Achim Kempf (University of Waterloo), Alexander Smith (Dartmouth College & Saint Anselm College), Flaminia Giacomini (Perimeter Institute), Lucien Hardy (Perimeter Institute)

Whatever the final theory of quantum gravity turns out to be, it will need to reconcile the incongruent ways in which time appears in quantum mechanics and general relativity. Quantum mechanics treats time as a classical background parameter, which is different than the way other observables, such as position and momentum, are treated. In stark contrast, general relativity promotes time to a dynamical quantity in the sense that Einstein’s equations relate how clocks behave in relative motion or differing gravitational fields. The aim of this conference, geared at graduate students and above, is to discuss the full consequences of treating time as a quantum phenomena in light of the recent progress on information-theoretic and operational descriptions of time as quantum observable. Topics discussed will include indefinite causal structures, the Page-Wootters formalism, relational quantum mechanics, quantum reference frames, the problem of time, and experimental implications.

Poster: https://events.perimeterinstitute.ca/event/6/images/9-Quantizing_Time.PNG

PIRSA:  http://pirsa.org/C21004


Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land.

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land.

  • A.W. Peet
  • Abhay Ashtekar
  • Abhay Srivastav
  • Abhilash Hoskere Nagaraj
  • Abhishek Roy
  • Achim Kempf
  • Adamantia Zampeli
  • Ajeet Kumar
  • Alexander Schmidhuber
  • Alexander Smith
  • Ali Yoonesyaan
  • Amanda Gatto Lamas
  • Andrea Calcinari
  • Andrea Di Biagio
  • Anirban Ganguly
  • Anne-Catherine de la Hamette
  • Anniela Melissa Rodriguez Zarate
  • Arkapal Mondal
  • Ashwin Balaji
  • Augustin Vanrietvelde
  • Ayesha Khan
  • Barbara Jasser
  • Benliang Li
  • Bianca Dittrich
  • Bryan Roberts
  • Carlo Cepollaro
  • Carlo Rovelli
  • Caroline Lima
  • Carolyn Wood
  • Caslav Brukner
  • Christophe Goeller
  • Claus Kiefer
  • Connor Wolfe
  • Cristian Mariani
  • Dana Mihai
  • Daniele Iannotti
  • Daniele Oriti
  • David Jackson
  • Dean Alvin Pablico
  • Dekhil Roukaya
  • Diego Paiva Pires
  • Doreen Fraser
  • Emily Adlam
  • Eric David Kramer
  • Erik Curiel
  • Ernesto Frodden
  • Esteban Castro
  • Eyo Ita
  • Flaminia Giacomini
  • Flavio Mercati
  • Francesco Ticozzi
  • Francisco Pipa
  • Francisco Zuniga Frias
  • George Matsas
  • Harkirat Singh Sahota
  • Harshit Rajgadia
  • Harvey Brown
  • Ian Durham
  • Ibai Asensio
  • Ilaria Gianani
  • Jack Davies
  • James Rantschler
  • Jasel Berra-Montiel
  • Jef Pauwels
  • Job Feldbrugge
  • Jochen Rau
  • John Jaykel Magadan
  • Jorge Pullin
  • Juliette Benitez
  • Julio Alcántara
  • Julio Alcántara
  • Kanak Sharma
  • Karen Morenz Korol
  • Kartik Kakade
  • Kaustubh Singhi
  • Ken Wharton
  • Kiran Adhikari
  • Kuntal Sengupta
  • Laurent Freidel
  • Lee Smolin
  • Lemuel John Sese
  • Leon Loveridge
  • Leonardo Chataignier
  • Leonardo Sanhueza
  • Lin-Qing Chen
  • Liujun Zou
  • Lorenzo Catani
  • Lorenzo Maccone
  • Luca Marchetti
  • Luciano Gabbanelli
  • Lucien Hardy
  • Lucía Menéndez-Pidal de Cristina
  • Luis Pedro Garcia-Pintos
  • Magdalena Zych
  • Marc Geiller
  • Marcos Basso
  • Marina Cortês
  • Mario Montero
  • Marios Christodoulou
  • Martim Lourenço Oliveira Vieira
  • Matteo Lostaglio
  • Mauro Paternostro
  • Maxime Savoy
  • Maximilian Lock
  • Mehdi Ahmadi
  • Mesbah Alsarraj
  • Michael Watson
  • Mischa Woods
  • Namrata Joshi
  • Nathan Argaman
  • Nelson Novais Júnior
  • Nicola Bortolotti
  • Nicolas Gisin
  • Nitica Sakharwade
  • Nuriya Nurgalieva
  • Patrick Fraser
  • Philip Flores
  • Philipp Hoehn
  • Prajwal Jadhav
  • Pratyusha Chowdhury
  • Preety Shreya
  • Purnima Ghale
  • Rajeev Singh
  • Rakesh Saini
  • Ralph Farrales
  • Ramon Jose Bagunu
  • Raúl Hidalgo-Sacoto
  • Renato Renner
  • Robert Spekkens
  • Rodolfo Gambini
  • Romin Stuart-Rasi
  • Sampreet Kalita
  • Sathvik Lakkaraju
  • Sebastian Mizera
  • Shabeeb Alalawi
  • Shadi Ali Ahmad
  • Shashaank Khanna
  • Shivam Naonit
  • Siddhant Das
  • Sijing Tao
  • Souparna Nath
  • Stefan Aimet
  • Stefan Ludescher
  • Stefano Pironio
  • Steffen Gielen
  • Suhail Malik
  • Sylvain Rossi
  • Tatevik Vardanyan
  • Thomas Andersen
  • Thomas Galley
  • Tiago Martinelli
  • Timo Kist
  • Timothée Hoffreumon
  • Veronika Baumann
  • Viktoria Kabel
  • Vilasini Venkatesh
  • Vivek Pandey
  • Weifeng Zhou
  • William Jin
  • Yidong Liao
  • Álvaro Mozota
Stephanie Mohl
    • 1
      Welcome and Opening Remarks
      Speakers: Alexander Smith (Saint Anselm College & Dartmouth College), Flaminia Giacomini (Perimeter Institute)
    • 2
      Composite quantum particles as ideal quantum clocks — operational approach to quantum aspects of time

