Let me tell you what happened in my classical mechanics class a few months ago.
We were solving an exercise on the Coriolis force. The question was: if you drop a mass from the top of a skyscraper, how far from the base will it land because of Earth’s rotation? This is a very simple problem which all my colleagues knew how to solve, you just applied the Coriolis force formula knowing the angular velocity of the Earth and your latitude. But at the end, the professor asked something different: why does this actually happen? In particular, why does the mass land slightly forward, in the direction of Earth’s rotation? I had thought about this while solving the exercise, because at first, you might think that since the Earth rotates while the mass is falling, it should land behind the skyscraper. But that’s not what happens. So, I raised my hand and asked if it was because the mass has a greater tangential velocity at the top of the skyscraper than at the surface of the Earth. Since it’s farther from the axis of rotation, it’s moving slightly faster. So, when it falls, it keeps that extra velocity and lands a bit forward. Turns out I was right.
But this is a unique anecdote in which we are told in class to fully understand what happens. We are often not trained to explain or understand physical phenomena, but just to compute predictions with the given equations. In fact, if you are very good a mathematics, you can go through a physics degree without too much struggle. If you can solve differential equations and correctly match the parameters to the problem, you can do almost everything they asked you for in exams. But that doesn’t necessarily mean you understand what’s happening physically.
And understanding what’s going on gives you much more insight into the model and the physics itself. We know that progress in physics has often come from thought experiments, such as those of Einstein and Newton, and without understanding what’s really happening, you just can’t make thought experiments and come up with new physics.
Dialect has also done a video about how symmetries are often regarded as explanations for phenomena, when they are just a consequence of the mathematical model you are using to describe the system. I will leave the video in the references below. Following the example of the Coriolis force, you can guess by looking at the equation that such force will appear whenever you have a velocity with respect to the rotating reference frame, because there is a velocity term in the equation. But still, this is not a complete picture or explanation, it’s a property of the mathematical equation.
The true question is why do we need an additional ad hoc force to describe such phenomenon and why Newton’s laws do not work in non-inertial systems as they very well do in inertial ones. We discussed inertia before in other posts.
The same problem happens in Modified Newtonian Dynamics. We explained MOND in our previous post and how impressive it is that it can predict the rotation curves of galaxies without dark matter by introducing a single new universal constant of acceleration. But after Milgrom presented MOND in 1983, research has been focused on building Lagrangian and relativistic formulations that reduce to MOND, but that do not explain where does that constant comes from. Lagrangian formulation introduce it ad hoc into their equations, and relativistic formulations introduce even more constants and fine-tuned free parameters. But it looks like that acceleration constant is a derived parameter, because you can construct it from multiple cosmological parameters.
Here in Independent Physics, we are not just raising these questions, but we actively researching theoretical gravitation and in particular, this new approach to understand where does MOND come from.
References: