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"?

To measure the position of a subatomic particle, we need to use some kind of probe, like light or other particles. When we do this, the probe interacts with the subatomic particle which results in a disturbance to the system. In other words, the act of measuring the position changes the particle's position, and even its momentum. This is the essence of the uncertainty principle described by Heisenberg.

Schrödinger's cat thought experiment illustrates the concept of measurement in quantum mechanics. In this experiment, a cat is placed in a box containing a radioactive atom, a Geiger counter, a vial of poison, and a hammer. If the Geiger counter detects the decay of the radioactive atom, it triggers the release of poison, killing the cat. According to quantum mechanics, the radioactive atom is in a superposition state of decayed and not decayed until it is measured or observed. The connection to the uncertainty principle is that the act of observing or measuring the system (in this case, the cat in the box) affects the system's state. In the thought experiment, the cat is both alive and dead until the box is opened, and the observer measures the state. This illustrates the paradox of measurement in quantum mechanics: until a system is measured, it exists in multiple states simultaneously. Similarly, we cannot measure a subatomic particle's position without disturbing its state, as explained in part (a).