This poster points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties.
This poster points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties.
THE PROBLEM IN A NUTSHELL CONCLUSION This poster points out an internal tension between quantum collapse and expressions which set eigenstates equal to superposition states in a different basis and thereby imply that pre-measurement and immediate post-measurement states are of the same kind. Its resolution appears to be either to discard the collapse postulate or to consider such states to be of distinct kinds with respect to their association with a superposition of properties. OVERVIEW Quantum collapse is a postulate in orthodox quantum mechanics, but it is poorly understood, though much has been written about it [1]. Here we point out that it also leads to a subtle internal tension in the theory when it is considered in conjunction with expressions that equate eigenstates with superposition states in a different basis because such expressions are consistent with a symmetry between states and observables under quantum superposition that is broken by quantum collapse. The tension can be relieved either by discarding the collapse postulate or by keeping it and considering pre-measurement and immediate post-measurement states to be of distinct kinds, in which case quantum collapse must be considered a transformation between two kinds of states. The basic strategy employed here is to convert a standard quantum mechanical relation into a logical equivalence, and then show that the imposition of the collapse postulate makes it possible to formulate an argument such that the truth value of the conclusion depends on which of the implications that are part of the equivalence is used, from which it is then possible to derive a contradiction.
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.
We present the quantum measurement problem as a serious physics problem. Serious because without a resolution, quantum theory is not complete, as it does not tell how one should - in principle - perform measurements. It is physical in the sense that the solution will bring new physics, i.e. new testable predictions, hence it is not merely a matter of interpretation of a frozen formalism. I argue that the two popular ways around the measurement problem, many-worlds and Bohmian-like mechanics, do, de facto, introduce effective collapses when "I" interact with the quantum system. Hence, surprisingly, in many-worlds and Bohmian mechanics, the "I" plays a more active role than in alternative models, like e.g. collapse models. Finally, I argue that either there are several kinds of stuffs out there, i.e. physical dualism, some stuff that respects the superposition principle and some that doesn't, or there are special configurations of atoms and photons for which the superposition principle breaks down. Or, and this I argue is the most promising, the dynamics has to be modified, i.e. in the form of a stochastic Schrödinger equation.
We propose an information-centric interpretation of quantum mechanics. According to this interpretation, a quantum mechanical system, A, can always choose a basis in which its own state is an eigenstate; it never sees itself in a superposition. This holds true even if, from the perspective of another system B, A is entangled with system S. In this case, A and S are in eigenstates (in their own systems) with their counterpart subsystem wave functions collapsed in the entangled degrees of freedom, but they are entangled according to B. This interpretation does not introduce new physics, and is consistent with the experimental predictions of quantum mechanics. At the same time, it avoids many ambiguities and potential inconsistencies associated with other interpretations. We further clarify concepts of measurement, macroscopic superposition, entanglement, and the dichotomy between the classical and quantum realms, in accordance with our interpretation.
The measurement problem is to explain why a system which is in a linear combination of states appears, upon measurement, to be in just one of those states. The solution given here is to first show that if one assumes linear, unitary, no collapse, no particle quantum mechanics, the different versions of reality are completely isolated from each other. This then implies only the eigenstates appropriate to the measurement setup will be perceived. In a Stern-Gerlach experiment, for example, only spin up or spin down will be perceived, but never a combination of the two.