      In general relativity time requires an operational description, for example, associated with the reading of an idealised clock following some world line. I will show that in quantum physics idealised clocks can be modelled as composite quantum particles and discuss what foundational insights into the notion of time is enabled by this approach. Moreover, since quantum particles do do not follow classical trajectories a question arises to which extent idealised quantum clocks can be associated with semi-classical paths — in analogy with quantum particles in Gaussian states being associated with semi-classical trajectories? I will show that for quantum clocks semi-classical propagation is not described by Gaussian but by a new class of quantum states derived from a new uncertainty inequality for configuration space rather than for phase space variables of the quantum clock.

      Speaker: Magdalena Zych (University of Queensland)
    • 3
      Kappa-Minkowski: physics with noncommutative time

      The kappa-Minkowski noncommutative spacetime has been studied for a long time as an example of quantum spacetime with nontrivial commutation relations between spatial and temporal coordinates which, at first sight, seem to break Poincaré invariance. However kappa-Minkowski is invariant under a Hopf-algebra deformation of the Poincaré group, which involves some noncommutative structures that prevent the sharp localization of reference frames. I will describe recent progress towards the consistent construction of quantum field theories on this spacetime, and the identification of physical predictions that genuinely distinguish kappa-Minkowski from ordinary, commutative Minkowski spacetime.

      Speaker: Flavio Mercati (University of Burgos)
    • 10:20 AM
    • 4
      Quantizing causation

      "Spatio-temporal relations are often taken to be more primitive than causal relations. Such a relationship is assumed whenever it is suggested that it is part of the definition of a causal relation that the cause must precede the effect in time. There are good reasons, however, to take causation to be the more primitive notion, with spatio-temporal relations merely describing aspects of causal relations. In such an approach, to understand what possibilities there are for an intrinsically quantum notion of time, it is helpful to understand what possibilities there are for an intrinsically quantum notion of causation. In short, how time is quantized is informed by how causation is quantized. The latter question will be the focus of this talk. I will describe a research program wherein the transition from classical to quantum is understood as an innovation to the notions of causation and inference. This is done by introducing the notion of a causal-inferential theory: a triple consisting of a theory of causal influences, a theory of inferences (of both the Boolean and Bayesian varieties), and a specification of how these interact. The possibility of defining causal-inferential theories by the axioms they satisfy provides a means of providing abstract and structural characterizations of the notions of causation and inference. In other words, within this approach, the new notions of causation and inference will stand to the traditional notions in much the same way that the notions of points and lines in nonEuclidean geometry stand to their traditional counterparts in Euclidean geometry.
      Based on: D. Schmid, J. Selby, and R. Spekkens, Unscrambling the omelette of causation and inference: The framework of causal-inferential theories, arXiv:2009.03297 (quant-ph)."

