As a physics student, one of the most fascinating things I've learned so far is how purely mathematical transformations can derive new insight into physical phenomena.* While a pure Physics degree was my first choice, I changed it later to Math & Physics and I don't regret it. Also, understanding WHY mathematics is so powerful in material world is a fundamental question that physics should be able to answer -- not philosophy.
* When I was studying basic physics in high school I recall being intrigued by the fact that in many scenarios (not always) a macroscopic body movement can be calculated from both the energy conservation framework (E kinetic/E potential, E=mgh, and so on), as well as from the mechanics framework {x/v/a(t)}. Both approaches yield identical numeric results through totally different formulas and input values. A somewhat deeper example from my current study would be one particular simplification of the Schroedinger's equation where it is rearranged into a tuple of functions with separated Time and Space variables (t/x). Resulting formulas, derived purely mathematically, show something very counter-intuitive: the formula for time-dependent change of a quantum system is universal for all such systems. Only the spatial change psi(x) is system-specific. Still wrapping my head around the physical meaning of it (which I do recognize as a primary sin in modern physics, asking those "why" questions, and I don't care).
Overall, I hate that modern physics shrugs off the most interesting parts of it and gives it away to philosophy, which speculates it away into unprovable/unfalsifiable chew of semantic nothing. Physics should be able to look into those parts that Copenhagen Interpretation outlawed, it also *should* be able to derive concrete (non probabilistic) calculations on the quantum phenomena, and not to shy away from rigorously incorporating consciousness and "subjectivity" into into the scientific framework. This would be my general solution to the current state of physics.
* When I was studying basic physics in high school I recall being intrigued by the fact that in many scenarios (not always) a macroscopic body movement can be calculated from both the energy conservation framework (E kinetic/E potential, E=mgh, and so on), as well as from the mechanics framework {x/v/a(t)}. Both approaches yield identical numeric results through totally different formulas and input values. A somewhat deeper example from my current study would be one particular simplification of the Schroedinger's equation where it is rearranged into a tuple of functions with separated Time and Space variables (t/x). Resulting formulas, derived purely mathematically, show something very counter-intuitive: the formula for time-dependent change of a quantum system is universal for all such systems. Only the spatial change psi(x) is system-specific. Still wrapping my head around the physical meaning of it (which I do recognize as a primary sin in modern physics, asking those "why" questions, and I don't care).
Overall, I hate that modern physics shrugs off the most interesting parts of it and gives it away to philosophy, which speculates it away into unprovable/unfalsifiable chew of semantic nothing. Physics should be able to look into those parts that Copenhagen Interpretation outlawed, it also *should* be able to derive concrete (non probabilistic) calculations on the quantum phenomena, and not to shy away from rigorously incorporating consciousness and "subjectivity" into into the scientific framework. This would be my general solution to the current state of physics.
