Quantum Physics

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.

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.

"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 .)"

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

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.)

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.

"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)"

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.

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.

"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"

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.