      Speaker: Robert Spekkens (Perimeter Institute)
    • 5
      Non-causal Page-Wootters circuits

      "The process matrix framework was invented to capture a phenomenon known as indefinite or quantum causal structure. Due to the generality of that framework, however, for many process matrices there is no clear physical interpretation. A popular approach towards a quantum theory of gravity is the Page-Wootters formalism, which associates to time a Hilbert space structure similar to spatial position. By explicitly introducing a quantum clock, it allows to describe time-evolution of systems via correlations between this clock and said systems encoded in history states. We combine the process matrix framework with a generalization of the Page-Wootters formalism in which one considers several observers, each with their own discrete quantum clock.
      This allows for implementing processes with indefinite casual order. The description via a history state with multiple clocks imposes constraints on the implementability of process matrices intros framework and on the perspectives of the observers. We describe how to to implement processes were the different definite causal orders are coherently controlled and explain why certain non-causal processes might not be implementable within this setting."

      Speaker: Veronika Baumann (IQOQI Vienna)
    • 12:00 PM
    • 6
      Quantum reference frames for space and space-time

      In physics, a reference frame is an abstract coordinate system that specifies observations within that frame. While quantum states depend on the choice of reference frame, the form of physical laws is assumed to be covariant. Recently, it has been proposed to consider reference frames as physical systems and as such assume that they obey quantum mechanics. In my talk, I will present recent results in the field of "quantum reference frames" (QRF). In particular, I will formulate the covariance of dynamical physical laws with respect to non-relativistic QRF transformations and show how relativistic QRFs can be used to solve a long-standing problem in relativistic quantum information or to address typical quantum gravity scenarios.

      Speaker: Časlav Brukner (University of Vienna)
    • Discussion Session: Discussion Session 1
    • Informal Hang Out Time: Informal Hang Out Time via Remo
    • 7
      A New Perspective on Time Reversal Motivated by Quantum Gravity

      Time Reversal T is usually discussed in the traditional framework of quantum mechanics in which T is represented by an anti-unitary operator. But quantum gravity may well need generalization of standard quantum mechanics which may not preserve even its linear structure, let alone the unitarity of dynamics and anti-unitarity of T. Then the currently used arguments to conclude that T violation is a fundamental aspect of Nature will break down. Fortunately, it turns out that one can analyze the T-violation experiments in a much more general setting, of which classical and quantum mechanics are special cases. The setting does not require a Hilbert space, or linearity of either dynamics or symmetry operations such as T. Nonetheless, somewhat surprisingly, one would still be to use the current experiments to conclude that there is T violation at a fundamental level under rather minimal assumptions on the structure of the final quantum gravity theory.

      Speaker: Abhay Ashtekar (Pennsylvania State University)
    • 8
      Space and Time in a Lorentzian path integral

      I will present a quantum gravity approach based on a Lorentzian path integral for quantum geometries. The properties of quantum space time can be measured using geometric operators. This allows also to discuss fluctuations of causal structure as well as violations of (micro-) causality. I will explain how the Lorentzian path integral comes with various options regarding which quantum space times to sum over: e.g. whether to include causality violations or not, or whether to allow also for space times with Euclidean signatures in Lorentzian path integrals. I will sketch some consequences for the resulting theories.

      Speaker: Bianca Dittrich (Perimeter Institute)
    • 10:20 AM
    • 9
      "TIME IN QUANTUM GRAVITY - From the fundamental level to the classical limit"

      Time cannot be both absolute (as in quantum mechanics) and dynamical (as in general relativity). I present general arguments for the absence of time at the most fundamental level of quantum gravity. I discuss possible concepts that could replace it and present the recovery of standard time as an approximate concept. My discussion is restricted to quantum geometrodynamics, but I argue for the validity of my conclusions beyond that scheme.

