I know that such events would cancel out in the math, but if an extreme event were to happen in the future (say a black hole forming or something on that par), would a particle in the present react to it? If not, why?
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The path integral is a broad idea, which comes in several different flavors. In non-relativistic quantum mechanics for one particle, you calculate the propagator matrix element $\langle {\bf x}_f| U(t_f,t_i) | {\bf x}_i \rangle$ by summing $\exp(i\, S[{\bf x}(t)]\, /\hbar)$ over paths connecting $(t_i, {\bf x}_i)$ to $(t_f, {\bf x}_f)$ which travel forward in time, so there's clearly no retrocausality. In relativistic quantum field theory, you typically use the LSZ formalism, which involves integrating $\exp(i S[\varphi(x)] / \hbar)$ with $S[\varphi(x)] := \int_{t_i}^{t_f} dt\, \int d^3 {\bf x}\, \mathcal{L}(\varphi(x), \partial_\mu \varphi(x); x)$ in the limit $t_i \to -\infty$ and $t_f \to +\infty$, so that the incoming and outgoing particles are thought of as far-separated and asymptotically noninteracting. (In practice, this limit is carried out through the use of the "$i\epsilon$ trick" in the denominator of the propagator, which sets the boundary conditions.) In neither case are paths that extend later than $t_f$ considered, so there is no retrocausality. (You do find acausal correlations across spacelike separations, but they cannot transmit acausal influences.)
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