The h Bar

Mostafa

3:01 PM

$\partial_\gamma M^{\alpha \beta \gamma}=0$
@ACuriousMind Is this 6 equations (or 12)?

Slereah

Depends how many dimensions?

Mostafa

greek letters= spacetime?

Slereah

Spacetimes can have arbitrary dimensions

Also does $M$ have symmetries

Otherwise it's 64 equations

Well

16

Mostafa

yeah 4*4=16 for $\alpha$ and $\beta$

but this is supposed to be only 6 equations

Slereah

What is $M$

Mostafa

3:04 PM

(conservation of rotation and boost angular momenta)

Slereah

oh, so antisymmetrical

Antisymmetrical tensors have $(16 - 4) / 2$ independant elements

So 6 yeah

Mostafa

Thanks
and sorry for the *extremely* dumb question, without reading the basics first.

0celo7

@Slereah Pf.?

Slereah

Total number of components minus the diagonal divided by two since off diagonal is antisymmetrical

0celo7

good

Yashas Samaga

3:11 PM

0

Q: How to find speed of light in glass

Light travels slower in glass than in air, and if the index of air is $1$, then the index of glass should be higher. I got that the index of glass was $1.12$ with the formula $n= \frac{v}{c}$ which was given to us by our teacher. How do I calculate the speed of light? If the index of glass is eq...

is that a homework question?

no research effort type

Ramanujan

Hello @YashasSamaga

Yashas Samaga

hi, what's your question?

Ramanujan

@YashasSamaga, Actually I have some exam questions.. Not the homework questions!

Q1. On what condition a body is weightless in earth's gravitational field?

Yashas Samaga

1. freefall

2. revolving in an orbit

I shouldn't be giving answers this way :/

I am not going to give answers anymore. You should think. You are asking very simple questions. I don't know how you are going to pass your exams.

Ramanujan

@YashasSamaga, how is free fall possible in earth's gravitational field?

Yashas Samaga

3:16 PM

Do you know what Earth's gravitational field means?

AccidentalFourierTransform

@0celo7 of course I shower daily. But I do not wash my hair daily, that is bad for your hair! You should wash it once or twice a week, three tops

Ramanujan

Yeah.. @YashasSamaga, the space around the earth upto which its gravity is felt.

Yashas Samaga

@Ramanujan The gravitational field of the earth extends till infinity but it becomes negligible after sufficiently long distances as it falls over as $\frac{1}{r^2}$. Moreover, the effect of the sun's gravitational field begins to dominate over the earth's gravitational field at distances far away from the earth.

@Ramanujan In Newton's times, people hated the idea of 'action at distance' very much.

People couldn't believe that a force could be felt magically through air.

People were used to pushing and pull but were surprised that gravity can pull things downwards through air/vacuum.

Faraday introduced the concept of field for the first time.

The idea was to assume that the an object creates a field around itself.

Other objects interact with the field and feel a force.

Earth creates a field > object interacts with the field > object feels a force

Ramanujan

@YashasSamaga, I just wanted to know can a body fall freely on the earth?

Yashas Samaga

I am coming there.

0celo7

3:21 PM

@AccidentalFourierTransform that's disgusting

Yashas Samaga

Gravitational field is given by = $G\frac{M}{r^2}$

0celo7

you have horrible hair

Yashas Samaga

@Ramanujan mass * field_strength = force

0celo7

you smell btw

Yashas Samaga

@Ramanujan so the strength of the gravitational field = accleration due to gravity at that point

0celo7

3:22 PM

just FYI

Mostafa

13

Q: How do higher-order optical chiralities look like?

The optical chirality of the electromagnetic field is a conserved quantity, analogous to the energy density, linear momentum density, and angular momentum density, which describes how chiral the EM field is at each point, and it is given by $$ C=\frac{\varepsilon_0}{2}\mathbf E\cdot\left(\nabla\t...

electromagnetism electromagnetic-radiation conservation-laws chirality

Does this mean there are infinitely many conserved quantities (in classical EM)?
(The 2nd paragraph)

AccidentalFourierTransform

my hair smells great

Yashas Samaga

@Ramanujan In the presence of a gravitational field, you feel a force.

