The h Bar

naturallyInconsistent

00:59

@imbAF It doesnt work. Throw it aside.

Silly Goose

03:02

why does $S'_{pp}$ make perfect sense for massless particles?

qwerty

03:18

ooo finally a q from silly goose I know something about :) qmechanic talked about it in some of his answers on the main site. it makes sense because the einbein which is here eta is unspecified. it's like a gauge freedom

you've removed the sqrt from the original action

what book did you get this from btw?

the reason the sqrt action is senseless for the massless case is because when you try to vary it you get space like parts of the curve and time like parts

this is mentioned in wald :)

that book skips a few lines of working

sorry forgot to reply ping you @SillyGoose

PM 2Ring

@imbAF The Dirac sea model was a first step to interpret the negative-energy quantum states predicted by the Dirac equation. It was proposed before the positron (or any other antiparticle) was discovered. It's totally superseded by QFT. It's only interesting for historical reasons, like Bohr's orbitals.

@imbAF When posting handwritten mathematics, please consider my suggestions here: math.meta.stackexchange.com/a/33091/207316

> if you really must post an image, please try to make it neat and clear, with good lighting and no shadows, and no crossed-out material or inscrutable little blobs. Use a clean page, not one with pen impressions on it, or with anything showing through from the other side.

2

Silly Goose

03:37

@qwerty this is from polchinski's string theory vol. 1

qwerty

@SillyGoose I think I downloaded that for this section :)

Silly Goose

@qwerty hehe

naturallyInconsistent

@SillyGoose I'm seriously suspicious of this text. Yes, we use the word tetrad even if it is not 4D, but tetrad is synonymous with vierbein and there is a n-D version, vielbein. However, that is not at all what this text is using. This $\eta$ is not a tetrad at all. It is an einbein, which is totally something else. You should have written down $S_{pp}$ so that we can talk about this easier.

Silly Goose

here is $S_{pp}$

qwerty

but yeah the einbein $\eta$ is unspecified for $m=0$ and if you pick for $m >0$ the choice $\eta = \frac{1}{mc} $ you get affine parameterised curves

:) I really liked this when I learnt it

Silly Goose

03:43

in what context did you all learn about this einbein business 0:

qwerty

I self learnt it when writing up my PhD thesis and qmechanics answers helped out for some of it

twas not in the literature for my field

Silly Goose

what was your phd thesis on?

qwerty

like a lot of what I thought was important

@SillyGoose mhmm I don't want to get more specific than late universe / non HEP cosmology

I had a bone to pick with a lot of the lit lol

twas non rigorous

(for a specific part, not even just non rigorous, handwaving where handwaving = step clearly not permissible)

PM 2Ring

@Slereah Yeah. The spatial incoherence is an instant giveaway that it wasn't created by a human. Ok, sometimes humans do that kind of thing deliberately, like Escher, but you can tell there's some artistic purpose to their bending of the rules. But GenAI image synthesizers don't give that impression, it just looks like a mistake.

There's a simple example in meta.stackexchange.com/a/403417/334566 The scene is mostly coherent, apart from her right arm. Here's one from chat.stackexchange.com/rooms/155368/thinking-out-loud produced via OakBot i.sstatic.net/1KIH07l3.jpg What's going on with the hair and scarf / hood of the girl in the foreground?

GenAI can easily draw hands with real fingers, but it often has problems drawing hands with integer fingers. ;)

naturallyInconsistent

Anyway, $S_{pp}$ is linearly proportional to $m$ and clearly is nonsense when $m=0$, whereas this answer by Qmechanic said that the einbein is not integrated out when $m=0$, in which case then you can see manifestly that it is sensible.

2

A: Massive vs. massless relativistic point particle in einbein form: Difference in the gauge structure?

The action (1) has a world-line (WL) reparametrization gauge symmetry in both the massive and massless case. An important difference is that in the massless case one cannot eliminate/integrate out the einbein field $e$, cf. e.g. this Phys.SE post. In contrast such elimination in the massive cas...

