aspect in the traditional Schrödinger cat argument which can be overcome through its extension with a proper macroscopic preparation device; the deliberate creation of a cat state and its identification then turns into a non-trivial problem requiring the determination of the evolution of a quantum system entangled with a macroscopic reservoir. We describe a new type of wave-function correlator testing for the appearance of Schrödinger cat states and discuss its implications for theories deriving the wave function collapse from a unitary evolution.
The basic idea of quantum mechanics is that the property of any system can be in a state of superposition of various possibilities (or eigen states).This state of superposition is also known as wave function and it evolves linearly with time in a deterministic way in accordance with the Schrodinger equation.However, when a measurement is carried out on the system to determine the value of that property (say position), the system instantaneously transforms to one of the eigen states and thus we get only a single value as an outcome of the measurement.Quantum measurement problem seeks to find the cause and exact mechanism governing this transformation.In an attempt to solve the above problem, in this paper, we will first define what the wave function represents in real-world and will identify the root cause behind the stochastic nature of events.Then, we will develop a model to explain the mechanism of collapse of the quantum mechanical wave function in response to a measurement.In the process of development of model, we will explain Schrodinger cat paradox and will show how Born's rule for probability becomes a natural consequence of the measurement process.
This paper reviews and suggests a resolution of the problem of definite outcomes of measurement. This problem, also known as ‘Schrodinger’s cat’, has long posed an apparent paradox because the state resulting from a measurement appears to be a quantum superposition in which the detector is in two macroscopically distinct states (alive and dead in the case of the cat) simultaneously. Many alternative interpretations of the quantum mathematical formalism, and several alternative modifications of the theory, have been proposed to resolve this problem, but no consensus has formed supporting any one of them. Applying standard quantum theory to the measurement state, together with the analysis and results of decades of nonlocality experiments with pairs of entangled systems, this paper shows the entangled measurement state is not a paradoxical macroscopic superposition of states. It is instead a phase-dependent superposition of correlations between states of the subsystems. Thus Schrodinger’s cat is a non-paradoxical ‘macroscopic correlation’ in which one of the two correlated systems happens to be a detector. This insight resolves the problem of definite outcomes but it does not entirely resolve the measurement problem because the entangled state is still reversible.
A misunderstanding of entangled states has spawned decades of concern about quantum measurements and a plethora of quantum interpretations. The "measurement state" or "Schrodinger's cat state" of a superposed quantum system and its detector is nonlocally entangled, suggesting that we turn to nonlocality experiments for insight into measurements. By studying the full range of superposition phases, these experiments show precisely what the measurement state does and does not superpose. These experiments reveal that the measurement state is not, as had been supposed, a paradoxical superposition of detector states. It is instead a nonparadoxical superposition of two correlations between detector states and system states. In this way, the experimental results resolve the problem of definite outcomes ("Schrodinger's cat"), leading to a resolution of the measurement problem. However, this argument does not yet resolve the measurement problem because it is based on the results of experiments, while measurement is a theoretical problem: How can standard quantum theory explain the definite outcomes seen experimentally? Thus, we summarize the nonlocality experiments' supporting theory, which rigorously predicts the experimental results directly from optical paths. Several previous theoretical analyses of the measurement problem have relied on the reduced density operators derived from the measurement state, but these solutions have been rejected due to criticism of reduced density operators. Because it avoids reduced density operators, the optical-path analysis is immune to such criticism.
In most textbooks, measurement does not receive the full attention it deserves and sometimes is even not treated at all, apart a brief and cryptic mention of the “reduction of the wave packet.” However, in the last decades, the situation has profoundly changed and it is time to consider measurement a fundamental part of quantum mechanics, even, to a certain extent, an important generalization of the traditional theory (see also Chs. 14–15). This chapter consists of three major parts. In the first block (Secs. 9.1–9.4) we develop the main physical features of the measurement process: the heart of the argument is here represented by the aspects related to the interpretation. In the second part (Secs. 9.5–9.8) we discuss several special (and partly interdependent) topics of measurement: the heart here is represented by experimental aspects. In the third part (Secs. 9.9–9.12) we deal with the measurement process on a more formal plane, making use, in particular, of the generalization represented by the concepts of effect and positive operator valued measure (POVM). As we have said, the measurement problem is one of the most fundamental issues in the conceptual structure of quantum mechanics (as described in Sec. 9.1) and has a long history that will be examined in Sec. 9.2. In this context, the existence of apparently paradoxical quantum states comes about: the so-called Schrödinger cat states (see Sec. 9.3).
The purpose of this paper is to resolve two paradoxes, which occur in quantum theory, by using the discussion of the theory of measurement presented in two earlier papers by the author [3], [4], [5]. The two paradoxes discussed will be the Schrödinger cat paradox and the Einstein, Podolski, Rosen paradox [2]. An introductory section will be included which summarizes the relevant results from the author's previous papers. Also a discussion will be made regarding the author's interpretation of the density operator.