|Intuitively, we expect physical quantities such as energy to be continuous and single-valued, like a dimmer switch. At very small scales, however, they are both discrete and multivalued, like a light switch that can be on and off at the same time.|
Of all the scientific theories that have broken out into public consciousness, none have ranged as far as quantum mechanics. This subject is sometimes presented as an erudite abstraction, as a smokescreen of uncertainty, as an almost mystical philosophy or as evidence that physicists have lost their minds. It’s rarely said that quantum mechanics makes sense.
There is good reason for that. Quantum mechanics is as hard to believe as anything can be while being demonstrably true. Feynman’s famous quote, “I think I can safely say that nobody understands quantum mechanics,” is sometimes taken out of context as suggesting that if you think you get it, you don’t. This defeatist attitude is unnecessary. Quantum mechanics is bizarre, but it can be understood.
The rules of quantum mechanics are logical, yet unfamiliar. For example, we expect a physical quantity like the position of a particle to be a single number, something that could be measured by a ruler. It is here and not there. That number may vary continuously as the particle moves, and it may be imprecisely known if we have not measured it well, but we intuitively expect it to be a specific number at a specific time.
What physicists have learned is that the position of a particle is not a single number: It is multivalued. The particle is here and there in a way that can be quantified, called the wavefunction. We imagine the wavefunction as a blob filling space, describing the degree to which the particle is in each place: thicker here, thinner there. It can be measured and charted, but our brains don’t like it because we evolved to manipulate the macroscopic world, everything larger than a splinter and smaller than a mammoth. Studying quantum mechanics forces us beyond our comfort zone, to apprehend something truly alien and shed our macrocentrism.
When I first learned about quantum mechanics, I was bothered by the crispness of quantum properties almost as much as their fuzziness. Not only is the energy of a particle multivalued, but each of those values is a whole number, never a fraction. It is as though the sliding dimmer light of our intuition has been replaced by an on-off switch with no middle value, but one that can be 30 percent on and 70 percent off, or any other ratio. Quantities have surprisingly little freedom in what values they can take, but surprisingly much freedom in how many they can take at once.
This is the first in a four-part series on quantum mechanics. In the next article, I will present the time paradoxes, followed by wave-particle duality and an overview of how we know what we know.