The h Bar

DanielSank

12:14 AM

@BernardoMeurer Really?

0celo7

1:25 AM

@JohnRennie Maybe all the Americans have left the chat or something. It's completely dead during prime time.

Tanuj

2:26 AM

@Semiclassical @Alex Are you guys around ? I need some help understanding a question on probability.

Jake Rose

hey

You know when you use an integrating factor method for an exact differential

Do you need to include the integration constant present in the integrating factor?

And if not why not?

Tanuj

2:40 AM

Ah nvm i got it !

Secret

3:59 AM

Random thought to be checked: Process that can catalyse the production of Hawking radiation hence speeding up the evaporation of a black hole

Also to be checked: What happens when an observer falls through the event horizon while the black hole just evaporated completely shortly after

journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.031103

The speculation here is that perhaps, with Hawking radiation providing an escape route of information from the black hole, the non determinacy of that spacetime beyond the Cauchy horizon can still be exposed to the rest of the universe

vzn

4:17 AM

@0celo7 lol then maybe you should think about what you write here (being one of the main ones...) :P btw, huh, "Americans" in 3rd person?

0celo7

@vzn I don't consider myself American

Tanuj

4:50 AM

@JohnRennie Good Morning :)

John Rennie

Morning :-)

Tanuj

@JohnRennie Can you help me understand what it really means ?

John Rennie

It's less complicated than it sounds ...

Suppose you are looking at a reaction where A oxidises B, and you're using an indicator I.

Tanuj

@JohnRennie Okay

John Rennie

You want A to oxidise I, and you want B to reduce I. That way the indicator I will reliably show whether there is an excess of A or B.

And you want A to oxidise I about as strongly as B reduces I. That is, in terms of oxidation potential you want I to be roughly halfway between A and B.

That's all there is to it.

Tanuj

5:04 AM

what you mean by halfway ? That oxidation potential of I should be midway between A and B ?

John Rennie

Yes

Tanuj

@JohnRennie Okay so lets suppose we are titrating KMnO4 with Oxalic acid using phenolpthalein as indicator

Cows

damn been stuck in my seat trying to wire up some next level oop code together. I want to stop but I think I want the promised money so I will continue.

John Rennie

Offhand I don't know how phenolpthalein works as a redox indicator. I've only ever used it as an acid-base indicator.

Tanuj

@JohnRennie Sorry , my bad , i got it all wrong.

@JohnRennie So what is happening is , as we are adding KMnO4 to oxalic acid solution , there comes a point where violet color of KMnO4 stops disappearing and a light pink color(permanent) is obtained

@JohnRennie So , is oxalic acid acting as a self indicator here ?

John Rennie

5:10 AM

OK, permanganate acts as its own indicator because it has such a dramatic colour change.

Tanuj

Oh so KMnO4 is the indicator ! Okay .

@JohnRennie After preparing the oxalic acid of some known concentration , we add dil. H2SO4 to it .Why is it done ? And does it affect the end point of the reaction in any way ?

John Rennie

I think H+ catalyses the reaction. It doesn't participate in the redox reaction.

Tanuj

Ah okay

@JohnRennie I found the explanation to it

it says dil H2SO4 is added "to prevent the formation of any precipitate of
manganese dioxide during the course of the titration".

Secret

yesterday, by Blue

"To Ahed and all the children in Israeli jails: We stand by your side, and are holding you in our hearts. We will not give up until you are free. You are not alone."

it's done

as in, mentioned

Tanuj

Oh , thank god :)

Cows

6:21 AM

Ok, I can learn some math now

I've decided! I will get a camera, super extra hd and start doing math(scary math . . .) on camera. . . .Mostly for the lolz, and to show off

Cows

7:22 AM

Listening to boys II men lolz

Boyz II Men - I'll Make Love To You

►

hehe

Rumplestillskin

Hello one and all! Does anyone have any idea about removing non-orthogonal components of a line element? I have the following line element $(ds)^2 = a dt^2 + b dr^2 + 2 c dr d\theta + d d\theta^2 + dz^2$ and I want to remove the off diagonal component? Where to start?

Cows

write it in matrix form first

Rumplestillskin

As a quadratic form?

@Cows

Cows

@Rumplestillskin something like that. . . but to be fair, I don't feel too comfortable giving advice on this. Just hang tight someone with hands on experience should be here soon

ACuriousMind

@Rumplestillskin You cannot, in general, diagonalize a metric - best you can do is make it so it is diagonal at a point, that's called Riemannian normal coordinates at that point.

Rumplestillskin

7:33 AM

@ACuriousMind So I am thinking about the usual starting point for a Schwarzschild metric where they have $(ds)^2 = A dt^2 + 2B drdt + c dr^2 + ...$ and they perform some magic and remove the off diagonal component. But I want to do it for $(ds)^2 = a dt^2 + b dr^2 + 2 c dr d\theta + d d\theta^2 + dz^2$? Is this possible do you think?

