On the limits of quantum theory: Contextuality and the quantum–classical cut

Abstract

This paper is based on four assumptions: 1. Physical reality is made of linearly behaving components combined in non-linear ways. 2. Higher level behaviour emerges from this lower level structure. 3. The way the lower level elements behaves depends on the context in which they are imbedded. 4. Quantum theory applies to the lower level entities. An implication is that higher level effective laws, based in the outcomes of non-linear combinations of lower level linear interactions, will generically not be unitary; hence the applicability of quantum theory at higher levels is strictly limited. This leads to the view that both state vector preparation and the quantum measurement process are crucially based in top-down causal effects, and helps provide criteria for the Heisenberg cut that challenge some views on Schrödinger's cat.

Spacetime and the Passage of Time

“…Through a kinetic energy term, the interaction Hamiltonian somewhat mysteriously introduces an effective time into the wave function for the system. If one accepts this proposal, it is a way that an effective time variation is induced at the quantum level due to top-down effects from the environment -a proposal that is in consonance with the broad suggestions of the effectiveness of top-down effects in quantum physics presented in [26]. Once this has occurred, one has an effective EBU situation at the micro as well as the macro level.…”

“…As emphasized so well by Eddington ( [19]:246-260), our mathematical equations representing the behaviour of macro objects are highly abstracted versions of reality, leaving almost all the complexities out. The case made in [26] is that when true complexity is taken into account, the unitary equations leading to the view that time is an illusion are generically not applicable except to isolated micro components of the whole. The viewpoint expressed by Carroll supposes a determinism of the future that is not realised in practice: inter alia, he is denying the existence of quantum uncertainty in the universe we experience.…”

“…This is sometimes justified by saying that as there can be no external measuring apparatus for the universe as a whole to interact with, no measurement or wave function collapse can take place: only unitary evolution will occur. However one can advocate an emergent view of higher level laws of causation from lower level physical interactions [26]. On this view, the wave function of the universe |ψ U is the wave function obtained by composition of all its components: it is a sum of terms of the form…”

Hybrid classical-quantum formulations ask for hybrid notions

“…Furthermore, such hypothetical theory would surely be more apt to describe our perception of the world, in which its macrovariables seem to have as much relevance in its evolution as its microvariables (see, e.g., the discussion in Ref. [1]). In this paper, among other specific developments, we want to put forward the view that the study of hybrid classical-quantum constructions suggests that it is indeed possible to build consistent hybrid theories, but at the (reasonable) cost of allowing them to be populated by subsystems which are neither purely classical nor purely quantum: Every subsystem would have a certain degree of classicality and of quantumness, with pure notions being applicable only to ideal situations.…”

“…In all these approaches one starts with initially separated purely classical and quantum sectors and then makes them interact in order to analyze the outcome. Without pretending to be exhaustive, we can classify these approaches in the following categories: (1) approaches that try to maintain the use of quantum states (or density matrices) to describe the quantum sector and trajectories for the classical sector [2,3], (2) those that first formulate the classical sector as a quantum theory [4][5][6] and then work with a formally completely quantum system [7][8][9][10][11], (3) conversely, those that first formulate the quantum sector as a classical theory [12] and then work with a formally completely classical system [13][14][15][16], and (4) approaches that take the quantum and the classical sectors to a common language and then extend it to a single framework in the presence of interactions, for instance, using Hamilton-Jacobi statistical theory for the classical sector and Madelung representation for the quantum sector [17][18][19] or modeling classical and quantum dynamics starting from Ehrenfest equations [20]. This classification is not sharp and in some cases is subject to interpretation, but it may be useful as a way to organize the possible procedures and conceptual viewpoints in the enterprise of constructing a hybrid theory.…”