The h Bar

Jake Rose

00:01

@DanielSank hyperphysics.phy-astr.gsu.edu/hbase/magnetic/larmor.html says it should be possible for a normal current loop

@amanuel2 it has to be a $sin(x)$ function due to the $y(0) = 0$

You could actually get the answer down to two options by just considering the form of the asnwer

amanuel2

@JakeRose So Im guessing its the 1/2dsin() function. But can u explain more why its sin?

uhoh

04:13

0

Q: Simple on-line laboratory logbook functionality for a small research group

We need a basic laboratory logbook function that can be accessed via the internet, possibly even at least viewed on phones. This is a modest university laboratory. Currently all we need is logging of events (time and name) and discussion of status of the parts of the experimental system: X is ...

Any thoughts?

Knight

04:34

@skullpatrol Hello Pal

Sir Cumference

05:12

feels like i can only see the sun once a month

vzn

05:41

in theory salon, 32 secs ago, by vzn

Sand dunes can 'communicate' with each other / physorg

in theory salon, 7 hours ago, by vzn

Mathematicians Prove Universal Law of Turbulence / quanta

↑ fluid dynamics + fractals + emergent behavior, a theme for 21st century physics! o_O :)

skullpatrol

@Knight welcome back pal

Knight

06:49

@skullpatrol What is meant by “old sport” ? Friends call each other “old sport”.

skullpatrol

here you go pal @Knight

skullpatrol

07:15

also

15

Q: What is the meaning of "old sport"?

In the film "The Great Gatsby," Mr. Gatsby says "Sorry, old sport, I thought you knew"; what is the meaning of old sport?

meaning cinema

Johan Liebert

2020 is quite a special year. Wildfire in Australia, Coronavirus in China, locust swarm attacks Pakistan and Africa,...etc. Who knows what else is going to come.

skullpatrol

yeah, 11 months to go!

Johan Liebert

@skullpatrol Currently 25000 people got infected with Coronavirus, 500 dead. Though I am a bit surprised as India isn't that hard hit by it (just 3 cases as of now). I think if this virus ever reaches India many more would die.

Novalium Company

@vzn Cool but it still doesn't feel like you are in the VR world. You can't lean in stuff, touch stuff and feel their shape... I want a machine that literally makes you feel like you are in the VR world.

There exists a really cool tech but I forgot it's name. Kinda like a hologram but with cube sticks coming out of it.

skullpatrol

if it spreads globally, who knows how many will die @JohanLiebert

Knight

07:29

@skullpatrol Some are saying that coronavirus is failure of experiments that china was doing for making an organic weapon.

Johan Liebert

@Knight So what were Africans doing with Ebola then? I think this is a false accusation.

skullpatrol

@Knight could be, they were the first with the cloning of a monkey

Novalium Company

Does anyone know the name of a device I have seen on youtube. It's like a table with pistons which push long cubic sticks in and out to create like a physical hologram.

skullpatrol

@JohanLiebert Africa is where AIDS started

Johan Liebert

@skullpatrol how did it came to humans from chimps?:-)

skullpatrol

07:37

mutation, I think

viruses are tricky

Knight

Chimpanzee? They had AIDS? Wow! They are so smart

skullpatrol

virology

Noun: virology (usually uncountable, plural virologies)

The branch of microbiology that deals with the study of viruses and viral diseases.

John Rennie

Viruses regularly jump from animals to humans. The virus often exists in a mild form in animals but when it jumps to humans it becomes a lot more dangerous.

In the UK a few years ago we had a scare with a virulent version of coronavirus in wild birds that was infecting humans.

This is it

Knight

I heard corona virus comes from having a soup of bats

John Rennie

Bats have been implicated as a source of viruses before. The recent Ebola outbreak was linked with bats.

Knight

07:42

Bats are nice, we should tame them

Johan Liebert

@Knight yeah these rumors are spreading in India too! Though who knows. There aren't any conclusive evidences yet.

Novalium Company

Thinking more about it, making a realistic VR world experience would be very very hard since it would require a machine that is able to exert force on on every point on the person's body in any direction. Something like the force from Star Wars.

