The h Bar

Captain Bohemian

05:53

the weather becomes cool, not so hot as the previously several days, because it rained from last morning intermittently.

It is still raining now, so it's not convenient to go out without umbrella.

So the price to have cool weather is raining.

Captain Bohemian

06:19

The best use of advertisement paper is using it as calculation paper.

JingleBells

07:39

@JohnRennie i traid to seldet mai wife four indernet conecshan

Charlie

Could anyone give me a hand understanding how to go from the first to the second line here? I see how the first and third term give the KG-equation bit, but how can we get the second term in the form it is in on the second line?

scisyhP

08:20

0

Q: Force on dielectric slab

I have a doubt regarding the procedure of calculating force on dielectric while it is being inserted between the capacitor plates (with or without battery). This is what I understood from the theory I was taught. Consider a capacitor which is charged and disconnected from the battery. Now the e...

anyone?

JingleBells

08:44

Does anyone know about pull-up resistors?

I'm a bit confused about them.

John Rennie

@JingleBells What about them?

JingleBells

When there is a pushbutton and the Arduino pin will read a series of alternations between high and low due to EMI

John Rennie

So you want to use a pullup resistor on the input?

JingleBells

To fix that, we put a pull-up resistor between 5V (VDD) and the Arduino read pin

How does the R1 and VCC connection solve the issue?

I mean, does current flow from VCC to input pin?

When the button is pushed, why doesn't current go to the input pin?

John Rennie

The input has a very high resistance, so the circuit is effectively (diagram incoming):

JingleBells

08:48

lol voltage divider?

John Rennie

Where R2 >> R1

@JingleBells yes, it is acting as a voltage divider.

JingleBells

thx, let me think about if for a min :P

So current takes the path of less resistance and when the button is pressed the current from VCC will go through the button instead through R2

That's why the input pin reads LOW, cuz no current is flowing through it

and when the pushbutton is not pressed, there's current between VCC through R1 then R2 and GND, and that's why the input pin reads high

John Rennie

When the button is open the voltage at the input is Vi = Vcc x R2/(R2 + R1). Yes?

JingleBells

Sorry, how did we get to R2/(R2 + R1) I forgot my formulas :P

the "x" is multiplication there?

Vi = Vcc - I1R1 - I2R2?

kirchkoff's stuff, voltage drops, no...?

John Rennie

R1 and R2 are in series, so the total resistance is R1+R2. The current is given by Ohm's law $I = V/R$ so in this case the current is I = Vcc/(R1+R2). OK so far?

JingleBells

08:57

Sorry I learned those stuff last year

@JohnRennie Yup

John Rennie

And the voltage across R2 is also given by Ohm's law V = IR so in this case the voltage across R2 is V2 = I x R2 = Vcc/(R1+R2) x R2

JingleBells

@JohnRennie I got confused here. I = Vcc/(R1 + R2) is the current flowing from VCC to GND (through R1 and R2)?

John Rennie

Yes

JingleBells

V2 = I2 * R2, no?

oh wait, current was constant wasn't it?

John Rennie

The two resistors are in series so the same current flows through both resistors.

JingleBells

09:02

Yup, got it

@JohnRennie got it

John Rennie

So with the switch open Vi = Vcc R2/(R2+R1)

And since R2 >> R1 the denominator is approximately equal to R2 giving Vi ~ Vcc

JingleBells

V2 = Vcc R2/(R2+R1) no?

that's the voltage across R2

Vi = V1 + V2 no?

John Rennie

Yes, and the input voltage is equal to V2 because the input is connected to the top of R2.

JingleBells

Got it

@JohnRennie got it

John Rennie

OK :-)

Now suppose we close the switch. Now the (closed) switch is in parallel with R2.

And the resistance of the closed switch is zero (or close to zero) so the combined resistance of the closed switch and R2 is zero.

So the input voltage is now Vi = Vcc x 0/(R1 + 0) = 0

JingleBells

09:11

Got it

Was that it?

John Rennie

Yes.

JingleBells

Thanks! :--)

John Rennie

The pullup resistor ensures the voltage is equal to Vcc when the switch is open.

JingleBells

I think my IQ jumped with 5 points after this

John Rennie

Without the pullup resistor the input voltage would be undefined when the switch was closed.

JingleBells

09:15

@JohnRennie How do you know this stuff? How do you make all the mathematical relations in your brain? I wanna know your IQ :D

John Rennie

Practice

3

Captain Bohemian

10:08

how to interpret $r<r_s$, where $r_s$ is the Schwarzschild radius, in the Schwarzschild metric?

John Rennie

@CaptainBohemian what do you mean by how to interpret?

Captain Bohemian

@JohnRennie after coordinate transformation in the Schwarzschild metric, the region of $r<r_s$ seems to become strange, e.g. in Kruskal coordinates and the associated Penrose diagram.

