> Heisenberg's starting point was the philosophical judgement, that a physical theory should not concern itself with things like electron orbits in atoms that can never be observed. This is a risky assumption, but it served Heisenberg well.
@DanielSank:No , that doesn't but I go on to say "Hence he fastened on the energies of atomic states, and the rates at which atoms spontaneously make radiative transitions from one state to another state, as the observables on which to base a physical theory."
@MoziburUllah Ok fine but that's like someone asking why the sky is blue and you explain why train engines work. Trains are useful, but it doesn't answer the question :-)
If you feel patronized then I'm not sure what to do.
I have learnt that matrix mechanics came before Schroedinger's wave mechanics, however introductory quantum mechanics textbooks introduce you to wave mechanics first. The way in which the transition to matrix mechanics is made is by defining the matrix elements:
$$ H_{mn} = \int _{-\infty}^{+\in...
@DanielSank: And was that done before Heisenberg? Had matrices been used in physics before he used them, or was his discovery of matrices what made them promiment.
@danielSank: This answer that you're concerned with I wrote over a year ago; I, right now, recall very little about the circumstances in which I wrote it; most likely I'd read Weinbergs historical summary in his book and wrote a brief summary of that in the answer.
> "Up until this time, matrices were seldom used by physicists; they were considered to belong to the realm of pure mathematics. Gustav Mie had used them in a paper on electrodynamics in 1912 and Born had used them in his work on the lattices theory of crystals in 1921."
@ACuriousMind I mean, I don't even know what the domain of $W$ is, or if the two $W$'s are supposed to be exactly the same thing. Nothing is defined properly. How do physicists do this?
@Slereah All QFT is "diffeomorphism invariant". The Yang-Mills action is "diffeomorphism invariant" in precisely the same sense as the E-H action is, and yet it has a well-known and consistent quantum theory.
I mean, clearly SUGRA theory also must include this "diffeomorphism invariance" Rovelli is talking about, yet no one working on them claims their n-point functions are trivial.
The $W$ is a scalar function of n points in spacetime, a coordinate change or a diffeomorphism does precisely nothing to it.
@BalarkaSen Had to study that poem for my English lit GCSE - can't remember much of it to be honest. Although my friend's applied for English lit at uni and he always laughs at shakespeare like wtf dude.
I guess $\gamma_5$ in the RS action $ = - \frac{1}{2} \int d^4 x \, \varepsilon^{\mu \nu \rho \sigma} \overline{\Psi}_{\mu} \gamma_5 \gamma_{\nu} \partial_{\rho} \Psi_{\sigma}$ is put in as a 'pseudo-scalar' to counter the behaviour of $\varepsilon$?
You know the feels when you answer a question then the more you read it the more wrong things you see and you end up editing it like 20 times over the course of 10 minutes...
In susy when you make the infinitesimal spinor generator local you add an index which leads to spin 3/2 and rarita-schwinger unavoidably as far as I understand, and consistency somehow follows
I always plan on looking into such things when I finish the main things I want to do, there's just so so so so so so so much stuff left to do, and re-do
Maybe the Schrodinger equation with a relativistic Hamiltonian (the thing that leads to the dirac equation by squaring) is fine when you expand that square root, books just say it isn't because locality is scary, no idea why! ahh