      Speaker: Claus Kiefer (University of Cologne)
    • 10
      The emergence of quantum mechanics and space, from a fundamental, active time

      "We propose a realist completion of quantum mechanics, in the sense of a complete description of individual events. The proposed fundamental theory assumes that time, events, causal structure, momentum and energy are fundamental. But space and the wave function are emergent.

      The beables of the theory are the views of the events, which are a subset of their causal pasts. Thus, this theory asserts that the universe is a causal network of events, which consists of partial views of itself as seen by looking backwards from each event.

      The theory is based on a simple action principle, which
      extremizes the variety of the universe, which is a measure of the diversity of its partial views. The Schroedinger equation is derived, while to higher order, there are computable corrections, non-linear in the wave function, from which new physical effects may be predicted.

      Finally, a relativistic version is sketched, in wqhich the views are built on the celestial sphere. "

      Speaker: Lee Smolin (Perimeter Institute)
    • Discussion Session: Discussion Session 2
    • 12:40 PM
      Lunch & Conference Photo
    • 11
      (Quantum) frame covariance: from foundations via gauge theories to gravity

      I will sketch how the perspective-neutral approach to (quantum) frame covariance brings together some recent developments on dynamical reference frames in quantum foundations, gauge theories and gravity. The survey will touch on spatial frames, quantum clocks and the problem of time, edge modes, and the relativity of subsystems.

      Speaker: Philipp Hoehn (University College London)
    • 12
      Quantum measurements of time

      "We propose a time-of-arrival operator in quantum mechanics by conditioning on a quantum clock. This allows us to bypass some of the problems of previous proposals, and to obtain a Hermitian time of arrival operator whose probability distribution arises from the Born rule and which has a clear physical interpretation. The same procedure can be employed to measure the ""time at which some event happens"" for arbitrary events (and not just specifically for the arrival time of a particle).

      This talk is based on the paper: L. Maccone, K. Sacha, Quantum measurements of time, Phys. Rev. Lett. 124, 110402 (2020)."

      Speaker: Lorenzo Maccone (University of Pavia)
    • 10:20 AM
    • 13
      Relative subsystems and quantum reference frame transformations.

      Transformations between reference frames play a crucial role in our understanding of physical processes. In practice, reference frames are realised by physical systems, which are standardly treated as classical. However, assuming that every physical system is ultimately quantum, it is interesting to ask how a theory of transformations wrt quantum reference frames would look like, and what implications it would have for our description of spacetime. Recently, there has been a lot of effort towards developing a quantum generalisation of reference frame transformations, unveiling novel phenomena that are absent in the classical treatment of reference frames. Here, we develop a first-principles framework for quantum reference frame transformations which clarifies important conceptual issues of previous treatments. Based on the algebra of relative observables between a system and a reference frame, our operational perspective leads naturally to a mixed-state approach (incoherent twirling), in contrast to current pure-state approaches (coherent twirling). Within our framework, the full invariant quantum subsystem contains not only the algebra of relative observables between the system and the reference frame but also an “extra particle,” related to the invariant degrees of freedom of the reference frame itself. Importantly, this extra particle contains information about the “quantumness” of the reference frame and is essential to the unitarity of quantum reference frame transformations. Our approach is general, in the sense that it can be applied to a vast set of symmetry groups and to any type of system. We illustrate the physical meaning of the concepts developed by analysing quantum reference frame transformations with respect to the (centrally extended) Galilei group.

      Speaker: Esteban Castro Ruiz (ETH Zurich)
    • 14
      Relational dynamics: interacting clocks and systems and quantum time dilation

      Time is absolute in quantum mechanics, whereas it is dynamical in general relativity. This is considered as one of the main obstacles towards unifying quantum theory and gravity. Relational quantum dynamics offers a possible solution by treating clocks as internal quantum systems, which promotes time to a dynamical quantity. This talk begins with a quick overview of time in relational quantum dynamics. We then explain that the inclusion of an interaction term coupling the clock and system causes the system dynamics to be governed by a time-nonlocal Schrödinger equation. Moreover, we demonstrate a quantum time dilation phenomena wherein we analyze the effect of non-classical states of quantum clocks on relativistic time dilation.

