In previous chapters we presented and discussed the standard, generally accepted Copenhagen interpretation of quantum mechanics according to which there exists in nature at the most fundamental level an irreducible and ineliminable indeterminism. Although we saw that what historically constituted the Copenhagen interpretation of quantum mechanics is difficult to specify with precision, three central commitments do characterize it. (1) In general, no particle trajectories can exist in a space–time background. (2) No deterministic description of fundamental physical phenomena is possible. (3) There exists in the laws of the fundamental physical phenomena of nature an essential and ineliminable indeterminism or probability (unlike the probability of classical physics, that there reflects our ignorance of the finer details of complex physical phenomena). A flavor of these features of the Copenhagen interpretation of quantum mechanics can be gotten from the quotations at the beginning of Part VIII (Some philosophical lessons from quantum mechanics). On this view, it is in principle impossible to predict, say, the exact future behavior of an electron (that is, to give its position and velocity as functions of the time). According to the Copenhagen school, there can be no causal description of microphenomena in terms of a continuous space–time background (as there is in classical physics). It is generally believed that a causal interpretation of quantum mechanics is impossible, although no proof of this exists.

As we indicated previously in Chapter 3, there is an element of belief in the very foundation of what is usually seen as the objective scientific enterprise. Traditionally, science has assumed that basically simple laws exist that explain the myriad phenomena of nature. This is a belief and science cannot prove it is a correct one. Throughout the history of Western thought there has been a tendency to reduce the phenomena of nature to a few simple laws or principles. One obvious motivation for this could well be a desire or felt need to make the world seem understandable to us. Today it is not uncommon to see the claim made that modern man has a view of the world based on science and that science has replaced religion. In addition to its acceptance of a basic simplicity in the fundamental laws of nature, this world view is often characterized as being philosophically materialistic, in the sense that matter and its interactions are regarded as comprising the entire universe, with the mind (or spirit) assigned a dependent reality (if any at all). Such a description of the world is typically taken, especially in older writing, to be completely deterministic, although quantum mechanics is widely believed to have changed this aspect of the philosophical materialism of modern science. (We return to determinism versus indeterminism in the quantum world in Chapters 21–24.)

In this chapter we discuss a few of the classic views of science that were popular from the time of the Renaissance until the early part of the twentieth century and then indicate some later changes in the conception of science. We return to a more complete overview of the current status of the philosophy of science as a retrospective in Chapter 25.

ORIGINS OF SCIENTIFIC METHOD

In the previous chapter we used Bacon as an example of a proponent of what developed into one important aspect of the modern scientific method. We also referred to Descartes as the father of modern philosophy and scientific reasoning. Galileo is often credited as being the first working scientist to apply modern scientific method in his investigations. (Chapter 6 will discuss the scientific writings and research of Galileo.) Although it is simplest for purposes of exposition to focus on the works of specific individuals such as Bacon, Descartes or Galileo to illustrate the rise of modern scientific thought and practice, these seventeenth-century thinkers were not the first to break with Aristotelian tradition. They did have predecessors. For instance, in the thirteenth century an experimental dimension for science was already advocated by the English Franciscan friar Roger Bacon (c. 1220–1292). And, as we shall see in more detail in Chapter 6, some of the fourteenth-century Ockhamists in Paris applied mathematical methods to the problem of motion and obtained results that contributed to the foundations of modern mechanics and of calculus.

The form of the Ptolemaic system, as depicted in Figure 4.7, was in accord with the general thinking of the day, fit past observational data and predicted fairly well the future positions of the then-known planets. In his De Revolutionibus, published at his death in 1543, and in his earlier Commentariolus (Sketch of the Hypotheses for the Heavenly Motions), about 1514, Nicolaus Copernicus seriously attacked the Ptolemaic model. He did this largely because he felt that some of the devices (in particular, the equant) used to compound circular motions in Ptolemy's system produced motions that were not uniform enough.

When we are presented with apparently bizarre properties of microsystems governed by quantum mechanics (as in our discussion of the double-slit experiment in the previous chapter), we naturally ask whether it might be possible to find another theory, or at least another story to go with the equations, that would make more sense to us. We might seek a theory and a view of fundamental physical processes that would accord more with our classically based, everyday common sense. This typically takes the form of the question of the possibility of the existence of a more detailed description of atomic processes than that afforded by the wave function (that is, by the Copenhagen interpretation of the previous chapter). In this chapter we discuss some of the central interpretive problems of the Copenhagen version of quantum mechanics. Then, in the next two chapters, we look at the severe, general restrictions that are placed on any such completion of quantum mechanics and at one particular extension of quantum mechanics. First, though, we begin here with the struggle that ensued over the status of causality in quantum theory.