Well I should say the Schwarzschild metric at that point but it is normally the starting point to derive the S metric

John Rennie

@Rumplestillskin I? suspect that geometry has a non-zero angular momentum in which case you won't be able to diagonalise it. The comparison is with the kerr metric, which can't be diagonalised either.

ACuriousMind

For some metrics it's possible to do it at more than a point, but I don't think there's a general procedure for that, so you just have to guess good coordinates. I'd have to try it myself but I'm on mobile on my way to work :P

Rumplestillskin

@ACuriousMind my skills at guessing good coordinates leaves a lot to be desired. This is unfortunately evident at my most recent post :) Thanks though!

@JohnRennie Do you mean it is potentially a rotating space via the $drd\theta$ term?

John Rennie

Yes

I guess the question is whether it's a rotating geometry or just rotating cordinates

If the latter the off diagonal term can be transformed away but if the former it can't

Rumplestillskin

My god! Looking for solutions to the field equations that are non-trivial is proving to be quite the task!! I would be interested to see if anyone has a particular choice of coordinates that could remove the off diagonal though.

John Rennie

7:49 AM

Incidentally, in your example of the Schwarzschild metric the off diagonal term appears because the $r$ coordinate is translating. Those are the Gullstrand Painleve coordinates, often referred to as the river model because the coordinates are flowing inwards.

Rumplestillskin

8:00 AM

I noticed that if you introduce a new radial coordinate $R = r + (c/b) d\theta$ you do remove the off diagonal term but then you have a metric of the form $(ds)^2 = a dt^2 + b dR^2 + (bd-c^2)/b d\theta^2 + dz^2$. not sure if it really does anything though as we still have the same amount of unknown functions

On a different note, what are peoples thoughts on the Post-Newtonian approximation to GR? This also seems incredibly involved! However, reading articles and doing some leg work of my own it seems quite nice. Any body have any experience with it?

John Rennie

Not personally. It's mostly used for numerical work because it greatly simplifies calculations.

Mikhail

8:15 AM

Yo, why is it called the "reduced wave equation", whats been reduced?

John Rennie

8:26 AM

The Helmholtz equation you mean?

Mikhail

Yeah, that threw me off. I get it now...

John Rennie

I guess the term reduced means simplified

Mikhail

That negative sign... Now I feel bad.

Rumplestillskin

8:58 AM

@JohnRennie it seems to me that if you want to do anything applied with GR you are forced in that direction. It's quite interesting how GR is incorporated into real systems such as orbit determination software for near-Earth objects. It is simply linearly added in to a Newtonian force model as an external gravitational force and thats it...

John Rennie

@Rumplestillskin the PPN formalism is only useful in the weak field limit. For example you wouldn't use it for calculating black hole mergers.

Rumplestillskin

@JohnRennie you may be interested in this article. Here is an excerpt from the afforementioned article "The post-Newtonian approximation is a method for solving Einstein’s
field equations for physical systems in which motions are slow compared
to the speed of light and where gravitational fields are weak.
Yet it has proven to be remarkably effective in describing certain
strong-field, fast-motion systems, including binary pulsars containing
dense neutron stars and binary black hole systems inspiraling

The post-Newtonian approximation is a method for solving Einstein’s
field equations for physical systems in which motions are slow compared
to the speed of light and where gravitational fields are weak.
Yet it has proven to be remarkably effective in describing certain
strong-field, fast-motion systems, including binary pulsars containing
dense neutron stars and binary black hole systems inspiraling
toward a final merger.

arxiv.org/pdf/1102.5192.pdf

@JohnRennie appologies about the double post. I was trigger happy with CTRL+V

@JohnRennie it's actually the PN approximation ( or the EIH equations ) that are used by JPL to calculate the ephemeris data for approximately 300 objects in the solar system to first order I think!

I? think the ephemeris file is called DE421

Slereah

9:57 AM

Topologists

If I have a manifold with some fundamental group

What is the fundamental group of the punctured manifold

I can only find for the 2 dimensional case

ACuriousMind

10:43 AM

@Slereah In more than 2D there is no difference.

skullpatrol

how long is your commute to work? @ACuriousMind

Slereah

Sorry my work isn't commutative

skullpatrol

I need a vacation :P

user929304

Hi everyone, can I ask a question about extracting diffusion coefficient from a mean-squared-displacement plot?

Slereah

11:50 AM

"Dai Nianzu, a senior Chinese historian of science, has recently attempted to attribute the quick embrace of relativity to ancient Chinese thought. For instance, he claims that as early as the first century B.C. there existed in China an idea that was exactly the same as the Galilean principle of relativity;
he also asserts that the Chinese expression yu-zhou, commonly translated as “the Universe” and meaning more literally “space-time,” demonstrates the traditional Chinese idea that “time and space are inseparable.”"

