>>11221254Two particles don't become "essentially the same entity". Entanglement means they share highly correlated statistics which violate Bell inequalities (at least, strong entanglement does). This rules out any local hidden variable theory.
Why does it happen? Because Hilbert space is a big place. Quantum degrees of freedom are coupled by a tensor product structure, whereas classical degrees of freedom are coupled by a direct sum structure. There is way more room in a product of spaces than a sum of those same spaces.
It's really not that wild to see what crates it. There is an interaction Hamiltonian describing how the two particles interact with each other (eg spin-spin, coulomb force, whatever). When you time evolve under that Hamiltonian, you create a path through Hilbert space that probably touches a lot of entangled states (Hilbert space is so large, after all, and is mostly entangled states), even if you start in an unentangled state.
Basically: if you take "particles interact with each other" (through a VAST variety of phenomena, call them forces if you like) and "particles evolve under the Schrodinger equation", you get entanglement. Nothing more mysterious than that.
As an exercise, try writing down the propagator for just 2 qubits in an Ising field. Don't even bother with local fields, just take . Compute (don't worry about units). Then apply that to a simple unentangled state, like both qubits spin up, . At what times t do you obtain maximally entangled states, i.e.
