The Philosophy of Quantum Mechanics (Handout Eight) 1. The Copenhagen Interpretation Bohr interpreted quantum theory as showing that there is a fundamental partition in nature, between the microphysical and the macrophysical. The macrophysical world could be understood employing the concepts of classical realism, for every macrophysical observable (e.g. position and momentum) has a sharp definite value at all times. The microphysical world, on the other hand, could be classical concepts; indeed those classical concepts are not even well-defined in the microphysical universe. The Copenhagen Interpretation claims that the quantum mechanical state description is complete, that there are no hidden variables, and that the existence of superposed states and the uncertainty relations merely shows that for the microphysical realm classical concepts derived from the study of macrophysical phenomena cannot in general be applied. Accordingly, when we perform a measurement on a previously isolated system, that measurement should be conceived of as an interaction which brings about some changes in a macrophysically observable property of the measuring apparatus. Thus, the result of a measurement involving as it does change in a macrophysical (classical) parameter (for example, a flash on the screen) is appropriately describable using classical concepts. But it is only when such a measurement is made that the classical properties with sharp, definite values (e.g. definite position) are applicable. There is, however, a major difficulty with the Copenhagen interpretation, stemming directly from the claim that quantum mechanics will allow that classical macrophysical parameters will always have definite sharp values. How this problem arises is best illustrated by the famous thought-experiment of Schrödinger s cat. (Cats tend to have a bad time in physics, quantum and classical!) In this experiment we imagine that a cat is placed in a box and connected up to a device which emits a single photon towards a half silvered mirror. If the photon passes through the mirror (an event which according to quantum mechanics has probability 1 /2 ) then a detecting device closes a circuit which electrocutes the cat. If the photon fails to pass the mirror, the circuit remains open and the cat remains alive. The entire system of box, cat, mirror, detecting device and photon emitter, forms an isolated system. According to quantum mechanics, as soon as the photon is emitted the entire isolated system is in a superposed state described by the superposition of the wave(-state) corresponding to
passage of the photon through the mirror (and electrocution of the cat) and of the wave(-state) corresponding to failure of the photon to pass the mirror (and a live cat). Providing the system remains isolated, this is the correct (and complete) description of the entire cat-apparatus complex. In short, it is in a superposition of the live cat -state, and the dead cat -state. But in such a superposed state, the classical macrophysical observable cat living (or cat dead ) has no definite value. But this is inconsistent with the macrophysical realism (that all macrophysical observables should have sharp, definite values) of the Copenhagen interpretation. The Copenhagen Interpretation requires a sharp divide between the micro- and the macro-world. Schrödinger s thought experiment crosses that divide. Suppose that we now interact with the system by opening the box to see if the cat is alive or dead. According to quantum mechanics, at the instant of interaction, a discontinuous change of stage occurs (reduction of the wave packet) and the entire system jumps into a definite state in which the observable cat alive has a precise value (Yes or No). However, the observable takes on the value only at the instant of interaction with the catapparatus system, that is, when we perform the measurement of looking to see how the cat is! It would appear, therefore, that we the observers may be responsible for the electrocution of the cat. The Schrödinger cat-experiment appears to show classical macrophysical observables do not after all have a sharp value. A natural reply, however, is that the real interaction which collapses the wave packet and throws the cat into a definite state is not when we open the box to see, but when the photon is emitted and passes, or fails to pass, the half silvered mirror. Hence, the cat is never really in the strange superposed state of neither alive nor dead but in a definite state as soon as the emitted photon does or does not trigger the detector. But this reply will not do. For it simply asserts that the cat s feeling or not feeling the bolt of electricity itself constitutes a measurement. But this certainly does not follow from quantum mechanics, and it amounts to no more than stipulating that classical macrophysical observables always have definite sharp values, and that that will be the criterion for a measurement s having occurred. Hence, this attempt to deflect the criticism of the Copenhagen interpretation is hardly philosophically satisfactory, since it presupposes the correctness of the interpretation rather than providing an independent reason why the objection is incorrect.
