**UCSD Workshop on Time's Arrows**

Time: October 14-15, 2023

Conference location:

Department of Philosophy, University of California, San Diego, CA

Arts and Humanities Building, 4th Floor

9625 Scholars Drive North, La Jolla CA 92093

Conference location:

Department of Philosophy, University of California, San Diego, CA

Arts and Humanities Building, 4th Floor

9625 Scholars Drive North, La Jolla CA 92093

Saturday, October 148:30 Breakfast 9:30-11:00 Charles Sebens (CalTech) 11:00-12:30 Tim Maudlin (NYU) Lunch Break 2:00-3:30 Ali Raza Mirza (Surrey) 4:00-5:30 Jenann Ismael (JHU) 6:15 Conference Dinner |
Sunday, October 158:30 Breakfast 9:00-10:30 Martin Voggenauer (Cologne) 10:45-12:15 Emily Adlam (Chapman) 12:15-1:00 Short talk / open discussion |

Organizers: Craig Callender (UCSD) and Eddy Keming Chen (UCSD)

This workshop is made possible through the John Templeton Foundation grant "Life on the Edge: Quantum Thermodynamics, Quantum Biology, and the Arrow of Time"

Practical information:

Conference hotel: La Jolla Shores Hotel (8110 Camino Del Oro, La Jolla, CA 92037)

Conference attendance is free but space is limited. Please contact Eddy Chen at [email protected] to register for the conference.

Charles Sebens. "How do Laws Produce the Future?"

Abstract: The view that the laws of nature produce later states of the universe from earlier ones (prominently defended by Maudlin, 2007) faces difficult questions as to how the laws produce the future and whether that production is compatible with special relativity. This project grapples with those questions, arguing that the concerns can be overcome through a close analysis of the laws of classical electromagnetism. The view that laws produce the future seems to require that the laws of nature take a certain form, fitting what Adlam (2022) has called “the time evolution paradigm.” Making that paradigm precise, we might demand that there be temporally local dynamical laws that take properties of the present and the arbitrarily-short past as input, and return as output changes in such properties into the arbitrarily-short future. In classical mechanics, Newton's second law can be fit into this form if we follow a proposal from Easwaran (2014) and understand the acceleration that appears in the law to capture how velocity (taken to be a property of the present and the arbitrarily-short past) changes into the arbitrarily-short future. The dynamical laws of electromagnetism can be fit into this form as well, though because electromagnetism is a special relativistic theory we might require that the laws meet a higher standard: linking past light-cone to future light-cone. With some work, the laws governing the evolution of the potentials and the evolution of charged matter for electromagnetism in the Lorenz gauge can be put in a form that meets this higher standard.

Tim Maudlin. "On the Emergence of Relativistic Structure From a Discrete Space-Time”

Abstract: It would help solve the problem of implementing non-locality in physics if there were a preferred foliation in space-time. And it would help solve problems about singularities if space-time were discrete. Both of these features are absent in Relativistic space-times, so if one postulates them there must be some compelling account of why a discrete space-time with a preferred foliation gives rise the the appearance, at macroscopic scale, of Relativistic structure. I will discuss some discrete space-time structures in which it appears that exactly this can happen.

Ali Raza Mirza. "Master equation incorporating the system-environment correlations present in the joint equilibrium state"

Abstract: We present a general master equation, correct to second order in the system-environment coupling strength, that takes into account the initial system-environment correlations. We assume that the system and its environment are in a joint thermal equilibrium state, and thereafter, a unitary operation is performed to prepare the desired initial system state, with the system Hamiltonian possibly changing thereafter as well. We show that the effect of the initial correlations shows up in the second-order master equation as an additional term, similar in form to the usual second-order term describing relaxation and decoherence in quantum systems. We apply this master equation to a generalization of the paradigmatic spin-boson model, namely, a collection of two-level systems interacting with a common environment of harmonic oscillators, as well as a collection of two-level systems interacting with a common spin environment. We demonstrate that, in general, the initial system-environment correlations need to be accounted for in order to accurately obtain the system dynamics.