John Rennie

In GR coordinates are just labels we use to identify points in spacetime. So we might identify a point inside the event horizon as $(t, r, \theta, \phi)$ but this is a label and you should not just assume there is a direct physical relevance to the values of the coordinates.

There are physically relevant quantities related to the coordinates. For example you might ask what is the time taken to fall into the singularity starting from the radial coordinate $r$?

Captain Bohemian

10:25

@JohnRennie can you interpret the diagram, which is the Penrose diagram of the Schwarzschild metric in Kruskal coordinates? I can't quite understand this diagram.

John Rennie

This is a bit advanced for someone who doesn't have a basic foundation in GR.

Captain Bohemian

@JohnRennie I have the foundation of GR.

But I can't understand a lot of places in this diagram.

John Rennie

OK. What aspects of the diagram are unclear? Incidentally that's not a Penrose diagram.

That's just the geometry drawn using the KS coordinates.

Captain Bohemian

@JohnRennie ok, maybe you are correct. I pick this diagram from a lecture which puts this diagram after writing xxx (the Schwarzschild metric in Kruskal coordinates) is the basis for constructing the Penrose diagram of the Schwarzschild black hole, so I consider this is the Penrose diagram.

John Rennie

10:40

You get a Penrose diagram by starting with the diagram for the black hole in KS coordinates then applying a further transformation that puts infinity at a finite distance on the diagram.

That's what your book means by the basis for constructing the Penrose diagram

Captain Bohemian

@JohnRennie so is the above the Penrose diagram?

John Rennie

Yes, that's the Penrose diagram

Captain Bohemian

11:03

@JohnRennie i feel the diagram doesn't correspond with Kruskal coordinates: $T=\sqrt{\frac{r}{r_s}-1}e^r/2r_s sinh(t/2r_s), X=\sqrt{\frac{r}{r_s}-1}e^r/2r_s cosh(t/2r_s) $ in some places. Like it denotes $t=0$ on the T axis. Does it mean the whole T axis is t=0 or just the point where the blue curve intercepts the T axis. But I think neither is correct because t=0 corresponds to T=0.

John Rennie

To be honest I'm pretty rusty on the interpretation of Penrose diagrams so I'm not the person to ask.

Captain Bohemian

@JohnRennie but you said this is not a Penrose diagram; it's just a pre-Penrose diagram.

John Rennie

@CaptainBohemian I thought you were referring to the Penrose diagram. Did you mean the KS diagram you posted first?

Captain Bohemian

@JohnRennie yes.

John Rennie

That one

Captain Bohemian

11:13

@JohnRennie yes. Is that blue curve in II region the singularity of the black hole and the green curve in the IV region the singularity of the white hole?

John Rennie

@CaptainBohemian Yes

Madame Akira

Good Afternoon sir @JohnRennie

:-)

John Rennie

@MadameAkira hi :-)

Madame Akira

You've got tonne of knowledge of physics. How do you cope up with failure in understanding something ?(if you had any haha)

@JohnRennie

peterh - Reinstate Monica

@FakeMod 99% of the deleted posts is trash. 1% would be interesting, you can see roughly in that what you can see even without them.

@FakeMod What to me worked at best: 1. Finding the most interesting deleted posts by the SEDE ( data.stackexchange.com , in contains many deleted post metadata, but no content), and then using archive.org to see their previous versions.

Captain Bohemian

11:26

@JohnRennie then can answer my above question? that is, what does the denotation t=0 near the interception of the T axis and the blue curve mean? as I think t=0 corresponds to T=0.

peterh - Reinstate Monica

@FakeMod You can also find many of your deleted posts by checking your flag history - if you flagged anything below that, the link remains in your flag history forever. It is also pretty useful if you save the link of all your posts in a text file. Make it a habit - you can not be ever sure, when will you need them.

@FakeMod 10k is actually not so hard, there are some tricks to get to it, but it still requires years, if you are not a prof.

John Rennie

@CaptainBohemian as I recall, on the KS diagram lines of constant t are straight lines passing through the origin.

So the T axis is a line of constant time, and it's the constant time $t=0$.

The label on the diagram isn't intended to mean $t=0$ only where the T axis intersects the singularity.

peterh - Reinstate Monica

@FakeMod You could also develop a script which crawls the whole site. I don't suggest it to do, even if you take care to not overload anything. Probably some automatism will detect, what are you working on and it will intervene.

@FakeMod There are also various backups, mirrors of the network around on the net, you can also grab them. The problem is that most deleted posts are deleted quickly, so they have only little chance to get into them.

@FakeMod However, the 10k is a little bit over-mystified: what you really get with it, is access to the wastebasket. Making this to the top privilege looks for me more like a psychological hack (note also, wastebask privilege is named as "community moderator").

