In the context of quantum mechanics, how does the complementarity principle relate to the uncertainty in measuring both the energy and the position of entangled particles?

In quantum mechanics, the complementarity principle says that certain pairs of properties, like energy and position, cannot be known precisely at the same time because they are linked by the uncertainty relation. For entangled particles, measuring the energy of one particle immediately fixes the energy of its partner, but this act disturbs the position information of both, making their exact positions uncertain. The reasoning follows from the fact that the operators for energy and position do not commute, so their measurement outcomes are statistically linked and cannot be simultaneously sharp. For example, if two photons are entangled and you measure one photon's energy very accurately, the other photon's position becomes highly uncertain, illustrating how complementarity enforces the trade‑off between energy precision and positional certainty.