The h Bar

I mean I just write raw SVG on my articles

there's no file involved

Of course, the SVG code has to be well-behaved. It can use SVG or CSS animation techniques, but not JavaScript.

also it has <foreignobject> tags which I don't think will behave nicely here

Probably not.

I don't know what Sage does to handle MathJax in a SVG. I doubt it's compact, but it's most likely totally portable. Matplotlib embeds any fonts you use into your SVG...

My article on GR measurements is a giant mess

I need to edit it a bit I think

and more to the point, finish it

I just need to learn functional analysis first, a small task I'm sure

1:13 PM

Here's some Python-generated SVG. An equilateral pentagon inscribed in an ellipse.

sagecell.sagemath.org/…

Here's a temporary file of that. It should display for a while, until it gets kicked off the SageMathCell server.

Why do analysis people use $\Omega$ for subsets of $\mathbb{R}^n$

One of the least pleasant letter to write

Omega's easy. But I've been writing since I was a kid, doing electronics. I'm not fond of $\zeta$ or $\xi$, though. :)

You'd think xi would be easy, but I tend to mess up the relative sizes of the various loops, in my effort to make sure it doesn't look like $\varepsilon$, or something else.

I can write omega but it will be a little curvy

1:29 PM

Another annoying one is $\varpi$. It looks too much like $\bar\omega$

How often do you use the varpi

I'm not sure I've ever used it for a paper

I never use it myself, but I've seen it in maths papers. Eg, number theory stuff about frequency & sums of primes. IIRC.

2:34 PM

Why is all the functional stuff about elliptic equations

You'd think hyperbolic equations would be also important

7:02 PM

@ACuriousMind @Slereah Yo

Do you guys know this normal ordering crap

Sure

aye

In Polchinski vol 1 page 239 there's some field $X(z, \overline{z})$ that breaks into the holomorphic and antiholomorphic part $X = X_L(z) + X_R(\overline{z})$ and the guy writes the vertex operator $V_{k_L, k_R}(z, \overline{z})$ as $: e^{i k_L X_L(z) + i k_R X_R(\overline{z})} :$

Can you explain me what this means?

now that's an advanced application of normal ordering :P

How do I normal order something defined just in a single hol-antihol coordinate pair

Not my question, a friend's

7:06 PM

that's CFT normal order, see physics.stackexchange.com/q/46975/50583

but see also physics.stackexchange.com/q/232705/50583 for Polchinski's idiosyncrasies

I'll relay this back to him and get back to you if he has queries

note that the "ordering" comes in here because the Taylor series expansion of the exponential contains arbitrary products of the two $X_{L/R}$, and physicists would probably describe the intention here as "just apply normal ordering order by order to the Taylor expansion"

@BalarkaSen I was going to ask what madness overtook you that you were reading string theory :P

oh sure

Age old excuse

@ACuriousMind OK now I want to understand: the exponential contains terms which are products of bunch of $X_L$, $X_R$'s. Pick a particular term, how do you normal order it? Polchinski's normal order is defined for a product of a pair of operators in $z_1, \bar{z}_1$ coordinates and $z_2, \bar{z}_2$ coordinates respectively

My question, not his

@BalarkaSen The $X_L(z)$ or $X_R(\bar z)$ are implicitly functions $X_L(z,\bar z)$, $X_R(z,\bar z)$

the notation just means that $\partial_{\bar z} X_L = 0$ and $\partial_z X_R = 0$

7:15 PM

OK, what is $:A(z, \bar{z}) B(z, \bar{z}) :$? I only understand $:A(z_1, \bar{z}_1) B(z_2, \bar{z}_2):$

ah, just normal order the thing on the right and then take $z_1 \to z_2$

But $:A(z_1, \bar{z}_1) B(z_2, \bar{z}_2): = A(z_1, \bar{z}_1) B(z_2, \bar{z}_2) + \eta^{\mu \nu} \log(|z_1 - z_2|)^2$

If you take that limit my guy goes to zero

Well, blows up

Wouldn't want your guy to blow up

@BalarkaSen well, the thing is that the non-ordered $A(z_1,\bar z_1)B(z_2,\bar z_2)$ is divergent, too

the normal order is (see the posts I linked) exactly the non-divergent part

Yeah I was reading that post, that's relevant

Shit seems to have essential singularities kek

7:23 PM

happens a lot in QFT!

well, it's the old "quantum fields are really distributions and you shouldn't be multiplying their values at a point" :P

but physics is like "but I want to" and so we are blessed with OPEs

Normal ordering is essentially baby's first renormalization

Remove divergences from the Hamiltonian

Can anyone help me understand this : The surface currents are induced by the magnetization of the medium by the applied magnetic field and therefore depend on the magnetization M of the specimen.

The currents (because of electron movement in atoms and because of spin_ are always present in the material,

so what exactly is induced here?

induced means, that something which wasn't present, because of reason now becomes present

How exactly the external magnetic field induces something which was present all along?

