i.imgur.com/wAs9tWQ.mp4

I carry an assault rife with me everywhere I go

never know when you might need suppressing fire on some crazy dude with a cat fetish

I dont do weird stuff with my cats though

I sometimes allow Mr Whiskers do as he pleases

but thats on him, not me

Gross

What did you do with the cat you accidentally took the Fourier transform of?

He took the inverse, obviously

@0celo7 youtu.be/K2mcO6l-0cY?t=98 ?

its 1 am anyway

so bye

cya

@0celo7 Real life :P

wb to virtual life :P

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.

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 you only get to ask one thing and that was it :-P

just kidding... it's fine. Don't ask whether you can ask, just ask.

I've got a vacuum chamber with a ~50kv hv supply

connected to a few electrodes

All part of a sort of crt system

The chamber has a lexan lid, so X ray permeable

So I'm kind of wondering, a. is there any way for me to determine if I got irradiated

and b. How thick should my shielding be if I want to be decently safe next time I try this?

(I do have a geiger counter, but it's only sensitive to hard gamma)

@ACuriousMind If you are still up, I need halp

@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.

@Giskard42 I'm assuming you don't have a scintillator?

@Giskard42 Leaded glass is your friend here -- if you do the dosimeter test, you could have some shielding layers in between.

@rob He's going to have a hard time with the usual dosimeters if they're weak electrons.

@0celo7 I thought he was making 50 keV cathode rays and worried about x-rays from bremsstralung.

Oops, somehow I thought electrons

a geiger counter should pick up even weak gammas, no?

@0celo7 Nope, don't have a scintillator

@0celo7 My geiger counter is one of those phone-based ones that just counts hot pixels

@0celo7 Every photon detector has some efficiency that depends on energy, including a cutoff.

So I wouldn't trust it with anything

@rob yes, obviously

@Giskard42 hmm

maybe get a better GM if you're working with gamma rays

@Giskard42 Do you have some budget for real equipment?

@rob Depends on your values of "budget"

:p

@0celo7 I guess a geiger that'll work for weak gamma will work for most x rays, right?

@Giskard42 The boundary between hard x-rays and soft gamma rays is squashy.

@Giskard42 Do you have institutional support for radiation safety?

@rob Nope, this isn't a uni. lab

@Giskard42 I have an X-ray source in my lab

I can test tomorrow

for 50 kV x-rays (not 50 keV), hardened with a 2 mm Al filter, I find an attenuation factor of 10^-7 with 1 mm lead shielding in my book

Just a dude playing around in a downstairs basement

wish me luck

@Giskard42 what was the target material, the current and the exposure time?

@Loong So, that's a dentist's apron, yes?

@Loong Copper sheet, about 5 seconds exposure, not sure about the current

@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.

System wasn't sensitive enough to determine

@rob yeah I guess so, since 50 kV does generate a continuous spectrum with a maximum energy of 50 keV

@Loong Okay, that was my thinking.

So a bit of lead, like a doctor's x-ray gown should be okay?

@Giskard42 get body armor

doubles as body armor in case of an assassination attempt

@Giskard42 1 mm lead, 6.5 mm iron, 31 mm baryt concrete, 130 mm normal concrete, or 200 mm brick are equivalent for 50 kV x rays

How much air, just out of curiosity?

@Giskard42 The inverse-square law is your friend in air. Distance is good.

@Loong Thanks for running those numbers, that's really great.

@rob actually, soft x rays do not exactly observe the inverse-square law since there is some shielding in air

200 mm brick Okay, so I just need to get a wall built in the lab, do you think the mexicans will pay for it? :P

:D

@Giskard42 Isn't that one 4"x8" brick, the long way? Importing labor seems extreme.

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.)

Dear h-bar

Could you guys take a look at the bibliography for my mechanics and waves course this semester and tell me which books are worth getting?

@Loong True. But since lead is 10^4 times denser than air, unless the x-rays are pretty well collimated, the inverse square law is the bigger effect.

@0celo7 good luck my friend.

Thanks everyone for your help, I'll vacate for others now :)

@BernardoMeurer Do you have any already? Most of those are intro texts.

@rob None, these will be my first physics books ever

It's my first physics course ever

apart from silly high school stuff

@BernardoMeurer Oh! Cool.

@rob :D

Mechanics and waves are not highschool stuff? :P

^

@BernardoMeurer In that case, you should buy the one that your instructor tells you to buy.

@ACuriousMind I guess we'll be seeing more real stuff

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.

@ACuriousMind @rob Go here, there's and english button on the top right. This is the syllabus

@Giskard42 for 50 kV without filter, 1 m air reduces the radiation to about half the value compared to vacuum

@rob I know Calc I, taking Calc II this semester

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.

@BernardoMeurer I have Giancoli

it's good

@0celo7 body armor makes you slow, which increases exposure time ;-)

> Conservation laws and space-time symmetries.

Is this a theoretical course where you'll be doing Noether's theorem?

@ACuriousMind no

@ACuriousMind I have no clue :)

Definitely get Fundamentals of Physics: D. Halliday, R. Resnick, J. Walker 2004

@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

@ACuriousMind can you halp me or not

@0celo7 With what?

