How do Laws Produce the Future?

TL;DR

This paper analyzes how classical mechanics and electromagnetism laws can be understood as producing the future, addressing questions about their compatibility with relativity and the nature of dynamical laws.

Contribution

It provides a detailed analysis showing that classical laws can be formulated to produce the future within the time evolution paradigm, even in relativistic contexts.

Findings

Classical mechanics laws can be expressed as local dynamical laws.

Electromagnetic laws can be formulated to link past and future light-cones.

The analysis supports the view that laws produce the future within a precise framework.

Abstract

The view that the laws of nature produce later states of the universe from earlier ones (prominently defended by Maudlin) faces difficult questions as to how the laws produce the future and whether that production is compatible with special relativity. This article grapples with those questions, arguing that the concerns can be overcome through a close analysis of the laws of classical mechanics and electromagnetism. The view that laws produce the future seems to require that the laws of nature take a certain form, fitting what Adlam 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, returning 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 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 vector and scalar potentials in the Lorenz gauge, as well as the evolution of charged matter, can be put in a form that meets this higher standard.