THE COMPLETENESS OF QUANTUM MECHANICS

Although the Heisenberg uncertainty principle (Section 20.4) and the lack of absolute predictive power are an inherent feature of quantum mechanics, there have been attempts to preserve an in principle completely deterministic structure for physics. Even classically, in a macroscopic sample of gas there are so many molecules that it would be hopeless, as a practical matter, to predict the future locations of all these molecules from Newton's laws of motion.

A central assumption of this book is that general philosophical discussions about science should be based upon specifics from the actual history of science. Therefore, we begin by considering the model of the universe accepted by the ancients and then we analyze some of the philosophical implications of this episode. In this chapter we present a summary of the naked-eye observations available to the ancients and outline the model of the universe that they built using this data. The next chapter then gives a description of the present-day theory that overthrew it. In Chapter 12 we discuss in more depth the profound shift in philosophical perspective necessitated by this change, as well as the contributions of several of the major precursors and shapers of that revolution.

ELEMENTARY OBSERVATIONS

In order to get into the proper frame of mind to appreciate a discussion of an ancient model of the universe in which the earth was pictured as being at rest, the modern reader who ‘knows’ that the earth moves around the sun and also spins on its axis might ask the following question. How would you demonstrate that the earth makes an orbit about the sun and that it turns on its own axis? Just use naked-eye observations – no photographs from satellites allowed. You will find that this is not such a simple exercise. Perhaps then the view the ancients had of their universe will seem less bizarre to you.

The theory of relativity is essentially the culmination of classical physics. Although revisions in our concepts of space and time are necessitated by both the special and general theories of relativity, the notion of causality, in which a cause precedes its effect, remains intact in the relativistic formulations of electrodynamics and mechanics and of gravitation. An upper limit is set on the speed of bodies, and of the propagation of energy, and physical quantities are often defined operationally, but once we adjust ourselves to these new rules, our representations of physical processes proceed pretty much as they did in classical physics. On the other hand, quantum theory seems to require a much more profound philosophical revision of our thought patterns. Even the viability of the usual meaning of a causal connection between one event and another is there called into question.

SOME HISTORICAL BACKGROUND

We begin with a brief and highly selective review of the experimental and theoretical problems that formed the conceptual backdrop to the emergence of quantum theory. We focus attention first on an important phenomenon – blackbody radiation – that was instrumental for the formulation of quantum mechanics. A blackbody is defined as a surface that absorbs all of the electromagnetic radiation that falls onto it. It is picturesquely so named since any light incident on such a body would be absorbed, making it appear black (at least at typical temperatures in our environment). A blackbody also emits radiation.

A typical textbook summary of Newton's theory of gravitation presents his reasoning as a model in the application of scientific method. The scenario is roughly the following. Newton considered the rate at which the moon must ‘fall’ toward the earth in order to remain in its circular orbit and asked what centripetal acceleration was necessary to produce this motion. He concluded that the gravitational acceleration produced by the earth at the position of the moon decreased as the inverse square of the distance from the center of the earth compared to the known value of g at the surface of the earth. A bold generalization or induction from this yielded the law of universal gravitation between any two particles. Newton worried about the fact that the earth and moon were extended bodies, not point particles. By inventing the calculus he was able to prove that, as long as one was external to a uniform spherical mass, the sphere produced the same gravitational force as a point particle of equal mass situated at the center of the sphere. Then, using the law of gravitation plus his laws of motion, he deduced Kepler's three laws of planetary motion.

As we indicated in previous chapters and as we now show in more detail here and in the next chapter, the actual development, even as presented by Newton in his Principia, was a bit more circuitous and reflects his own philosophical view of the nature of science.

We shall see in Chapter 14 that, with Maxwell's great work, A Treatise on Electricity and Magnetism (1873), our conception of an electromagnetic wave (of which ordinary light is but one example) became that of a wave consisting of electric (E) and magnetic (B) fields propagating along at the speed of light (c). However, most waves of which we have some immediate experience, such as water waves, sound waves in air and waves in a vibrating string, are transmitted through some material medium. The obvious question, then, is what is the nature of the medium that transmits optical and other electromagnetic effects. At first sight this may not appear to pose much of a problem when these effects are transmitted through a material medium such as air, water or a solid. But electromagnetic waves do propagate through what we usually term a vacuum, as between the sun and the earth. In this chapter we review the history of certain ideas concerning light and electromagnetism.

EMERGENCE OF THE OPTICAL AETHER

As we saw previously, Descartes believed that all space was a plenum, everywhere filled with matter so that there were no voids and could exist no vacuum. An aether permeated all of space. For him, interactions could take place only via pressure and impact; that is, through the tangible action of some intermediary agent or matter.