@FakeMod I think, the highest privilege / effort ratio is at the 3k. This is important.

@FakeMod Note also, there are no "post (un)deletion" review queues, the del/undel votes are unretractable, and the 10k tools page is mostly informative. Really important infos are only for the mods, but for example, not even they have access to vote data.

@FakeMod With an experient usage of the SEDE + archive.org combo, you can roughly see what a 10k user can see, without any privileges on the site itself.

Captain Bohemian

@JohnRennie you mean t=constant (on the diagram only $t=-\infty, t=-2, t=-1, t=0, t=1, t=2, t=\infty$ are denoted) are those shaded straight blue and pink lines passing through the origin?

bolbteppa

11:55

@Charlie just apply the derivatives

The middle term on the first line becomes the last term on the second line, the first term on the first line becomes the first and third terms on the second line

peterh - Reinstate Monica

12:26

1. a BEC of D2 molecules. 2. a BEC of He4 atoms. 3. Coherent photons, out of the system. 4. The D2 BEC + the He BEC should interact to quantum tunnel the D2 molecules into He atoms, and the released energy should appear as (3). 4. Photons should work on a way to induce current in the superconducting coils out of the system. 5. The whole system should be made self-stabilizing. <- I believe, such a system could be designed by quantum computers and built by nanotechnology.

That would be... really cold fusion.

user434058

@peterh-ReinstateMonica Thanks for the extensive explanation, however I am not so serious about viewing deleted posts :-)

John Rennie

12:41

@CaptainBohemian yes

JingleBells

13:05

OOohh you cAn U SIIIIII

laallalllalalaldilallaaaa

naaanananaaaaaa nana nana n anaaaaa

Jake Rose

13:58

How can you have $\langle x | x' \rangle = \delta$ AND $ \langle p |\ p' \rangle = \delta$

i.e. the particle is definitely there, and it's momentum is definitely that

Doesn't this go against the uncertainty principle?

never mind that was such a stupid quesiton

bolbteppa

$\delta(x - x')$ and $\delta(p - p')$

Jake Rose

@bolbteppa Yeah didn't type them out of laziness if I'm honest

Captain Bohemian

14:31

@JohnRennie then do $r=$constant correspond to those shaded blue and pink curves (on the diagram only $r=0, r=0.4, r=0.6, r=0.8, r=1, r=1.2, r=1.4, r=1.6$ are denoted)?

John Rennie

@CaptainBohemian Yes, lines of constant $r$ are hyperbolae.

@CaptainBohemian the power of the KS diagram is that it makes some situations easy to analyse without even having to calculate anything. For example look at my question:

129

Q: Does someone falling into a black hole see the end of the universe?

This question was prompted by Can matter really fall through an event horizon?. Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event horizon the result is infinite. This implies that the universe ages by an infinite time before someone ...

general-relativity black-holes spacetime observers event-horizon

Reading Michael Brown's answer to that was the first time I really grasped how useful the KS diagram could be.

Jake Rose

$\langle x | p | x' \rangle$

I'm getting the derivative of a delta function...

Which seems awfully unlikey

Captain Bohemian

@JohnRennie here comes to what I feel strange on the diagram I previously said. First, I notice when $t=0$ and $r=0$, T is indefinite because $\frac{e^{\frac{0}{0}}-e^{-\frac{0}{0}}{2}}$ is indefinite, but on the KS diagram, $t=0$ and $r=0$ corresponds to the point where the curve $r=0$ intercept with the line $t=0$.

Jake Rose

Oh wait

I must be right

That's unusual

Captain Bohemian

@JohnRennie sorry that I missed something in LaTeX above. Let me try again. here comes to what I feel strange on the diagram I previously said. First, I notice when t=0 and r=0, T is indefinite because $\frac{e^{\frac{0}{0}}-e^{-\frac{0}{0}}{2}}$ is indefinite, but on the KS diagram, t=0 and r=0 corresponds to the point where the curve r=0 intercept with the line t=0.

John Rennie

14:44

$$ T = \sqrt{\frac{r}{2M} - 1} \exp\left(\frac{r}{4M}\right) \sinh\left(\frac{t}{4M}\right) $$

Why does that become indefinite for $t=0, r=0$?

Captain Bohemian

@JohnRennie so $T=0$ when $t=0, r=0$?

John Rennie

Oh wait ...

