Making sense of particles going backwards in time

Question

Physicists sometimes talk about particles going backwards in time. Help me make sense of this. I thought things don't "go" in any particular direction in time. They just "are" there at every moment. And you can imagine playing the tape "forwards" or "backwards" but that has no physical meaning.

Answer 1

It's unfortunately common for popular science accounts to use the "going backwards in time" when talking about zigzag causal structures in Feynman diagrams and retrocausal quantum models. It's unfortunate, because as you correctly note, that phrase isn't logically coherent; it uses time in two different senses in quick succession. Feynman himself never used that phrase, I'm almost certain, and in my Rev. Mod. Phys. piece of retrocausal accounts of entanglement we certainly did not use anything like that terminology, instead adopting the block-universe perspective of spacetime events. (The set of those events, as you correctly note, can be "played" forward or backwards, and don't "go" in either direction.)

But instead of dismissing such phrases out of hand, it's perhaps worth analyzing why it's so common for people to use this particular phrase in these contexts. The central point that is being (clumsily) attempted is that the causal order is opposite the temporal order. Any careful and precise way to make this point requires the "interventionist" account of causation popularized by Judea Pearl, and frequently used in the zigzag context by Huw Price.

Suppose you had a zigzag structure $\text{/\/}$ in spacetime, as in one of Feynman's examples of an electron which annihilates the positron from an electron-positron pair. A lazy and technically incorrect way to talk about this would be that the electron "goes forward in time" (on the left), then "goes back in time" (as a positron) in the middle, and then "goes forward in time" (on the right). But the meaningful sentiment of these statements is that the causal structure of this event looks like a directed acyclic graph (Pearl's DAGs), with zigzagging arrows pointing up to the right, then down to the right, then up to the right.

The key here is that interventionist causation doesn't quite work in a single block universe, as it requires counterfactuals; you have to imagine how the events would be different given potential interventions at different points. The causal arrows tell you in what direction to expect the effects of those interventions. Those counterfactuals can't all fit on one spacetime diagram – they refer to counterfactual universes – but they do tie into how we innately think about causation, imagining what would be different under different external interventions. With this in mind, those statements might make a bit more sense: the word "going" is meant to be causal, not temporal, not anything which would be meaningful in a single block universe without imagining counterfactuals.