2physics

12:09 PM

@EmilioPisanty yea, I got it. thanks for the answer

Slereah

12:28 PM

"In my opinion, this kind of criticism is not helpful for physics; it only creates confusion and hinders the development of natural sciences. We would rather have one Einstein than a hundred philosophers of this kind. "

nbro

I am very new to quantum mechanics.

Slereah

"The critics included mainly physicists, engineers, philosophers, and journalists of the younger generation, who charged that relativity was based on a groundless hypothesis, advocated reactionary “idealist relativism” and bourgeois viewpoints, and represented “one of the biggest obstacles now blocking the advance of natural sciences.”"

"Qin Yuanxun, a 1947 Harvard Ph.D. in mathematics and a contributor to the design of China’s first nuclear bomb, inaugurated the debate series by publishing a paper on his own “new theory” of space-time, which abandoned Einstein’s “controversial” assumption of the constant speed of light."

lol

nbro

Apparently, the expectation value is the expected value of a result (measurement) of an experiment. The EV is associated with an operator. Is this because an operator is what allows us to measure an experiment?

Slereah

"Except for those involving military projects, most scientific research institutes were dismantled and researchers sent down to work in factories or the countryside. "

@0celo7 is this good for the GDP

That Chinese paper on relativity is Dengsu tiaojian xia de kongshi duicheng lilun

Theory of symmetry between space and time under the condition of uniform velocity

It doesn't seem to be available translated

"The foundation of the basic [scientific] theories is Marxist philosophy; the most basic theory is Marxism. Without Marxism, where do scientific theories come from?"

skullpatrol

12:48 PM

In other news, they did show the world how far ahead they are in cloning research.

Slereah

Did they clone Mao yet

skullpatrol

I guess his partial clone is the leader of North Korea :P

Slereah

wulixb.iphy.ac.cn/EN/article/…

found the paper

strangely enough it seems to even include the Schwarzschild metric

skullpatrol

You, sir, are a Google-fu master.

Slereah

I wonder if there's weirder versions of the "Reception of relativity" papers

Like how was it received in Togo or something

"One of the major achievements found in Africa was the advance knowledge of fractal geometry and mathematics. The knowledge of fractal geometry can be found in a wide aspect of African life from art, social design structures, architecture, to games, trade, and divination systems."

heh

bolbteppa

1:06 PM

In $ay'' + by' + cy = 0$ is $b^2 - 4ac - 2b'$ anything, it's like the discriminant with the extra $-2b'$

2physics

@ACuriousMind. Hi , I'm here with another question again lol (I've already asked others idea about it too). We know time varying electric field on a point in space causes magnetic field, right? We also know a moving charge with a constant velocity changes the electric field in space with respect to time. there fore this time varying E field should cause a time varying magnetic field and again that magnetic field should create an electric field and it should continue for ever.

then why it is said that a moving charge with constant velocity doesn't radiate?

Fawad

Why isolated spherical capacitor has much less potential than spherical capacitor? I don’t know how to answer

2physics

I would be grateful if anybody else says his idea on that.

Fawad

1:21 PM

wait for John rennie sir

Slereah

Poor @JohnRennie

A slave to the public

Fawad

This is how selfish people think 🤔 💭 ^

Slereah

You're a mean one, Mr Grinch (Original 1966 Version)

►

its me

2physics

1:37 PM

@Slereah haha

bolbteppa

@2physics radiation depends on acceleration as in the Larmor formula en.wikipedia.org/wiki/Larmor_formula

Slereah

1:52 PM

If you think this is too hard on literary criticism, read the Wikipedia article on deconstruction.

3

heh

Secret

2:19 PM

I am the final panal for most topics except logic and number theory (and when someone deliberately test me)

Slereah

A fraud?

Secret

nah, it's more like:

People have the tendency to fill in the blanks, so even if I don't fully understood what certain jargon mean, I knew enough to give relevant response and then the expert then fill in the rest assuming what I said is what they think

and it gets more interesting in that 80% of the time, the answer they give actually answers my question, thus I get to learn without them dumbing down their explanation level

I then read books and google to help myself to comprehend the expert's answer

That's how I learn in most conferences

thus only when they ask about my background, will they knew I am from chemistry and not from <insert field of the conferece>

Put it simply, most of the time when people not from my field explains things to me, I don't understand the jargon, but I knew enough on what they are trying to say

Slereah

Are you quite sure about this self-image of yourself

From my perspective you seem to go on about a lot of nonsense

7

Secret

Well, eh, it is accurate for the questions that are based on some topics people read in journal articles. Here's an h bar example:

(but I agree it gets horribly wrong when I ask a question completely out of nowhere, where the half bakedness is obvious)

but in my real life, people from various conference often said I am like a sponge and learnign fast

Recent example here:

