There is a common misconception that quantum particles get entangled after they collide. But the "collision" has no particular beginning. The colliding particle have always been entangled-- since the beginning of the Universe. Am I the only one thinking this way?
@BartoszMilewski But if you have a pair of particles i and j approaching each other from "independent" sources you can, for reasons I don't fully understand (and probably a consequence of decoherence), model them as a tensor product of states ψᵢ⊗ψⱼ, despite them having entanglement in their history. So you can talk of them as not being entangled.
The situation seems similar to the way we assume independence (in the math sense) of "independent" events (in the common sense) in probability theory.
@dpiponi We can *approximate* them as a tensor product. But my question is, if they are on a collision course, at what point do they get entangled? Is it a gradual process? Can we describe it mathematically? And what about time reversal?
@BartoszMilewski The entanglement emerges from the equations of motion. exp(itH/ℏ) will map simple tensor products to linear combinations of tensor products and you should be able to compute how the linear combination evolves as a function of t. This is all perfectly reversible from a mathematical perspective. (But there are shades of Boltzmann's H-theorem of classical physics here.)
@dpiponi @BartoszMilewski If we imagine, say, two non-relativistic massive charged particles having a collision, the interaction Hamiltonian is never strictly zero (assuming they've existed forever), but wouldn't the degree of entanglement be small until they have gotten somewhat close to one another (and the influence of the interaction Hamiltonian becomes large) with this entanglement then persisting afterward? In reality, with other environmental degrees of freedom being present (thermal photons, gas particles, etc.), it may be the case that there is significant decoherence that more strongly limits the degree of entanglement (in, say, positional degrees of freedom) except when they get close and the rate of entanglement generation overcomes the rate of decoherence to perhaps produce some non-negligible degree of entanglement. Depending on the details, this may then decohere again afterward leaving mostly just a correlated mixed state once you get far enough from the collision event.