      Speaker: Mehdi Ahmadi (Santa Clara University)
    • 12:00 PM
    • 15
      The Issue of Time in Generally Covariant Theories

      A possible solution of the problem of time in quantum gravitational systems is presented based on a relational description between the parameterized Dirac observables of the system under consideration and the clocks. The use of physical clocks required by a quantum gravitational description of time is shown to induce a loss of unitarity. The evolution is described by a Lindblad-type master equation unless it is possible to construct a perfect clock. I show that fundamental uncertainties in time measurements could arise due to quantum and gravitational effects, leading to the conclusion that there is always a loss of unitarity induced by the use of physical clocks. The extension of the analysis to physical reference frames in totally constrained systems is sketched.

      Speaker: Rodolfo Gambini (Universidad de Montevideo)
    • Discussion Session: Discussion Session 3
    • 16
      What can information theory tell us about time?

      Information theory is an invaluable tool for studying questions around the foundations of physics. In thermodynamics, for example, it provides the key to resolving apparent contradictions, such as the famous Maxwell's demon paradox. Conversely, information theory lends itself to the conception of novel paradoxes, such as the black hole information paradox, which helps us sharpening our physical intuition. One may therefore ask whether an information-theoretic perspective can also yield insights on the nature of time. In this talk, I will explain some of the conceptual problems that arise when one tries to capture time with information-theoretic methods, and discuss possible routes to move forward.

      Speaker: Renato Renner (ETH Zurich)
    • 17
      Time and Noether's (first) theorem

      "It is widely believed that the homogeneity of time is the symmetry related by Noether's (first) theorem to the conservation of energy, and indeed that it explains energy conservation. Both claims are questionable, and in particular seemingly hard to reconcile with the modern version of Noether's first theorem due independently to Martínes Alonso (1979) and Olver (1986).
      The talk is based on: 'Do symmetries ""explain"" conservation laws? ...'

      Speaker: Harvey Brown (University of Oxford)
    • 18
      God does not play dice (He plays sudoku)

      I argue that modern physics gives us good reason to take seriously the possibility of laws which are non-local, global, or in some other way non-dynamical. I set out a general framework for lawhood which does not presuppose the standard kinematical/dynamical split, and I apply it to the problem of giving a generalized definition of determinism for the non-dynamical context. Finally I make some suggestions about how to draw conclusions about the global structure of the laws of nature from the local observations we are able to make.

      Speaker: Emily Adlam (Basic Research Community for Physics)
    • 10:20 AM
    • 19
      Time in Physics and Intuitionistic Mathematics

      "Physics is formulated in terms of timeless axiomatic mathematics. However, time is essential in all our stories, in particular in physics. For example, to think of an event is to think of something in time. A formulation of physics based of intuitionism, a constructive form of mathematics built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality and may help bridging the gap between static relativity and quantum indeterminacy.
      Historically, intuitionistic mathematics was introduced by L.E.J. Brouwer with a very subjectivist view where an idealized mathematician continually produces new information by solving conjectures. Here, in contrast, I’ll introduce intuitionism as an objective mathematics that incorporates a dynamical/creative time and an open future. Standard (classical) mathematics appears as the view from the “end of time” and the usual real numbers appear as the hidden variables of classical physics. Similarly, determinism appears as indeterminism seen from the “end of time”.
      Relativity is often presented as incompatible with indeterminism. Hence, at the end of this presentation I’ll argue that these incompatibility arguments are based on unjustified assumptions and present the “relativity of indeterminacy”.

      C. Posy, Mathematical Intuitionism, Cambridge Univ. Press, 2020.
      N. Gisin, Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real?, Erkenntnis (2019), https://doi.org/10.1007/s10670-019-00165-8
      N. Gisin, Real Numbers are the Hidden Variables of Classical Mechanics, Quantum Studies: Mathematics and Foundations 7, 197-201 (2020).
      Flavio Del Santo and N. Gisin, Physics without determinism: Alternative interpretations of classical physics, Physical Review A 100.6 (2019).
      N. Gisin, Mathematical languages shape our understanding of time in physics, Nature Physics 16, 114-119 (2020).
      N. Gisin Indeterminism in Physics and Intuitionistic Mathematics, arXiv:2011.02348
      Flavio Del Santo and N. Gisin, The Relativity of Indeterminacy, arXiv:2101.04134"

      Speaker: Nicolas Gisin (University of Geneva & Schaffhausen Institute of Technology-Geneva)
    • 20
      Measuring time with stationary quantum clocks