Feb 17 at 14:46, by Slereah

I should find out if it's possible to have rotating thin-shell wormholes

Feb 17 at 14:51, by Secret

what happens if a wormhole is rotating

Feb 17 at 14:58, by Slereah

@Secret The Teo wormhole isn't spherically symmetric, but 'course it's not a thin-shell wormhole

Feb 17 at 14:59, by Slereah

the thin-shell case would be that the homeomorphism between the two mouthes is of the form $f(t, \theta^i) = R(t, \theta^i)$

Feb 17 at 14:59, by Slereah

With $R$ some rotation matrix

Feb 17 at 15:00, by Slereah

just gotta show that there's no such homeomorphism that is also an isomorphism

Feb 17 at 15:01, by Slereah

For a spherical embedding, anyway

Here's the point: Often when people explain things to me, they rarely find the need to dumb down the explanation level and go full jargon. While For example here the fact is that I have no background on wormhole metrics which will mean I don't completely understand the explanation, I understoof some of the words here thus the whole thing flows and does not sound contradictory to me

So what I understood here is that there is a type of wormhole called the Teo wormhole, which has an asymmetry (arxiv goolging on the paper then reveal to me it is an axial symmetry), and then the two mouths are related by a homeomorphism, and the form of that homeomophism suggests the two mouths are rotated at some angle wrt each other, but all of the above analysis only applies in the case of a spherical embedding

2physics

2:37 PM

@bolbteppa well, in my example the charge's movement creates E & M varying fields; why don't we call it radiation?

Secret

So basically in my perspective, your answer to my question boils down to: There is some homeomophism that relates the two mouths of the wormhole in the thin shell case such that it is a rotation, but that does not apply to this case

Avantgarde

Is there a way to see papers (of a particular category) on arxiv from today till the desired past date?

And not just in the past week. Say, last month papers.

Slereah

use the advanced search

arxiv.org/find

it can only do years though

Secret

and so, while I only understood part of the answer that is given, it contains enough leads for me to work out the rest

Slereah

otherwise you can use inspire HEP

It allows for finer search

Avantgarde

2:43 PM

Oh thanks, I think I got it.

Secret

But I actually prefer it that way, for there are explanations that one simply cannot throw away all that jargon without distorting its real meaning

Slereah

inspirehep.net/info/hep/search-tips#dates

Secret

> and the form of that homeomophism suggests the two mouths are rotated at some angle wrt each other

As for whether this interpretation of the answer is reflecting what the answer mean, it is where I don't have the knowledge to judge. Using that xkcd example, if someone ask me a question based on the above, that will be the scenario when they knew I am not an expert and just a laymen

30 mins ago, by Slereah

A fraud?

And so to wrap that all up, basically the reason I have this self image is that: The answerer have give their explanation, and think that the asker understood the answer fully, while the asker think that they understood at least enough of what the answer mean, thus result in an illusion of both parties thinking they mutually understood the question and answers

(but again this is how I view it, perhaps in your perspective, you know I have almost no knowledge on GR solutions, thus you actually knew I don't understand fully what you said, but you said anyway, which is good, because I still learn something)

bolbteppa

3:03 PM

@2physics in Griffiths he talks about the difference between charges flying off to infinity, which is radiation, vs. charges following along, and how you see it in the velocity vs. acceleration terms in deriving the Larmor formula, in ch. 11, that might help in seeing it

Secret

(For anyone who is still following the above) The aforementioned analysis on how I get that self image could be wrong if the following premise I have is wrong:

> An expert will only go full jargon in their explanations and conversations if they think the asker is also an expert in the field

otherwise, some kind of analogy simplification or other devices should be present

and as usual, I don't know if anyone is bother enough to check this premise for me, given how most people don't like to read long messages

2physics

@bolbteppa I haven't studied Griffiths ; what's your personal idea about why the charge movement of my example does not radiate? according to the basic EM concepts (Maxwell's equations)

Secret

45 mins ago, by Slereah

Are you quite sure about this self-image of yourself

As for why I wrote the above long analysis: I don't like unanswered questions from either side of the party. All questions must be paired with an answer, even if a perceived one All conversations must be traceable to the smallest thought chain

John Rennie

@2physics suppose you switch to the rest frame of your moving charge. If the charge was radiating EM waves then in the rest frame you would see energy appearing from nowhere.

