Past events

Abstract: According to quantum mechanics, it is fundamentally impossible to predict with certainty the outcome of a future measurement on a system prepared in a pure state, unless the state is an eigenstate of the observable to be measured. The best prediction is probabilistic, given by the Born rule. This absolute limitation on our ability to predict certain future events constitutes a radical difference from classical mechanics. In the reverse time direction, however, the analogous limitation does not hold: it is in practice possible to know with certainty the outcome of any type of measurement on any type of state, since all such events can have records at present. What is the origin of this time-reversal asymmetry, and how should we think about quantum theory if we believe that a microscopic theory should be time-symmetric?

It has been suggested that quantum theory in its usual predictive form is already time symmetric, if suitably applied back in time, while the observed asymmetry in the information we have about the past and the future can be traced to the thermodynamic irreversibility of macroscopic phenomena. In this talk, adopting a specific operational way of thinking about quantum theory, I will argue that the above asymmetry can be understood as a consequence of a special form of a joint past-future boundary condition at the level of quantum theory itself, without invoking considerations of macroscopic coarse-graining. Improving on an argument originally suggested in [O. Oreshkov and N. J. Cerf, Nature Phys. 11, 853-858 (2015)], I will explain how such a boundary condition implies the inability of a local observer in spacetime to predict future events better than the Born rule, in contrast to past events. I will argue that this can accounts for our perceived ability to influence the future and not the past, as well as to remember the past but not the future, and will speculate on the link between this arrow of time and the thermodynamic arrow. I will argue that a meaningful time-symmetric formulation of quantum theory requires rules that work for all physically admissible situations, hence the Born should be regarded as a special case of a more general rule. Adopting this generalization allows us to reformulate quantum theory in a way that makes sense without predefined time, which may be important for quantum gravity.

This talk will describe a model quantum universe consisting of a very large box containing a screen with two slits and an observer (us) that can pass through the slits. We apply the modern quantum mechanics of closed systems to calculate the probabilities for alternative histories of how we move through the universe and what we see. After passing through the screen with the slits, the quantum state of the universe is a superposition of classically distinguishable histories. We are then living in a superposition. Some frequently asked questions about such situations are answered using this model. In particular we will discuss whether or not if we are living in a superposition we would in some way feel it.

The standard operational framework of quantum theory is time-asymmetric. This asymmetry reflects the capabilities of ordinary agents, who are able to deterministically pre-select the states of quantum systems, but not to deterministically post-select the outcomes of quantum measurements. However, the fundamental dynamics of quantum particles is time-symmetric, and is compatible with a broader class of operations where pre-selections and post-selections are combined in general ways that do not presuppose a definite direction of time. In this talk I introduce a framework for quantum operations with indefinite time direction, providing an example, called the quantum time flip, where an unknown, time-symmetric process is accessed in a coherent superposition of two alternative time directions. To highlight the potential of quantum operations with indefinite time direction, I will show a game where a hypothetical agent with access to the quantum flip can in principle outperform all agents who operate in a definite time direction.

In earlier work, sometimes referred to as quantum linguistics [NewScientist], or as grammatical quantum field theory [by quantum gravity specialist Louis Crane], we for the first time combined grammatical structure with the distributional meanings of machine learning [CSC], which are typically represented in an inner-product space. The key insight was that grammar as well as more general linguistic structure perfectly matches the diagrams of categorical quantum mechanics [CKbook]. Our recipe was not restricted to inner-product space representations, for example, we also used density matrices, and we can also use spacetime as a representation of meanings. In fact, much in language has direct spatio-temporal connotations, either direct or metaphorical, e.g. prepositions like in, after, above etc. In joint work with Vincent Wang we constructed a linguistic model of spacetime, and how it extends to account for many more cognitive features [ConcSpacI] e.g. shape, taste, colour etc. We will argue that linguistic structure is really an interaction/process logic of things happening in the world out there. Hence this work could be a stepping stone to an alternative formalism for combining quantum structure with spacetime, at the crossroads of AI. This is joint work With Vincent Wang.

REFERENCES: [NewScientist] J. Aron. Quantum links let computers read. New Scientist nr 2790, pages 10-11. [CSC] B. Coecke, M. Sadrzadeh, and S. Clark. Mathematical foundations for a compositional distributional model of meaning. In: A Festschrift for Jim Lambek, volume 36 of Linguistic Analysis, pages 345–384. 2010. arxiv:1003.4394. [CKbook] B. Coecke and A. Kissinger. Picturing Quantum Processes. A First Course in Quantum Theory and Diagrammatic Reasoning. Cambridge University Press, 2017. [ConcSpacI] J. Bolt, B. Coecke, F. Genovese, M. Lewis, D. Marsden, and R. Piedeleu. Interacting conceptual spaces I: Grammatical composition of concepts. In: Concepts and their Applications, Synthese Library. 2018. arXiv:1703.08314

We analyse a gedankenexperiment previously considered by Mari et al. that involves quantum superpositions of charged and/or massive bodies (“particles”) under the control of the observers, Alice and Bob. In the electromagnetic case, we show that the quantization of electromagnetic radiation (which causes decoherence of Alice’s particle) and vacuum fluctuations of the electromagnetic field (which limits Bob’s ability to localize his particle to better than a charge-radius) both are essential for avoiding apparent paradoxes with causality and complementarity. We then analyze the gravitational version of this gedankenexperiment. We show that the analysis of the gravitational case is in complete parallel with the electromagnetic case provided that gravitational radiation is quantized and that vacuum fluctuations limit the localization of a particle to no better than a Planck length. This provides support for the view that (linearized) gravity should have a quantum field description.

I will discuss the challenges and prospects for isolating and exploring gravity as a relevant coupling mechanism in table-top quantum experiments. This includes quantum states of the metric generated by a quantum source mass and possible schemes to measure it. Experimentally, a central role is played by the possibility to achieve quantum control over motional states of levitated solid-state particles.