I failed my third year Quantum Mechanics course the first time I took it. I passed on the second attempt, but I think more out of the professor’s pity than any firmer grasp of the material.
Which is slightly unfair. I more-or-less understood QM. The issue is that it’s fundamentally nigh-impossible to actually understand QM without the underlying mathematics, and I have never been any good with the mathematics.
Let’s take a simple example: the Heisenberg Uncertainty Principle. This is familiar to some non-scientists, but it is most often summarized as “The more accurately you know an object’s velocity, the less accurately you know that object’s position.” Keep in mind this only applies to quantum-level physics (hence the ridiculous joke where a police officer pulls over Heisenberg and says “Did you know that you were going 100 km/h?” and Heisenberg throws up his hands and says “Great, now I’m completely lost!”), but the concept sort of makes sense.
Except that’s not the Heisenberg Uncertainty Principle. The HUP is more along the lines of “Any pair of canonically conjugate variables are connected such that there is an upper limit to the accuracy of any measurement of those variables in relation to each other,” and that is defined by an equation. And it doesn’t matter if it makes sense… quantum mechanics, if you will excuse the oversimplification, doesn’t need to make sense: it just has to be true. So the age-old question of “Is Light a wave or particle” has the answer “Yes, and no, and both, but sometimes neither, depending on the circumstances.”
What are the circumstances? Just plug the variables into this equation…
Hopefully you understand what I’m getting at. Classical mechanics is all about grasping and understanding how objects interact: a cannonball has a parabolic trajectory, so how does that relate to gravity? The sun’s mass allows us to understand the Earth’s mass and the way that our moon orbits us is the same way, albeit simpler, than the way Titan or Io orbit their planets. But QM? Doesn’t care. It doesn’t need to make sense, but it has to be mathematically solid.
This long tirade brought to you by trying to explain the Uncertainty principle to somebody last night. It did not go well… but that’s in part because it’s a very difficult concept once you get into the weeds of it.
Hope everyone out there is staying safe and healthy!