Most physics PhDs pursue grad school with some hopes of academia. However, there simply aren’t enough academic positions to sustain the influx of wide-eyed graduate students. As a result, most PhDs do not stay on in physics. What then, is the benefit of studying physics for 6+ years simply to never look at it again? In my opinion, the main skill of getting a physics PhD isn’t the esoteric knowledge but instead the ability to work with mental models efficiently and effectively.
As a physicist, you collect many tools in your toolbox. You might learn a little about how fluids work, things like how water or air flows. But those equations won’t do you very good if you want to study subatomic particles. Instead, you’ll sooner or later discover that there is another set of rules that describe how electrons behave around nuclei. This realization is an example of realizing that your mental model of the problem is wrong. You shouldn’t be treating the electron as if it’s a fluid!
A lot of times mental models are like analogies. They aren’t perfect, but they help you understand certain aspects of a system. Often, they are contradicting. It’s weird to think of an electron as a fluid, but in fact, it behaves a lot like a wave! Would I be worried about drowning in a sea of electrons? Definitely not.
It can feel like traversing a booby-trap-laiden maze when dealing with mental models. Just when you think an analogy helps you, it can lead you astray and give complete nonsense when taken literally. But that just comes with the territory. Learning to figure out when different tools fit the bill is a skill in itself.
Physics in particular is a discipline where most of the mental models are expressed in the language of mathematics. Not all mental models have to be based on math. However, they do have a special power in that mathematics is predictive. If you say that something is growing exponentially, that is a very quantifiable prediction that can either be born out or not. STEM fields tend to have a bias towards this, in part because it leads to better feedback on how good your reasoning was.
PhDs don’t always realize that they’ve rewired their brain in this way, but once they do, it becomes more clear what employers really want in “people who are good at math”. The ability to swap in and out mental models for the situation at hand, and the ability to pick up new ones as you see fit is something that doesn’t come naturally. It requires a sort of mental flexibility that takes time to develop and is invaluable in today’s knowledge economy.