Despite its extraordinary predictive successes, quantum mechanics has, since its inception some seventy years ago, been plagued by conceptual difficulties. The basic problem, plainly put, is this: It is not at all clear what quantum mechanics is about. What, in fact, does quantum mechanics describe?
It might seem, since it is widely agreed that the state of any quantum mechanical system is completely specified by its wave function, that quantum mechanics is fundamentally about the behavior of wave functions. Quite naturally, no physicist wanted this to be true more than did Erwin Schrödinger, the father of the wave function. Nonetheless, Schrödinger ultimately found this impossible to believe. His difficulty was not so much with the novelty of the wave function [2, page 156 of ,]: ``That it is an abstract, unintuitive mathematical construct is a scruple that almost always surfaces against new aids to thought and that carries no great message.'' Rather, it was that the ``blurring'' suggested by the spread out character of the wave function ``affects macroscopically tangible and visible things, for which the term `blurring' seems simply wrong.''
For example, Schrödinger noted that it may happen in radioactive decay that ``the emerging particle is described ... as a spherical wave ... that impinges continuously on a surrounding luminescent screen over its full expanse. The screen however does not show a more or less constant uniform surface glow, but rather lights up at one instant at one spot....'' And he observed that one can easily arrange, for example by including a cat in the system, ``quite ridiculous cases'' with ``the -function of the entire system having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.''
It is thus because of the ``measurement problem,'' of macroscopic superpositions, that Schrödinger found it difficult to regard the wave function as ``representing reality.'' But then what does? With evident disapproval, Schrödinger describes how ``the reigning doctrine rescues itself or us by having recourse to epistemology. We are told that no distinction is to be made between the state of a natural object and what I know about it, or perhaps better, what I can know about it if I go to some trouble. Actually--so they say--there is intrinsically only awareness, observation, measurement.''
Schrödinger's portrayal of the views of his contemporaries was quite accurate. Niels Bohr [4, page 210,], the founder of the ``Copenhagen interpretation,'' insisted upon the ``impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the conditions under which the phenomena appear'' and claimed [4, page 235,] that ``in quantum mechanics, we are not dealing with an arbitrary renunciation of a more detailed analysis of atomic phenomena, but with a recognition that such an analysis is in principle excluded.'' Werner Heisenberg [6, page 129,] claimed that ``the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them ... is impossible ...'' and that [7, page 15,] ``We can no longer speak of the behavior of the particle independently of the process of observation. As a final consequence, the natural laws formulated mathematically in quantum theory no longer deal with the elementary particles themselves but with our knowledge of them. Nor is it any longer possible to ask whether or not these particles exist in space and time objectively.''
Many physicists pay lip service to the Copenhagen interpretation, and in particular to the notion that quantum mechanics is about observation or results of measurement. But hardly anybody truly believes this anymore--and it is hard for me to believe anyone really ever did. It seems clear that quantum mechanics is fundamentally about atoms and electrons, quarks and strings, and not primarily about those particular macroscopic regularities associated with what we call measurements of the properties of these things. But this, of course, does not really provide an answer to the question with which I began. After all, if these entities are not to be somehow identified with the wave function itself--and if talk of them is not merely shorthand for elaborate statements about measurements--then where are they to be found in the quantum description?
There is, perhaps, a very simple reason why there has been so much difficulty discerning in the quantum description the objects we believe quantum mechanics should be describing. Perhaps the quantum mechanical description is not the whole story, a possibility most prominently associated with Albert Einstein.
On the basis of more or less the same considerations as those of Schrödinger quoted above, Einstein concluded that the wave function does not provide an exhaustive description of individual systems, while noting [8, page 672,] that ``there exists ... a simple psychological reason for the fact that this most nearly obvious interpretation is being shunned. For if the statistical quantum theory does not pretend to describe the individual system ... completely, it appears unavoidable to look elsewhere for a complete description of the individual system.'' In relation to this more complete theory, ``the statistical quantum theory would ... take an approximately analogous position to the statistical mechanics within the framework of classical mechanics.'' Earlier, Einstein, Boris Podolsky and Nathan Rosen concluded their famous EPR paper  as follows: ``While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.''
Regarded as a response to the measurement problem, the position of Bohr and Heisenberg seems excessive in comparison with that of Einstein. After all, the latter denied merely that the wave function is a complete description of an observer-independent physical reality, while the former seemed to deny that there is any such reality, at least insofar as atomic phenomena are concerned! And as regards the plausibility of their conclusions, Einstein's insistence on the possibility of a more complete description seems rather modest when contrasted with the categorical assertions of ``impossibility'' and ``in principle'' exclusion of Bohr. Nonetheless, it is generally believed in the physics community that Bohr vanquished Einstein in their great, decades-long, debate. At the same time, it is also widely believed that their debate was merely philosophical and hence not susceptible to any clear cut resolution.
However, the Bohr-Einstein debate has already been resolved, and in favor of Einstein: What Einstein desired and Bohr deemed impossible--an observer-free formulation of quantum mechanics, in which the process of measurement can be analyzed in terms of more fundamental concepts--does, in fact, exist. Moreover, there are many such formulations, the most promising of which belong to three basic categories or approaches: decoherent histories, spontaneous localization, and pilot-wave theories. The simplest pilot-wave theory, Bohmian mechanics, has in fact existed almost since the inception of quantum theory itself. These approaches can be regarded, each in its own way, as minimal responses to the problem of formulating a quantum theory without observers. Each of these, I will argue, can also be regarded as realizations of Einstein's insight that the wave function does not provide us with a complete description of physical reality, and of his belief that a more complete theory is possible.