@Ramanujan If you don't h ave an opposing force, the gravitational force will cause the object to acclerate.

user228700

@JohnR: One month until I am held responsible for all my actions in the eyes of the Law :-P

Yashas Samaga

@Ramanujan The object is said to be in free fall in such a scenario.

0celo7

3:23 PM

If you wash your hair once a week I guarantee it does not smell great

John Rennie

@Kaumudi.H 18th birthday next month?

Ramanujan

@YashasSamaga, isn't there air resistance on earth

Emilio Pisanty

@Mostafa yes

Ramanujan

hello @JohnRennie

user228700

@JohnRennie Yep! U forget a lot and don't give me "Irrelevant data", I remember even some of that!

Yashas Samaga

3:24 PM

@Ramanujan If you consider air resistance, then no object will ever freefall.

John Rennie

@Kaumudi.H I'm terrible with birthdays. I even forget my own occasionally.

Emilio Pisanty

@Mostafa The answer to that question describes one such series

AccidentalFourierTransform

@0celo7 I wash it twice a week. And I use a conditioner that smells great. And I dont know why Im explaining this to you.

Yashas Samaga

0

A: Quadrupole moment of point charges?

Go here. What you are describing is called a linear electric quadrupole.

user228700

@JohnRennie ...and that I know. IIRC, it was I who reminded you of it a week before :-P

Jaime Gallego

3:25 PM

Yashas Samaga

are such answers allowed?

Mostafa

@EmilioPisanty Is this possible according to Noether's 1st theorem? I mean, Zilch is obtained using the duality symmetry of Maxwell's equations (From your other question). Can this (finite) set of symmetries give rise to infinitely many conserved quantities?

Yashas Samaga

flaggable as low quality?

John Rennie

@Kaumudi.H anyway, happy "next months birthday" in case I forget :-)

Jaime Gallego

AFT's hair

0celo7

3:25 PM

@AccidentalFourierTransform because you're embarrassed by your terrible hygiene

user228700

@JohnRennie Lol, OK, thanks :-P

0celo7

@AccidentalFourierTransform your hair looks like this I presume

John Rennie

@Kaumudi.H so what do you plan to do that you can't (legally) do now?

AccidentalFourierTransform

lol I wish

some day Ill get dreadlocks for sure

0celo7

oh god

why?

what is wrong with people

AccidentalFourierTransform

3:27 PM

but I want to be original. Maybe one big, fat dreadlock

user228700

@JohnRennie This might sound boooring but I might attempt to procure my driver's license before heading off to college seeing as there won't be much to do in the summer.

Ramanujan

@YashasSamaga, would not it be at the center of earth, where g=0?

Yashas Samaga

@Ramanujan Yes

ACuriousMind

@AccidentalFourierTransform uhhhh...that won't look great. If you want to be original, better go for an unusual color

AccidentalFourierTransform

an unusual color is the opposite of original

ACuriousMind

3:28 PM

@AccidentalFourierTransform Only if it is an unusual color that is usual among people with unusual colors :P

John Rennie

@Kaumudi.H Not boring at all - go for it!! :-) I didn't get my car licence until I was about 24, because up till then I rode a motorcycle.

Ramanujan

@YashasSamaga, why are wooden slippers used under railway track?

Yashas Samaga

@Ramanujan no idea

Mostafa

@ACuriousMind sorry for pinging you for that question about indices...I thought you were here.
(I still feel guilty about it)

AccidentalFourierTransform

so what colour would be truly original? something around $200\ \mathrm{nm}$?

0celo7

3:29 PM

@JohnRennie wtf

@AccidentalFourierTransform x rays

AccidentalFourierTransform

so, bald

ACuriousMind

@Mostafa np, I saw it got resolved without me ;)

Emilio Pisanty

@Mostafa there's a corresponding hyerarchy of symmetries

John Rennie

@Ramanujan sleepers not slippers :-)

user228700

@JohnRennie Ah, OK :-) It might be some trouble getting both in the span of 60 days but hey, I literally came up with that just now and now I'm taking it seriously so thanks!! (:-P)

0celo7

3:30 PM

maybe you'd die of head cancer

@JohnRennie I need chemistry help

Ramanujan

@JohnRennie. Why are they used?