The only thing I can understand is that the magnetic field, redirects the magnetic moment of the atoms, and that's it.

Is this what it;s meant with induced ?

@imbAF well, yes - and the "redirection" of the magnetic moment happens by the magnetic fields "inducing" the electron current to orient themselves differently

I think you got the idea, this is just using "induce" in a slightly looser sense that you seem to expect

yes it induces

redirection

not the current itself

@ACuriousMind I have one question for the dielectrics. As you know the following equation is true: $D = \epsilon_0 E + P$

is E in this case, the electric field inside the dieelctric ?

7:38 PM

oh no, I'm horrible with EM in media!

I don't want to say anything wrong about that

I see

@ACuriousMind If you want to make it relatable, it's related to the Gordon decomposition of the Dirac field, IIRC

lol

Gordon decomposition

In mathematical physics, the Gordon decomposition (named after Walter Gordon) of the Dirac current is a splitting of the charge or particle-number current into a part that arises from the motion of the center of mass of the particles and a part that arises from gradients of the spin density. It makes explicit use of the Dirac equation and so it applies only to "on-shell" solutions of the Dirac equation. == Original statement == For any solution ψ {\displaystyle \psi } of the massive Dirac equation, ( i...

is a particle divisible in infinity or it has an end, and if yes, which is that end ?

7:47 PM

whaaaat

your science fiction answer would be?

Also that

I'm not even sure what you mean

well

molecule - atom - proton - quark -??-??....

As far as we know for now quarks are elementary

hmmm

their gyromagnetic factor even in QED is not an exact number

but smth like 2.000 and a bunch of numbers

and even if that wasn't the case

7:50 PM

yeah but quantum effects are involved

nothing is build by itself, pretty paradoxical thing to be true

from*

Another question : what's the difference between a dead human and an alive one in terms of quantum mechanics ?

I think you can find the difference with just plain old classical mechanics

let's stick to the micro world tho

like for example, do they have both the same stored energy at rest?

why stick to the micro world

Might as well ask the difference between a bowl and a cup in terms of quantum mechanics

8:06 PM

hmm...primary change I can think of, nr of electrons rotating around the nucleus

should be an indicator of different materials?

+ studying the human life, you are trying to have a quantum explanation of life and death.

can't apply those concepts to a bowl and a cup

if you want a fairly boring definition, the most fundamental one I've read was that a living thing will draw Gibbs free energy from their environment

although of course that's not true of just living things, but that's a pretty basic difference between a living and dead organism

@imbAF reductionism doesn't work like that

a rectangular plate and a circular plate have no "quantum explanation" of their difference, the difference is purely classical and macroscopic

yes, if you would look it like that, only via a classical viewpoint you can talk about their shape (in this case).

likewise, a living and a (freshly) dead multicellular organism don't differ in their molecular makeup or anything like that, just their neurons have stopped firing/their blood has stopped flowing/whatever

But all I was trying to say is that, you can study human biology etc from an inanimate pov

8:16 PM

if you're doing biology you're pretty much by definition not studying inanimate systems

And find solutions about different deceases etc simply observing the micro world

I'm sure there's plenty of molecular differences between a live and dead cell, but those probably don't boil down to a simple QM argument, except maybe in that free energy idea

just because the molecules aren't "alive" when looking at molecular biophysics doesn't mean it's a science of "inanimate" things - it's the science of what happens inside of living things on a molecular level

Also "alive" is probably a bit hard to define here

I'm sure from a microscopic point of view, a lot of biological processes still happen after an organism dies

you can have many "biological" processes happening in a test tube

8:18 PM

just less and less so as time goes on

just...that doesn't explain anything about the difference between a living thing and a dead thing

Example : Someone who suffers from Diabetes, if you would speak as a biologist/ doctor you would recommend some medicine, which had some side effects. But you could look it this way: Someone who suffers from diabetes, on a quantum mechanical level has a certain "group" of subatomic particles on a lower amount then another body. So how do we try and change that, so this number can increase to the same levels, that a normal entity has them

Yeaah sloppy explanation, but can't do better

@imbAF but that's not the case - diabetes isn't caused by "subatomic particles"

not caused

it's a complex defect of the biological processes that normally process sugar

8:20 PM

but there is a difference in chemicals or w/e else in your body

you lack insulin for example

sure, insulin isn't subatomic

It's build from molecules,

everything is build from subatomic particles, at least what is considered as matter

insulin is a (very complex) molecule

yes

My idea is that there is no real difference between living things and objects. A bunch of particles arranged differently

in different quantity / different arrangement / different movement etc etc

I think you're confusing reductionism and monism here. Our modern understanding of living things is that they're just the same as everything else - made of matter, and everything they do is ultimately explainable by the same laws that govern all matter

that's monism

8:23 PM

and reductionism ?

