Conference

In classical mechanics, only the initial state of the system is needed to determine its time evolution. Additional information on the final state is either redundant or inconsistent. In quantum mechanics, however, the initial state does not convey all measurements’ outcomes. Only when augmented with a final quantum state, which can be understood as propagating backwards in time, a richer, more complete picture of quantum reality is portrayed. This time-symmetric view leads to a subtle kind of a local hidden-variables theory, where true collapse never occurs, yet can be effectively observed. Moreover, the Born rule and the borderline between classical and quantum systems can be derived from, respectively, the requirements of stability and “macroscopic robustness under time-reversal.’’ The significant role of macroscopic systems in amplifying and recording quantum outcomes then directly follows. Some possible cosmological consequences of this construction are discussed, especially those related to the breakdown of the “Pigeonhole principle” and our on-going work on the concept of “Quantum Holism”. The talk will be partially based on: 1. Y. Aharonov, E. Cohen, E. Gruss, T. Landsberger, Quantum Stud.: Math. Found. 1 (2014) 133-146. 2. Y. Aharonov, E. Cohen, A.C. Elitzur, Ann. Phys. 355 (2015) 258-268. 3. Y. Aharonov, E. Cohen, to be published in “Quantum Nonlocality and Reality”, M. Bell and S. Gao (Eds.), Cambridge University Press, arXiv:1504.03797. 4. E. Cohen, Y. Aharonov, to be published in “Quantum Structural Studies: Classical Emergence from the Quantum Level”, R.E. Kastner, J. Jeknic-Dugic, G. Jaroszkiewicz (Eds.), World Scientific Publishing Co., arXiv:1602.05083.

Bell's inequality is often stated as proving that quantum mechanics is non-local (rather than non-realistic, which apparently shows that physicists have more problems with non-realism than with non-locality). I will argue that the purpose of the use of locality in Bell's argument (in the CHSH form) is to make the classical system as close to the quantum system as possible, not to differentiate it from the quantum, and that non-realism is a more reasonable interpretation than is non-locality.

The two-state vector formalism of Aharonov and collaborators introduces a backwards-evolving state in order to restore time symmetry to quantum measurement theory. The question then arises, does any time-symmetric account of quantum theory necessarily involve retrocausality (influences that travel backwards in time)? In [1], Huw Price argued that, under certain assumptions about the underlying ontology, an interpretation of quantum theory that is both realist and time-symmetric must be retrocausal. Price’s argument is based on an analysis of a photon travelling between two polarizing beam-splitters. One of his assumptions is that the usual forward-evolving polarization vector of the photon is a beable, i.e. part of the ontology. He argues, on the basis of this and his other assumptions, that a backward-evolving polarization vector must also be a beable. The assumption that the forward evolving polarization vector is a beable is an assumption of the reality of the quantum state. But one of the reasons for exploring retrocausal interpretations of quantum theory is that they offer the potential for evading the unpleasant conclusions of no-go theorems, such as Bell’s theorem and, in particular, recent proofs of the reality of the quantum state [2]. In this talk, I will show how Price’s argument can, in fact, be generalized so that it does not assume the reality of the quantum state. I also reformulate the common assumptions of Price’s and our arguments to make them more generally applicable and to pin down the notion of time-symmetry involved more precisely. The notion of time-symmetry used in the argument is stronger than the notion of time-symmetry usually used in physics, but is still a true symmetry of quantum theory that ought to be taken seriously. This talk is based on joint work with Matt Pusey. [1] H. Price. Does time-symmetry imply retrocausality? How the quantum world says “maybe”. Stud. Hist. Phil. Mod. Phys., 43(2):75–83, 2012. arXiv:1002.0906 [2] For a review see M. Leifer. Is the quantum state real? An extended review of psi-ontology theorems. Quanta, 3:67-155, 2014. arXiv:1409.1570

According to the many worlds interpretation (MWI), quantum mechanics in its simplest form (no collapse or hidden variables) is complete. A primary objection to the MWI is that it fails to account for the Born rule. The most prominent response to this objection comes from the decision-theoretic program, which aims to derive a rationality postulate according to which a believer in the MWI ought to act as if the Born rule is true. I argue that the existence of alternative coherent rationality postulates undermines this response. A different response, based on self-locating uncertainty, avoids this objection and may explain the Born rule in the MWI. I conclude by considering whether this framework is capable of explaining the weak trace of particles in certain difficult cases.

Our universe is at its heart quantum mechanical, yet classical behaviour is seen everywhere. I will discuss the scales that determine the quantum to classical transition and the prospects for the observation of ever more macroscopic quantum behaviour. I will then discuss how paradoxes in quantum mechanics can be understood and visualized with Bohmian trajectories, how these trajectories can be measured, and the implications for the ontology of the Bohmian picture.

The weak value, as an expectation value, requires an ensemble to be found. Nevertheless, we argue that the physical meaning of the weak value is much more close to the physical meaning of an eigenvalue than to the physical meaning of an expectation value. Theoretical analysis and experimental results performed in the MPQ laboratory of Harald Weinfurter are presented. Quantum systems described by numerically equal eigenvalue, weak value and expectation value cause identical average shift of an external system interacting with them during an infinitesimal time. However, there are differences between the final states of the external system. In the case of an eigenvalue, the shift is the only change in the wavefunction of the external system. In case of the expectation value, there is an additional change in the quantum state of the same order, while in the case of the weak value the additional distortion is negligible. The understanding of weak value as a property of a single system refutes recent claims that there exist classical statistical analogue to the weak value.

The products of weak values of quantum observables have interesting implications in deriving quantum uncertainty and complementarity relations for both weak and strong measurement statistics. We show that a product representation formula allows the standard Heisenberg uncertainty relation to be derived from a classical uncertainty relation for complex random variables. This formula also leads to a strong uncertainty relation for unitary operators which displays a new preparation uncertainty relation for quantum systems. Furthermore, the two system observables that are weakly and strongly measured in a weak measurement context are shown to obey a complementarity relation under the interchange of these observables, in the form of an upper bound on the product of the corresponding weak values. Moreover, we derive general tradeoff relations, between weak purity, quantum purity and quantum incompatibility using the weak value formalism. Our results may open up new ways of thinking about uncertainty and complementarity relations using products of weak values.