Jenann Ismael. "Reflections on the Asymmetry of Causation"

Abstract: I examine the status of the causal arrow, assuming a broadly boltzmannian account of the foundations of thermodynamics and the interventionist account of causation. I argue that there is an objective asymmetry rooted in the thermodynamic gradient that underwrites the asymmetry of interventionist causal pathways: along a thermodynamic gradient, interventionist causal pathways—scaffolded intervention-supporting probabilistic relationships between variables—will propagate influence into the future, but not into the past. The reason is that the present macrostate of the world, in the presence of a low entropy boundary condition, will screen off probabilistic correlations to the past. The asymmetry, however, emerges only under the macroscopic coarse-graining and that raises the question of whether the arrow is simply an artefact of the macroscopic lenses through which we see the world. The question is sharpened and examined.

Martin Voggenauer. "From an Intrinsic Arrow of Time to Entropic Arrows in Time"

Abstract: The problem of the direction of time consists in an apparent contradiction between the time-reversal invariance of the fundamental laws of physics and many temporal asymmetries we experience in our world. In particular, we experience many irreversible processes in nature suggesting that entropy increases only in one temporal direction. However, since the fundamental laws of nature are time-reversal invariant, the question arises as to what the temporal asymmetry of these irreversible processes is grounded in. In this talk, I focus on approaches that attempt to interpret the direction of time as an intrinsic feature of the temporal dimension of spacetime, and explore how local entropic arrows can be explained by such an intrinsic arrow of time. To this end, I first explore whether these approaches can be strengthened by considering assumptions from contemporary cosmology that provide physical reasons for the direction of time as an intrinsic feature of spacetime. In a second step, I examine whether a general constitution principle in the form of a local statistical postulate can help to recover the local entropic arrows from such a physically motivated intrinsic arrow of time.

Emily Adlam. "The Temporal Asymmetry of Influence is Not Statistical"

Abstract: I argue that the temporal asymmetry of influence is not merely the result of thermodynamics: it is a consequence of the fact that the modal structure of the universe must admit only processes that cannot give rise to contradictions. I appeal to the process matrix formalism developed in the field of quantum foundations to characterize processes that are compatible with local free will while ruling out contradictions, and I argue that this gives rise to “consistent-chaining” requirements that explain the temporal asymmetry of influence. I compare this view to the perspectival account of causation advocated by Price and Ramsey.

This workshop is made possible through the John Templeton Foundation grant "Life on the Edge: Quantum Thermodynamics, Quantum Biology, and the Arrow of Time"

Practical information:

Conference hotel: La Jolla Shores Hotel (8110 Camino Del Oro, La Jolla, CA 92037)

Conference attendance is free but space is limited. Please contact Eddy Chen at [email protected] to register for the conference.

**Talk abstracts:**Charles Sebens. "How do Laws Produce the Future?"

Abstract: The view that the laws of nature produce later states of the universe from earlier ones (prominently defended by Maudlin, 2007) faces difficult questions as to how the laws produce the future and whether that production is compatible with special relativity. This project grapples with those questions, arguing that the concerns can be overcome through a close analysis of the laws of classical electromagnetism. The view that laws produce the future seems to require that the laws of nature take a certain form, fitting what Adlam (2022) has called “the time evolution paradigm.” Making that paradigm precise, we might demand that there be temporally local dynamical laws that take properties of the present and the arbitrarily-short past as input, and return as output changes in such properties into the arbitrarily-short future. In classical mechanics, Newton's second law can be fit into this form if we follow a proposal from Easwaran (2014) and understand the acceleration that appears in the law to capture how velocity (taken to be a property of the present and the arbitrarily-short past) changes into the arbitrarily-short future. The dynamical laws of electromagnetism can be fit into this form as well, though because electromagnetism is a special relativistic theory we might require that the laws meet a higher standard: linking past light-cone to future light-cone. With some work, the laws governing the evolution of the potentials and the evolution of charged matter for electromagnetism in the Lorenz gauge can be put in a form that meets this higher standard.

