As discussed in the A Closer Look box on "Measurement and the Uncertainty Principle," the essence of the uncertainty principle is that we can't make a measurement without disturbing the system that we are measuring. (a) Why can't we measure the position of a subatomic particle without disturbing it? (b) How is this concept related to the paradox discussed in the Closer Look box on "Thought Experiments and Schrödinger's Cat"?

(a) We cannot measure the position of a subatomic particle without disturbing it because at the subatomic scale, the interaction between the particle and probing photons (used for measurement) can significantly change the state of the particle. Obtaining an accurate position measurement requires higher energy photons, which in turn causes a greater disturbance in the particle's momentum. This is in accordance with the Uncertainty Principle, which states that it is impossible to simultaneously measure both the position and momentum of a quantum object with absolute certainty. (b) The Uncertainty Principle and Schrödinger's Cat experiment are related as they both demonstrate the limitations and paradoxes of applying quantum mechanics to real-world scenarios. In the Schrödinger's Cat case, measuring the radioactive atom forces the superposition to collapse, resulting in a single outcome: the cat being either alive or dead. This highlights the central idea of the Uncertainty Principle: measurements inevitably disturb the system, preventing us from simultaneously determining some properties with absolute certainty.