Since the chat room is quiet and I can do so without hijacking an ongoing conversation, I have a request to make.
Please don't use the chat message edit/delete functions to "temporarily" say things.
Editing is intended for quick, minor changes to typos and the like, not to substantially replace the meaning of a message.
And deleting is for removing messages that shouldn't have been posted at all --- for instance if you accidentally send a message while you're still in the middle of typing a sentence.
These are more or less the same guidelines as on the main site.
Hello everyone! I'm wondering if I could just barge in for a sec and ask a quick question about X ray shielding; I think I've accidentally made a hard x-ray generator and given myself a decent dose and I want to avoid that in the future.
@Giskard42 Past exposure is hard. One thing you could do would be to buy some dosimeters, set them where the dose is expected to be large, run the machine for some known amount of time, and analyze the dosimeter for its exposure.
@Loong Why distinguish between kV (electron source drive voltage) and keV (photon energy)? I can start to make guesses, but maybe you know things I don't.
The classic lab accident happens when adjusting the beam for X-ray crystallography while the system is running. (You have to override a safety switch for this.)
I remember Giancoli being appropriate for an introductory course where the students don't have calculus yet, but I haven't actually looked at a Giancoli in years.
I have a Halliday/Resnick/Walker on my desk and found a calculus-based treatment of moments of inertia, so maybe that one is at a slightly higher level.
@BernardoMeurer Yeah, that's where you want to be.
@Loong Hmm. Thing is, I don't really know what the initial radiation amount would be, so I can't really determine if attenuating by half is good enough :p
@BernardoMeurer We teach our freshman majors out of Chabay and Sherwood. Every time I reread a chapter, I think "Yes, that's totally how real physicists think about this sort of problem." I like that text a lot.
@ACuriousMind You know how a Turing machine works, right? it having a certain number of states and performing a certain number of steps, and so on right?
@ACuriousMind So I finally understand this a little. Given $l=0,\frac{1}{2},1,\dotsc,$ I can find a vector space on which there's an irrep of $\mathfrak{so}(3)$
Okay, so this guy Radó wanted to mess with the limits of the halting problem, so he defined a @busy beaver function", $\beta$ that is the maximum number of steps a machine with $n$ states that halts can perform. So basically, the number of steps the most complex program defined for $n$ states does
@rob It's an amazing work, so basically if ZFC is consistent $\beta(7918)$ couldn't be described, but the function is well defined so there's no reason for it to not be described
@BernardoMeurer Most axiomatic systems cannot prove its own consistency, you need some sort of meta-theory. The statement "ZFC is consistent" doesn't make sense within ZFC itself. In fact, it is a theorem that if ZFC is consistent, it cannot prove its own consistency.
@0celo7 Well, all reps of $\mathfrak{so}(3)$ lift to those of $\mathrm{SU}(2)$ - and since the kernel of $\mathrm{SU}(2)\to\mathrm{SO}(3)$ is $\{\pm 1\}\cong \mathbb{Z}_2$, exactly thsoe representations descend to a representation of $\mathrm{SO}(3)$ where $\pm 1\in\mathrm{SU}(2)$ is represented as the identity.
@BernardoMeurer In what framework are you making the statement "If ZFC is consistent, then $\beta(7918)$ cannot be described"? What does "described" mean? These logical issues get very subtle very fast, and mostly relate to us switching between the formal and informal meaning of words without expressly saying so
@0celo7 $\exp(\mathrm{i}\alpha/2 \vec n \cdot \vec S)$, for $\vec S$ the spin operator (Pauli matrices for $l = 1/2$) and $\vec n$ the rotation axis and $\alpha$ the rotation angle
It's a bit difficult to explicitly write down actual projective representation maps - that's why we use the equivalency to the linear reps of the universal cover to classify them
@0celo7 No - the actual projective representation map would be a map $\mathrm{SO}(3)\to \mathrm{PU}(H)$, but maps into $\mathrm{PU}(H)$ are horrible to write down because you can't write the latter naturally as matrices/operators on $H$.
So you pick an associated map $\Sigma: \mathrm{SO}(3)\to\mathrm{U}(H)$ as in my post.
The map $(\vec n,\alpha)\mapsto \exp(\alpha/2 \vec \sigma\cdot \vec n)$ is such a choice.
It's associated $C$ (again, in my notation), is a function that's $-1$ if the two angles of the inputs are together larger than $2\pi$, and $1$ otherwise
I'm reluctant to actually write down this map. I know what it does, but writing it down is still horrible
So thankfully we use the equivalence to the linear reps of the universal cover, and we can have nice maps again