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Time in Physics and Intuitionistic Mathematics

Nicolas Gisin
Université de Genève
June 17, 2021

PIRSA:21060107
Quantum Foundations
Dynamics of Primordial Black Holes in the Early Universe

Derek Inman
Canadian Institute for Theoretical Astrophysics (CITA)
June 17, 2021

PIRSA:21060128
Strong Gravity
God does not play dice (He plays sudoku)

Emily Adlam
Chapman University
June 17, 2021

PIRSA:21060106
Quantum Foundations
Time and Noether's (first) theorem

Harvey Brown
University of Oxford
June 17, 2021

PIRSA:21060105
Quantum Foundations
Discussion Session 3
June 16, 2021

PIRSA:21060104
Quantum Foundations
The Issue of Time in Generally Covariant Theories

Rodolfo Gambini
Universidad de la Republica Uruguay
June 16, 2021

PIRSA:21060108
Quantum Foundations
Relational dynamics: interacting clocks and systems and quantum time dilation

Mehdi Ahmadi
Santa Clara University
June 16, 2021

PIRSA:21060102
Quantum Foundations
Relative subsystems and quantum reference frame transformations.

Esteban Castro Ruiz
Université Libre de Bruxelles (ULB)
June 16, 2021

PIRSA:21060101
Quantum Foundations
Oscillator-to-oscillator codes do not have a threshold

Lisa Hanggli
Ludwig-Maximilians-Universitiät München (LMU)
June 16, 2021

PIRSA:21060003
Quantum Information
Quantum measurements of time

Lorenzo Maccone
University of Pavia
June 16, 2021

PIRSA:21060100
Quantum Foundations
(Quantum) frame covariance: from foundations via gauge theories to gravity

Philipp Hoehn
Okinawa Institute of Science and Technology Graduate University
June 16, 2021

PIRSA:21060099
Quantum Foundations
TBA

Mikhail Solon
University of California, Los Angeles
June 15, 2021

PIRSA:21060000
Particle Physics

Time in Physics and Intuitionistic Mathematics

Nicolas Gisin
Université de Genève
June 17, 2021

PIRSA:21060107
Quantum Foundations
"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”. References: 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"
Dynamics of Primordial Black Holes in the Early Universe

Derek Inman
Canadian Institute for Theoretical Astrophysics (CITA)
June 17, 2021

PIRSA:21060128
Strong Gravity
If dark matter is composed at least partially of primordial black holes (PBHs) then structure formation occurs very differently than in standard particle dark matter scenarios. PBH binaries, halos and other structures can form at very early redshifts and the resulting nonlinear dynamics can change constraints on the abundance of PBHs. In this talk I will describe this structure formation history using results from cosmological simulations and discuss constraints on solar mass and heavier PBHs from LIGO and the CMB. Lastly, I will discuss how the baryons may be impacted by such nonlinear structures.
God does not play dice (He plays sudoku)

Emily Adlam
Chapman University
June 17, 2021

PIRSA:21060106
Quantum Foundations
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.
Time and Noether's (first) theorem

Harvey Brown
University of Oxford
June 17, 2021

PIRSA:21060105
Quantum Foundations
"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? ...' arXiv:2010.10909v1"
Discussion Session 3
June 16, 2021

PIRSA:21060104
Quantum Foundations
The Issue of Time in Generally Covariant Theories

Rodolfo Gambini
Universidad de la Republica Uruguay
June 16, 2021

PIRSA:21060108
Quantum Foundations
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.
Relational dynamics: interacting clocks and systems and quantum time dilation

Mehdi Ahmadi
Santa Clara University
June 16, 2021

PIRSA:21060102
Quantum Foundations
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.
Relative subsystems and quantum reference frame transformations.

Esteban Castro Ruiz
Université Libre de Bruxelles (ULB)
June 16, 2021

PIRSA:21060101
Quantum Foundations
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.
Oscillator-to-oscillator codes do not have a threshold

Lisa Hanggli
Ludwig-Maximilians-Universitiät München (LMU)
June 16, 2021

PIRSA:21060003
Quantum Information
It is known that continuous variable quantum information cannot be protected against naturally occurring noise using Gaussian states and operations only. Noh et al. (PRL 125:080503, 2020) proposed bosonic oscillator-to-oscillator codes relying on non-Gaussian resource states as an alternative, and showed that these encodings can lead to a reduction of the effective error strength at the logical level as measured by the variance of the classical displacement noise channel. An oscillator-to-oscillator code embeds K logical bosonic modes (in an arbitrary state) into N physical modes by means of a Gaussian N-mode unitary and N-K auxiliary one-mode Gottesman-Kitaev-Preskill-states.
Here we ask if - in analogy to qubit error-correcting codes - there are families of oscillator-to-oscillator codes with the following threshold property: They allow to convert physical displacement noise with variance below some threshold value to logical noise with variance upper bounded by any (arbitrary) constant. We find that this is not the case if encoding unitaries involving a constant amount of squeezing and maximum likelihood error decoding are used. We show a general lower bound on the logical error probability which is only a function of the amount of squeezing and independent of the number of modes. As a consequence, any physically implementable family of oscillator-to-oscillator codes combined with maximum likelihood error decoding does not admit a threshold.
Quantum measurements of time

Lorenzo Maccone
University of Pavia
June 16, 2021

PIRSA:21060100
Quantum Foundations
"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)."
(Quantum) frame covariance: from foundations via gauge theories to gravity

Philipp Hoehn
Okinawa Institute of Science and Technology Graduate University
June 16, 2021

PIRSA:21060099
Quantum Foundations
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.
TBA

Mikhail Solon
University of California, Los Angeles
June 15, 2021

PIRSA:21060000
Particle Physics
Abstract: TBD

Zoom Link: https://pitp.zoom.us/j/96516977019?pwd=WVlpZG5WTTUwbFJVZ2wvcXdNWUR5Zz09

Title	Date	Collection	Type	Info
Time in Physics and Intuitionistic Mathematics	2021‑06‑17	Quantizing Time	Conference	View details
Dynamics of Primordial Black Holes in the Early Universe	2021‑06‑17	Strong Gravity	Scientific Series	View details
God does not play dice (He plays sudoku)	2021‑06‑17	Quantizing Time	Conference	View details
Time and Noether's (first) theorem	2021‑06‑17	Quantizing Time	Conference	View details
Discussion Session 3	2021‑06‑16	Quantizing Time	Conference	View details
The Issue of Time in Generally Covariant Theories	2021‑06‑16	Quantizing Time	Conference	View details
Relational dynamics: interacting clocks and systems and quantum time dilation	2021‑06‑16	Quantizing Time	Conference	View details
Relative subsystems and quantum reference frame transformations.	2021‑06‑16	Quantizing Time	Conference	View details
Oscillator-to-oscillator codes do not have a threshold	2021‑06‑16	Perimeter Institute Quantum Discussions	Scientific Series	View details
Quantum measurements of time	2021‑06‑16	Quantizing Time	Conference	View details
(Quantum) frame covariance: from foundations via gauge theories to gravity	2021‑06‑16	Quantizing Time	Conference	View details
TBA	2021‑06‑15	Particle Physics	Scientific Series	View details

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