@SillyGoose Polchinski definitely knows that einbein isnt the same thing as tetrad, so this is an egregious mistake

qwerty

04:00

@naturallyInconsistent I thought you could still vary a curve even if you have $m=0$ and it being proprotional, it's the sqrt thats problematic. this was according to wald iirc

123

Hello Everyone...

naturallyInconsistent

@qwerty see Qmechanic's answer

I'm not claiming to be an expert on this; sqrt or m, something breaks down

qwerty

@naturallyInconsistent as far as I can tell it's not in contradiction with what I was saying. but yes. it breaks down.

Lucky Chouhan

04:16

Greetings @naturallyInconsistent (~~Miao Miao ),

naturallyInconsistent

Miao miao~~

Lucky Chouhan

Pineapple Island is in danger :(

naturallyInconsistent

why????

Silly Goose

oh no

qwerty

04:38

seeee

it comes up ALL the freaking time

F :<

naturallyInconsistent

@qwerty nothing a little ignoring cannot handle~

qwerty

too late, I've made it a side quest >=]

I am basking in the glory of once again, the freedom to make my own mistakes and not someone elses'

highly underrated! :D

naturallyInconsistent

lol

enjoy~~

qwerty

thank you! ❤️

think_meaning_builds

04:53

🙈🙉🙊

Lucky Chouhan

@naturallyInconsistent Because of China,

@qwerty What does this mean? I've not got it :'|

qwerty

@LuckyChouhan your academic/intellectual freedom as a grad student is heavily dependent on your advisor. the power imbalance is pretty extreme

you can find yourself in sticky situations.

Lucky Chouhan

@qwerty Yeah, I agree. It is very crucial in research to get an advisor who matches your frequency, that's why when I see many Abel and Nobel Prize laureates most of them are professors and they really had good advisors,

qwerty

05:11

there are so many variables I don't think much of it is in our control. a lot of it is just luck: right place, right time, right project, right person.

your experience can be drastically different if those variables differ.

Lucky Chouhan

@qwerty yeah, what do you think do you have the type of advisors or colleagues you want?

qwerty

@LuckyChouhan me? now, or during my academic career?

Lucky Chouhan

@qwerty yeah, I don't know you're a student or working professional:') So yeah in your academic career..

qwerty

05:29

I don't know if I can go into the sort of specifics that would make my story understandable in a public chat; I will think about what exactly to answer later tonight and get back to you. I do want to answer as I believe this is an important topic

naturallyInconsistent

@LuckyChouhan did something happen?

qwerty

I'm conscious that oftentimes and especially on the internet people throw around loaded words without regard for accuracy or acknowledgement of their weight. I don't want to give the impression I'm doing that if I say something vague.

John Rennie

05:51

Cooking with physics!

PM 2Ring

CERN should make sauerkraut to help pay their electricity bill.

Nov 24, 2023 at 12:23, by PM 2Ring

Early this year, someone asked Hank Green what a spoon of protons would taste like. https://youtube.com/shorts/vJMvFIqU8hk?si=r_aKCWLyHRxS-coc So I got curious about how hot it would be. If I'm calculating correctly, ~1 mg of protons confined to a ball of radius 1 cm would be a little more energetic than LHC beam protons.

Lucky Chouhan

06:13

@qwerty sure,

@naturallyInconsistent we all know about the tension between China and Taiwan, so I don't have much to say China says Taiwan is their territory (Remember one China Policy) and they will make it happen and there is also possibility of war in Korean peninsula. Oh god, war war war all the sides. Israel doesn't care about UN's resolutions and banned UN Chief :( What is happening in Aisa, huh

naturallyInconsistent

@LuckyChouhan but if there is no immediate event to consider, miao miao would be confused as to what it is you are referring to. The people here have been threatened with war from them for decades; it is usually ignored, and mostly safely so.

Ryder Rude

07:19

hi

think_meaning_builds

hi

ACuriousMind

07:56

@naturallyInconsistent The einbein is the 1d version of the vielbein, Polchinski is correct. Note that one defining characteristic of the vielbein is that its square (suitable interpreted) is the metric and that's what the einbein is.

(the names could've told you that - the vierbein (tetrad) is German for "four-legs", the vielbein is the generic form meaning many-legs, and einbein means one-leg)

qwerty

@ACuriousMind I thought that was the case but wasn't confident enough to say anything

is the einbein the same as a threading lapse function or does it just squeak the same?