Self-referential consistency and inconsistency

Universality implies self-referentiality

In the preceding chapters, we have mentioned on several occasions that there are good reasons to consider quantum mechanics as universally valid. Indeed, during the last 70 years quantum mechanics has not been disproved by a single experiment. In spite of numerous attempts to discover the limits of applicability and validity of this theory, there is no indication that the theory should be improved, extended, or reformulated. Moreover, the formal structure of quantum mechanics is based on very few assumptions, and these do not leave much room for alternative formulations. The most radical attempt to justify quantum mechanics, operational quantum logic, begins with the most general preconditions of a scientific language of physical objects, and derives from these preconditions the logico-algebraic structure of quantum mechanical propositions [Mit 78,86], [Sta 80]. There are strong indications that from these structures (orthomodular lattices, Baer*-semigroups, orthomodular posets, etc.) the full quantum mechanics in Hilbert space can be obtained. Although simple application of Piron's representation theorem [Pir 76] does not lead to the desired result, [Kel 80], [Gro 90], there are new and very promising results [Sol 95] which indicate that the intended goal may well be achieved within the next few years. Together with the experimental confirmation and verification of quantum mechanics, these quantum logical results strongly support the hypothesis that quantum mechanics is indeed universally valid.

Historical remarks

The quantum mechanical formalism discovered by Heisenberg [Heis 25] an Schrödinger [Schrö 26] in 1925 was first interpreted in a statistical sense by Born [Born 26]. The formal expressions p(φ,ai) = |(φ,φai)|2, i ∈ N, were interpreted as the probabilities that a quantum system S with preparation φ possesses the value ai that belongs to the state φai. This original Born interpretation, which was formulated for scattering processes, was, however, not tenable in the general case. The probabilities must not be related to the system S in state φ, since in the preparation φ the value ai of an observable A is in general not subjectively unknown but objectively undecided. Instead, one has to interpret the formal expressions p(ai, ai) as the probabilities of finding the value ai after measurement of the observable A of the system S with preparation φ. In this improved version, the statistical or Born interpretation is used in the present-day literature.

On the one hand, the statistical (Born) interpretation of quantum mechanics is usually taken for granted, and the formalism of quantum mechanics is considered as a theory that provides statistical predictions referring to a sufficiently large ensemble of identically prepared systems S(φ) after the measurement of the observable in question. On the other hand, the meaning of the same formal terms p(φ,ai) for an individual system is highly problematic.

This book, on the interpretation of quantum mechanics and the measurement process, has evolved from lectures which I gave at the University of Turku (Finland) in 1991 and later in several improved and extended versions at the University of Cologne. In these lectures as well as in the present book I have aimed to show the intimate relations between quantum mechanics and its interpretation that are induced by the quantum mechanical measurement process. Consequently, the book is concerned both with the philosophical, metatheoretical problems of interpretation and with the more formal problems of quantum object theory.

The book is based on the idea that quantum mechanics is valid not only for microscopic objects but also for the macroscopic apparatus used for quantum mechanical measurements. We illustrate the consequences of this assumption, which turn out to be partly very promising and partly rather disappointing. On the one hand we can give a rigorous justification of some important parts of the interpretation, such as the probability interpretation, by means of object theory (chapter 3). On the other hand, the problem of the objectification of measurement results leads to inconsistencies that cannot be resolved in an obvious way (chapter 4). This open problem has far-reaching consequences for the possibility of recognising an objective reality in physics.

The manuscript of this book was carefully written in TEX by Dipl. Phys. Falko Spiller. In addition, he proposed numerous small corrections and improvements of the first version of the text.

The concept of measurement

Basic requirements

In this chapter we give a brief account of the quantum theory of measurement. As already mentioned in the preceding chapter, the quantum theory of measurement treats the object system, as well as the measuring apparatus, as proper quantum systems. Here we restrict our considerations to a proper quantum mechanical model of the measuring process that makes use of unitary premeasurements. Furthermore, we will be mainly concerned with ordinary discrete observables of the object system that are measured by an apparatus with a pointer observable which is also assumed to be an ordinary discrete observable. These restrictive assumptions are made here and throughout the entire book in order to simplify the problems as much as possible. The remaining open problems of consistency, completeness, self-referentiality, etc. can then be discussed without unnecessary additional complications.

In order to characterize the concept of measurement in quantum mechanics, we formulate some basic requirements that must be fulfilled by any measuring process. In many situations, one can add further postulates, but these additional requirements are not essential for the concept of measurement. The basic requirements are in accordance with the most general interpretation of quantum mechanics, the minimal interpretation, which has already been mentioned in chapter 1. There is a general interplay between interpretation and the quantum theory of measurement, since the postulates that characterize a given interpretation must be compatible with, and capable of being satisfied by, a corresponding model of the measuring process.