The definitions of T and X are different inside and outside the event horizon, and the one I've given you is for outside the horizon. Inside the horizon the definition is:

$$ T = \sqrt{1 - \frac{r}{2M}} \exp\left(\frac{r}{4M}\right) \cosh\left(\frac{t}{4M}\right) $$

So $T=1$ and $X=0$ for $t=0,r=0$

Captain Bohemian

14:59

@JohnRennie Ok,yours looks correspondent with the KS diagram. The lecture only gave the $T$ and $X$ for $ r>r_S$ (as I typed here earlier, which is like yours with $r_S=2M$)

John Rennie

Wikipedia gives the definitions of T and X both inside and outside. I actually got them from Schutz's book, but obviousy they are the same.

Captain Bohemian

15:18

@JohnRennie Thank you, I'll read about it to get more about the detail of the KS diagram. but what do the region above the blue curve $r=0$ and the region below the green curve represent?

John Rennie

Those regions do not exist i.e. values of T and X in those regions do not map to any real values of r and t

Captain Bohemian

15:32

@JohnRennie actually the Wikipedia doesn't define the formulas of $T$ and $X$ at $r=0$. It only defines the formulas of $T$ and $X$ at $r>r_s$ and $0<r<r_s$.

Slereah

Hm

Should I order a book

let's see

John Rennie

@CaptainBohemian technically the point $r=0$ doesn't exist as it's not considered to be part of the manifold.

ACuriousMind

@Slereah another ancient GR tome?

Slereah

@ACuriousMind Maybe a nudie mag

or a GR book

John Rennie

@CaptainBohemian I suspect that's why Wikipedia says $0 \lt r \lt r_s$ rather than $0 \le r \lt r_s$

ACuriousMind

15:35

I'm sure GR is the more corrupting influence on the youth of the two :P

John Rennie

More fun too :-)

Slereah

Oh wait

Maybe I can get that GR poetry book

it is expensive, tho

JMac

Holy crap Canada post has the worst online tracking ever. I wake up this morning and it says I missed them and they left a notice. There's no notice in my mailbox or door. So I go to Canada post, and they say "oh yeah, they might have put that in the system early". I go back home, and sure enough, they came while I was at the post office looking into it (marking that they came ~3 hours earlier on the slip, even though I had checked after that time)

bolbteppa

Get GSW

BioPhysicist

16:27

@JMac Sneaky Canadian post. Maybe they had excess notices, so they forced you to be gone so they could issue one.

SE pet peeve: when users essentially say the same thing as answers in the question that has been proposed as a duplicate.

Charlie

17:37

thank you again @bolbteppa

Just as a follow up, a as in that example a derivative term like $\partial_\mu(\partial^\mu\phi\partial^\nu\phi)$ can just be treated with the product rule right? So this becomes $(\partial_\mu\partial^\mu\phi)\partial^\nu\phi+(\partial^\mu\phi)\partial_\mu\partial^\nu\phi$.

bolbteppa

Yeah

Charlie

tyvm

user434058

Yo, this is nice! The Universe is really trying hard to stop me from answering. Whenever I click the answer box to start typing out the answer, I see a notice saying that there's a new answer to the question and that answer is practically the one I was about to write. Thank you, the mystical Universe :-)

Charlie

17:53

god works in mysterious ways

user434058

@Charlie yes, God does :) And that makes me wonder everyday Simulation hypothesis might be true...

Charlie

I also see you've given up on the dream of being inactive :P

Everyone needs their fix

user434058

Though, I have also been doing my part and have stopped visiting the review queues now that my number of reviews in all categories have reached a multiple of 5 :)

Charlie

greatness achieved

user434058

@Charlie I just removed it to stop confusing others and stop deceiving myself

user434058

17:57

@Charlie lol

Charlie

no more living in denial :)

user434058

@Charlie though, I might get over SE soon.

user434058

Said The Sky - Over Getting Over You (feat. Matthew Koma)

►

user434058

Not very related, but a good song ☝️

JingleBells

In the Hitchhiker's Guide to the galaxy, doesn't the question of life, the universe and everything get answered?

The movie ended in the stupidest way possible

Charlie

19:49

Am I allowed to make a manipulation like $(\partial_\mu\phi)A^\mu=(\partial^\mu\phi) A_\mu$ because this is just multiplication by the identity $\delta_\mu^\nu$?

bolbteppa

Yes, you can see it as $(\partial_{\mu} \phi) A^{\mu} = \eta_{\mu \nu} (\partial^{\nu} \phi) A^{\mu} = (\partial^{\nu} \phi) A^{\mu} \eta_{\mu \nu}= (\partial^{\nu} \phi) A_{\nu}$

Madame Akira

Is Qmechanic a person ? I mean he's like online 24*7.
It's not even 2 minutes I posted my question and he has already edited it.

Charlie

tyvm

bolbteppa

In true quantum spirit, even when (s)he's not here, (s)he could be here

Captain Bohemian

21:51

@JohnRennie Don't those regions map to negative values of r rather than imaginary values of r? But negative values of r are also unacceptable.

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