Schrödinger's cat states A prerequisite to getting quantitative information on the microscopic world is the existence of measuring apparatuses that indicate definite measuring results.The idea that a pointer of a measuring device is itself in an indeterminate state waiting for someone to make the wavefunction for the combined system (object + measuring apparatus) collapse by simply having a look on the apparatus, thus reading it out, appears absurd. I think, there is no doubt that measuring devices will behave like other objects in the macroscopic world in which there is no place for ‘intrinsic’ uncertainty. Actually, this fact becomes questionable, at least it needs further theoretical investigation, when it is claimed that the quantum mechanical description applies also to macroscopic bodies, in particular measuring devices. (There are physicists who do not shrink back from attributing a single wavefunction even to the whole universe!) The dilemma originates from the quantum mechanical rule following from the linearity of the Schrödinger equation, that a pure quantum state remains a pure quantum state during its evolution. So, assuming that both the microscopic system to be observed and the measuring apparatus are initially in a pure state each, the combined system (object + measuring apparatus) will still be in a pure state after the interaction has taken place. Hence one will need ‘someone’ to bring about the collapse of the wavefunction. (In a realistic approach to this problem, the agent is recognized to be the environment with its virtually infinite number of degrees of freedom.) Schrödinger, being fully aware of this dilemma, illustrated it ingeniously through a fictitious ‘diabolic device’.
Schrödinger's cat states A prerequisite to getting quantitative information on the microscopic world is the existence of measuring apparatuses that indicate definite measuring results.The idea that a pointer of a measuring device is itself in an indeterminate state waiting for someone to make the wavefunction for the combined system (object + measuring apparatus) collapse by simply having a look on the apparatus, thus reading it out, appears absurd. I think, there is no doubt that measuring devices will behave like other objects in the macroscopic world in which there is no place for ‘intrinsic’ uncertainty. Actually, this fact becomes questionable, at least it needs further theoretical investigation, when it is claimed that the quantum mechanical description applies also to macroscopic bodies, in particular measuring devices. (There are physicists who do not shrink back from attributing a single wavefunction even to the whole universe!) The dilemma originates from the quantum mechanical rule following from the linearity of the Schrödinger equation, that a pure quantum state remains a pure quantum state during its evolution. So, assuming that both the microscopic system to be observed and the measuring apparatus are initially in a pure state each, the combined system (object + measuring apparatus) will still be in a pure state after the interaction has taken place. Hence one will need ‘someone’ to bring about the collapse of the wavefunction. (In a realistic approach to this problem, the agent is recognized to be the environment with its virtually infinite number of degrees of freedom.) Schrödinger, being fully aware of this dilemma, illustrated it ingeniously through a fictitious ‘diabolic device’.
One of the main goals of no-collapse interpretations of quantum mechanics is to show how results of measurements are objectified, or, in a more poignant terminology, how in a measurement situation facts arise. One needs to show how in their dynamical evolution the measured system and, perhaps more importantly, the measuring apparatus acquire, or at least appear to acquire, the definite properties that are otherwise explained by the collapse of the state. This can be seen as a special case of the problem whether quantum mechanics alone can account for the classical behaviour of macroscopic systems; in particular, the permanent definiteness of at least those properties of macroscopic systems that are directly observable, such as the position of the pointer of a measuring apparatus. In other words, whether quantum mechanics can account for macrofacts of the familiar kind.
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.
Abstract Chapter 15 deals with various unresolved issues, such as how measurements are to be described, whether they induce collapse of linear superpositions, and if so, what the result should be. Another is whether quantum mechanics applies to macroscopic measuring devices, and if not, why not. Some of these issues are addressed via the Schrödinger cat-in-the-box experiment, in particular whether the cat is ever half alive and half dead; analogs of the corresponding Schrödinger-cat state (not involving a cat) have been studied experimentally. For Schrödinger, it was ridiculous to apply quantum mechanics to macroscopic situations, nevertheless, it has been explored by many physicists. Whether measurements induce collapse and whether collapse arises in various formulations/interpretations of quantum mechanics is examined in the context of generic measuring instruments known as pointer devices. Various conclusions have been reached, though consensus has not, despite only one interpretation having been verified experimentally.
The decoherence approach to the measurement problem invokes dissipative interactions between a measuring apparatus and its environment to explain, within the context of ‘pure’ quantum mechanics (QM), why such devices appear to possess definite pointer readings. By ‘pure’ QM, I mean Schrödinger evolution with no wavefunction collapse. Several classes of interpretations of pure QM can rely on decoherence. One class is the ‘modal’ interpretations of van Fraassen (1979), Dieks (1989), Healey (1989), and others. Another class is the relative-state and many-world interpretations. I will argue that decoherence cannot help these interpretations address the general metaphysical challenges raised against them. But decoherence can help pick out a ‘special’ basis that determines which observables receive definite values. I'll explore to what extent decoherence rescues the modal (biorthogonal) basis-selection rule, and Zurek's (environmental interaction) basis-selection rule, from the basis degeneracy problem and the imperfect measurement problem.
One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.