The phenomenon you're referring to is known as quantum entanglement, where two or more particles can become correlated in such a way that the state of one particle is dependent on the state of the others. When two particles are entangled, their individual quantum states become inseparable, even when they are physically separated.
According to the principles of quantum mechanics, the state of a system is described by a wave function, which represents the probabilities of different outcomes when measurements are made. When a measurement is performed on an entangled particle, the wave function of the combined system collapses into a specific state, and this collapse appears to be instantaneous, regardless of the spatial separation between the particles.
However, it's important to note that the collapse of the wave function does not allow for instantaneous communication or transfer of information between the entangled particles. The collapse is a change in our knowledge or information about the system rather than a direct physical influence. This is known as the no-communication theorem in quantum mechanics.
To address your question, the reason we know that both wave functions weren't collapsed at separation is based on experimental evidence and the violation of certain Bell inequalities. Experiments have been conducted to measure the correlations between entangled particles at different locations and orientations. These experiments have consistently shown that the correlations observed cannot be explained by classical (non-quantum) theories, indicating the existence of non-local correlations between the entangled particles.
The violation of Bell inequalities provides a statistical test that distinguishes between classical correlations and the non-local correlations predicted by quantum mechanics. These tests have been performed in numerous experiments and have consistently demonstrated that the correlations observed in entangled systems are incompatible with classical explanations.
These experimental results strongly support the idea that the collapse of the wave function upon measurement is indeed a real and instantaneous effect, and that the entangled particles retain a non-local connection even when separated in space. However, it's important to note that the exact nature and mechanism of this non-locality are still subjects of ongoing research and debate in the field of quantum mechanics.