Tim Maudlin. "On the Emergence of Relativistic Structure From a Discrete Space-Time”

Abstract: It would help solve the problem of implementing non-locality in physics if there were a preferred foliation in space-time. And it would help solve problems about singularities if space-time were discrete. Both of these features are absent in Relativistic space-times, so if one postulates them there must be some compelling account of why a discrete space-time with a preferred foliation gives rise the the appearance, at macroscopic scale, of Relativistic structure. I will discuss some discrete space-time structures in which it appears that exactly this can happen.

Ali Raza Mirza. "Master equation incorporating the system-environment correlations present in the joint equilibrium state"

Abstract: We present a general master equation, correct to second order in the system-environment coupling strength, that takes into account the initial system-environment correlations. We assume that the system and its environment are in a joint thermal equilibrium state, and thereafter, a unitary operation is performed to prepare the desired initial system state, with the system Hamiltonian possibly changing thereafter as well. We show that the effect of the initial correlations shows up in the second-order master equation as an additional term, similar in form to the usual second-order term describing relaxation and decoherence in quantum systems. We apply this master equation to a generalization of the paradigmatic spin-boson model, namely, a collection of two-level systems interacting with a common environment of harmonic oscillators, as well as a collection of two-level systems interacting with a common spin environment. We demonstrate that, in general, the initial system-environment correlations need to be accounted for in order to accurately obtain the system dynamics.

Jenann Ismael. "Reflections on the Asymmetry of Causation"

Abstract: I examine the status of the causal arrow, assuming a broadly boltzmannian account of the foundations of thermodynamics and the interventionist account of causation. I argue that there is an objective asymmetry rooted in the thermodynamic gradient that underwrites the asymmetry of interventionist causal pathways: along a thermodynamic gradient, interventionist causal pathways—scaffolded intervention-supporting probabilistic relationships between variables—will propagate influence into the future, but not into the past. The reason is that the present macrostate of the world, in the presence of a low entropy boundary condition, will screen off probabilistic correlations to the past. The asymmetry, however, emerges only under the macroscopic coarse-graining and that raises the question of whether the arrow is simply an artefact of the macroscopic lenses through which we see the world. The question is sharpened and examined.

Martin Voggenauer. "From an Intrinsic Arrow of Time to Entropic Arrows in Time"

Abstract: The problem of the direction of time consists in an apparent contradiction between the time-reversal invariance of the fundamental laws of physics and many temporal asymmetries we experience in our world. In particular, we experience many irreversible processes in nature suggesting that entropy increases only in one temporal direction. However, since the fundamental laws of nature are time-reversal invariant, the question arises as to what the temporal asymmetry of these irreversible processes is grounded in. In this talk, I focus on approaches that attempt to interpret the direction of time as an intrinsic feature of the temporal dimension of spacetime, and explore how local entropic arrows can be explained by such an intrinsic arrow of time. To this end, I first explore whether these approaches can be strengthened by considering assumptions from contemporary cosmology that provide physical reasons for the direction of time as an intrinsic feature of spacetime. In a second step, I examine whether a general constitution principle in the form of a local statistical postulate can help to recover the local entropic arrows from such a physically motivated intrinsic arrow of time.

Emily Adlam. "The Temporal Asymmetry of Influence is Not Statistical"

Abstract: I argue that the temporal asymmetry of influence is not merely the result of thermodynamics: it is a consequence of the fact that the modal structure of the universe must admit only processes that cannot give rise to contradictions. I appeal to the process matrix formalism developed in the field of quantum foundations to characterize processes that are compatible with local free will while ruling out contradictions, and I argue that this gives rise to “consistent-chaining” requirements that explain the temporal asymmetry of influence. I compare this view to the perspectival account of causation advocated by Price and Ramsey.