# A Lenient Causal Arrow of Time?

## Abstract

**:**

## 1. Introduction

## 2. Retrocausal Toy-Models

#### 2.1. A Simplistic Toy-Model

#### 2.2. Hall’s Toy-Model

#### 2.3. Criticism of the Superdeterministic Approach

- (i)
- $a$ and $b$ are free variables;
- (iI)
- The causal arrow of time, with $\lambda $ associated with a time earlier than that of $a$ and $b$.

## 3. Toward a General Retrocausal Theory

## 4. Summary and Discussion

The unlikelihood of finding a sharp answer to this question [the measurement problem] reminds me of the relation of thermodynamics to fundamental theory. The more closely one looks at the fundamental laws of physics the less one sees of the laws of thermodynamics. The increase of entropy emerges only for large complicated systems, in an approximation depending on “largeness” and “complexity.” Could it be that causal structure emerges only in something like a “thermodynamic” approximation, where the notions “measurement” and “external field” become legitimate approximations? Maybe that is part of the story, but I do not think it can be all. Local commutativity does not for me have a thermodynamic air about it. It is a challenge now to couple it with sharp internal concepts, rather than vague external ones.

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Sketch of a spacetime region permeated by fluctuating fields, with an external perturbation applied at times near ${t}_{1}$, and with the field configuration at an early time, ${t}_{0}$, fixed as initial conditions. If the fields are described by a deterministic theory, the field configurations before ${t}_{1}$ are unaffected by the external perturbation; in contrast, for stochastic theories the probability distribution of the fields at times between ${t}_{0}$ and ${t}_{1}$, indicated by the filled ovals, may depend on the perturbation. Nevertheless, the firing rate of a “detector” placed at or near these ovals must not depend on the perturbation (or else the no-signaling condition would be violated).

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