The h Bar

1:27 PM

1

Q: Mathematical quirk

It is written in the Goldstein's Classical Mechanics text that $$\frac{\mathrm d}{\mathrm dt}\left(\frac{\partial {r_i}}{\partial {q_j}}\right) = \frac{\partial {\dot r_i}}{\partial {q_j}}=\sum_k \frac{\partial^2{r_i}}{\partial {q_j}\partial{q_k}}\dot q_k+\frac{\partial^2{r_i}}{\partial {q_j}\pa...

boy, that title should be changed

if duplicates are waymarkers to the canonical version, this is a useless waymarker

but

the only titles I can think of are basically the title of the open duplicate

anyone have better ideas?

2:00 PM

@EmilioPisanty yeah. Eg “why aren’t canonical velocities functions of canonical coordinates?”

That’s basically all that’s being asked, and it’s pretty much a duplicate of the older question’s title

(as is the explicit version: "Why does $\partial \dot{q}_i/\partial q_j$ vanish in classical mechanics?")

Q: How come $\frac{d}{dt}\left(\frac{\partial {r_i}}{\partial {q_j}}\right) = \frac{\partial {\dot r_i}}{\partial {q_j}}$ in Lagrangian mechanics?

2:42 PM

1

It is written in the Goldstein's Classical Mechanics text that $$\frac{\mathrm d}{\mathrm dt}\left(\frac{\partial {r_i}}{\partial {q_j}}\right) = \frac{\partial {\dot r_i}}{\partial {q_j}}=\sum_k \frac{\partial^2{r_i}}{\partial {q_j}\partial{q_k}}\dot q_k+\frac{\partial^2{r_i}}{\partial {q_j}\pa...

classical-mechanics lagrangian-formalism coordinate-systems differentiation

eh

not great

but as long as it's descriptive

yeah

could equally well say that as "Why do the Euler-Lagrange equations hold in Lagrangian mechanics?" if one wanted to avoid the latex in the title

3:21 PM

Is this a big deal? I don't know how valid the claim of potentially observable effects is, but I imagine it could be a big thing if that's a reasonable claim physics.aps.org/articles/v11/127

The idea that a black hole is linked to an expanding universe dates back decades. It's actually quite easy to patch together a Schwarzschild geometry and an FLRW geometry in a way that makes mathematical sense - whether it makes physical sense is debatable.

Lee Smolin used this idea as the basis for his book The Life of the Cosmos.

there's also the distinction between "makes physical sense" and "has observable effects"

And, it's been known for a long time that in a drastically simplified version of loop quantum gravity called loop quantum cosmology the Big Bang is replaced by a bounce. In effect gravity becomes repulsive at extraordinarily high densities so a collapsing universe reaches this density then bounces.

I hadn't realised the idea had been applied to a black hole, but I guess it's not unexpected. A collapsing ball of dust actually has a similar interior metric to a collapsing universe, so the fact a bounce exists isn't shocking.

But ...

The last I heard LQG was proving very hard to extend to a classical limit i.e. no-one has been able to show it corresponds to GR when you go to larger scales than the Planck length.

I would be pretty sceptical about any claims made for showing LQG predicts anything useful about macroscopic black holes.

@JohnRennie that's one instance of 'semiclassical physics' that I basically have no insight into

(which illustrates the problem of the word 'semiclassical', insofar as it doesn't clarify between quantum vs. classical vs. relativistic)

3:36 PM

and yet it's your name

your whole life is a lie

yup

I tried looking into semiclassical EM once

but snore

Aha, the article says:

> The result was obtained through an approximation of the full loop-quantum-gravity equations - similar to the one employed in previous work aimed at resolving the big bang singularity

So it will be the same approach as used in loop quantum cosmology.

Somehow I had never heard that the "big bounce" came from LQG...interesting

I also thought that LQG started with GR and would have a trivial classical limit for some reason. Don't know how far that's off

LQG is pretty darn complicated

But then again most QG theories are

3:52 PM

I have a book that's all of 120 pages and goes from introducing SR to what are supposedly details of LQG...I learned nothing

I've been meaning to take a look at Rovelli's book to see if that makes sense

Rovelli's pretty rough

Hope you know your QFT and GR well

Those both get a solid nope

Gravity has to be an emergent property. Non-linearity is always emergent. The universe is fundamentally linear.

Why must it fundamentally be linear?

It just is. Trust me on this one :-)

3:56 PM

b/c it'd be a huge headache if it weren't :P

Anyhow, it means LQG makes about as much sense as trying to quantise the Navier-Stokes equations.

starting paradigm stopwatch now

Damn, I've mislaid the Nobel prize application form.

@JohnRennie This statement bothers me.

I feel like there's a theorem that if you combine a bunch of linear systems, you get a linear system.

@rob it wasn't intended to be a serious statement about physics :-)

4:06 PM

@JohnRennie Okay. My sarcasm detector is on the fritz today.

I guess the operators which generate rotations are infinitesimally linear.

Unreasonable effectiveness of mathematics, blah blah.

