“In the future, maybe quantum mechanics will teach us something equally chilling about exactly how we exist from moment to moment of what we like to think of as time.” -Richard K. Morgan
It’s absolutely true that, in quantum mechanics, there are certain pairs of properties that we simply can’t measure simultaneously. Measure the position of an object really well, and its momentum becomes more uncertain. Measure its energy, and its time becomes more uncertain. And measure its voltage, and the free charge becomes more uncertain. Although this is disconcerting to some, it’s a fundamental part of the quantum nature of the Universe.
An illustration between the inherent uncertainty between position and momentum at the quantum level. Image credit: E. Siegel / Wikimedia Commons user Maschen.
But there’s also more to it than that! Not only are pairs inherently uncertain, but each component has some built-in uncertainty that you can never take away. Moreover, it arises from a simple fact that isn’t true classically: the order of operations — whether you measure position or momentum first — makes a fundamental difference in what you get out. This quantum commutation relation is where so much of the fundamental quantum weirdness in ...