John Rennie

@Kaumudi.H Yeah! Learn to ride a motorbike - I'm sure your parents would approve :-)

Emilio Pisanty

@Mostafa Zilch does not correspond to the duality symmetry (that's the optical helicity if I remember correctly). Zilch corresponds to a more complicated symmetry transformation.

Yashas Samaga

@ACuriousMind is this flaggable?

0

A: Quadrupole moment of point charges?

Go here. What you are describing is called a linear electric quadrupole.

ACuriousMind

@Ramanujan Have you tried to google it instead of asking random people in here?

3

user228700

3:31 PM

@JohnRennie :-P On the contrary, actually. My father has asked if I want to learn to ride his bike.

AccidentalFourierTransform

@YashasSamaga why do you want to flag stuff so hard?

dmckee

@YashasSamaga When I first saw that I had a moment of hope that someone was asking about the experimental methods of doing reasonable precise bench-top measurements.

AccidentalFourierTransform

they do not give you points for valid flags :-P

Emilio Pisanty

The naive duality symmetry is $A^\mu \mapsto A^\mu +\theta C^\mu$

0celo7

@JohnRennie :(

Emilio Pisanty

3:32 PM

Zilch corresponds to $A_\mu\mapsto A_\mu-\xi^{\alpha\beta}\partial_\alpha G_{\beta\mu} ,\quad C_\mu\mapsto C_\mu+\xi^{\alpha\beta}\partial_\alpha F_{\beta\mu}$

John Rennie

@0celo7 Chemistry? I can try to answer ...

Yashas Samaga

@AccidentalFourierTransform Has been 2 years and I haven't figured out how to flag questions and answers.

ACuriousMind

@YashasSamaga You know that there is a "link only" deletion reason in the review queue, right? So that's certainly worth a VLQ flag.

AccidentalFourierTransform

lol

dmckee

There are some very nice ways of using interferometers to get three to four digits of precision in a very simple measurement. (You are limited by your thickness measurement, because the instrument has dynamic range to spare.)

John Rennie

3:33 PM

@Ramanujan You have to fix the rails to something to stop them moving. Since the rails have to pass over all sorts of different types of ground the simple solution is to put a base under the rails. That's what the sleepers are.

0celo7

@JohnRennie what the hell does the 3s, 3p, etc. notation mean

dmckee

But, alas, it was someone's homework. And misunderstood at that.

Emilio Pisanty

Higher-order members of the hierarchy would come from higher-order derivatives of the fields.

@Mostafa

AccidentalFourierTransform

@0celo7 spherical harmonics?

0celo7

I think the number means the energy level, and the letter denotes some $\ell$ value

but why the hell couldn't they make things simple

AccidentalFourierTransform

3:33 PM

you know the Legendre thingy $P^n_\ell(x)$

dmckee

@AccidentalFourierTransform Well, for the s, p, d. The numbers are the radial part.

Emilio Pisanty

@0celo7 yes

@0celo7 because history

Jaime Gallego

@Ramanujan As @JohnRennie says, they balance the train's weight to the ballast below, keep the rails spaced evenly (because of expansion, etc.), and other stuff.

Mostafa

@EmilioPisanty Thanks a lot! Do higher order conserved quantities of the zilch tensor have physical significance? (like chirality)

0celo7

@EmilioPisanty I have selection rules $\Delta n\ne 0$ and $\Delta\ell=\pm 1$

AccidentalFourierTransform

3:34 PM

@dmckee ah right

0celo7

what does that mean in that strange chemistry notation?

John Rennie

@0celo7 It's a historical artefact. I think they refer to the appearance of the related lines in spectra.

Emilio Pisanty

@0celo7 it means you can only jump one step in the s,p,d,f,g,h,... series

you can move right or left by one slot

@Mostafa what do you mean by "physical significance"?

Mostafa

Physical interpretation

(Like chirality, for example)

John Rennie

@dmckee particle scattering question for you ...

This question:

1

Q: Random directions of the trajectories in a cloud chamber

It is easy to construct a home-made cloud chamber. In observation, one finds that the directions of the trajectories are quite random. Does this mean that all the particles detected are secondary cosmic rays?

particle-physics cosmic-rays

Emilio Pisanty

3:37 PM

@Mostafa they can be expressed as functions of $\mathbf E$ and $\mathbf B$

so in one sense you're sort of done

John Rennie

points out that in a cloud chamber we see only the secondary electrons not the cosmic rays themselves. Why don't the cosmic rays (high energy protons) leave a trail in the cloud chamber?

