Three qRules governing the collapse of a wave function are given in another paper. In most situations the predictions of this theory are identical with the predictions of other foundation theories. However, there is at least one experiment in which the qRules predict results that are characteristically different from other theories. These results are shown to be a function of molecular collisions in an experiment proposed by Collett and Pearle. Wave reductions in other collapse theories are distinctly not a function of collisions. Keywords: foundation theory, measurement, qRules, state reduction, wave collapse.
Three qRules governing the collapse of a wave function are given in another paper. In most situations the predictions of this theory are identical with the predictions of other foundation theories. However, there is at least one experiment in which the qRules predict results that are characteristically different from other theories. These results are shown to be a function of molecular collisions in an experiment proposed by Collett and Pearle. Wave reductions in other collapse theories are distinctly not a function of collisions. Keywords: foundation theory, measurement, qRules, state reduction, wave collapse.
Three qRules governing wave collapse are given in this paper that provide a foundation theory of quantum mechanics. They are empirical regularities that are known to be valid in macroscopic situations. When projected theoretically into the microscopic domain they predict a novel ontology, including the frequent collapse of atomic wave functions. Future experiments can potentially discriminate between this and other foundation theories of quantum mechanics. Important features of the qRules are: (1) they apply to individual trials not just to ensembles of trials, (2) they are valid independent of size or mass (microscopic or macroscopic), (3) they allow all observers to be continuously included in the system without ambiguity, (4) they account for the collapse of the wave function without introducing new or using old physical constants, (5) they allow energy and momentum to be conserved in an individual collapse, (6) they generate wave reductions that are independent of any outside observer or measuring device, (7) they provide a high frequency of stochastic localizations of microscopic objects independent of macroscopic objects, and (8) they are formulated in a covariant language that makes them useful beyond non-relativistic quantum mechanics. Keywords: foundation theory, measurement, qRules, state reduction, wave collapse.
It is claimed in another paper that the collapse of a quantum mechanical wave function is more than invariant, it is trans-representational. It must occur along a fully invariant surface. The obvious surface available for this purpose is that of the backward time cone of the collapse event as proposed by Hellwig and Kraus. This collapse is widely believed to result in paradoxical causal loops that cannot be removed by special relativistic or standard quantum mechanical considerations alone. However, the paradox is resolved when we apply the qRule foundation theory that is developed in the other paper. The causal and temporal orders of state reduction are then found to be in agreement with one another, and the resulting boundaries in Minkowski space are shown to have a novel architecture that limits the range of a Hellwig-Kraus reduction in space and time. Although these boundaries have been worked out using the qRules, they should be the same for any foundation theory that treats the collapse of a wave in an invariant way, and requires that a collapse destroys the possibility of any further influence on itself, as do the qRules. Keywords: measurement, state reduction, wave collapse.
The collapse postulate in quantum mechanics is problematic due to the measurement problem. The problem lies not with collapse per se, but with the appeal to measurement; a theory that could underwrite the collapse process without ineliminable reference to measurement would constitute a solution to the measurement problem. This is the strategy pursued by dynamical (or spontaneous) collapse theories. But dynamical collapse theories face a number of challenges. First, they make different empirical predictions from standard quantum mechanics, and hence are potentially empirically refutable. Second, there are difficulties reconciling the dynamical collapse mechanism with special relativity. Third, the post-collapse state is not the same as the post-measurement state of standard quantum mechanics, raising the possibility that dynamical collapse theories do not solve the measurement problem after all. Assuming that these challenges can be met, dynamical collapse theories can lay claim to being serious contenders for the correct description of the quantum world. And the description they provide has a number of interesting consequences. First, it makes indeterminism an irreducible fact about the physical world. It has been argued that this has important consequences for the foundations of statistical mechanics, for free will, and for consciousness. Second, many dynamical collapse theories can be taken to imply that the quantum wave function is fundamental, giving rise to a new kind of vagueness, since a wave can be fuzzy around the edges in a way that a particle cannot. Furthermore, the quantum wave function is defined over a high-dimensional space, not the three-dimensional space of experience, suggesting to some that three-dimensionality is an illusion.
Quantum mechanics gives many versions of reality but we perceive only one. One potential explanation for this, the one considered here, is that the wave function collapses down to just one version. The experimental situation is briefly reviewed, with no evidence found for collapse. The theoretical position is also reviewed and found wanting. Collapse-by-observation schemes are logically untenable. A mathematical theory of collapse must be nonlinear, a significant departure from current quantum theory. In addition, the primary candidate theory, the GRW-Pearle model, requires instantaneous, non-local transmission of information. It also requires transmission of information across versions of reality, which is forbidden in current quantum mechanics. And there is no apparent physical quantity, such as particle number, that can provide the mechanism for collapse in all cases. Further, these aspects, which are in disagreement with current theory, seem to be necessary for any mathematical theory of collapse. The conclusion is that the outlook for mathematical collapse schemes is not encouraging.
We consider theories in which the Schr\"odinger equation is modified so that the reduction of the state vector becomes a dynamical process characterized by a mean reduction time ${\ensuremath{\tau}}_{R}$. It is generally believed that such a theory and quantum theory differently predict the outcome of any two experiments performed in rapid enough succession (separated by a time interval $\ensuremath{\lesssim}{\ensuremath{\tau}}_{R}$), such as Papaliolios's successive measurements of a photon's polarization. It is shown that the predictions of a plausible class of dynamical reduction theories (for which the ensemble average of ${|〈{\ensuremath{\varphi}}_{n}|\ensuremath{\psi}〉|}^{2}$ remains constant during the reduction process, where $|\ensuremath{\psi}〉$ is the state vector, and $|{\ensuremath{\varphi}}_{n}〉$ is any one of the basis states to which it may reduce) and quantum theory do not differ for any Papaliolios-type experiment. However, there are deviations from the predictions of quantum theory if the second experiment measures interference between the superposed states created by the first measurement. As an example, the result of a recent two-slit neutron interference experiment by Zeilinger et al. is applied to the theory of Pearle, placing an upper limit ${\ensuremath{\tau}}_{R}\ensuremath{\gtrsim}5$ sec on the neutron self-reduction time.