The h Bar

3:30 AM

@PM2Ring nice! thanks for alerting me to this phenomena. i have to bookmark this for later, as i'm not equipped for QED level - but it's fantastic & seems to confirm my suspicion that even vacuum EM has nonlinearity

5:45 AM

@TejasDahake If magnetic charges existed they would be a source of a magnetic field in the same way an electric charge is a source of an electric field. However as far as we know they don't exist.

You may have heard them referred to as magnetic monopoles.

7:57 AM

Today I learned the fancy name for the many roles a tensor can have : en.wikipedia.org/wiki/Tensor-hom_adjunction

Wikipedia is unreadable after these changes in format

yeah idk what they're doing

Jan 19 at 17:29, by ACuriousMind

the new Wikipedia layout is making me consider to make a Wiki account just to be able to customize it to the old layout

Yeah you can change it back apparently : en.wikipedia.org/wiki/Wikipedia:Skin

ugh yeah i hate it

8:12 AM

cohost.org/two/post/868713-on-the-subject-of-ch

i presume someone has a plugin to append ?useskin=vector-2022 to all wiki urls

oh nice @bolbteppa

Man the old one is just miles better

The old one is very old school internet

Some people probably said they needed a more modern design, daddy-o

Which is how websites are typically ruined

Aren't you a bit young to be grumpy old men? That's my job :-)

just setup @bolbteppa's link solution. works nicely :)

lol @JohnRennie

8:23 AM

@JohnRennie it's a mindset, it's not about age :P

I hate when things change

FWIW I don't like the change either. But I still find the site usable, it's just that it will take some getting used to.

Oh well, when I used to play videogames I hated every update changing game mechanics even in the slightest. Change can be frustrating :P

In the case of Wikipedia I don't care much because I rarely make extensive use of the site

@JohnRennie oh, it's usable, I just dislike that it's following this design trend of having a lot of empty space on the sides

reddit is another one the do-gooder format changers helped wreck

That's why mobile is less frustrating

8:29 AM

I understand that generally this increases focus and seems to guide most people better, but I like my screen cluttered :P

A Professor of mine used to say physicists tend to be a bit conservative at times, I guess I agree

@ACuriousMind Agreed :-)

And btw, after that he proceded to smear books that call $\vec{B}$ the magnetic field :P

@Mr.Feynman Only if they derive from Lagrangian

@Mr.Feynman That is what it is

"We can also make Vect into a monoidal category with direct sum as the ‘tensor product’ — this may seem perverse, but it’s actually very useful."

@Slereah I never said I agree :P

I was talking about $B$ and $H$ though

8:40 AM

Still, $B$ is the magnetic field in that context!

Once again, I didn't say I agree :P

Although old books call $H$ the magnetic field and $B$ the magnetic induction

I prefer to stick with the $H$- Field and the magnetic field $B$

I don't believe in $H$ anyway

That's just a fake field made by ignoring your matter term

Maxwell equations in matter are ugly :D

Fortunately you don't use such things much in QFT

The matter is in the current term

8:57 AM

Yeah, I mean those written in terms of $D$ and $H$

10:14 AM

also they hid 'random article'. so if you're not doing kb shortcuts its 2 clicks away

10:57 AM

Gotta do some data analysis on emails and boy that is not good

Emails have no standards

it's chaos

11:22 AM

@Slereah are you talking about technical standards or about the fact that people have very different ideas about how emails should be structured or what they should contain :P

11:55 AM

@ACuriousMind The body of the email

Basically you have a header, the text, a signature and quotations of previous emails

and there are no standards at all for all this

It's all mail provider dependent

I mean if you're unlucky the mail body is a bunch of HTML

Oh no, things are very dire most of the time

Except for like company chainletters, nothing is in HTML

You just have <p>[all the email]</p>

also most corporate people have gigantic signatures which doesn't help

12:20 PM

Time's up

1:11 PM

@bolbteppa oeis.org/…

oeis.org/A053016

what about the platonic solid of zero faces

ah, the infamous d0

The {0,0} polyhedron

Considering the respective contexts in which each of them operated, do you find more astonishing Newton's or Einstein's work on gravitation?

1:18 PM

I don't really know the context of the Newton era that well

I do know that Einstein certainly struggled with GR his whole life

I don't really think people understood GR that well until the 60's at least

at least broadly

Newton-era mechanics is hard to get into because it was a very Euclid-based kind of formalism

I tend to think that what Einstein did was far more impressive but I feel like I might be biased from 4 centuries of Newtonian gravitation :P

It was based on Hooke's work on central forces from what I remember

@Mr.Feynman why do you assume I find either "astonishing" :P

@ACuriousMind Because you'd be lying if you said you don't think coming up with GR is at the very least remarkable!

@Slereah Newton's worst enemy

1:33 PM

I mean, yes, these were clever people. Why do I have to rank them?

