There are reasons to doubt that making sense of the wave function (other than as a probability algorithm) will help with the project of making sense of quantum mechanics. The consistency of the quantum-mechanical correlation laws with the existence of their correlata is demonstrated. The demonstration makes use of the fact (which is implied by the indeterminacy principle) that physical space is not partitioned "all the way down," and it requires that the eigenvalue-eigenstate link be replaced by a different interpretive principle, whose implications are explored.
There are reasons to doubt that making sense of the wave function (other than as a probability algorithm) will help with the project of making sense of quantum mechanics. The consistency of the quantum-mechanical correlation laws with the existence of their correlata is demonstrated. The demonstration makes use of the fact (which is implied by the indeterminacy principle) that physical space is not partitioned "all the way down," and it requires that the eigenvalue-eigenstate link be replaced by a different interpretive principle, whose implications are explored.
We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of a state, its dynamical evolution rule and another rather trivial postulate proposed here (Read-Off Postulate). The wave function collapse and the probability rule are replaced with intrinsic properties of the theory, i.e. decoherence and relative frequency, respectively. Interpretation of the wave function as a faithful representation of the reality naturally emerges, although quantum reality has a peculiar feature which distinguishes it from classical reality.
We take it for granted that our physical environment communicates information, making things observable and measurable. However, there are very strong constraints on the fundamental physics of any universe that can do this. Measuring or communicating any kind of information always requires an appropriate interactive context, and these contexts are necessarily complex, involving other kinds of information determined in different contexts. This makes measurement hard to grasp theoretically, since every measurement depends on other kinds of measurements. Even so, we can identify some basic functional requirements for a physics that determines and communicates facts. These are sufficient to explain the peculiar features of quantum mechanics, combining the unitary evolution of superpositions with the mysterious "collapse" that occurs whenever the context allows new facts to be defined. Moreover, the precise determinism of classical physics can be understood on the same basis. It seems likely, in fact, that most of the complexity and fine-tuning we see in our most fundamental theories is needed to make any kind of information measurable.
We outline how Bohmian mechanics works: how it deals with various issues in the foundations of quantum mechanics and how it is related to the usual quantum formalism. We then turn to some objections to Bohmian mechanics, for example the fact that in Bohmian mechanics there is no back action of particle configurations upon wave functions. These lead us to our main concern: a more careful consideration of the meaning of the wave function in quantum mechanics, as suggested by a Bohmian perspective. We propose that the reason, on the universal level, that there is no action of configurations upon wave functions, as there seems to be between all other elements of physical reality, is that the wave function of the universe is not an element of physical reality. We propose that the wave function belongs to an altogether different category of existence than that of substantive physical entities, and that its existence is nomological rather than material. We propose, in other words, that the wave function is a component of physical law rather than of the reality described by the law.
All the concepts and principles necessary to understand quantum mechanics on an initial level are given in a form suitable for the non-expert. The concepts explained include visualizing the wave function, wave-particle duality, the implications of Schrodinger's cat, probability, the uncertainty principle, collapse of the wave function, and others. However, because of the peculiar, non-intuitive nature of quantum mechanics, one must understand the potential interpretations of its mathematics before one can properly understand these concepts. Thus the paper is organized aorund interpretations, conceptual pictures that explain the peculiar properties of the theory. The only interpretation that currently satisfies all the constraints imposed by experiments and the theory itself makes use of a perceiving Mind which is outside the laws of quantum mechanics.
This article presents a novel interpretation of quantum mechanics. It extends the meaning of “measurement” to include all property-indicating facts. Intrinsically, space is undifferentiated: There are no points on which a world of locally instantiated physical properties could be built. Instead, reality is built on facts, in the sense that the properties of things are extrinsic, or supervenient on property-indicating facts. The actual extent to which the world is spatially and temporally differentiated (that is, the extent to which spatiotemporal relations and distinctions are warranted by the facts) is necessarily limited. Notwithstanding that the state vector does nothing but assign probabilities, quantum mechanics affords a complete understanding of the actual world. If there is anything that is incomplete, it is the actual world, but its incompleteness exists only in relation to a conceptual framework that is more detailed than the actual world. Two deep-seated misconceptions are responsible for the interpretational difficulties associated with quantum mechanics: the notion that the spatial and temporal aspects of the world are adequately represented by sets with the cardinality of the real numbers, and the notion of an instantaneous state that evolves in time. The latter is an unwarranted (in fact, incoherent) projection of our apparent “motion in time” into the world of physics. Equally unwarranted, at bottom, is the use of causal concepts. There nevertheless exists a “classical” domain in which language suggestive of nomological necessity may be used. Quantum mechanics not only is strictly consistent with the existence of this domain but also presupposes it in several ways.
After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics persists to this day. Most of these endeavors assume the validity of standard quantum formalism and proceed to ponder the ontic nature of wave functions, operators, and the Schödinger equation. The present essay takes a different approach, more epistemological than ontological. I endeavor to give a heuristic account of how empirical principles lead us to a quantum mechanical description of the world. An outcome of this approach is the suggestion that the notion of discrete quanta leads to the wave nature and statistical behavior of matter rather than the other way around. Finally, the hope is to offer some solace to those older of us who still worry about such things and also to provide the neophyte student of quantum mechanics with physical insight into the mathematically abstract and often baffling aspects of the theory.