The image that should give you pause
How does a particle get from A to B? Classical answer: it follows the one path of least action — the trajectory that minimizes energy or some related quantity. Newton's mechanics says this. Common sense says this. It's almost right.
The deeper answer, due to Feynman in the 1940s: the particle takes every possible path from A to B, with each path contributing an amplitude (a complex number, like a probability). The amplitudes from all paths interfere. Most paths cancel each other out. The few paths that constructively interfere — clustered around the classical least-action path — are what survive and produce the observed motion.
This is the path integral formulation of quantum mechanics. It's mathematically equivalent to the Schrödinger picture, but conceptually more striking: the actual motion of the particle is the sum over every conceivable history. The classical trajectory is the one where most of the histories agree.
Why this is more than a math trick
Sit with it. To compute where a photon will land on a screen after passing through two slits, you don't ask which slit did it go through; you sum over both slits and every other path you can imagine. The answer matches experiments to absurd precision. The math doesn't care about "which slit really" — it cares about the sum.
This is the deepest source of the famous "weirdness" of quantum mechanics. Particles don't choose paths; they explore all of them in superposition until measurement collapses the sum down to one. The world as you see it is the constructive-interference residue of every path the universe could have taken to get here.
Many-worlds, lightly
Some physicists take the path integral literally — every path is happening, in some sense, in a parallel branch of a broader reality. This is the many-worlds interpretation. Other interpretations (Copenhagen, pilot wave, etc.) treat the path integral as a calculation tool that doesn't necessarily mean every path is "real" in a strong sense. The math is the same; the metaphysics is contested. We are not going to resolve it; we're not even going to try.
What survives across interpretations: the world doesn't pick a single history when no one is looking. The histories interfere. Measurement is what selects one. That's the headline.
What this means for choice
The previous lesson hinted at this; the path integral makes it sharper. Before a decision, your future is a path integral over all the choices you might make. The amplitudes for different futures are weighted by your context, your history, your dispositions. When you decide, you collapse the integral to one path. The other paths' amplitudes don't necessarily vanish (in the literal quantum sense) — but in your lived life, they're not the path you walked.
This is also why the idea that tiny everyday choices matter is mathematically defensible. Small amplitudes can interfere constructively over long sums. Habit, character, repeated small acts — they shift the amplitude of certain futures over time. The classical least-action path of your life is the path your accumulated decisions have made most likely.