Knight

@JohanLiebert yeah

Johan Liebert

@Knight are there any recent cases of this virus in your state? I heard that there are total 15 cases of coronavirus in the USA.

skullpatrol

who knows, the coronavirus may mutate to the Heinekenvirus if it gets to Germany :P

Knight

07:50

@JohanLiebert No, USA is not concerned about it’s own people, USA is worrying what would happen if China would annex its neighbors by this organic weapon

Novalium Company

Thanks for your time

skullpatrol

np pal

VR is so last decade

Novalium Company

I just came up with a great VR idea

Johan Liebert

@Knight for the time being it can only annex Pakistan! :-)

Knight

@JohanLiebert :)

@JohanLiebert Can you give links to some strict comments of Dmckee? I want to see his comments

skullpatrol

07:55

search his profile under "comments"

Novalium Company

billion dollar idea

boom.

Johan Liebert

@Knight I have never seen any strict comment from his side. He was always kind and gentle (as far as I know). His comments used to quite informative.

John Rennie

@Knight dmckee is very easy going. I doubt he makes many harsh comments.

Johan Liebert

Feb 2 at 5:12, by dmckee --- ex-moderator kitten

In an effort to provide some kind of continuity for those who asked, I've started a blog just so there is a place to get me on the internet.

This is his recent comment in chat.

Knight

@JohnRennie Yes sir. That's what I believe too.

Novalium Company

08:00

VR marionette doesn't work. People will get tied up pretty easily

I thought you could make a machine that will control you like a marionette doll but you'll get tied up constantly.

@JohnRennie tasteofhome.com/recipes/southwestern-beef-and-rice-skillet/… for u

John Rennie

@NovaliumCompany That looks nice :-)

skullpatrol

yummy

Virtual food would be a good way to diet?

Knight

But the mind will become fat

skullpatrol

yeah, the brain would get used to having "food"

Knight

08:16

Yeah

How is NFL going on?

skullpatrol

The KC Chiefs won the SuperBowl

The raiders are oficially the LAS VEGAS raiders

>8(

Knight

I have a very difficult question for you all

When someone writes sends this " :) " do you just understand it or you literally turn the screen of laptop/mobile to see it upright ?

skullpatrol

I just understand it.

Knight

Earlier I used to turn up my screen but now I'm used to it.

It was very hard I hope you understand

John Rennie

I lie on my side on the desk

skullpatrol

08:29

In geometry didn't you have to rotate drawings mentally? @Knight

Knight

Wow! I never thought of that

@skullpatrol I was quite bad at that

@JohnRennie Did you have that desk already or you ordered it just for this purpose?

skullpatrol

@Knight yeah, it's a skill

John Rennie

I hate it when people post pictures that are upside down, because then I have to hang from the light fitting by my toes.

skullpatrol

Batman?

Knight

@JohnRennie Yes, it's no less than a crime to post a landscape image.

@skullpatrol And what about <3 , in this case we have to lie down oppositely as in the previous case

John Rennie

08:33

@skullpatrol oh no, my secret is revealed!

skullpatrol

@Knight :) equals (:

John Rennie

Even parity smileys

Knight

But we have passed that age that no one sends us <3 anymore (for me it's true I don't get these anymore)

skullpatrol

<3 are so last decade

Knight

How many you were receiving in last decades?

skullpatrol

08:39

over 9000

John Rennie

@Knight Ɛ>

Knight

Did person who was sending it receive something from you?

@JohnRennie Gentleman you can not use mathematics, this is the physics room

skullpatrol

It's Over 9000!

"It's Over 9000!", also known as simply "Over 9000!", refers to an internet meme and a form of trolling involving a particularly famous change made for English localizations of an episode of the Dragon Ball Z anime television series titled "The Return of Goku", which originally aired on April 19, 1997. The phrase refers to an alteration of the original line spoken in Japanese by the Saiyan character Vegeta, voiced in English by actor Brian Drummond, in the 21st episode of the Ocean Productions English dub. The phrase is typically used as an innumerable quantifier to describe a large quantity of...

John Rennie

:-) I don't think there is a reversed "3" in unicode so that was the closest I could get. You could probably do it with Latex.

