The measurement problem of quantum mechanics was probably born in 1926: ‘Thus Schrödinger’s quantum mechanics gives a very definite answer to the question of the outcome of a collision; however, this does not involve any causal relationship. One obtains no answer to the question “what is the state after the collision,” but only to the question “how probable is a specific outcome of the collision” (in which the quantum-mechanical law of [conservation of] energy must of course be satisfied). This raises the entire problem of determinism. From the standpoint of our quantum mechanics, there is no quantity that could causally establish the outcome of a collision in each individual case; however, so far we are not aware of any experimental clue to the effect that there are internal properties of atoms that enforce some particular outcome. Should we hope to discover such properties that determine individual outcomes later (perhaps phases of the internal atomic motions)? Or should we believe that the agreement between theory and experiment concerning our inability to give conditions for a causal course of events is some pre-established harmony that is based on the non-existence of such conditions? I myself tend to relinquish determinism in the atomic world. But this is [also] a philosophical question, for which physical arguments alone are not decisive.’ (Born, 1926a, p. 866; translation by the author) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The measurement problem of quantum mechanics was probably born in 1926: ‘Thus Schrödinger’s quantum mechanics gives a very definite answer to the question of the outcome of a collision; however, this does not involve any causal relationship. One obtains no answer to the question “what is the state after the collision,” but only to the question “how probable is a specific outcome of the collision” (in which the quantum-mechanical law of [conservation of] energy must of course be satisfied). This raises the entire problem of determinism. From the standpoint of our quantum mechanics, there is no quantity that could causally establish the outcome of a collision in each individual case; however, so far we are not aware of any experimental clue to the effect that there are internal properties of atoms that enforce some particular outcome. Should we hope to discover such properties that determine individual outcomes later (perhaps phases of the internal atomic motions)? Or should we believe that the agreement between theory and experiment concerning our inability to give conditions for a causal course of events is some pre-established harmony that is based on the non-existence of such conditions? I myself tend to relinquish determinism in the atomic world. But this is [also] a philosophical question, for which physical arguments alone are not decisive.’ (Born, 1926a, p. 866; translation by the author) These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The language of this first section is quite heuristic, as it only aims at a broad presentation of the problems we want to turn our attention to. A rigorous formulation of some of these questions, and of their answers, is reviewed in section 2. A few illustrative models are mentioned briefly in Section 3. Section 4 is entirely devoted to the question raised by the very existence of crystals in a world where the fundamental interactions are believed to be covariant at least under the group of rigid motions in IR 3 . These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Measurements play a specific role in quantum mechanics; only measurements allow us to catch a glimpse of the eluding physical reality. However, there is something deeply unsatisfactory with this specificity—a measurement is itself a physical process! Several varying modes of coping with this dilemma have been proposed and this article tries to describe how a now-century-long discussion has led to new insights about the transition from the quantum to the classical world. Starting from the pioneer’s view of the quantum measurement problem, it follows the development of formalisms, the interest from philosophers for its new aspects on reality and how different interpretations of quantum mechanics have tried to support our classically working brains in understanding quantum phenomena. Decoherence is a main topic and its role in measurement processes exemplified. The question of whether the quantum measurement problem is now solved is left open for the readers’ own judgment.
[I] think I can safely say that nobody understands quantum mechanics. Richard Feynman, The Character of Physical Law Quantum mechanics [is] that mysterious, confusing discipline, which none of us really understands but which we know how to use. It works perfectly, as far as we can tell, in describing physical reality, but it is a ‘counter-intuitive discipline’… Murray Gell-Mann, Questions for the Future [The quantum] postulate implies a renunciation as regards the causal space-time co-ordination of atomic processes. Niels Bohr, Atomic Theory and the Description of Nature It should be emphasized, however, that the probability function does not in itself represent a course of events in the course of time. It represents a tendency for events and our knowledge of events. The probability function can be connected with reality only if one essential condition is fulfilled: if a new measurement is made to determine a certain property of the system. [T]he 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 … Werner Heisenberg, Physics and Philosophy [In] quantum theory it is the principle of causality , or more accurately that of determinism , which must be dropped and replaced by something else.… We now have a new form of the law of causality.… It is as follows: if in a certain process the initial conditions are determined as accurately as the uncertainty relations permit, then the probabilities of all possible subsequent states are governed by exact laws. Max Born, The Restless Universe
Ever since the beginning of quantum mechanics, the measurement problem has been a subject of sometimes discontinued but nevertheless recurrent concern. As students, most physicists have raised questions about it, but the spectacular and renewed successes of quantum theory were a strong incentive for them to work out applications without further worrying about foundations. In each generation, however, some dissatisfaction reemerges, which leads to slow progress, and we may expect that the measurement problem will some day be cleared up rather than forgotten. The situation recalls statistical mechanics, the foundations of which still give rise to scientific discussions, in spite of more than one century’s achievements. Actually, the paradoxes of irreversibility and of Maxwell’s demon share some common features with quantum measurements, to wit, they involve probabilities in a crucial fashion and their explanation requires elucidating the role of the observer.
We wrap up the main outcomes of our investigations. Even if not all questions and issues could be addressed as precisely and persuasively as one would wish, we do find that the assumption of an underlying theory describing a single, definite world with completely deterministic evolution laws, can be maintained and pursued further. In the more distant future, it is hoped that the Cellular Automaton Theory will enable us to select credible models for grand unification an quantized gravity; in the mean while, the Cellular Automaton Interpretation will be helpful in visualizing what we are actually doing when we are involved with quantum mechanical calculations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The indeterminacy and stochasticity of quantum mechanics have nurtured an illustrious gathering of critics including Einstein, Schrödinger, Bell, and Penrose. This has been good for quantum mechanics since it has become the most ruggedized and most battle hardened branch of physics. The one criticism that is often alluded to, now days, is ‘the measurement problem.’ First of all, from a pragmatic perspective it can be categorically stated that there is no measurement problem. Quantum mechanics exquisitely agrees with experimental measurements. Secondly, the so called ‘measurement problem’ is often related, by supporters of this concept, to the alleged ‘collapse of the wave function’ which is an unobserved phenomenon. In this chapter, several aspects of this experimentally nonexisting problem are discussed in order to inform the reader on the measurement reality of quantum mechanics.