dextercioby said:
There’s always the feeling you get when you study physics really deeply that you’re doing no more than applied mathematics.
Unless you’re a modern Michael Faraday, i.e. a guy who works in a team who works in a (sometimes really big) laboratory from a (typically huge) facility or research institute like CERN or FermiLab, and your day-to-day job involves working with electronic equipment.
This paragraph is really weird. How can the author possibly label person working in team in a research facility/institute as "modern Michael Faraday"? The work they do in modern laboratories is rarely even close to what Michael Faraday was doing in his research. He did moderate-cost research of basic EM phenomena with a small-size self-made equipment (he studied EM induction with magnets and coils). In CERN, they do immense-cost research of subtle and exotic EM phenomena with expensive machinery which takes years to build (they study what detectors say happens after microscopic particles collide).
And why does the author suggest that everybody else is doing "no more than applied mathematics"?
I can say that whenever "I was thinking of physics deeply", how rare soever it was, I have never had a feeling like I'm doing applied mathematics. I am not sure what the author thinks doing applied mathematics means, but I guess it means you're not doing physics at all and you're either calculating consequences of a mathematical model given to you or you're developing such a model based on some mathematically formulated requirements.
I think that when you think about theoretical physics deeply, you're thinking about how the claims from professor, peers, textbook or paper are inconsistent either with themselves or with other physics known. You're trying to discern which ideas are experimental facts, which are questionable interpretations of such facts, which are just a popular way to think of them but not really necessary. You're thinking whether they can possibly be consistent with that or that theory and facts. Or you think about statements of a person who claims he solves some physics problem and you're trying to find whether he's right by analyzing the arguments and validity of the assumptions made. In many ways, deep thinking in theoretical physics is much like deep thinking in philosophy (it really originated in there). Applied mathematics is not a good name for such endeavour, I would say.
Do let a Heisenberg matrix be finite (Avogadro’s number of lines and columns) and you won’t have a quantum theory whatsoever. [as a side note: do let Planck’s constant be = 0 and you won’t have a quantum theory again].
It is true that the standard way to talk about Heisenberg matrices and Schroedinger operators is using the concept of infinity. However, neither matrices nor operators really are the core part of the theory that implies the predictions and explanations derived from it.
The core is the Schroedinger equation and the Born interpretation. The equation is a partial differential equation in coordinates and time.
This equation works with concepts of derivative and differentiable function, which are close to concept of infinity. But it can also be discretized and its solutions calculated in computer with no use of infinity. This can be done so it leads to predictions/explanations arbitrarily close to those you would get from the partial differential equation. The infinity has no more special significance for Schroedinger equation any more it has for the heat conduction equation or wave equation.