Emilio Pisanty

@Mostafa what are you understanding "the physical interpretation of optical chirality" to be?

John Rennie

Peresumably it's because they don't scatter strongly off the air atoms at very high energies, but if so why not?

dmckee

@JohnRennie We see mostly muons I would think, so yeah. They're secondary.

0celo7

@EmilioPisanty How does one TeX 3s?

dmckee

3:39 PM

And the azimuthal distribution is quite wide.

0celo7

3$s$?

Emilio Pisanty

@0celo7 ah, I'm never sure

Mostafa

@EmilioPisanty A sort of handedness. Like polarization, or vortex of an optical field

Emilio Pisanty

I usually $s$ the $s$s

Ramanujan

@JohnRennie, what happens if we use oil instead of water in hot water bags?

Emilio Pisanty

3:40 PM

@Mostafa that's pretty washy, though

you could say the same about the optical helicity

Mostafa

Isn't it the meaning of chirality?

0celo7

does cyanide smell like marzipan?

AccidentalFourierTransform

hmm no

why would it?

0celo7

there is a strong marzipan smell in my lab

AccidentalFourierTransform

oh, because the almond

0celo7

3:41 PM

@AccidentalFourierTransform people say it smells like almonds

AccidentalFourierTransform

yeah, I forgot about that

so, you got cyanide in your lab?

0celo7

maybe

if you don't hear from me I either got banned or killed

AccidentalFourierTransform

lol

Emilio Pisanty

@Mostafa there's other quantities that share the same meaning

so, for instance, you could take the optical helicity, $\mathrm{Hel} = \frac12 \left( \mathbf A^\perp \cdot \mathbf B - \mathbf C^\perp \cdot \mathbf E \right)$, and it's also "a sort of handedness".

So there's this big hierarchy of related quantities

and they're similar but different

0celo7

@EmilioPisanty how many $4p$ states are there? I'm still confused

Emilio Pisanty

3:45 PM

and not particularly easy to understand

John Rennie

@dmckee as I recall the droplets in a cloud chamber form around ions created by the charged particle. So that must mean the (low energy?) secondary muons are better at ionising atoms than the high energy protons in the cosmic rays. Why would that be?

Emilio Pisanty

at least in physical terms

that's what those questions were getting at

and I think Danu did an amazing job at explaining what the deal is

0celo7

assuming $p$ corresponds to $\ell=1$ states, then there should be three of them

Emilio Pisanty

@0celo7 three linearly independent ones

AccidentalFourierTransform

times 2 for spin

Emilio Pisanty

3:46 PM

^ plus that, yes

0celo7

oh jesus

dmckee

@JohnRennie The protons (and heavier nuclei) basically don't make to the surface level. There are 10 tons per square meter of stuff in their way.

Mostafa

@EmilioPisanty So, intuitively, they all correspond to the chiral properties of the field, right?

I'm asking because of the claim made here by D.J. Candlin: (p. 1394)

link.springer.com/article/10.1007/BF02783348

dmckee

In NuSea (Fermilab E866) we put about 3 tons per square meter of shielding in the cavity of the main magnet to remove most of the non-muon junk and it worked just find even though the mean energy of the detritus was higer than a mere GeV like cosmic rays.

John Rennie

@dmckee if you watch a home built cloud chamber you don't see lines spanning the chamber. You see tracks starting at random points in the chamber then travelling a few cm before fading out.

I assume those are electrons created when a muon scatters off an air molecule.

AccidentalFourierTransform

3:49 PM

no, those are probably neutrinos

John Rennie

The question is why the muons themselves don't leave tracks.

AccidentalFourierTransform

or axions, or dark matter

Emilio Pisanty

@Mostafa Эта статья у меня есть!

got it

John Rennie

@AccidentalFourierTransform don't be silly this is a serious conversation.

Emilio Pisanty

lemme have a look

dmckee

3:49 PM

@JohnRennie I would guess so. Muons have pretty low dE/dx, and a only slightly supersaturated detector might not notice them. But delta rays (scattered electrons) have much higher dE/dx.

