Instantaneous collapse of the wave function upon measurement of a single particle is one of the postulates of the Copenhagen interpretation of quantum mechanics. However, what happens when a many-body system in a macroscopic coherent state is measured one particle at a time? Here, we consider successive measurements of individual spins from a spin Bose condensate that starts in a Schrödinger cat state. When the spin measurements are done one particle at a time, the collapse of the spin condensate is not instantaneous but leads to probabilities for spin measurement that strongly depend on the previous measurements. What is surprising is that an almost complete collapse occurs in very few measurements. Even in a large system, a single cat component is emphasized quite quickly in the sequence of measurements. We examine the process by analysis of a simple two-Fock-state cat, as well as a cat state that has many components. Justification is given for our theoretical measurement process.
Instantaneous collapse of the wave function upon measurement of a single particle is one of the postulates of the Copenhagen interpretation of quantum mechanics. However, what happens when a many-body system in a macroscopic coherent state is measured one particle at a time? Here, we consider successive measurements of individual spins from a spin Bose condensate that starts in a Schrödinger cat state. When the spin measurements are done one particle at a time, the collapse of the spin condensate is not instantaneous but leads to probabilities for spin measurement that strongly depend on the previous measurements. What is surprising is that an almost complete collapse occurs in very few measurements. Even in a large system, a single cat component is emphasized quite quickly in the sequence of measurements. We examine the process by analysis of a simple two-Fock-state cat, as well as a cat state that has many components. Justification is given for our theoretical measurement process.
The entangled Schrodinger cat state obtained immediately upon measurement of a superposed two-state quantum system is often considered paradoxical because it appears to predict two macroscopically different outcomes, such as an alive and dead cat. However, nonlocal interferometry experiments testing momentum-entangled photon pairs over all phases demonstrate that the cat state does not fit this description and is not paradoxical. Both experiment and theory imply that it instead represents a superposition of two nonlocally coherent (i.e. phase-dependent) statistical correlations between its sub-systems. This is not paradoxical. Standard quantum theory rigorously predicts the experimentally-observed outcomes of this state. Neither sub-system is superposed; rather, the correlations between the states of the subsystems are superposed. This resolves the problem of definite outcomes. The nonlocal properties of entanglement then ensure that only one outcome occurs while the other outcome simultaneously does not occur, resolving a problem posed by Einstein in 1927. The single outcome that occurs then triggers an irreversible process leading to macroscopic registration of the outcome. This resolves the quantum measurement problem. Collapse occurs because of entanglement and does not require a special collapse postulate. Collapse is a consequence of standard quantum physics and the irreversible nature of the macroscopic registration.
In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950s development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrödinger cat states are the norm rather than curiosities generated in physicists’ laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr’s quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.
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.
Whether wave function collapses or not is a major remaining question in the theory of quantum measurement. This difficulty stems from following two facts. First, it has not been recognized that single-particle quantum mechanics and many-particle quantum mechanics must be treated separately. Second, quantum jump (QJ) and wave function collapse (WFC) need clearer definitions. We define a QJ as a process of selecting a set of system eigenvalues (SEVs) of an observable and a WFC as a process of determining the probability distribution (PD) of SEVs, both from a single measurement. The goal of quantum observation is to obtain the PD, which is determined from an ensemble of SEVs. The wave function becomes an observable when the PD is determined. In single-particle quantum mechanics, a single measurement results in only one set of SEVs and the PD is not observable. Therefore the WFC does not happen. In many-particle quantum mechanics, we focus on the occupation number of a singe quantum state. The wave function does not collapse in general, but there are exceptions. The occupation number can be huge and macroscopic for photons or for Bose-Einstein condensates. In such a case, the PD is determined from a single measurement of a real ensemble and the WFC occurs. We call it a macroscopic quantum jump, which effectively is a measurement of a classical observable.
The fully entangled Schrodinger cat state obtained immediately upon measurement of a superposed two state quantum system by a detector is often said to paradoxically predict macroscopically different outcomes simultaneously. However, nonlocal interferometry experiments and their accompanying quantum theoretical analyses, testing momentum entangled photon pairs over the full range of phases, demonstrate that the cat state does not fit this description. This state instead represents two nonlocally coherent correlations between its subsystems. Even if the detector is a cat, this state is not paradoxical. Furthermore, standard quantum theory correctly predicts the experimentally observed nonparadoxical outcomes. Thus both quantum theory and quantum experiments show there is no Schrodinger cat paradox associated with measurement. This resolves the problem of definite outcomes and, with it, the measurement problem. Upon entanglement with a detector, superpositions collapse nonlocally and unitarily to one definite macroscopic outcome. No special collapse postulate is needed.
Whether the wave function collapses or not is a major remaining question in the theory of quantum measurement. This difficulty stems from the following two facts. First, it has not been recognized that single-particle quantum mechanics and many-particle quantum mechanics must be treated separately. Second, quantum jump (QJ) and wave function collapse (WFC) need clearer definitions. We define a QJ as a process of selecting a set of system eigenvalues (SEVs) of an observable and a WFC as a process of determining the probability distribution (PD) of SEVs, both from a single measurement. The goal of quantum observation is to obtain the PD, which is determined from an ensemble of SEVs. The wave function becomes an observable when the PD is determined. In single-particle quantum mechanics, a single measurement results in only one set of SEVs, and the PD is not observable. Therefore, the WFC does not happen. In many-particle quantum mechanics, we focus on the occupation number of a single quantum state. The wave function does not collapse in general, but there are exceptions. The occupation number can be huge and macroscopic for photons or for Bose-Einstein condensates. In such a case, the PD is determined from a single measurement of a real ensemble, and the WFC occurs. We call it a macroscopic quantum jump, which effectively is a measurement of a classical observable.