Knight

All right

@skullpatrol Did you use to lie down to understand <3/ $\varepsilon$> these?

skullpatrol

08:45

nope

Knight

Means you were born as a genius

Salute to you

skullpatrol

lol

visualization is only one form of thinking, pal

thanx for the pirate salute :-)

Knight

HAHAHHHAHAH

Have you seen this?

3-year-old's priceless response after mom "ate all his candy"

►

skullpatrol

HAHAHA, nice

Knight

Have you seen Dr. Strangelove?

skullpatrol

08:52

yup, one of my favourites

gentlemen! NO fighting in here, this is the war room

Knight

I'm unable to understand

skullpatrol

He is quoting a song

Knight

What are his indications?

skullpatrol

None, he's being "sarcastic"

trolling doesn't require taking sides...it is more about the "sport"

nah, just move on

the question is closed

Knight

OH! the way @tpg2114 sir has said "don't take too much interest in dramas". I forgot that, thank you for reminding me.

skullpatrol

09:00

np, pal

Knight

:)

skullpatrol

drama = wasted time

Knight

Yes, and here we have full time dramas going on everyday.

skullpatrol

yup

focus on your objectives

Knight

Yes,

Slereah

10:03

@skullpatrol What?

I don't know of a specific joke about french mathematicians

So yesterday, I found an Ancient GR Secret

There is apparently

A secret tensor

Called the November Tensor

This was apparently one of the first candidate for the field equations

But it was dumb and not covariant

$$N_{\mu\nu} = {\Gamma^\sigma}_{\mu\nu, \sigma} - {\Gamma^\sigma}_{\mu\tau} {\Gamma^\tau}_{\sigma\mu}$$

It was basically half of the Ricci tensor

John Rennie

arxiv.org/abs/1904.02008

Slereah

that's the one, yes

It was apparently so bad that I have never seen it outside of the context of "Why did Einstein try this dumb tensor?"

You know I don't even know why there's a dispute over the paternity of GR

There might have been a close call for finding the field equations, but by that point Einstein had got the idea of curved spacetime for years

John Rennie

I've only glanced at that paper, but it does go though Einstein's notebooks explaining how he seems to have arrived at that tensor.

Slereah

Yeah apparently the November Tensor isn't great but it's like

Invariant under a variety of coordinate transformations

but not all of them

so it might have passed the low bar of "Gravity can be transformed away by an acceleration"

pitt.edu/~jdnorton/Goodies/Zurich_Notebook

if you want to see the SECRET NOTES

Also looking into old GR stuff, I think I can see where Duffield made his mistakes

Apparently "variable speed of light" is one of the very first attempt at doing GR

Going back to Abraham's relativistic gravitational theory

Duffield isn't a quack, he's just as dumb as Einstein

That poor sap

enumaris

11:39

pain

Knight

11:56

gain

Novalium Company

train

Knight

12:31

0

Q: sign of potential in double Atwood machine

I'm feeling very confused about which sign to the potential should I choose. A specific exercise I've had trouble with is in this link. in this exercise a double Atwood machine is given. when I tried calculating the potential, I drew gravity pointing downwards, and the axis system I chose was y p...

lagrangian-formalism potential

I think Jeff Atwood will be the best man to answer this.

Johan Liebert

12:55

1

Q: Can the mass of an object account for the total internal energy of the object?

While studying thermodynamics my book describes the quantity the internal energy of a system. My book states: The concept of internal energy of a system is not difficult to understand. We know that every bulk system consists of a large number of molecules. Internal energy is simply the sum of...

thermodynamics energy mass-energy

Please cast close vote on this question :"Needs Details or Clarity"

Slereah

13:18

" In a class I taught at Berkeley, I did an experiment where I wrote a simple little program that would let people type either “f” or “d” and would predict which key they were going to push next. It’s actually very easy to write a program that will make the right prediction about 70% of the time. Most people don’t really know how to type randomly. They’ll have too many alternations and so on. There will be all sorts of patterns, so you just have to build some sort of probabilistic model. Even a very crude one will do well.