Yashas Samaga

If I run out of votes to close, I can't flag it? -_-

dmckee

I'm used to working with detectors that have plenty of dynamic range and pick up muons with ease.

ACuriousMind

@YashasSamaga nope, 24 votes/day, that's it.

John Rennie

@dmckee is there an intuitive explanation of that? Assuming the scattering is mainly EM the only difference is the momentum of the particle. Why are high momentum muons bad at ionising atoms in the air while low momentum electrons are good at it?

Emilio Pisanty

@Mostafa ok, what claim?

dmckee

3:52 PM

@JohnRennie Uhhhh. I figured that out once, but I'll have to get back to you on it.

AccidentalFourierTransform

Bethe formula

The Bethe formula describes the mean energy loss per distance travelled of swift charged particles (protons, alpha particles, atomic ions) traversing matter (or alternatively the stopping power of the material). For electrons the energy loss is slightly different due to their small mass (requiring relativistic corrections) and their indistinguishability, and since they suffer much larger losses by Bremsstrahlung, terms must be added to account for this. Fast charged particles moving through matter interact with the electrons of atoms in the material. The interaction excites or ionizes the atoms...

Mostafa

> it seems unlikely that any special significance or application can be found for zilch.
(P. 1394; first paragraph of the page)

dmckee

^^ is the place to starts.

John Rennie

@dmckee OK, at least I don't feel guilty for not know the answer to a simple question :-)

dmckee

But it's complicated because it depends on the particle mass in an involved way.

John Rennie

3:53 PM

@AccidentalFourierTransform aha, thanks, I'll have a read through that.

ATHARVA

physics.stackexchange.com/questions/315371/fluid-mechanics @YashasSamaga should this answered looks like he has explained his work out in the image.

0celo7

I think I need a selection rule $\Delta j_z=0$ too

so that $\Delta m_s=0$

argh I hate physics

2

Jaime Gallego

@0celo7 Burn the witch!

Emilio Pisanty

@Mostafa meh

AccidentalFourierTransform

I dont think that there is an intuitive/physically obvious reason. Its just that when you plug in actual numbers, muons have low dE/dx while electrons have high dE/dx.

Emilio Pisanty

3:56 PM

I mean, it's useful enough, more useful than the higher terms in the hierarchy, not as useful as the stress-energy tensor.

it depends what you mean by "special"

AccidentalFourierTransform

Jan 8 at 14:20, by AccidentalFourierTransform

man I hate physics

Yashas Samaga

@ATHARVA It is unreadable and it is still a HW question.

Emilio Pisanty

but I find e.g. Robert Cameron's papers on the subject to be a pretty strong refutation of that claim

ATHARVA

@YashasSamaga Ok.

Mostafa

4:08 PM

@EmilioPisanty Ok, thanks a lot. Your questions on this were (actually are) extremely helpful for me.

Emilio Pisanty

@Mostafa I can only claim pretty limited credit for those

Danu did most of the work

but yeah, read those questions, plus the chat they link to

and anything by Robert Cameron referenced there

Slereah

ebay.com/itm/Springer-Handbook-of-Spacetime-Abhay-Ashtekar-/…

why

Yashas Samaga

4:26 PM

Every time I try to upload an image to imgur (while adding an image to a Q or an A), I get failed to upload image.

I have to try around 10 times before it succeeds.

John Rennie

What format? Imgur doesn't seem to like PNGs.

Yashas Samaga

It never used to happen before.

It's PNG :D

but it used to work without fail before

on first try

My answers always have images

John Rennie

Try a GIF instead.

0celo7

@ACuriousMind Why does $\mathbf J$ commute with $\mathbf S\cdot\mathbf r$?

Yashas Samaga

It uploaded as PNG but I had to try around 5-6 times.

0celo7

4:29 PM

@ACuriousMind If you say "rotational invariance" I will get upset

AccidentalFourierTransform

calculate the commutator and check that it, indeed, vanishes

if you want to know the reason, it is because $\boldsymbol S\cdot\boldsymbol r$ is a scalar operator

and so it has to commute with $\boldsymbol J$

0celo7

I just said don't say that

AccidentalFourierTransform

rotational invariance.

