Backtracking Influence

Abstract

Backtracking influence is influence that zigzags in time. For example, backtracking influence exists when an event E ₁ makes an event E ₂ more likely by way of a nomic connection that goes from E ₁ back in time to an event C and then forward in time to E ₂. I contend that backtracking influence is redundant in the sense that any existing backtracking influence exerted by E ₁ on E ₂ is equivalent to E ₁’s temporally direct influence on E ₂. I prove the redundancy of backtracking influence using several plausible physical principles without assuming any fundamental temporal or causal asymmetry. This explanation can play a prominent role in an account of why causation appears to be objectively asymmetric regardless of whether the fundamental laws are temporally symmetric.

Acknowledgements

This paper benefited from the comments of two anonymous referees of this journal.

Notes

[1] In the case of quantum mechanics, most fundamental properties are represented as part of the universal wave function, Ψ, which encapsulates the entanglements among position, momentum, spin, etc., for all the particles in the universe. Ψ’s degrees of freedom require a mathematical space of very high dimension called ‘configuration space’ for adequate representation. One way to interpret Ψ is to say that it represents a holistic relation among all the particles in the universe at some time t and thus occupies the infinitely extended time slice at t. However, one might wish to interpret this configuration space as a part of (or perhaps all of) the fundamental space (or arena) inhabited by all fundamental entities and properties. In that case, one would need to translate my talk of space‐time locations into talk of regions in this more general arena that includes space‐time and configuration space or perhaps just configuration space alone. Everything I say in this article is compatible with such interpretational manoeuvres, though for rhetorical convenience, I will presume space‐time as the arena of fundamental reality.

[2] A more thorough discussion of this approach towards causation is provided in Kutach (in prep.).

[3] In particular, I will not consider the prob‐influence exerted by spatio‐temporally disconnected contrastive events where the foreground part is located inside a compact region that lies to the future of a vast time slice. The prob‐influence exerted by such events does not count as backtracking influence because it exists only in virtue of the temporally direct probability‐fixing of the vast time slice. The conclusion I am defending here only concerns genuine backtracking influence. I discuss the prob‐influence exerted by such disconnected events in Kutach (in prep.), but in any case they do not constitute exceptions to any of the claims I make here.

[4] In classical gravitation, the events that play the key role in causation are determinants that span a full time slice of Galilean space‐time, specifying the relative location and speeds of every particle in the time slice and also specifying where the time slice is just a vacuum. Events that are smaller than a full time slice, even if they only omit specification of what happens at a single point p, will typically fail to determine (or fix probabilities) for anything else because what happens at other times depends on whether there is a massive particle at p. And such events do not determine or fix a probability for whether there is a particle at p. In some models of classical gravitation, one can postulate that the gravitational field is an ontologically independent quantity, which could lead to determination at space‐like separation, but I am assuming a model that omits the gravitational field from the fundamental ontology.