Slereah

13:38

Cartan–Karlhede algorithm

The Cartan–Karlhede algorithm is a procedure for completely classifying and comparing Riemannian manifolds. Given two Riemannian manifolds of the same dimension, it is not always obvious whether they are locally isometric. Élie Cartan, using his exterior calculus with his method of moving frames, showed that it is always possible to compare the manifolds. Carl Brans developed the method further, and the first practical implementation was presented by Anders Karlhede in 1980.The main strategy of the algorithm is to take covariant derivatives of the Riemann tensor. Cartan showed that in n...

This seems interesting

Aaron Stevens

13:54

@JohanLiebert Why do you want people to close your question?

Semiclassical

14:07

a quick knee-jerk question: is latent heat extensive or intensive?

@Slereah oh hey, john norton. i've met that guy. (he was the adviser of the physics history prof I know)

Johan Liebert

@AaronStevens actually the question isn't good and through it I ain't able to tell what really is in my mind. But as you can see I have got some answers so I can't delete it nor modify it in a significant way. So I thought it would be good for all if it was closed.

JMac

@Semiclassical I'd call it extensive. The required thermal energy scales with the mass. Specific latent heat is intensive though.

Semiclassical

same. but intro physics books seem to use "latent heat" when I'd use "specific latent heat"

which is annoying

if only because it means that latent heat doesn't have units of heat :P

the more common instance of this, I guess, is using "specific heat" when it should properly be "specific heat capacity"

JMac

Yeah I had to double check if "latent heat" was actually defined as "specific latent heat" since I know it gets used that way so often

Semiclassical

right

I definitely prefer to have specific/latent heats be extensive

because 1) it makes it clear that specific/molar/volumetric heat capacities are variations on the same concept, and 2) so that, when I refer to a particular experiment, I can refer to the amount of heat required to vaporize a given fluid as the latent heat of vaporization

otherwise I have to say that the latent heat of vaporization is different than "the heat required to vaporize my sample"

which is annoying

(It does lead to the following rule of thumb, I suppose: If your book talks about the difference between extensive and intensive variables, then specific/latent heat is probably extensive. If it doesn't, then it's probably intensive.)

Knight

14:47

I'm having some difficulty in calculating the divergence of Biot-Savart Law. Anyone interested?

Sir enumaris may I ask it from you?

Slereah

I didn't know @enumaris was knighted

enumaris

oh whoops, I forgot a 1x1 convolution in length is equivalent to a time-distributed feed forward

bowchicawowow

Uh...

Knight

was knighted? Really?

enumaris

I haven't done physics in a while so I'm not sure I'll know it lol

Slereah

I am joking about you calling him "sir"

enumaris

14:52

but go ahead and shoot

Knight

I'm going to shoot, wear your guards

enumaris

mmmk

Knight

I'm quoting Griffith's *"The biot-savart law for the general case of a volume current reads $$ \mathbf{B} \left(\vec{r} \right) =
\frac{
\mu_0}
{4 \pi} \int \frac
{
\mathbf{J} \left(\vec{r'}\right)\times \mathbf{\hat \mathcal{r}}
}
{\mathcal{r}^2} d\tau $$

enumaris

gotta fix it

Knight

I don't what I'm missing

Just be with me I'm gonna copy it to texmaker

enumaris

15:00

mmmk

Knight

$$ \mathbf{B} \left(\vec{r} \right) =
\frac{
\mu_0}
{4 \pi} \int \frac
{
\mathbf{J} \left(\vec{r'}\right)\times \mathbf{\hat \mathcal{R}}
}
{\mathcal{R}^2} d\tau'$$

Well it's working in my texstudion

enumaris

odd

Knight

enumaris

mmmk

Knight

So, this the equation. "this formula gives the magnetic field at a point $\mathbf{r} = (x,y,z)$ in terms of an integral over the current distribution $\mathbf{J} = (x', y', z')$. It is best to be absolutely explicit at this stage:

enumaris

15:08

For a static current eh

I think it's more common to call the elements $J_x, J_y, J_z$ for clarity

Knight

$$ \mathbf{B}~ \textrm{is a function of (x,y,z) } \\
\mathbf{J} ~ \textrm{is a function of (x', y', z') } $$
$$\vec{\mathcal {R}} = (x-x') \hat x + (y-y') \hat y + (z-z') \hat z \\
d\tau ' = dx' ~dy'~dz'$$