@ACuriousMind I asked you yesterday

@ACuriousMind Want to see the ZFC stuff?

@ACuriousMind representation theory

@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.

@0celo7 So, what do you want to know?

@rob @0celo7 I try to stay away from anything that has "for engineers" in the title. I HATE that title

@BernardoMeurer Shoot

@ACuriousMind Okay, so this is what I saw in the mini course that I will try to reproduce as well as I can

@BernardoMeurer One of the standard references for asymptotic analysis is "for engineers"

@rob This one?

@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?

@BernardoMeurer Yep

I'll assume you know then about the halting problem

@BernardoMeurer Yes. We haven't started requiring the new (4th) edition yet.

@BernardoMeurer I can never stop thinking about the halting problem.

@BernardoMeurer Yep

@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

now, if $l$ is an integer, then it lifts to a representation of $\mathrm{SO}(3)$ itself

@rob It's an amazing problem, and such an elegant solution

if it's a half-integer, you can only lift to the universal cover, $\mathrm{SU}(2)=\mathrm{Spin}(3)$

Sad solution though

@ACuriousMind But then, if we only want projective representations, we can in fact always lift to $\mathrm{SO}(3)$

Is all of that right?

@0celo7 Yes

@ACuriousMind So what the hell is a projective representation

now i don't mean the mathematical definition

I'm looking at Shankar and Sakurai and I don't see anything that really looks like it

@0celo7 Have you read my Q&A on it?

@ACuriousMind Last year people managed to craft a turing machine with 7918 states that tests ZFC for consistency

@BernardoMeurer I don't understand what that sentence means.

@ACuriousMind Last time I tried, I wasn't a mathematician.

Let me try again.

@ACuriousMind Read this en.wikipedia.org/wiki/Busy_beaver#Applications

It's basically what we saw

if ZFC is invalid, I will stop math

@BernardoMeurer The 8000th Busy Beaver number eludes ZF set theory: new paper by Adam Yedidia and Scott Aaronson

@rob Yeah! That was exactly the paper

@ACuriousMind what is this "group cohomology" I hear about

Does is have anything to do with the usual kind

Aaronson writes kind of a great blog.

@0celo7 Yes, it is the usual cohomology of the classifying space of the group

@ACuriousMind Is it weird that I recognize all of this from Weinberg?

@0celo7 No

@ACuriousMind Classifying space?

@ACuriousMind I don't think I was ready to appreciate Weinberg back in high school.

@BernardoMeurer Read it, still don't know what it means for a machine to "test ZFC for consistency".

@ACuriousMind It will run forever unless there's an inconsistency in ZFC

I still need to read the paper on how the machine is actually crafted

interesting

@BernardoMeurer That's a statement that's laden with pitfalls.

@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

@ACuriousMind Hm?

@BernardoMeurer I think that overstates the conclusion.

@ACuriousMind rubs eyes Wow I do not understand algebra

This is pretty dense

@ACuriousMind And I don't think this answers my question

It's a theorem-proving program: it generates theorems from axioms and theorems in the programmatic way that was invented by Godel

@ACuriousMind So looking at part 2. in the end, you just want to lift $\mathrm{SO}(3)$ to its cover

The proof is that if ZFC contains inconsistencies, the program will eventually halt.

And the action is just $\Bbb Z_2$?

But the only way to tell whether the program eventually halts is to run it literally for ever.

@rob Yes, but if we compute the busy beaver function for it's state count we could know whether it would halt or not once it reached $\beta(7918)$

@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.

Yes, the Second Inconsistency Theorem states that

@BernardoMeurer That's in interesting point ... but the Busy Beaver numbers are "noncomputable."

@rob noncomputable, yes, but still ""writable"", not sure which word to use for that

i.e. we can't compute $\beta(5)$ because of the Halting Problem, but we can still find it

@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.

Well, I agree that it's interesting, but I've already said a couple of wrong things about it. So I'm going to bow out for now.

cya

@rob Yeah, I'm not claiming to have proven ZFC is wrong, it's just a cool point :)

@rob thanks for the book recommendation

@skillpatrol You too

@BernardoMeurer My pleasure.

np pal

I should have gone for CS

I believe the axiom of choice

@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

@ACuriousMind By described I meant what I said here:

@ACuriousMind But that still doesn't answer my question. In the usual physicist approach to QM, what are the "projective representations?"

@BalarkaSen I don't

I couldn't say calculated, because it's easy to prove that the function is non-computable

@ACuriousMind take $l=\frac{1}{2}$ for definiteness

@0celo7 You don't even believe mathematical logic

So that's nothing unexpected

@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

I know that we have a rep of $\mathrm{SU}(2)$ given by $e^{-i \sigma\cdot n/\hbar}$, modulo stuff in the exponent

@ACuriousMind That's just an ordinary unitary representation of SU, no?

...which are projective representations of $\mathrm{SO}(3)$.

ahhhh, so when we lift to a unitary representation of SU, that same representation is a projective representation of SO?

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

I guess you have to project it down first?

@ACuriousMind So we just precompose the unitary rep of SU with the covering SU-->SO to get the projective rep of SO?

I didn't understand this point in Hall

Well no, that still doesn't give a map in the right direction

@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.

ugh

what?

I'm reading Hall again, one sec

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