Secret

3:19 PM

tbh, it would be much easier if this is real life, because I will then be able to see from the body language on whether people think my explanation on why I think about what I think is nonsense

cyberspace cut off this important feedback mechanism, thus I won't even know if I am actually making my point across

or I am just speaking to thin air and thus flooding the chat as a side effect on trying to give an explanation

Fawad

2 hours ago, by Fawad

Why isolated spherical capacitor has much less potential than spherical capacitor? I don’t know how to answer

@JohnRennie

😢

$\dfrac{a}{1-{\frac{b}{a}}} >= a$

Tanuj

3:43 PM

@JohnRennie Good Afternoon :)

bolbteppa

@2physics the wiki derivation explains the same thing Griffiths does

Larmor formula

The Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates or decelerates. This is used in the branch of physics known as electrodynamics and is not to be confused with the Larmor precession from classical nuclear magnetic resonance. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light. When any charged particle (such as an electron, a proton, or an ion) accelerates, it radiates away energy in the form of electromagnetic waves. For velocities that are small relative to the speed of light, the total power...

Summing that page up, the electric field created by a moving particle is given by the first equation, and they link to a derivation of it from the Lienard-Weichert potential, which is found immediately just by solving Maxwell's equations, one of the most basic equations in electrodynamics,

and you see in this expression for the E field terms representing both the velocity and acceleration of the moving particle, as the page says, and the dependence of the velocity part is $1/R^2$ so it dies off as $R$ gets large, while the dependence of the acceleration part is only $1/R$, so far away from the moving charge only terms related to the acceleration of the moving particle remain,

and this is called radiation, i.e. that which radiates away from moving particle, so already you can see for a non-accelerating particle the field doesn't radiate, but you justify this by deriving the formula for power radiated, i.e. the Larmor formula, as in that link

That is, the general solution of Maxwell's equations for a point charge is the Liénard–Wiechert potential, the electric and magnetic field for this potential is given in that link, and from the expression you get you see terms representing both the velocity and acceleration of the moving particle depend on $1/R^2$ and $1/R$ respectively, so we only expect accelerating particles to radiate, as the Larmor formula (radiated power) justifies

Tanuj

4:35 PM

@JohnRennie Hey !

CooperCape

5:47 PM

ohai

Anonymous

@CooperCape Hi!

CooperCape

@Blue Don't you think exclamation marks over the internet make people seem so much more excited than they are/

Anonymous

Heh. Maybe, yes. But I use the exclamation mark only when making a point, or when I'm excited or well, exclaiming!

CooperCape

I suppose it's in the name.

Not called a "I guess it's alright" mark

Anonymous

(Also I'm trying to prevent myself from dozing off, while studying for a boring test, tomorrow morning....so occasional excitations helps :P)

CooperCape

6:01 PM

anything mildly interesting?

I was happy to have finished the organic chemistry section of my course today

news of the year

Anonymous

It's a physical electronics test. Lots to memorize

bolbteppa

What goes on at irregular singular points

CooperCape

Agh the most annoying kind of revision

Anonymous

@CooperCape Congrats

CooperCape

At least for me

Anonymous

6:03 PM

:D

CooperCape

@Blue doesn’t mean I’ll do well at it, just means the knowledge is passed on lol

That’s a lotta memorisation as well

Anonymous

I think you'll again have organic chemistry in college

Anonymous

In the first year

Anonymous

I don't know the UK system though

Anonymous

@CooperCape True, true

Anonymous

6:04 PM

It's sad they don't teach reaction mechanisms much in school. They just focus on teaching students more and more reactions which they'll forget anyway (in the long run)

ACuriousMind

@skullpatrol A little under half an hour

CooperCape

@Blue if I turn up to a university and see an organic chemistry module I might drop out and take a gap life

Eh we got enough mechanisms

If I remembered them

Anonymous

Lol. That's a good idea

Anonymous

@CooperCape Mostly they can be deduced

Anonymous

It's more like math...you need practice

CooperCape

6:17 PM

Yeah that makes sense

It's just I have no motivation for it currently

Sure I will when exams start looming

nbro

Hi folks!

CooperCape

Anyway for know I have a physics project to finish

Anonymous

What project?

CooperCape

You know when you have a bright idea to do something, then it turns out to be really stupid but you continue it anyway, and then it's a day before and it's kinda finished but really crap and you regret the last few weeks...

It's for my A level, to show... that we can research? I think.

2000 words on anything which was nice

Anonymous

I've had that experience before :P

Anonymous

6:20 PM

Cool cool

Anonymous

What's the topic

nbro

Today, I had my second lecture on quantum computing. After two lectures, I can confidently say that the professor teaching us this course is the worst professor (I have ever had) in terms of being able to explain well. It's so ridiculous how bad he is.

CooperCape

Well fuckin me be fuckin me went "Hey let's do the Higgs mechanism"

I still don't know what a field is really.

Anonymous

I wonder if your school teacher will even understand your project, given the kind of topic you've chosen XD

CooperCape

Well it would make one of us if he did.

Turns out this isn't a topic where words are used more frequently than equations.

Anonymous

6:22 PM

I mean it is a pop-sci level essay then that makes sense

Anonymous

Not a bad idea

CooperCape

It just requires a lot of "this is true, okay, I read it online. No i don't get it, but, it's true"

Anonymous

:P

nbro

I hate those people who try to make a subject look more complicated than it actually is by using the old trick of explaining extremely badly (i.e. out of order, introducing clearly unknown concepts, etc) and ambiguously. What are these guys trying to prove?