@enumaris Yes

enumaris

mmmk

Knight

"The integration is over the primed coordinates; the divergence and curl of $\mathbf{B}$ are with respect to the unprimed coordinates"

enumaris

yarp

Knight

Should I send the picture of the figure or can we continue without it?

enumaris

15:12

I think you can continue

this all is familiar to me

though I still don't guarantee I can answer your final question at the end lol

Knight

No, you're a very educated and kind man.

I want to know why the divergence and curl of B is over the unprimed coordinates and what is the significance of saying that

Johan Liebert

worldometers.info/coronavirus

enumaris

So B is a function of unprimed coordinates so when you take its divergence, it must be over unprimed coordinates

the primed coordinates are integrated over on the right hand side of the equation. They are dummy coordinates.

Johan Liebert

@JohnRennie sir why is the no of patients and the days following quadratic relationship? Does it happen for other kind of viruses?

enumaris

The reason the book mentions that specifically is probably to try to avoid confusion

John Rennie

15:19

@JohanLiebert I have no idea. I would guess it isn't really quadratic. Given ideal transmission it would be exponential, but the quarantine in effect in Wuhan will be limiting transmission to give a subexponential dependence on time. I'd guess it looks quadratic simply because any curve is approximately quadratic over a short range.

Knight

But wouldn't $\mathbf{B}$ gonna exist even inside the material through which the current is flowing? For example if we have a slab of some conductor and current is flowing through every infinitesimal volume, then at point inside the slab we should a have magnetic field due to currents flowing somewhere else in the slab. Then in this case we would have the $\mathbf{B}$ with primed cooridnates.

John Rennie

@JohanLiebert they helpfully provide a log plot, and since that isn't a straight line we can see it's sub-exponential growth. Still, the rate of growth is on the scary side.

Johan Liebert

@JohnRennie I believe that the case is worse than they are being shown. Chinese government is good at hiding stuff.

Knight

@enumaris Are you with me?

enumaris

@Knight primed versus unprimed coordinates don't denote separate locations or something

primed just means they are dummy coordinates to be integrated over

so there are no primed coordinates

Suppose you have a sum $f = \Sigma_{i=1}^4 i^2$, then $i$ would be like your "primed coordinates"...it's just a dummy variable to be summed over, it's doesn't really exist

Knight

15:29

You also make mistakes?

enumaris

it's just helpful notation so you don't have to write out the sums explicitly

So you are asking a similar question as "why can't I take the derivative of $f$ with respect to $i$?"

gotta take a call

Knight

Okay we will continue

Sir FaceArea Good Morning !

Aaron Stevens

15:45

@JohanLiebert The question is fine. I don't think it should be closed. If it is not exactly what you were confused about then it would be fine to just ask a new question

Johan Liebert

@AaronStevens OK thanks!

Aaron Stevens

@JohanLiebert Just make sure it is not a duplicate of what you already asked :)

Johan Liebert

@AaronStevens I don't think I would be asking any related question any time sooner as I think there is a lag in my understanding of the topic and hence I might not be able to convey it properly.

Knight

@enumaris Are you free now? I apologize for disturbing you by pinging you again and again.

enumaris

yarp

Knight

16:02

My problem is this statement: "But $ \nabla \times \mathbf{J} = 0$, because J doesn't depend on the unprimed variables"

enumaris

can you back up a step

Knight

YES

enumaris

so you have $\nabla \times B = \nabla \times \int {stuff}$ then there's steps where you need to move the $\nabla$ inside the integral right

Knight

Yes

enumaris

so, show the whole derivation and then what's $\nabla \times B$ at the end of the day

cus you know from Maxwell that you need to get $\nabla \times B \propto J$

Knight

16:06

Sir, we are doing divergence first.

enumaris

but I don't recall the full derivation to go back and forth from the integral formulation to the differential formulation

it has to do with Stoke's theorem, that's about all I recall lol

ok, just show the full thing you're working on lol

you skipped a bunch of steps :)

