Many explanations about the uncertainty principle and its related EPR paradox state that it is impossible to measure opposite complementary variables on different entangled particles; for example, measuring the position of one particle and the momentum of the other at the exact time.
I fail to understand what it means for this to be "impossible" in this case. What would happen if such an attempt was made?
I can only think of 4 ways of interpreting this impossibility:
- For every known pair of complementary variables, we only know how to measure one of the two variables for any given particle; for example, we only know how to measure position, not momentum (or vice versa). This is obviously incorrect.
- It is impossible to measure any of the complementary variables of a particle at the exact time we measure any other complementary variable of another particle. For example, given any two particles, we cannot measure both of their positions at the same time. I'm guessing this is also incorrect.
- Same as #2, but exclusive for entangled particles, implying that there is something in the process of the creation of such a pair that prevents them from being measured at the same exact time.
- In the case of an entangled pair being measured at the same time for opposite complementary variables, these measurements would "somehow" no longer correlate between the two, thus rendering the particles entangled no more.
Furthermore, if #4 is the case, was it verified? Was there an experiment showing the measured particles indeed were no longer entangled, perhaps by proof of contradiction; i.e, observing a later measurement that could only occur if these values were different than the values assumed based on the original measurements and the correlation between the particles?
I would love it if the answer would be simple as possible, as I do not have a strong background in neither physics nor mathematics.