The h Bar

I need to revise combinatorics :P

Thanks btw :)

Balarka Sen

There're multiple ways you can do this. I am inclined to believe Tern's is the fastest.

No problem, I didn't help much. now I can go back to rehearing the instrumentals on Low.

I found another way just now $\frac{1}{5}(1.2.3.4(5-0) + 2.3.4.5(6-1) + .....)$ All the terms cancel out except the last and the first it seems

Mithrandir24601

@vzn If you've got the solution for something without some approximation as well as with some approximation, then you can just plug them into a computer and compare results to help figure out how good the approximation is, right [note: I don't actually have the 'solution', only some number of steps towards one]

[I also meant to put a '?' at the end of that]

skill patrol

9:27 AM

Chapter 1 of PHYSICS has been created

9:51 AM

If I have energy in an electric field, I can think of it as the potential energy associated to the Coulomb force.

If I have energy in a magnetic field, I can't seem to come up with a force associated to the energy.

What's the deal?

@DanielSank The magnetic force is not conservative (since it depends on velocity), so it has no potential associated to it.

Surely the problem is that the force fields associated with magnetism, i.e. when you change the current through a loop of wire, are not conservative.

jinx

:P

@ACuriousMind Yes, but somehow, there must be something conservative, else we wouldn't have energy stored in the B field in the first place.

I recall reading Purcell's E&M book as an undergraduate. There, it is clearly demonstrated that magnetism can be seen as electrostatics + relativity.

Somehow, the Coulomb force is hiding in the magnetic energy. But how?

Magnetism is just a lorentz transformed Coulomb force

9:55 AM

@Mithrandir24601 Sounds interesting.

@Slereah pretty sure that's equivalent to what I just said ;-)

Yes

@DanielSank I think that once you invoke relativity, you shouldn't really think in terms of separate electric/magnetic fields anymore. The proper relativistic object is the EM field strength tensor, and it has an associated stress-energy tensor. If you examine the energy density component of that one, you find it is $E^2 + B^2$ (modulo constants).

@ACuriousMind I understand that $F$ is the right way to think about stuff.

However, I am trying to visualize intuitively what $F$ does for me automatically.

Here is an analogy for what kind of thing I'm asking:

Suppose I have a bar with a big positive charged ball on either end.

We're in space, i.e. no gravity. I put the bar in a uniform $B$ field. Now I turn off the $B$ field. It's easy to see that the bar will spin. Where did the angular momentum come from?

Now you could say "There's angular momentum in the magnetic field", and you'd be right.

However, that sounds like a cop-out of the "dark matter" variety.

Why does it have to come from anywhere?

Assigning angular momentum to the magnetic field makes sense because if you think about the sources of that field, you have a current in a coil, a.k.a. moving charges going in circles, a.k.a. angular momentum. When you turn the field off, you're stopping those charges, so of course their angular momentum goes somewhere.

@ACuriousMind Because we're pretty darn sure that angular momentum is conserved.

10:02 AM

@DanielSank Okay, so why is it a "cop-out" to say the momentum was in the field? If angular momentum is conserved, and the only difference between the situation with the unmoving bar and the rotating bar is the presence of the magnetic field, the momentum must've been in the field.

@ACuriousMind It's a cop out in two senses:

1) The field itself originates as a way to keep track of inter-particle forces. In other words, it only makes sense if there are forces (I know you'll argue with this).

@Kenshin Name ?

Quantum Physics

2) Angular momentum is $m r \times v$, i.e. there's a mass and a thingy moving around.

@DanielSank No, I don't argue with that. It's true - fields are just bookkeeping devices. Amazingly useful bookkeeping devices.

10:05 AM

@Kenshin Eh..wouldn't be better to keep some common chapters at the beginning like Mechanics or Optics or Thermodynamics ?

common?

QP is for advanced readers

@DanielSank That is what I argue with. If that is your definition of angular momentum, then obviously there is no angular momentum in a field, and angular momentum is not conserved.

QM is the most common tag on Physics.SE

@Kenshin I mean in layman's terms...

10:06 AM

@anonymous there is no reason that I can't re-order the chapters

@Kenshin Oh...when you said CHAPTER 1 I thought....

@ACuriousMind So, in reality, I think fields are as real as anything else because "particles" are just a book-keeping device to help us reason about the experiences inside our brain-boxes anyway.

It is only when you define angular momentum in the Noetherian sense as the quantity associated to rotational symmetry that you can meaningfully assign angular momentum to a field.