@ACuriousMind Only one of them gets to live

No, no. I don't want to know "who's better"! Just asking who amazes you (if it's the case) more based on your personal thoughts

It can be a bit tough because I can roughly put myself in Einstein's place as far as where he was at prior to relativity, since physics education hasn't change that much since, but Newton is kind of a different bag

like using coordinates was cutting edge stuff

1:59 PM

@Mr.Feynman I don't really think about people that way

like, sure they're impressive, but ranking them feels very artificial to me

Newton did a lot more magic than Einstein

2:16 PM

@ACuriousMind I see

Btw, Landau had a log scale of physicists

3:28 PM

hello, i encountered a point in sakurai where he says "here, we have an important result: infinitesimal rotations about different axes do commute if terms of order $\epsilon^2$ and higher are ignored.", where the rotations are $R_x(\epsilon)$ and same format for y and z. i am wondering how one can know when they are in a situation where it is reasonable to ignore these terms? he cites an example as angular velocity, but im confused why this is a useful result in general.

also

SQUAWK

there was a sparrow flying through the corridor in my uni today. he was freed by a professor

3:46 PM

@Relativisticcucumber I mean, this is reasonably if and only if you're staying infinitesimally

$\epsilon^2 = 0$ is one possible definition of what $\epsilon$ being "infinitesimal" means

also I'm very puzzled why so many texts seem to think that "infinitesimal rotations commute to first order" is a statement worth stressing: It seems very natural to me that the commutator of two transformations parametrized by $\epsilon_1,\epsilon_2$ will at lowest order depend on the product $\epsilon_1\epsilon_2$ and so this is a statement completely unrelated to the fact that the infinitesimal transformations under consideration are rotations

very little rotations make a little square

all this is is the BCH formula: $\mathrm{e}^{\epsilon A}\mathrm{e}^{\epsilon B} = \mathrm{e}^{\epsilon A + \epsilon B + \epsilon^2 [A,B] + \mathcal{O}(\epsilon^3)}$ which at first order gives you $\mathrm{e}^{\epsilon A}\mathrm{e}^{\epsilon B} = \mathrm{e}^{\epsilon A + \epsilon B} = \mathrm{e}^{\epsilon B}\mathrm{e}^{\epsilon A}$, i.e. all transformations commute to first order!

seems like a rather useless observation to me :P

Physicists just love a good first order approximation

4:03 PM

what does BCH stand for

@Relativisticcucumber Baker-Campbell-Hausdorff

parz

Hello!

Q: Increasing radial velocity even if radial acceleration is zero

ah thank you

it is somewhat interesting to me that infinitesimal rotations commute, but large ones do not. i guess it is not that hard to explain tho. hmm is the idea just that these negligible terms will add up over many rotations, so in bulk they are not negligible ?

Tejas Dahake

0

In one of the lectures on Mechanics in polar coordinates, my professor gave an example in which he showed that even if the radial acceleration of a particle is zero it can have an increasing radial velocity which is quite ambiguous for me. How can that happen !! I asked him the reason but he didn...

newtonian-mechanics classical-mechanics

What is being asked in this question?

As the velocity is changing with time that means acceleration is present

@ACuriousMind there is a branch of Math called smooth infinitesimal analysis where this is postulated iirc

4:21 PM

Very smol rotation looks like a translation

@Relativisticcucumber Infinitesimal rotations (or well as ACM said any kind of continuous symmetry transformations) commute in the sense that the difference is at second order and "infinitesimal" means "consider first order pieces". The content of what you ask is exactly the BCH formula linked above, indeed commutators correspond to second order or higher

4:39 PM

oh, i see what you mean

okay thanks

A: Why are infinitesimal rotations commutative, whereas finite rotations are not?

20

Infinitesimal rotations don't commute exactly if you're accurate enough. An infinitesimal rotation may be written as $$ \exp( i a A ) $$ where $a$ is an infinitesimal "angle" and $A$ is a combination of generators. Such an object doesn't commute with the analogous object $\exp(ibB)$ in general. ...

@Mr.Feynman whether you call this "smooth infinitesimal analysis" or "synthetic differential geometry" is a matter of taste and how much you like categories :P

@Slereah again, any smol transformation looks like a translation!

4:57 PM

@ACuriousMind you've just thrown my future self straight into a rabbit hole

5:11 PM

@ACuriousMind I mean yeah

exponential map something something

7:55 PM

I'm interested to hear an opinion about this from people who have some "mileage" with General Relativity...
Do you think it's better to first learn the subject the "classical way" - which I would sloppily call the "Non-manifold" formulation? When I say better, I don't mean just as a matter of taste. I mean also practically how much of the modern approach using Manifolds and defining the Connection, Metric, etc. on them requires to unlearn and/or conflicts with the more classical approach. So it is also a question regarding simple "cost effectiveness"

it depends what you want to do I guess

you can just learn it as a field theory and then it's fine for doing gravitational physics

just work out the dynamics of stars and such

Yes that's a very relevant question. For me it's a matter of understanding the subject deeply, I am not learning to pass a test, nor even participate in any active research (probably)

So "field theory" I guess is what I find for example in Landau & Lifshitz Vol. 2? :)

Yeah

also Weinberg's book is very field theory focused

No dilly dallying with topology and such

I guess that's a big part of the question too. How much of it is dilly dallying, and how much of it really adds insight to the subject...

Perhaps I am making too much of it, and after some point (which I probably haven't reached yet) you can go back and forth between those languages without effort...

I...wouldn't worry about this too much? If you want to be able to converse with other people about the topic easily you need to learn most of the approaches anyway to some degree