      Time plays a fundamental role in our ability to make sense of the physical laws in the world around us. The nature of time has puzzled people –- from the ancient Greeks to the present day -– resulting in a long running debate between philosophers and physicists alike to whether time needs change to exist (the so-called relatival theory), or whether time flows regardless of change (the so-called substantival theory). One way to decide between the two is to attempt to measure the flow of time with a stationary clock, since if time were substantival, the flow of time would manifest itself in the experiment. Alas, conventional wisdom suggests that in order for a clock to function, it cannot be a static object, thus rendering this experiment seemingly impossible. We show that counter-intuitively, a quantum clock can measure the passage of time, even while being switched off, lending support for the substantival theory of time.

      Speaker: Mischa Woods (ETH Zurich)
    • 12:00 PM
    • 21
      Measuring Quantum Discreteness of Time in the Lab with Gravity Entanglement Interference

      The concrete perspective of using interference to measure Gravity Induced Entanglement in the lab is a very exciting development for quantum gravity. While the measurements considered so far only test the nonrelativistic regime, the same technique might allow access to genuine relativistic quantum effects. Among these, there might be the possibility of direct detection of time quantum discreteness.

      Speaker: Carlo Rovelli (Centre de Physique Theorique)
    • Discussion Session: Discussion Session 4
    • Informal Hang Out Time: Informal Hang Out Time via Remo
    • 22
      Relational observables and quantum diffeomorphisms on the worldline

      "Candidate theories of quantum gravity must answer the questions: how can the dynamics of quantum states of matter and geometry be defined in a diffeomorphism-invariant way? How are the quantum states related to probabilities in the absence of a preferred time? To address these issues, we discuss the construction and interpretation of relational observables in quantum theories with worldline diffeomorphism invariance, which serve as toy models of quantum gravity. In this context, we present a method of construction of quantum relational observables which is analogous to the construction of gauge-invariant extensions of noninvariant quantities in usual gauge (Yang-Mills) theories. Furthermore, we discuss how the notion of a physical propagator may be used to define a unitary evolution in the quantum theory, which is to be understood in terms of a generalized clock, as is the classical theory.  We also discuss under which circumstances this formalism can be related to the use of conditional probabilities in a generalization of the Page-Wootters approach. Finally, we also examine how our formalism can be adapted to calculations of quantum-gravitational effects in the early Universe.
      Refs.: L. Chataignier, Phys. Rev. D 101, 086001 (2020); 103, 026013 (2021); 103, 066005 (2021)"

      Speaker: Leonardo Chataignier (University of Cologne)
    • 23
      Relational dynamics in an emergent spacetime context

      I discuss the new dimension that the relational approach to the problem of time takes in quantum gravity contexts in which spacetime and geometry are understood as emergent. I argue that, in this case, the relational strategy is best realized at an approximate and effective level, after suitable coarse graining and only in terms of special quantum states. I then show a concrete realization of such effective relational dynamics in the context of a cosmological application of the tensorial group field theory formalism for quantum gravity.

      Speaker: Luca Marchetti (University of Pisa, LMU Munich)
    • 24
      Inequivalent clocks in quantum cosmology I

      Quantum cosmology faces the problem of time: the Universe has no background time, only interacting dynamical degrees of freedom within it. The relational view is to use one degree of freedom (which can be matter or geometry) as a clock for the others. In this talk we discuss a cosmological model of a flat FLRW universe filled with a massless scalar field and a perfect fluid. We study three quantum theories based on three different choices of (relational) clock and show that, if we require the dynamics to be unitary, all three make drastically different predictions regarding resolution of the classical (Big Bang) singularity or a possible quantum recollapse at large volume. The talk is based on [arXiv:2005.05357] and a second paper to appear on arXiv in May 2021. We plan to give two talks: one covering the foundations and general properties of the model, and one showing detailed results and physical interpretation. (We will merge these talks into one if the organisers decide to accept only one talk.)

