Heisenberg's uncertainty principle asserts a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position and momentum, can be known simultaneously. The more you know about one, the less you know about the other. Why does the following thought experiment not violate Heisenberg's uncertainty principle? Suppose you have a source that releases simultaneously two identical particles in opposite directions. The particles have the same momentum: being identical they have the same mass, and they were ejected from the source with the same speed. (You may think of the particles as being two protons resulting from the "explosion" of a dihydrogen molecule; because of the conservation of momentum, the two protons fly in opposite directions with the same speed). Now, at t=1s after the particles have been released from the source you carry out two measurements: 1) You measure the position of particle A and find a value, xA. Because of the conservation of momentum, you can deduce the position of particle B at that time, which will be -xA 2) You measure the momentum of particle B and find a value, pB. Because of the conservation of momentum, you can deduce the momentum of particle A, which will be -pB As a result, you have acquired precise knowledge at a given time of both the position and the momentum of particle A (and similarly for particle B). Therefore, Heisenberg's uncertainty principle is false. What's wrong with this thought experiment? It resembles a lot EPR's thought experiment, but is not identical. I'm pretty sure that there must be a mistake somewhere, but I can't figure out where. Any thoughts?