but it doesn't imply that you can usefully reduce every explanation of how a thing (living or not) works to quantum mechanical or subatomic explanations

and what's the counter argument to that?

thats (a common caricature of) reductionism

@imbAF note the usefully

I'm not saying you can't in principle do this, but in practice the reductionist explanation will be so hopelessly overcomplicated and intractable you can't actually do anything with it

with our current level of understanding and intellect sure

50k years later, who knows

take classical thermodynamics: In principle the behaviour of a gas in a container and the pressure and so on is just a function of the position and momentum of each particle of the gas

8:26 PM

But I like monism, apparently. I think you can explain everything in a fundamental way, qm way, if that's what fundamental means in this case

but no one thinks about gases like that - they do statistical mechanics and talk about pressure, temperature and equilibrum instead

in principle the explanation in terms of the individual gas particles is valid, but it's not useful in practice

and not because we lack understanding or anything

so basically we study living things in a classical way, right ?

not sure that's a useful statement, either - a lot of molecular chemistry/physics is based on our understanding of QM

but we're not doing QM like "particle in a well QM" there

But when you treat a disease, you talk about what will it do to your body, not to your building particles

sure

8:28 PM

so it's classical

but our "study of living things" is very broad - someone treating a broken leg might not care about details of protein folding, but people studying a particular process inside our body (perhaps one causing a disease by making the wrong protein) might

which is an attempt of a non classical way of dealing with the problem

it simply goes up to a certain level of complexity

classical/quantum isn't a hard border

at the lowest level, everything is quantum, but describing everything in those terms gets too complicated quickly, so we do approximations

I am not disagreeing with anything you said.

there's a sliding scale of approximations between "fully classical physics" and "fully quantum physics"

8:31 PM

I just think, that if we would be able to study living things in such a detailed way, maybe we would be able to cure things that we currently cannot

and I can't prove that xD

I'm pretty sure modern medicine is not currently limited by our understanding of quantum physics :P

the body is a very complicated thing, and it's the interactions between its countless subsystems that are hard to understand, not the molecular physics at a single receptor or whatever

Do I have to take out the metabolic pathway diagram

Yes ofc

@Slereah pls no

(this perhaps wasn't true some decades ago, but it's true today - we can model proteins and understand how one molecule fits into another, etc)

This is biology

8:34 PM

was fun for me, but not a deep dive into the micro world

hence I had to choose physics :D

@ACuriousMind one more question

How can, in this reality, energy conversion and Bing bang be true simultaneously ?

what is the bing bang

is that that strip club in the Sopranos

assuming those are typos, see physics.stackexchange.com/q/10309/50583

:D

bigus bangus*

if they aren't typos, I won't be converted into a follower of Bing Bang via energy or any other means

lmaooo

big bang*

so ?

8:39 PM

so what?

I already posted a link to that same question on the main site

Ok, gonna inspect that

The time-translational invariance is broken, so via Noether's theorem, one doesn't expect a conserved quantity. Also, if one defines the "total" stress energy tensor as a variation of the action with respect to the metric tensor, it vanishes in GR because the metric tensor is dynamical and the variation has to vanish because it's an equation of motion (Einstein's equations).

If the space is asymptotically flat or AdS or similarly simple, a conservation law - for the ADM energy - may be revived.

I need multiple books to be able to understand this answer

the simple answer is "energy conservation is not quite as absolute a law as you've been led to believe" :P

good

because if the universe would have been here all along, that would have been the lamest revelation ever

for me

or maybe it is conserved

in this reality and fabric of space time

as an after affect of the big bang?

Noether's theorem relies on the boundary conditions of your spacetime manifold to be not too bad to work

Hence why it is not gonna work well next to a singularity

Ehhh Physics is tough. specially for some1 like me who needs to know the answer to every tiny single why.

8:50 PM

As Earman would put it

This is what happens

It gets tiresome after a while

naked sigularity?

Q: I'm asking something really obvious. Why is is marked as "unpublished personal theory"?

9:03 PM

@Slereah could you help me with two illustrations and 2 explanations ?

Physics Meta

11:19 PM

0

I'm asking a really obvious question; many people told me that they had this thought and question, so why is this marked as a personal theory (Is mass the source of space-time?)? It should be possible, in my opinion, to ask questions like, "Why are we sure that Earth is a sphere and not a flat su...

discussion

DIRAC1930

If I have a Grassmann field $\psi^\alpha$, can I just commute the symmetry group elements with eachother?

I.e. with suppressed indicies is $G_1 G_2 \psi_1 \psi_2 = G_2 G_1 \psi_1 \psi_2 = G_1 \psi_1 G_2 \psi_2 $?

Sorry I meant $G_1 G_2 \psi_1 \psi_2 = G_1\psi_1 G_2 \psi_2$

DIRAC1930

11:49 PM

Are classical fermionic fields Grassmann numbers?