Are all operators infinitesimally linear?

Not sure that really makes sense as a statement.

Can a reflection be made infinitesimal?

@danielunderwood The harmonic oscillator potential is infinitesimally quadratic.

@Semiclassical ahh right pretty much everything I've read has gone to the tune of "except reflections, which we're going to ignore"

@Semiclassical C,P,T are discrete rather than continuous symmetries.

4:10 PM

Guess I ignored them too much

yes, and that's what I had in mind

they're not continuous symmetries, so asking about whether the corresponding operators are infinitesimally linear makes no sense

Well all infinitesimal operators of the CPT symmetries are linear

(vacuously)

Also, operators do tend to be linear in the sense that $H(u+v)=Hu+Hv$

@Semiclassical I mean, linear operators, sure

But there are nonlinear ones!

yeah. they just don't tend to be the ones you deal with in QM

(except T, since that's antilinear)

4:13 PM

yeah

although IIRC there's a bunch used in various areas

Well I was thinking of linear as $O = I + \epsilon G$...but that's not what linear is in the first place

T is the weird one.

@Semiclassical This is circular reasoning. I'm pretty sure we invent linear operators in QM because we know how to deal with them.

Well, no, we use linear operators in QM because the results they give match experiment.

One place where nonlinearity does show up is if you go down the Bohmian route. You still have linearity at the level of wavefunctions, but the way the wavefunction relates to the trajectories isn't

Mostafa

4:48 PM

Pageviews of "suicide methods" on Persian Wikipedia: tools.wmflabs.org/pageviews/…

so, is the chat session still going on?

Anonymous

@EmilioPisanty In theory, yes (started 56 mins ago) ;)

Loong

I could tell you that we are just unpacking our Christmas package from Oak Ridge. ;-)

@Loong Well, that's an effective way to pique curiosity.

whomp

5:03 PM

anyways, I have a story to tell

last Friday I finally told my PhD supervisor about this site

was he in awe of your 71k rep

I didn't mention any points system and it didn't come up, nor would he have been that interested

I did hint that I may have spent some nontrivial fraction of my working hours during my PhD answering random stuff on the internet

but then again, that became a much easier sell with the Nobel-prize post in hand

probably don't have to sell what you do in your free time...

but never know, maybe he would have been uber impressed with the 71k rep

@enumaris well, the question is what happens with the time I spent on PSE while ostensibly working

@enumaris I'm rather more proud of the google rank of the CPA post than of the rep, tbh

getting 71k rep is work

5:08 PM

@enumaris good thing I'm at 81k, then =P

XD

101k if you include bounties offered ;-)

that's a lot of bounties

well

I think it's the right amount

you've offered more bounties than my total rep count

5:09 PM

but who am I to judge

@enumaris don't worry, you're not alone there

6 times more

@enumaris I've also been on PSE six times longer than you

@EmilioPisanty I'm curious about your advisor's reaction to the site.

jaw dropped at dat physix

@rob I started with the CPA post

which he liked

and then it was much easier to mention that, yes, I've written a number of posts on this site

and by a number I mean ~1.8k answers

but yeah, he took it well, thankfully

5:15 PM

Neat.

I think that since the point of a science PhD is to learn to generate new ideas, there's a certain amount of tangentially-related goofing off "on the clock" that's tolerated where it wouldn't be in another type of a job.

@rob well

Since you're all graduated now, I'd have been more surprised if your PhD advisor had even feigned distaste at your habit of excellent science writing.

goofing off is an integral part of jobs

Anonymous

@EmilioPisanty Umm, so was your advisor aware of the existence of this site before you told him? I don't have much idea of how well known PSE is, among the professional physicists. It would be interesting to conduct a survey.

I'm not sure the amount of time I spent ( / spend) on PSE falls within that 'certain amount'

@Blue he'd probably seen it but not noticed

he didn't go "oh, stack exchange"

@rob more importantly, I would argue that the primary benefit has been the writing practice

Anonymous

5:21 PM

@EmilioPisanty Ah, was expecting that :P

though it's not necessarily a benefit that I might have been able to articulate (or successfully defend) in, say, 2014

Anonymous

Yeah, even my writing skills improved a lot after I joined SE. That's surely one plus. But then, I've also spent a considerable amount of time procrastinating here.

Example: the xkcd nerd sniping comic came out a couple of days after my PhD advisor and I spent more than an hour discussing the infinite grid of identical resistors.

nerd sniped yourself

3

In fact I think we ended our discussion with a comment like "how long have we been talking about this?"

5:25 PM

Good thing there weren't any buses nearby

heh

Anonymous

@rob It's a fun problem though. I still couldn't get myself through the whole solution

Anonymous

> Consequently we have the "well-known" result

Anonymous

Well known to whom, I wonder

resistance is futile

very well known

A: What is Chirped Pulse Amplification, and why is it important enough to warrant a Nobel Prize?

5:51 PM

Maybe it's one of those "obvious once you've done it" things

vzn

@EmilioPisanty what do you mean "nobel prize post in hand"?

Anonymous

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