@anonymous currently it is Ch1 but only because it is the first one i've done

it may end up as ch3 or 4 or whatever

I see

Good

10:07 AM

...but right now I'm drawing an arbitrary line between particles and fields and insisting on understanding stuff with only particles.

@Kenshin Do you have a preview ?

of the first chapter?

in pdf form ?

@anonymous it is in pdf format currently

Can I see?

@ACuriousMind Ah, but it is conserved if you insist on the field having a source!

@anonymous patients please lol

10:08 AM

@DanielSank Why would I? Maxwell's equations admit non-trivial vacuum solutions.

(Yes, free fields satisfy Maxwell but let's just ignore them for now since we already said we're in Particlesonly Land)

jinx

it was quite a lot of effort to select the best questions

@Kenshin I'm sort of excited :) Do show me a preview sometime if possible

Just 1-2 pages

alright I will :)

@DanielSank Well, if you want to be in particles-only land then I say that you cannot understand classical electromagnetism.

10:09 AM

@ACuriousMind I find that claim suspect.

::shrugs::

Obviously rejecting fields is unnatural. Any attempt to do that and still understand things like radio will fail unless we recreate fields in some less elegant form.

suspect?

how do you explain the double slit experiment with particles?

Koolman

Congrats @Kenshin

ty @Koolman :)

10:11 AM

Perhaps I should instead say that I'm trying to understand the original question about magnetic energy purely from the point of view of the source charges. Is that better?

Ahah @DanielSank doesn't know about angular momentum for fields

@Slereah Are you trolling?

@Slereah please don't tease ppl for what they know and don't know

@DanielSank Yeah, but my position is the same as for angular momentum - you need a new definition of energy (the Noetherian one) in field theories for energy to be conserved.

Hmm, based on recent experimental evidence, I hypothesize that @Slereah is a troll and @Kenshin is either illiterate or sarcastic :-P

3

10:13 AM

you can do EM classically without EM fields

but it's really heavy handed and boring

Jefimenko's equations

In electromagnetism, Jefimenko's equations (named after Oleg D. Jefimenko) describe the behavior of the electric and magnetic fields in terms of the charge and current distributions at retarded times. Jefimenko's equations are the solution of Maxwell's equations for an assigned distribution of electric charges and currents, under the assumption that there is no electromagnetic field other than the one produced by those charges and currents. == Equations == === Electric and magnetic fields === Jefimenko's equations give the E field and B field produced by an arbitrary charge or current ...

@Slereah Yeah but describing time delayed forces like with radio transmission must be ugly.

@Slereah Like I said, ugly. Those equations are horrible.

they are

and actually, the versions in Wikipedia are written in terms of the fields. So... that doesn't actually support the point you were making.

Surely you can just rewrite everything in terms of forces and pretend fields don't exist...

@DanielSank ...is that not what you wanna do here?

I'm still a bit confused what your actual question is, I guess

@DanielSank Well they are rewriting $E$ and $B$ in terms of sources

10:16 AM

Yes, that's what I want to do.

Which means you can get rid of $E$ and $B$

@Slereah Yep.

But while you can

i would not recommend it

Koolman

@Kenshin you should have a look at tags

@ACuriousMind actually I was hoping for a qualitative description of how to think of magnetic energy in terms of sources and electrostatic energy.

10:17 AM

There are many things you can do but that I would not recommend

^ LSD?

Bank robbing?

I meant more this

amazon.com/Einstein-Matrix-Form-Derivation-Relativity-ebook/dp/…

Read Jackson's E&M book?

@Koolman can you please clarify/

@DanielSank I think that's impossible: Consider a magnetic field generated by a current loop. There is no inertial frame where all the charges in the loop are at rest, so there is no frame where that magnetic field is purely electric.

10:18 AM

@Slereah EEEK! ::shoots ink and jets off to hide in den::

2

Koolman

@Kenshin qandaexchange

Few tags have spelling mistakes

that's terrible

thanks for letting me know

Perhaps I should have said "...in terms of sources, electrostatic energy, and time dilation / length contraction".

I can recover the attractive force of two current carrying wires in that way.

Also particles with spin have a magnetic field at rest :p

@Slereah I never totally understood that.

10:26 AM

I don't think there's something to understand - it's just an experimental fact that spin behaves like angular momentum with respect to the magnetic field. It's basically why we call it spin.

Note, perhaps, that "particle with spin at rest" is kind of an oxymoron, since in the quantum regime where "spin" is defined, "at rest" is not.

You can have classical fields with spin