@BenNiehoff Precisely, I think of it more as a good heuristic to find the objects you actually want to compute (such as invariants in many topological and supersymmetric theories)
@0celo7 No one is saying it's not kind of a mess. I personally just think that's what physics looks like when it's still "fresh". If physics actually proceeded like math by carefully defining everything before lunging forward, the two wouldn't need to be separate disciplines at all.
You can say you don't like that (and I share in that feeling to some degree), but I find your hyperbolic statements it's "nonsense" unnecessarily harsh and unjustified, given the success it's had as an actual physical theory (and not a mathematical framework).
And in particular I find it questionable to assault a newcomer who is trying to learn QFT with these complaints.
"The principles of QM" by Dirac appeared pretty soon to set a standard and clear way of doing QM. QFT is almost as old as QM and there is nothing similar
@Runlikehell Classical point particle mechanics is also infinitely easier than classical field theory
Classical field theory already can carry many subtleties, but it's rare that those are taught because they tend to have rather specialized applications
@0celo7 Talk to me again when your numerology predicts high-energy precision experiments with unparalleled accuracy, then. The difference between physics and numerology is predictive power.
@0celo7 Why would that change if it were any more mathematically rigorous? Why should mathematical rigor have anything to do with describing the world?
Have you ever read Wigner's eassy on The Unreasonable Effectiveness of Mathematics?
The miracle is that mathematical procedure can tell us so much about the world to begin with, not that the parts of physics which are not fully rigorous still describe the world!
@ACuriousMind Let's put it this way: take the same sets of physical axioms, and perform some computations. One way, you treat all operators as matrices, multiply distributions, etc. In the other you do everything correctly. The first computation says you need to move 1 foot to not get killed by a bomb blast, and 2 is fatal. The other says you need to move 2, and 1 is fatal. What do you do?
@0celo7 Of course I move 2. But that's not the situation we're in. The current situation is that one computation says I should move 1 and the rigorous one fails to give any output at all for any but the simplest toy problems. And once we would discover the non-rigorous one gave the wrong answer we would of course adjust it!
But that's not what happens. What happens is that the non-rigorous procedure, time and time again, gives the correct output to almost arbitrary precision given enough computation time.
(At least in the cases where we know how to compute anything at all :P)
Rigor is preferable to its absence, but non-rigorous physics is preferable to giving up.
@0celo7 I don't see any reason why rigorous mathematics should give accurate results and it be any more than a mere coincidence, either. Science, at its heart, is nothing more than figuring out which coincidences happen frequently enough that we don't call them that anymore.