Anonymous

I guess I should leave now and study for tomorrow's test. I don't even know what all is in the syllabus...

Anonymous

6:25 PM

Cya

CooperCape

Good start, good luck. bye :)

ACuriousMind

@nbro Never assume malice where simple incompetence suffices as an explanation :P

Emilio Pisanty

@nbro that argument has a bunch of hair that's aching to be cut with Hanlon's razor. How do you (could you possibly) know that it's because they're trying to teach it badly instead of just them being bad at teaching?

ACuriousMind

@EmilioPisanty Sniped ;)

Emilio Pisanty

@ACuriousMind yes

but link trumps quote

nbro

6:28 PM

During my studies, I have only had one or two good teachers. The rest is just a bunch of "clowns", with all respect.

Emilio Pisanty

@nbro that's unrelated to what we just told you

ACuriousMind

@EmilioPisanty As long as you believe that ;)

nbro

I don't just write to answer to you.

Emilio Pisanty

also, it might be indicative that your choice of university might've been suboptimal

nbro

I am not even sure if Occam's razor is actually a good principle to follow...

Furthermore, people interpret these quotations in different ways to please them

Cows

6:48 PM

At the dentist getting my teeth cleaned. And no I'm not going to close the gap.

Emilio Pisanty

0

Q: Extension of trigonometric functions (like Bessel functions)

This may be more related to math SE, but I got no answer from there, and maybe physics SE can tell me more about practicality of my question. I learned that the Bessel functions and that family are derived from the ODE $$ y''+y'/x+(1-\nu^2/x^2)y=0, $$ and $J_\nu(x)$, $Y_\nu(x)$, $H_\nu^{(1)}(x)$...

special-functions

close as off-topic? migrate and let MSE close as dupe? leave it open here?

Emilio Pisanty

7:15 PM

28

Q: How to discourage users from using the "functions" tag

The following is the tag info for the functions tags: In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. A function is defined by its set of inputs, called the domain; a set ...

discussion featured tagging tag-management

^ lolz

MSE've gone and got themselves into some trouble there

19k questions' worth of trouble

John Rennie

7:34 PM

@dmckee that's a bit harsh. While I agree with your sentiments I wouldn't have been quite so blunt.

dmckee

@JohnRennie Are we talking about the magnetic declination question?

Ditch the notion of "stupid question" entirely?

John Rennie

@dmckee we are :-)

dmckee

You're probably^W right. Is it better now?

John Rennie

My immediate reaction to the question was to ignore it - or I might vote to close as unclear. If I were to answer I'd take the question at face value and answer fully with a diagram of a globe.

2physics

7:50 PM

@bolbteppa thanks but actually I don't understand it.

Emilio Pisanty

@JohnRennie @dmckee Any idea where the 11.3° came from?

bolbteppa

@2physics what textbook are you using

2physics

I don't know why according Maxwell's equations it radiates but according the equations you explain it does not!

dmckee

@EmilioPisanty I think that approximately the current value on the west coast of the USA. Other than that, not a clue.

2physics

@bolbteppa don't you think it should radiate? why shouldn't a time varying electric field result in a magnetic field?

@bolbteppa engineering textbooks, they don't cover advanced arguments

Emilio Pisanty

7:54 PM

@2physics The term 'radiation' in EM is normally quite specifically restricted to fields whose strength goes asymptotically down as $1/r$ (as opposed to the electrostatic $1/r^2$)

This is because ${\sim}1/r$ fields have a nonzero energy flow at asymptotically-large distances, while ${\sim} 1/r^2$ fields do not

the fields of a point charge moving with constant velocity are in that second category

@dmckee maybe it's the latitude of the magnetic north pole? it's consistent with the data from 1994, but given how much the magnetic pole's been moving around...

2physics

@EmilioPisanty "fields whose strength goes asymptotically down as 1/r" why should their strength go down? suppose we don't have any energy loss and those E & M fluctuations can propagate through space and recreate each other

Emilio Pisanty

@2physics because space has a bunch of possible directions

bolbteppa

@2physics you asked for a way to see this starting only from Maxwell's equations, the proof is to actually set up Maxwell's equations for a moving charge, and then solve them, finding the general solution called the 'Lienard-Wiechert potential', which is the electromagnetic potential for a moving point charge, then you can use e.g. $E = - \partial_t \mathbf{A} - \nabla \phi$ and $B = \nabla \times \mathbf{A}$ to find the electric and magnetic fields from this solution of Maxwell's equations,

and it turns out the electric field breaks into two terms, one depending on the velocity of the particle, the other on the acceleration of the particle, and it just so happens the velocity part depends on $1/R^2$, while the acceleration part depends on $1/R$, so the velocity part goes to $0$ fast far away from the moving charge, and so does not affect anything,

however the acceleration term only goes as $1/R$, a lot slowed, and so far away from the moving charge this part does affect things, and radiation if what ends up far away from the moving charge

Emilio Pisanty

generally, if you're radiating energy, then the total energy flux through a sphere $S$ of radius $R$ should be constant as $R$ increases to infinity

however, the area of the sphere grows as $R^2$, so the energy density $u$ needs to go down

2physics

@EmilioPisanty I mean the strength of light doesn't decrease as long as there is no loss. What do you mean by its strength?