ACuriousMind

I don't know what a "threading lapse function" is

I know the lapse function from the ADM formalism

qwerty

oh well nvm then

yeah that's not the same when you do threading versus slicing

Slereah

The Einbein's a weird thing because it's the frame field, it's a vector field and it's a volume form all at once

And people aren't typically very clear about which meaning they mean when they write it

qwerty

08:16

I was told you can just think of it as a parameter like a Lagrange multiplier

I didn't think of it as any of those other things

ACuriousMind

It's only a proper Lagrange multiplier in the massless case

at least in the Lagrangian action - in the Hamiltonian action it's always a multiplier since it's what enforced the constraint $p^2 = m^2$

qwerty

what do you imply by an improper Lagrange multiplier?

ACuriousMind

a Lagrange multiplier $\lambda$ should occur in the action in a single term of the form $\lambda f(x)$, where $f(x)$ is its associated constraint

but in the massive Lagrangian action, both $e$ and $e^{-1}$ occur

qwerty

hmmmm

what's the physical intuition of this "should"?

sorry, I actually never used Lagrange multiplier more than a couple of times many years ago

ACuriousMind

I mean that's just the definition of what a Lagrange multiplier is :P

qwerty

08:29

@ACuriousMind it gives you the mass shell condition in the Lagrangian formulation too

so I kinda thought it just made sense that way

Ryder Rude

@think_meaning_builds hi

ACuriousMind

@qwerty oh, I'm not saying it's completely wrong to think about it that way - as I said, in the Hamiltonian formulation it's always a standard multiplier

I'm just pointing out that in the Lagrangian action it does not technically fulfill the definition of how a Lagrange multiplier looks

qwerty

but the comment about the mass shell condition?

ACuriousMind

What about it?

qwerty

I thought you were implying it only comes from the einbein in the Hamiltonian formulation and that tied in to why it was "proper"

Mr. Feynman

08:33

Why hasn't ACM mentioned QoGS yet? :P

naturallyInconsistent

@ACuriousMind but we dont use it like we use a vierbein? For the massive case, where it is most well-defined, going by how you said it, it is a mutated form of the Hamiltonian action's Lagrange multiplier into the Lagrangian action; we don't usually use the vierbein anywhere near like that.

Mr. Feynman

By the way, I think I also had some trouble understanding the einbein as a Lagrange multiplier

ACuriousMind

@naturallyInconsistent well that's because differential geometry in 1 dimension is not very interesting :P

doesn't change it's a vielbein for n=1

Mr. Feynman

Hey, 1D is the best for everything

1D calculus is so much neater than 2+D

naturallyInconsistent

@ACuriousMind interestingness or not is not my point here; I wont deny that you are saying that it is a vielbein for n=1; I'm saying that we dont use it like we use a vielbein at all.

qwerty

08:38

@naturallyInconsistent mutated is a bit rude ;( I like lagrangians

Hamiltonians are scary

naturallyInconsistent

@qwerty miao miao likes Lagrangians too; why would that be a rude anything??

ACuriousMind

@qwerty No, that's not what I meant. It's just that it's a proper constraint in the Hamiltonian formulation (in the sense of the constrained Hamiltonian formalism); in the Lagrangian formalism it's just an equation of motion

qwerty

@naturallyInconsistent I guess connotations of mutations - mutants

naturallyInconsistent

@ACuriousMind here you said it is a multiplier in the Hamiltonian action?

qwerty

I am so tempted to drop a link to my thesis here lol

naturallyInconsistent

08:41

@qwerty mutatis mutandis

ACuriousMind

@naturallyInconsistent yes?

I feel people are trying to interpret much more into my words here than I actually meant :P

naturallyInconsistent

@ACuriousMind and you say it is a proper constraint later; just to be clear, you mean that it is a proper constraint enforced via Lagrange multipliers?

qwerty

@ACuriousMind you only have yourself to blame for not being precise/rigorous! ;p

ACuriousMind

@naturallyInconsistent Constraints appear in the full Hamiltonian action via Lagrange multipliers

naturallyInconsistent

could it not be something else?