The Schrödinger s cat experiment can be used to make a further point. Some authors have argued (particularly the great mathematician Von Neumann) that, in contrast with the worldview of classical physics, the observer, and in particular consciousness, is shown by the quantum theory to play a crucial role in determining physical reality. Suppose we consider an isolated system S (like the cat and the associated apparatus in the Schrödinger experiment) and let the state of S be described by a superposition of states. Let M be a system which performs at some point some measurement of a classical macrophysical parameter of S (perhaps, M could register the heartbeat of the cat). Then we can regard the interaction between the systems M and S as a measurement by M of a parameter of S. As such, the treatment of this interaction, by quantum mechanics, will be that of a reduction of the wave packet associated with S, the interaction resulting in a discontinuous change in S, when the measured parameter takes on a definite value. But we can also regard the total system M+S as one single isolated system, in which case the evolution of the states of that system will be governed by the first type of quantum mechanical time evolution, namely, the deterministic Schrödinger equation, in which case there will be no reduction of the wave packet. We might think that we could look, and find out, what M had in fact registered as the value of the measured parameter of S. But now we have a situation in which the observer (0) performs a measurement on the isolated system (M+S). So again we must treat this as a case of the deterministic evolution of a new isolated system O+M+S. Then the classical parameter, to ascertain whose value O looked at M, would, from the quantum-theoretic account of the evolution of the isolated system O+M+S, have no definite value. If measurement is, therefore, to play the role of ultimately inducing sharp values for observables, a natural question to ask is: when does the measurement take place? It seems arbitrary to say that it is when M interacts with S, because that can, as we have seen, be treated as an interaction within an isolated system in which no discontinuous reduction occurs. We could, therefore, have a whole sequence of measuring apparatus, each registering the values of an observable, itself registered by a measuring apparatus further down the chain. No matter how long the chain was, it could still be treated as a whole isolated system undergoing time evolution given by the Schrödinger equation. Macrophysical parameters do have sharp definite values, when we observe them. But we are physically just like the measuring apparatus M interacting with the observed system S ( i.e. like the
system M+S). So how is it that we observe sharp values? What destroys the equivalence of the two ways of treating the interaction? The proposed solution is that the only way the symmetry can be destroyed is by appeal to human consciousness, to the fact that we are conscious observers and it is ultimately non-physical consciousness which is responsible for the fact that the observable properties of physical systems have the definite real values that they do. It will follow that consciousness and physical reality are intimately interlinked. 2 Indeterminacy How bizarre one finds this consequence of the Copenhagen interpretation will depend to a great extent on one s conception of consciousness. Clearly, if one adopts the materialistic view, that mental states are physical states of the brain or central nervous system, then consciousness cannot be relied upon to separate the micro- from the macrophysical. Indeed, the general tenor of the scientific revolution which has taken place over the last four hundred years, and has in fact culminated in a world-view of which quantum mechanics is a part, is that human beings are different from the animal kingdom, and from the rest of nature, not in kind but only in degree of complexity. Hence consciousness cannot mark any radical difference. The cat constitutes an observer, and a macrophysical phenomenon, as much as we do ourselves. It is, therefore, instructive to realise that there is a coherent interpretation of quantum mechanical phenomena which requires neither the postulation of hidden variables, nor that of a sharp divide between two realms, the macrophysical and the microphysical, phenomena only in the latter being affected by quantum uncertainty. This new interpretation agrees that quantum theory is in fact complete. To illustrate it, let us recall our discussion of a particle whose state is described as a superposition of the two states ψ1 and ψ2 (which we represented schematically as ψ1 + ψ2). According to this interpretation, a particle in such a state has no definite position. What is described is a propensity or tendency to produce a definite value for the position upon measurement. That is, when we perform a measurement to ascertain where the particle is (for example, by employing a screen in the two slit-experiment and allowing the particle to interact with the screen), that act of observation results in a potentiality being actualised. The particle has no actual position in the superposed state, merely a potentiality or propensity to have a given definite position when it interacts with the
measuring apparatus. That potentiality becomes actual in the discontinuous collapse of the wave packet (j1 + j2) at the instant of interaction with the measuring device. Quantum mechanics measures such potentialities by assigning to each interval available to the particle a definite probability that upon measurement it will actually be found there. In our example we used the observable position, but we could equally well have chosen momentum or energy, indeed any of the dynamical properties of the system. So, if quantum mechanics is taken to be a fundamental theory, this interpretation requires that the classical realist view of the world as made up of individuals with definite properties be replaced by one in which propensities or potentialities are the fundamental properties of the constituents of Nature. We seem, in consequence, forced to concede that quantum mechanics entails a revision in our classical realist conception of the nature of reality. A satisfactory metaphysical account able to sustain an intelligible interpretation of the theory requires that we jettison our intuitive conception of the world as consisting of objects with definite and determinate properties. The hidden variable interpretation, attempting to force classical realism onto the microphysical world comes up against Bell s inequality, and so cannot be sustained. The Copenhagen interpretation, trying to limit quantum uncertainty to a range of microphysical phenomena separate from the world of scientific observation clashes with the fact that there is straightforward interaction between the two realms. Only at the cost of an untenable, because essentially anti-scientific, dualism concerning the mental, can such a distinction be maintained. Such a radical distinction threatens to make the mind, and consciousness, inaccessible to scientific investigation, and so ultimately inexplicable. It follows that quantum mechanics shows that bivalence and classical realism are incorrect, albeit intuitively appealing, conceptions of the fundamental nature of the world. The world consists only of a statistical distribution of propensities, sometimes actualised, but incapable of total and complete actualisation. It is therefore indeterminate in a way radically in opposition to our natural beliefs.