@ACuriousMind I got a philosophy books recommended : "Being and Time" by Heiddeggar

Are you familiar with this stuff?

I see Heiddeggar's name a lot in philosophy discussions

Heidegger was important as a precursor to the existentialists

also he was a Nazi supporter

Omg

that's the two facts I know about Heidegger and I'm not really interested in learning any more :P

And I thought the book had a cool title :P

I will look for non-nazis at least

@bolbteppa Doesn't this change the interpretation of virtual particles? It is understood that only asymptotic states are real particles, but if you view virtual particles breaking conservation of proper energy instead of total energy (which is allowed), isn't this consistent with them being real?

I'm confused by this expression $\int dx' \partial_x[ \delta(x-x') f(x,x')]$. If the derivative and integral were with respect to the same variable, I would use integration by parts. Now, I would like to use Leibniz's integral rule, but I don't understand how it works with the $\delta$-function.

You know sometimes when I see some very elegant formula with no apparent obvious derivation I wonder if the guy who found it just tried a bunch of terms until he got it right

One of Feynman's exercize is to show that for the harmonic oscillator $$S_{cl} = \frac{m\omega}{2\sin(\omega T)} [(x_b^2 + x_a^2) \cos(\omega T) - 2 x_b x_a]$$

Which I can show knowing the answer

but how do you come up with it?

Do you just try a bunch of terms of $x_a$ and $x_b$

I guess it can't be that may different possible terms due to dimensional analysis, but still

From symmetry arguments it can only be in terms of $x_a, x_b, T$ and by dimensional analysis (if there's no rational terms) I guess it can only be something $x_a^2$, $x_b^2$, $x_a x_b$ since there's no constant that can absorb a length like that, but that's still not an amazing argument

Is there some amazing elegant proof to show that it is that without fumbling around to find it or did the Ancients just try a bunch of terms

On second thoughts nevermind

We can't transition to a virtual state at $t=+\infty$ due to the $\sin^2$ function becoming a delta function but does this mean that we can't transition to the state for any other $t$?

Sorry I am using virtual wrong here

When we have 2 asymptotic states in the mathematical formalism for scattering, are we really saying that we evolve from $t=-\infty$ to a finite time and the particles become dressed (but not interacting with eachother) and these are the particles we use in experiments?

In reality, do particles only interact for a very short time $\Delta t$?

squick

do you mean "magnetism" as in, the property of materials that produces magnetic fields?

or have you become a relativity denier and want to seperate magnetism from electrostatics :P

hm

I think the former. As in magnetism in matter yes

a relativity denier XD

e.g. stuff like this in griffiths is a little too far fetched for me, or maybe I am just not understanding it well

like you want to treat an electron as a current when it's convenient and then back as an orbiting particle when it's convenient :P

And the derivation ends with something to the effect of "it's all wrong anyways, so don't worry about the details"

I am confused about magnetisms relationship with all this business. From Bohr-Van Leeuwan theorem it seems like only in particular instances can diamagnetism and paramagnetism not be explained by classical physics. Okay, so use quantum mechanics when dealing with these situations. But in other cases like when you'd like to find the magnetic field due to a steady current, classical physics seems fine.

So it doesn't sound like magnetism as a whole needs quantum mechanical explanations, but I feel like that is how it is made out to be?

Basically a text which wrestles with where the classical theory of magnetism goes wrong and explains how quantum fixes the wrong, but then continues to explain classical magnetism just without lying to you about what our more modern understanding of magnetism is

ah, well, I'd guess there should be plenty of condensed matter texts that explain the quantum model of magnetism?

I don't think there's a deep explanation behind why "electrons as little currents" works: It's just that basic ferromagnetism doesn't depend on any specifics of the system (you can get it from "classical" Ising models), you just need these little magnetic moments that can be aligned

whether you think those magnetic moments come from little currents, electron spin, electron angular momentum or whatever doesn't matter for the basic idea

there's this general phenomenon about phase transitions (and the formation of magnetic domains is a phase transition I think, but I'm really a bit out of my depth here) that the specific dynamics don't matter for the essential features of the transition, cf. universality

so the texts say that you shouldn't worry about the details because they really don't matter :P

hmm okay then maybe i should try to get the quantum picture. i would basically just like to associate with these results in magnetic fields in matter a toy model for what goes on beneath

that is better than the griffiths toy model*

wait, do you mean the "the electron is effectively a tiny current" model

yes

the quantum version is just "the electron state has orbital angular momentum, and charged states with angular momentum have a corresponding magnetic moment"

it's just assigning the magnetic moment to the electron without claiming it's a current :P

in order to get any sort of explanation for the magnetic moment to have to go to QED where the moment can be computed by a series of Feynman diagrams (and the tiny corrections to the naive moments from classical or QM are a celebrated prediction of QED), but I don't feel this contributes any sort of mental picture :P

the precise proportionality between the angular momenta and the magnetic momenta is called the g-factor

or you can start from somewhere in-between and derive a g-factor of 2 for the spin from the Dirac equation coupled to the EM field, see physics.stackexchange.com/a/503163/50583

but there I feel the coupling between spin and magnetic field also just "pops out" from the EM interaction - it's correct, but there's not really anything "going on underneath", it's really just that charged spinning things couple to magnetic fields "because" they're like currents :P

@B.Brekke that's a rather strange expression, how did you get it?

I think you're right to be confused by this, this is physics notation (i.e. pretending $\delta$ is a function) gone wrong :P

$$-\frac{t^3}{xyz} \frac{\partial^4}{\partial t^4} H(t,x,y,z) -\frac{3t^2}{xyz} \frac{\partial^3}{\partial t^3} H(t,x,y,z) -\frac{t}{xyz} \frac{\partial^2}{\partial t^2} H(t,x,y,z) = \frac{\partial}{\partial x}\frac{\partial}{\partial y} \frac{\partial}{\partial z} H(t,x,y,z)$$

Does this show up in GR or in Physics?

@DanielSank I'm interested

in investigating the origins of flux etc.

I remember in first year labs we did the JJ thompson experiment (I think) where you found the mass to charge ratio of an electron. I wish I could do it again so I could take it in properly this time

@bolbteppa This sin^2 function appears again in L&L 4 QED when discussing the S matrix in the footnote of page 248

But it is not really relevant

@ACuriousMind Have you thought about this energy-time uncertainty in relation to QFT?

@DIRAC1930 which one? Generally I think there are only two "energy-time uncertainties" that really make sense: The one for explained here which holds for all quantum mechanics ("Mandelstam-Tamm uncertainty relation"), and the one for the spectral width and life time of resonances.

I think the L&L argument is really just a heuristic; the proper argument about position not being meaningful in relativistic QM has to be about Newton-Wigner operators and Pauli's theorem forbidding the existence of a time operator for anything but a free particle

Also, what is the difference between the Gell-Mann Low theorem and the adiabatic theorem? It is just that Gell-Mann and Low also connected the interaction and Heisenberg representations?

The Mandelstam-Tamm paper is very interesting btw daarb.narod.ru/mandtamm/mt-eng.pdf

@geocalc33 Send your resume to [email protected].

@DanielSank Where is the job located?