What is the ultimate sensitivity with which one can continually measure an object’s position? Sensitivity is often limited by thermal noise, and in some situations amplifiers set the noise floor. But classical physics argues that, with proper experimental design, the position uncertainty can be made arbitrarily small. Nearly 80 years ago, though, Werner Heisenberg posited his now-famous uncertainty relation, in which quantum mechanics places a fundamental limit on measurement precision: The product of the uncertainties in an object’s position and momentum must be at least ħ/2. A single position measurement will cast an object into a position eigenstate, but the resulting uncertain momentum will make the next position measurement uncertain.
Not only is the object being measured subject to quantum mechanics, so too are the measurement apparatus and the interaction between the object and the apparatus. And back action—the effect of the measurement system on the object being measured—is inescapable....