      Speaker: Steffen Gielen (University of Sheffield)
    • 25
      Times of arrival and gauge invariance

      "We revisit the arguments underlying two well-known arrival-time distributions in quantum mechanics, viz.,
      the Aharonov-Bohm and Kijowski (ABK) distribution, applicable for freely moving particles, and the quantum
      flux (QF) distribution. An inconsistency in the original axiomatic derivation of Kijowski’s result is pointed out,
      along with an inescapable consequence of the “negative arrival times” inherent to this proposal (and generalizations thereof). The ABK free-particle restriction is lifted in a discussion of an explicit arrival-time setup
      featuring a charged particle moving in a constant magnetic field. A natural generalization of the ABK distribution is in this case shown to be critically gauge-dependent. A direct comparison to the QF distribution,
      which does not exhibit this flaw, is drawn (its acknowledged drawback concerning the quantum backflow effect

      Based on a recent paper (https://arxiv.org/abs/2102.02661), to be published in Proceedings of the Royal Society A."

      Speaker: Siddhant Das (Ludwig Maximilian University of Munich)
    • 10:20 AM
    • 26
      What does the Path Integral imply for Quantizing Time?

      "Even though path-integral formulations of quantum theory are thought to be equivalent to state-based approaches, path-integrals are rarely used to motivate answers to foundational questions. This talk will summarize a number of implications concerning time and time-symmetry which result from the path-integral viewpoint. Such a perspective sheds serious doubt on dynamical collapse theories, and also pushes against efforts to extend configuration space to include multiple time dimensions. A recently-developed map between all possible two-qubit entangled states and spacetime-based path-integrals sheds further doubt on any need to extend spacetime to a large ontological configuration space.
      (References include arXiv:2103.02425, 1512.00740, 1103.2492 .)"

      Speaker: Ken Wharton (San Jose State University)
    • 27
      An experiment to detect the Discreteness of time

      To this date no empirical evidence contradicts general relativity. In particular, there is no experimental proof a quantum theory of gravity is needed. Surprisingly, it appears likely that the first such evidence would come from experiments that involve non relativistic matter and extremely weak gravitational fields. The conceptual key for this is the Planck mass, a mesoscopic mass scale, and how it relates with what remains of general relativity in the Newtonian limit: time dilation. Indeed, current technological capabilities can amplify differences in time dilation superposition that are much smaller than the smallest time interval that can be measured by an atomic clock. Inspired from recent proposals to detect non--classicality of the gravitational field, we devise and examine the feasibility of an experiment that could detect a granularity of time at the Planck scale.

      Speaker: Marios Christodoulou (The University of Hong Kong)
    • 28
      Representing time and time's arrow

      What does it mean to say that a curve in state space describes change with respect to time, as opposed to space or any other parameter? What does it mean to say it's time is asymmetric? Inspired by the Wigner-Bargmann analysis of the Poincaré group, I discuss a general framework for understanding the meaning of time evolution and temporal symmetry in terms of the representation of a semigroup that includes "time translations", amongst the automorphisms of a state space. I discuss the structuralist and functionalist philosophical underpinnings of this view, and show how time reversal, parity, matter-antimatter exchange, and CPT are best viewed as extensions of a representation of continuous symmetries, whose existence is sensitive to the underlying structure of state space. I conclude with some comments on how an arrow of time can be defined in this framework, as well as prospects for such an arrow in the context of gravitation.

      Speaker: Bryan Roberts (London School of Economics & Political Science)
    • 29
      Arrows of time and locally mediated toy-models of entanglement

      "Making progress in quantum gravity requires resolving possible tensions between quantum mechanics and relativity.  One such tension is revealed by Bell's Theorem, but this relies on relativistic Local Causality, not merely the time-reversal symmetric aspects of relativity.  Specifically, it depends on an arrow-of-time condition, taken for granted by Bell, which we call No Future-Input Dependence.  One may replace this condition by the weaker Signal Causality arrow-of-time requirement -- only the latter is necessary, both for empirical viability and in order to avoid paradoxical causal loops.  There is then no longer any ground to require Local Causality, and Bell's tension disappears.  The locality condition which is pertinent in this context instead is called Continuous Action, in analogy with Einstein's ""no action at a distance,"" and the corresponding ""local beables"" are ""spacetime-local"" rather than ""local in space and causal in time.""    That such locally mediated mathematical descriptions of quantum entanglement are possible not only in principle but also in practice is demonstrated by a simple toy-model -- a ""local"" description of Bell correlations.  Describing general physical phenomena in this manner, including both quantum systems and gravitation, is a grand challenge for the future.
      [K.B. Wharton and N. Argaman, ""Colloquium: Bell's Theorem and Locally-Mediated Reformulations of Quantum Mechanics,"" Rev. Mod. Phys. 92, 21002 (2020).]"

