Well research is always done off existing foundational theory. But one thing I know about modern physics is people are bad at explaining their work. I remember working through some of a book on statistical mechanics and there was two equation lines directly adjacent to one-another and it took me two and a half pages of work to show how to get there. I will hand it to them, though, it was terse.
this post was submitted on 03 Jul 2023
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Yeah I've been through a couple of textbooks that do the same. I think Griffiths QM can be pretty egregious in that regard, actually.
Are you high? I kid, I kid.
I know what you mean. Physics without calculus is kind of useless. Physics with calculus is elegant and powerful. Although you are talking about QM and Hilbert spaces, the same thing goes for Newtonian mechanics and Newton/Leibniz, as well as E&M.
Actually I was just talking yesterday with my husband about relativity vs string theory, and the same thing: one produces (edit: spelling) falsifiable predictions, the other doesn't. And Einstein was a real ballsy dude predicting gravitational lensing, which is so completely counter-intuitive. It speaks to his incredibly deep grasp of what his theories actually are (I know that seems like "duh" but clearly he wasn't just doing math).
Yeah I agree, it's pretty incredible. I am no mathematician, in fact I'm pretty far from one, so it often blows my mind that there are/were people out there than can read through the numbers and make deep connections between seemingly abstract mathematics and physical reality. I've found that I generally approach physics intuitively, meaning I try to intuitively understand a system before deciding on what relevant maths or concepts I'll need to solve/quantify the system. I think that stands in contrast to those who start with the mathematics, and maybe tease out an intuitive understanding ex post facto.
Also, nice username!
I am right there with you, I use math but I develop an intuitive understanding of the system generally. And thanks re: username! I work in nuclear materials.