Emilio Pisanty

8:02 PM

@2physics I mean the intensity, i.e. the energy flux, i.e. the amount of energy that passes a window of unit area in a unit time, as that same window goes further and further away

by 'strength' I mean the electric field

2physics

@bolbteppa this and what @EmilioPisanty added is clarifying it

bolbteppa

I can't figure out how to post a pic of the equation for the electric field here

Larmor formula

The Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates or decelerates. This is used in the branch of physics known as electrodynamics and is not to be confused with the Larmor precession from classical nuclear magnetic resonance. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light. When any charged particle (such as an electron, a proton, or an ion) accelerates, it radiates away energy in the form of electromagnetic waves. For velocities that are small relative to the speed of light, the total power...

But the first formula there

Depends on $1/R^2$ in the first term, and $1/R$ in the second term, which is how you see what was said above explicitly

Emilio Pisanty

@2physics it's a bit technical, but you should look at this solution

Liénard–Wiechert potential

Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Built directly from Maxwell's equations, these potentials describe the complete, relativistically correct, time-varying electromagnetic field for a point charge in arbitrary motion, but are not corrected for quantum-mechanical effects. Electromagnetic radiation in the form of waves can be obtained from these potentials. These expressions were developed in part by Alfred-Marie Liénard in 1898 and independently by Emil...

the Liénard-Wiechert fields are the EM fields emitted by a single point particle moving in arbitrary motion

2physics

I will

Emilio Pisanty

the electric field comes out in the form

$$
{\displaystyle \mathbf {E} (\mathbf {r} ,t)={\frac {1}{4\pi \varepsilon _{0}}}\left({\frac {q(\mathbf {n} -{\boldsymbol {\beta }})}{\gamma ^{2}(1-\mathbf {n} \cdot {\boldsymbol {\beta }})^{3}|\mathbf {r} -\mathbf {r} _{s}|^{2}}}+{\frac {q\mathbf {n} \times {\big (}(\mathbf {n} -{\boldsymbol {\beta }})\times {\dot {\boldsymbol {\beta }}}{\big )}}{c(1-\mathbf {n} \cdot {\boldsymbol {\beta }})^{3}|\mathbf {r} -\mathbf {r} _{s}|}}\right)_{t_{r}}}
$$

where you have one ("electrostatic") term that goes down as $1/r^2$ and one ("radiative") term that goes down as $1/r$ and actually transmits power at infinity

that radiative term is proportional to the acceleration, $\dot{\boldsymbol\beta}$, so if there is no acceleration, there's no radiated energy

2physics

8:12 PM

yes the energy density goes down as R increases..

Emilio Pisanty

@dmckee @JohnRennie whatcha make of this review?

physics.stackexchange.com/review/low-quality-posts/206639

doesn't it normally take three Looks OKs to knock stuff out of the queue?

(mind the timeline between the reviews and the latest edit, though)

2physics

@EmilioPisanty yes but the intensity of the electric field doesn't go down.

I mean

as R increases, field intensity is constant but energy density goes down

no no

I got it. you are talking about static field

@EmilioPisanty isn't it possible to explain it with out the help of those formulas?

don't consider the charge at all

Emilio Pisanty

@2physics yes it does.

2physics

we create a time varying E field in space

Emilio Pisanty

@2physics depends on what you mean by "explain"

@2physics No. This is a time-varying electric field. $\mathbf r_s = \mathbf r_s(\mathbf r,t)$ is a function of space and time, as is $t_r$ and everything ($\mathbf n$, $\boldsymbol \beta$, $\gamma$) that depends on it.

2physics

8:20 PM

why does it matter whether it is created by an accelerating charge or a charge with zero acceleration or a time varying magnetic field

you don't consider the charge at all

Emilio Pisanty

@2physics matter for what?

generally, it doesn't.

that's the point of the field description.

2physics

we have created a time varying electric field in space.

Emilio Pisanty

the electric and magnetic fields are local descriptions

the local behaviour does not depend on how those fields were created

2physics

alright! so you mean it doesn't matter how we have created that time varying field, right?

Emilio Pisanty

@2physics locally it doesn't

2physics

8:23 PM

what do you mean by locally?

