@BernardoMeurer I was born in the wrong generation

watching old apple keynotes

steve was amazing

oh god a book question with words Q___Q

@GPhys just words?

@GPhys Would you rather have a question without words? (If yes, how would that work?)

I think I figured this one out :P

@ACuriousMind Suppose I have a curve going once around a torus the long way. Is there an isotopy of the torus that takes the curve to a "standard" one?

No self-intersections of course...

:O this question is free :O :O :O

@0ßelö7 Can't say more than "sounds reasonable" about that one.

@ACuriousMind ah, I don't need that one anyway

oh god this question is actually QFT

stop freaking out...

every physicist knows QFT, you will survive

@0ßelö7 lol, no

I know plenty of physicists who have never taken QFT :P

that's like a mathematician who doesn't know module theory

what does a physicist who doesn't know QFT do?

@0ßelö7 Medical physics, environmental physics, material science, astronomy,...

engineer, ???, engineer, they need QFT

@0ßelö7 For what does an observational astronomer need QFT? Or someone doing simulations on star formation?

Observational astronomy is a legitimate field? People do that as a profession and nothing else?

Computational people need to understand fusion, hence the strong force.

@0ßelö7 Pretty sure one can "understand" fusion at a sufficient level without ever touching QFT. You're being a bit narrow-minded here.

@ACuriousMind Understand maybe, but why on Earth wouldn't one take QFT if there's even a chance of understanding it better?

I think you're being narrow minded because anyone whose field even peripherally touches QFT should be interested.

@0ßelö7 Because it's one of the harder theory courses and plenty physics students already find the rest of theory hard and/or uninteresting.

These are some narrow-minded students you're describing.

@ACuriousMind I have a question about particle physics :3

my book says the GZK limit for cosmic ray protons is from the interaction $\gamma+p\to \Delta^+$

I don't even know what the GZK limit is, you're asking the wrong guy

ACM is my dude but since when is he a particle guy?

@ACuriousMind no no no theq uestion is independent of htose kind of details it's very simple

it's special realtivity level question

Ah yes

int he CoM reference frame, there's only one total energy that can work to make this interaction

The old switcheroo

but a professor used this as if the energy in that scenario was the minimum such energy

and not the only such energy

can something like $\gamma+p\to \Delta^+$ occur if the starting particles have more energy than necessary, as long as the Delta+ decays again into more particles immediately?

@GPhys You mean kinematically?

yeah

in this particular situation for the problem the gamma was fixed, meaning there was only one proton energy could work, but it was used in a situation where they were talking about the minimum such proton energy

implying this still occurs when proton energy is higher than that, for some reason

can interaction still occur if the gamma and p have more energy than the rest mass of the Delta in the CoM reference frame as long as what actually happens is osmething like $\gamma+p\to \Delta^+\to p+\pi^0$

@BernardoMeurer find a good analogy and run with it

@GPhys Well, this is a sort-of delicate question. If the $\Delta^+$ decay immediately, then it is more of a "resonance" than a particle in the classical sense. Whether you want to call a resonance a "particle", a "bound state", an "excited state" or simply a resonance is sort-of opinion based and none of these terms is really better than another.

'metastable state' is another term, if I remember right

Resonances have "widths", they are Breit-Wigner peaks centered around the "rest mass" of whatever you want to call the resonant state, so technically you would have to admit the idea of the formation and decay of the $\Delta^+$ at both above and below the necessary energy.

(This is probably one origin of the confusing idea that virtual particles can "borrow" energy from the HUP to be slightly off-shell, because it erroneously identifies the resonant state with a specific line in a Feynman diagram, which is sort of understandable if you're not being purist about what the diagrams mean)

the primary reason I ask is if such a thing can't occur then it's not justified as a bound in the way they used it (so I supposed that it could, but I had never heard of such a thing in quite this sense)

@GPhys As I said, resonances are B-W peaks, so if this is what is meant, the "threshhold" is not a hard threshhold at all - since $\Delta$s are short-lived, though, it's probably sharp enough