Knight

$$\nabla \cdot \mathbf{B} = \frac{
\mu_0}{4\pi
}
\int \nabla \cdot \left( \mathbf{J} \times \frac{
\mathcal{\hat R} \right)
}
{\mathcal{R^2} } d\tau'$$

enumaris

painful

Knight

$$\nabla \cdot \mathbf{B} = \frac{
\mu_0}{4\pi
}
\int \nabla \cdot \left( \mathbf{J} \times \frac{
\mathcal{\hat R}
}
{\mathcal{R^2} } \right) d\tau'
$$

@JohnRennie I did what you taught me, identation.

enumaris

mmk, looks legit so far :)

John Rennie

16:12

@Knight :-)

I was just looking at the MathJax but you beat me to it!

enumaris

although...I'm not 100% sure if you can just move the divergence inside the integral like that...but probably...

I don't really remember stoke's theorem very well lol

maybe it's not even stoke's theorem for this...

LOL it's been too long

Knight

*"Invoking the product rule"* $$ \nabla \cdot \left(
\mathbf{J} \times \frac {\mathcal{\hat R}}{\mathcal{R^2}}\right) = \frac{\mathcal{\hat R}}{\mathcal{R^2}} \cdot \left(\nabla \times \mathbf{J} \right) - \mathbf{J} \cdot \left(
\nabla \times \frac{\mathcal{\hat R}}{\mathcal{R^2}}\right)$$

OH My God I have done that in one go!

enumaris

sounds legit

And then they say the first term is 0 due to that statement right?

Knight

"But the $\nabla \times\mathbf{J}=0$ doesn't depend on the unprimed variables"

I having trouble in the above statement.

enumaris

you means $\times$

Knight

16:17

Yeah, sorry

enumaris

Probably easier to try an analogy with 1 variable

Knight

Can you please explain with that summation example?

enumaris

consider $f(t)=\int g(t,t')h(t')dt'$ then $df/dt = \int dg(t,t')/dt h(t')dt'$ right and you don't get a term like $dh(t')/dt$ since h(t') doesn't actually depend on $t$

That's essentially what that step is doing, except it's in 3-dimensions

maybe the notation I used is not great lol...

but you get the gist...

Knight

I'm unable to understand why J doesn't depend on x, y and z ?

enumaris

cus it's being integrated over. It's the analogue of $h(t')$ in my example

$h(t')$ doesn't depend on $t$

It's the thing being integrated over

Knight

16:23

Yes. But what's the difference between t' and t?

enumaris

t' is the thing being integrated over and t denotes where you are evaluating $f$

t' is a dummy variable

hmmm...how to explain this clearly lol...

Knight

In this example $$ f = \sum_{1}^{n} i^2$$ I know that $f$ is a variable of n and not of i.

enumaris

well that example was to illustrate the fact that $i$ is a "dummy" variable

just like $t'$ and just like $x',y',z'$

Knight

lol

enumaris

It's being summed over

that example doesn't have an actual independent variable in it

Knight

16:28

Can you invent a new one like that one?

enumaris

It would be like $f(t) = \Sigma_{i=0}^\infty g(t,i) i^2$

then when you do $df/dt$ you will only have a term that has $dg/dt$ you don't have a $di/dt$ term since $i$ is just being summed over

it's a dummy variable

Knight

Sir my apologies but may please use $$ for that summation statement?

enumaris

$$f(t) = \sum_{i=0}^\infty g(t,i)i^2$$

instead of $i^2$ you can think of any other function of $i$ like

Knight

Yes I can see that $f$ is a function of $t$

enumaris

$$ f(t) = \sum_{i=0}^\infty g(t,i)J(i)$$

then when you take the derivative of $f$ with respect to $t$, then $J$ explicitly doesn't depend on $t$

Knight

16:32

Yes, yes, I'm getting some good feelings :)

enumaris

so no derivative shows up

So now instead of sum, replace with integral

and you have the result you want

well and then make it 3-dimensional lol

Knight

$J(i)$ would work as a constant during the differentiation ?