John Rennie

@EmilioPisanty the north pole and magnetic north are 11.3 degrees apart

Emilio Pisanty

the same thing that "locally" means in every other instance it is used in in physics

@JohnRennie when?

John Rennie

@EmilioPisanty now (ish)

Emilio Pisanty

@JohnRennie not really. it was observed at ~11° in 1994, but it was much closer to 6° in 2007

at least if you believe Wikipedia

2physics

@EmilioPisanty what is the non-local behavior in this example?

Emilio Pisanty

8:25 PM

@2physics the contrast is to a global picture of the fields

i.e. knowing the fields throughout all space

in which case the Maxwell equations uniquely specify the sources

John Rennie

@EmilioPisanty now \pm 25 years

Emilio Pisanty

@JohnRennie =P

it does look like the magnetic pole is heading to Russia, dunnit? suspicious...

2physics

you mean one can't answer to this question properly with out knowing about the source of the E field: does a time varying electric field which is created at a point in space result in a magnetic field around it?

Emilio Pisanty

@2physics what do you mean by "is created at a point in space"? Do you mean that the field's source is at that point, or just that there is a source (somewhere) that produces that field?

2physics

@EmilioPisanty I mean there is a source (somewhere) that produces that field.

anywhere , I don't say anything about the source. Does it matter at all?

Emilio Pisanty

8:32 PM

@2physics then your statement is a local statement and it does not depend on the source

and yes, you can always answer that question. If there is a time-varying electric field at a given point in space, then there is always a magnetic field at that location.

(barring some implausible cases where there's a current density at that point that exactly cancels that magnetic field, I guess)

2physics

@EmilioPisanty does a moving charge with a constant velocity create a time varying E field in space?

Emilio Pisanty

@2physics Yes. It also creates a magnetic field.

And no, we don't call that time-varying field "radiation"

2physics

@EmilioPisanty alright! not radiation. lets call it fields' fluctuations!

Emilio Pisanty

@2physics that's even worse

you just call it "a time-varying electric field"

as I said, the name "radiation" is restricted to fields with nonzero asymptotic energy flow

2physics

wait wait , suppose a ray of light has caused that time varying E field

are they different?

what is the difference? both of them are E(x,y,z,t)

Emilio Pisanty

8:39 PM

@2physics the ray of light transfers energy

bolbteppa

@2physics Your original question was:
"We know time varying electric field on a point in space causes magnetic field, right? We also know a moving charge with a constant velocity changes the electric field in space with respect to time. there fore this time varying E field should cause a time varying magnetic field and again that magnetic field should create an electric field and it should continue for ever.
then why it is said that a moving charge with constant velocity doesn't radiate?"
so it seems like you've been confusing the definition of radiation with 'fluctuations'

2physics

@EmilioPisanty doesn't a time varying E field created by the uniform movement of a charge transfer energy?

Emilio Pisanty

@2physics Not asymptotically.

the surface integral of the Poynting vector over a sphere at radius $R$ tends to zero as $R$ goes to infinity

locally there is a nonzero energy flow parallel to the particle's velocity, but there is no radial energy flow

bolbteppa

Hopefully now you see radiation comes from an accelerating charge and only due to it's acceleration, which is why it is said a moving charge with constant velocity doesn't radiate, this is different from fields interacting with each other

2physics

"asymptotically" .. I have never seen Maxwell and his friends mention this evil word explicitly among their equations... lol

Emilio Pisanty

8:44 PM

@2physics then you haven't looked for long enough.

"I haven't seen X" ≠ "X doesn't exist"

2physics

@bolbteppa @EmilioPisanty yes I think now I understand it.. the problem was in what I meant by radiation! I was talking about fluctuations.

bolbteppa

Yeah, radiation is a technical concept with a specific meaning :p

Emilio Pisanty

@2physics "fluctuation" is another ~protected term with a specific technical meaning. I would discourage you from using it unless that specific technical meaning is in fact what you have in mind.

2physics

of course fluctuations will go to zero at infinity because the static E field of the charge goes to zero at infinity I think.

Emilio Pisanty

@2physics if by "fluctuations" you just mean "changes in the electric field over time", then that statement is true but insufficiently descriptive

the variations will go down to zero at infinity, but the rate at which they go to zero makes a lot of difference

2physics

8:54 PM

I mean changes in the electric field over time and space

bolbteppa

I'm not sure what the question is then

The real problem in learning this stuff is remembering the results, the size of the derivations is such a problem but it'd be fine if I could even remember that formula for the electric field :p

2physics

yup

@EmilioPisanty what would be the differences?

@EmilioPisanty the only time that the variations go to zero is when the charge moves at a constant speed. isn't it?

Emilio Pisanty

@2physics whether the fields and their time derivatives go down as $1/r$ or as $1/r^2$ (or an even higher power, of course)

... as previously explained.

Transcript for