      Speaker: Nathan Argaman (NRCN)
    • 12:00 PM
    • 30
      Time Symmetry in Decoherence and Stable Facts

      It has been previously discussed how events (interactions) in quantum mechanics are time-symmetric and an arrow of time is only due to the arrow of inference in the paper “Quantum information and the arrow of time”, arXiv:2010.05734 by Andrea Di Biagio, Pietro Dona, and Carlo Rovelli. In the relational interpretation of Quantum Mechanics, these interactions are relative facts. Stable facts result from relative facts through the process of decoherence as shown in the paper "Di Biagio, A., Rovelli, C., Foundations of Physics 51, 30 (2021)". They are separate from observed facts in laboratories due to the reason that they do not depend on a decision-making agent for their creation. In my talk, I will discuss my work with Carlo Rovelli and Andrea Di Biagio where we show that the process of decoherence and the notion of stability of facts is indeed time-symmetric. This is in contrast to the observed facts of our everyday world where an arrow of time emerges due to the presence of agents and traces.

      Speaker: Anirban Ganguly (Aix-Marseille Université)
    • 31
      Hierarchy of Theories with Indefinite Causal Structures: A Second Look at the Causaloid Framework

      "The Causaloid framework [1] is useful to study Theories with Indefinite Causality; since Quantum Gravity is expected to marry the radical aspects of General Relativity (dynamic causality) and Quantum Theory (probabilistic-ness). To operationally study physical theories one finds the minimum set of quantities required to perform any calculation through physical compression. In this framework, there are three levels of compression: 1) Tomographic Compression, 2) Compositional Compression and 3) Meta Compression.

      We present a diagrammatic representation of the Causaloid framework to facilitate exposition and study Meta compression. We show that there is a hierarchy of theories with respect to Meta compression and characterise its general form. Next, we populate the hierarchy. The theory of circuits forms the simplest case, which we express diagrammatically through Duotensors, following which we construct Triotensors using hyper3wires (hyperedges connecting three operations) for the next rung in the hierarchy. Finally, we discuss the implications for the field of Indefinite Causality.

      [1] Journal of Physics A: Mathematical and Theoretical, 40(12), 3081"

      Speaker: Nitica Sakharwade (Perimeter Institute)
    • 32
      Interaction and Evolution in Classical and Quantum Physics, and Indefinite Causal Structure

      In classical mechanics, the representations of dynamical evolutions of a system and those of interactions the system can have with its environment are different vector fields on the space of states: evolutions and interactions are conceptually, physically and mathematically different in classical physics, and those differences arise from the generic structure of the very dynamics of classical systems ("Newton's Second Law"). Correlatively, there is a clean separation of the system's degrees of freedom from those of its environment, in a sense one can make precise. I present a theorem showing that these features allow one to reconstruct the entire flat affine 4-dimensional geometry of Newtonian spacetime---the dynamics is inextricably tied to the underlying spacetime structure. In quantum theory (QT), contrarily, the representations of possible evolutions and interactions with the environment are exactly the same vector fields on the space of states ("add another self-adjoint operator to the Hamiltonian and exponentiate"): there is no difference between "evolution" and "interaction" in QT, at least none imposed by the structure of the dynamics itself. Correlatively, in a sense one can make precise, there is no clean separation of the system's degrees of freedom from those of the environment. Finally, there is no intrinsic connection between the dynamics and the underlying spacetime structure: one has to reach in and attach the dynamics to the spacetime geometry by hand, a la Wigner (e.g.). How we distinguish interaction from evolution in QT and how we attach the dynamics to a fixed underlying spacetime structure come from imposing classical concepts foreign to the theory. Trying to hold on to such a distinction is based on classical preconceptions, which we must jettison if we are to finally come to a satisfying understanding of QT. These observatons offer a way to motivate and make sense of, inter alia, the idea of indefinite causal structures.

      Speaker: Erik Curiel (Munich Center for Mathematical Philosophy )
    • 33
      Goodbye & Closing Remarks
      Speakers: Alexander Smith (Saint Anselm College & Dartmouth College), Flaminia Giacomini (Perimeter Institute)
    • Informal Hang Out Time: Informal Hang Out Time via Remo