enumaris

yarp

it doesn't depend on $t$ at all right

Knight

yes

enumaris

Hope that makes sense now lol

$t$ and $t'$ or $x,y,z$ and $x',y',z'$ are totally unrelated things...it's only confusing cus you generally use the same letters to denote them

maybe it's easier if you rewrite your equation like

$$B(x,y,z) = \frac{\mu_0}{4\pi}\int J(a,b,c)\times \hat{R}/R^2 dadbdc$$

the notation $\int J(a,b,c) dadbdc$ is the integral equivalent of something like $\sum_a J(a)$

Knight

16:37

Yes, and now taking the derivatives with respect to x, y and z, ha?

enumaris

yep

Knight

I have a silly doubt, isn't (a,b,c) lies in the space of (x, y, z) ?

enumaris

no

I mean physically yes, but mathematically no

It's the same physical space...but (a,b,c) are just being summed over

Knight

Please explain that mathematical 'no' . I think that is causing me (and bcoz of me to you too) enough stress

enumaris

lol, maybe don't think of it in terms of what space these variables lie in...

mathematically a,b,c are just a set of symbols that tell you what you're integrating over

Literally they are totally analogous as the $i$ in $\sum_i$

Knight

16:44

If we write $$ \frac{d}{dx} \mathbf{J}\left(a , b, c \right) $$

then wouldn't $a$ gonna vary as $x$ varies?

I mean J will change as $x$ will change, and hence a function of $x$? becuase moving in $x$ direction would result in change in current density.

enumaris

nope, cus $a$ is independent of $x$

how does $i$ vary as $t$ vary in $f(t)=\sum_i g(t,i) i^2$?

$i$ is literally just a dummy variable to be summed over

it's not dependent on $t$

and so $a$ is not dependent on $x$

Knight

If we have slab whose corners are $(0,0,0) ; (0,0,2) ; (0,2,2) ; (2,2,2) ; (2,2,0)$

and let the current is flowing in this slab. So, any point in this slab is represented as $(a,b,c)$ , isn't it?

enumaris

sure

I don't know how else to explain this lol

a, b, and c get summed over

they get integrated over

they are exactly like the $i$ in a summation

they don't depend on $x,y,z$

Knight

Then if we move along the $x-axis$ the $a$ will vary, will it not?

enumaris

no it won't lol

you have 2 different vectors

both in 3-D space

vector $r$ and vector $p$

why is it that if I move $r$ around

$p$ has to move around?

$p$ doesn't care about $r$ at all

but they both live in the same 3-D space...

Knight

16:55

lol

I thought we could write $ 0 \lt a \lt 2$ and hence $a$ will change as we move from 0 to 2

enumaris

As far as $p$ and $r$ are concerned, they are totally independent of each other, they couldn't care less about what the other is doing

I really don't know how else to explain lol

why do you think that just because things are in the same space, they all have to move at once?

Knight

lol (I think I'm making you angry lol)

enumaris

I mean...say you have two times $t$ and $t'$

is $t$ dependent on $t'$?

is $t'$ dependent on $t$?

Knight

no

enumaris

they are both times though

they both live in the same space

if you can accept that $t'$ and $t$ are independent why can't you accept $x$ and $a$ are independent lol

gotta take another call

Knight

16:59

Yeah! Now, I have got you! $t'$ is changing as $t$ but it doesn't care whatever $t$ is doing or just sitting and seeing the dying sun.

enumaris

cool beans :)

Knight

(I respect you sir, that gif is only friendly thanks)

enumaris

17:53

lol

Spoilt Milk

19:29

Hey all! Does anyone know the exact form the trace of extrinsic curvature tensor, $\Theta$ takes in AdS_4?

by a different just $K$ in AdS_4

*notation

Novalium Company

19:54

China

I SAID, CHINA

JMac

21:10

Man SE loves to put up banners that seem to imply "we only want feedback from coders".

skullpatrol

22:04

yeah, I noticed that also

Milan

Anybody know why Ben Crowell deleted his physics SE account?

JMac

@Milan Geez I didn't even notice that until now. I never saw him mention anything about it.

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