If A and B are entangled photons and one measures the position of photon A just before photon B encounters a double-slit experiment, it will not directly determine whether photon B behaves as a wave or a particle. The behavior of photon B will still depend on the specific experimental setup and conditions.
The entanglement of two particles, such as photons A and B, means that they are correlated in certain ways, regardless of their spatial separation. When one of the entangled particles is measured or observed, it can affect the state of the other particle instantaneously, even if they are far apart. This phenomenon is known as quantum entanglement.
However, the act of measuring the position of photon A does not provide information about the specific behavior of photon B in a double-slit experiment. The behavior of photon B, whether it exhibits wave-like interference or particle-like behavior, will be determined by the experimental setup and the conditions under which the experiment is conducted.
In a standard double-slit experiment, the behavior of photon B will be influenced by factors such as the slit widths, the distances involved, the type of detectors used, and the interaction between the photons and the experimental apparatus. These factors will determine whether photon B exhibits interference patterns characteristic of wave-like behavior or a localized pattern consistent with particle-like behavior.
It's worth noting that entanglement does not directly determine the behavior of individual particles. Instead, it establishes correlations between measurements made on entangled particles. The behavior of each particle is still subject to the laws of quantum mechanics and the specific conditions of the experiment.