0celo7

Are you trolling me?

AccidentalFourierTransform

your question doesnt make much sense though. They commute because when you calculate the commutator, it is zero

thats why

if you want to know the reason for why we expect it to commute to begin with, or why we know that it has to commute, then it is because rotational invariance

Jaime Gallego

4:33 PM

I'm trying to wrap my head around the difference between the $B$ and the $H$ fields, and reading up is just getting me more confused.

AccidentalFourierTransform

I dont believe in magnetic fields

I mean, I know they exist. I just dont believe they do

0celo7

I don't believe path integrals exist

Emilio Pisanty

what on Earth is going on with physics.stackexchange.com/revisions/315380/1 ?

0celo7

interesting question!

Emilio Pisanty

i.e. why does $ϴ$ ( $ϴ$ ) look so horrible and so different to $\theta$?

Slereah

4:37 PM

it's a fat theta

Emilio Pisanty

ah, yes, it's marked as a capital theta

U+03F4 : GREEK CAPITAL THETA SYMBOL

doesn't look very capitalized, though

ϴ

0celo7

no unicode pls

Jaime Gallego

⸘‽

ACuriousMind

@EmilioPisanty It's capital in that the outer thingy is round, not ellipsoid

Slereah

$\Theta$

$\huge \Theta$

ACuriousMind

4:40 PM

...or at least, not as ellipsoid as the non-capital one :P

Emilio Pisanty

@Slereah yeah, that is how capital theta's meant to look like

Slereah

$$\Huge{\Theta \omega \Theta}$$

I'm a goat

Emilio Pisanty

including a distinctly non-connected middle bar

0celo7

what is that?

Slereah

It's a goat

0celo7

4:41 PM

I...don't get it

Slereah

Goats have freaky eyes

Emilio Pisanty

@Slereah oh, indeed

0celo7

learn something new every day

Cham

Are you guys really talking about physics ?

dmckee

@Cham That only happens in here by mistake.

John Rennie

4:48 PM

@Cham trust me, compared to some of the stuff that gets discussed here goats eyes are nothing! :-)

AccidentalFourierTransform

no, if you want to talk about physics youll have to goat-to another chat.

Jaime Gallego

Ba dum tss

John Rennie

Take my wife ...

AccidentalFourierTransform

ok sorry for that

0celo7

@JohnRennie Goat =/= sheep

John Rennie

4:49 PM

How very biblical of you :-)

0celo7

You're not a...well. Better not continue that line of thought.

John Rennie

Oh you mean the take my wife comment? That's an old music hall joke from the Victorian era.

0celo7

He prolly think it's a club light, But really it's the red dot. - Quavo

Jaime Gallego

I just received an SSD, and by god, it is tiny.

Slereah

Take my wife, please!

Thank you, I'll be here all night

0celo7

4:51 PM

Shut up, Rodney

John Rennie

4

Q: Is the phrase "Take my wife – please!" a paraprosdokian?

I was reading the wiki page about paraprosdokians and I don't understand why the phrase: Take my wife – please! is classified as one.

jokes humor paraprosdokian

Cham

I'm a physics teacher in my classroom right now, watching my students doing their astrophysics exam. And watching you guys doing physics. LOL !

John Rennie

Hey! I'm trying to calculate whether we could measure gravitational time dilation caused by lab scale masses (the answer appears to be no).

0celo7

@JohnRennie You should tell me if you don't want to learn any topology

Slereah

@0celo7 No respect at all!

0celo7

4:52 PM

I'm tired of asking

Jaime Gallego

@Cham Oh well, I guess we just diversify topics.

Cham

What was the original topic here anyway ?

John Rennie

@0celo7 In principle I would like to understand how to define a manifold, but in practice I lack enthuisiasm for the amount of work required. I think you should assume I'm a lost cause unless I suddenly discover I have a lot more free time.

Slereah

Manifolds aren't terribly complicated to construct

Jaime Gallego

@Cham Unicode. Long story.

Slereah

4:54 PM

You just stitch together pieces of Euclidian space

John Rennie

But thanks for trying. Genuinely thanks that is - I mean no irony.

Cham

Manifolds are dull to define precisely in physics.

0celo7