Like, Dirac had a whole spiel about constrained Hamiltonians

ACuriousMind

08:43

yes, I mean exactly that formalism; the condition $p^2 = m^2$ is exactly a Hamiltonian constraint in Dirac's and Bergmann's sense

naturallyInconsistent

I never understood the many things Dirac was pioneering in all that constrained Hamiltonian bits

so didn't want to say the wrong stuff

But look, I'm trying to point out that we dont use vielbeins as a constraint anything, but einbeins are. The intended usage is way too different.

123

Hello @RyderRude

ACuriousMind

When you try to Legendre transform the action, you get $p^2 = m^2$ as a first-class constraint, and the gauge symmetry generated by it is the reparametrization invariance of the action. See e.g. this answer by Qmechanic

Mr. Feynman

@naturallyInconsistent I don't really know very much about this, so don't take this message too seriously. That's probably because typically einbeins appear in the description of a 1D submanifold (e.g. a string in spacetime), while vielbein in GR describes the geometry of spacetime itself

So you're not constraining anything in the second case

Ryder Rude

@123 hello

123

08:51

Now i am free

Ryder Rude

great

123

I have question yesterday. But there was problem in internet

inertial mass and gravitational mass has relation with quantity of matter.

naturallyInconsistent

@Mr.Feynman not like miao miao is any more informed than you are; the ones who know what is happening is ACM, Slereah, and Qmechanic.

123

Gravitational mass also depend on type of matter. like steel of planet and soil of planet same size and density can have different gravitational mass.

Ryder Rude

@123 what is ur question

ACuriousMind

08:56

@naturallyInconsistent The thing is that 1d is so degenerate a case that many concepts that are distinct in higher dimensions coincide here. You can view the einbein as the 1d version of the vielbein (square-root of the metric), you can view it as the 1d ADM lapse function (that's the analogue to choose for the constraint view), ...

123

@RyderRude gravitational mass also depend on type of matter e.g planet made of steel and planet made of soil has different gravitational mass?

Mr. Feynman

Those "..." are scary

qwerty

@ACuriousMind I don't think it's the adm lapse function for massless or massive particles

Ryder Rude

@123 what do u think the answer is and why

qwerty

I think it's the threading one as I mentioned

123

08:58

@RyderRude Because inertial mass and gravitational mass experimentally found to be equal. Then i think yes type of does matter in gravitational mass also

Ryder Rude

@123 that is correct...

123

Thanks

@RyderRude It is weird to think material has two characteristics resistance against velocity change and force of attraction.

Means one property resisting motion change. and same material have property cause of motion change

ACuriousMind

@qwerty I do - ADM writes $\mathrm{d}s^2 = N^2\mathrm{d}t^2 + \text{terms not there in 1d}$ and the einbein has also $\mathrm{d}s^2 = e^2\mathrm{d}t^2$

Ryder Rude

@123 right. But it is what the experiments tell us. Galileo was able to know this even without experiments

123

Material have resistance against acceleration and also cause of producing acceleration.

Ryder Rude

09:02

16

Q: Is Galileo's argument about falling bodies logically flawed?

Galileo's famous argument against the Aristotle's theory of falling bodies goes like this (taken from THEP forum, now defunct):"Let's say heavy objects do fall faster than light ones. Then it seems the heavier weight will fall with the lighter weight acting, as it were, a bit like a parachute. In...

ACuriousMind

I don't know what the threading lapse is but I would not be surprised if it also coincides with the einbein in 1D

Ryder Rude

@123 Galileo made an armchair argument about why the falling acceleration does not depend on quantity of matter

and he also tested it famously

123

@RyderRude Pls explain.

Ryder Rude

before that, people thought heavier things fall faster

123

Ookay...

Ryder Rude

09:05

@123 take two bodies made of identical matter and identical density. one has bigger size than the other. this means one has more inertial mass.

now, assume that the bigger one falls faster than the smaller one

we will see that this is impossible

123

Yes

naturallyInconsistent

@ACuriousMind that is one superposition that miao miao did not wish to be attacked by

Ryder Rude

what happens if u glue these bodies together and drop them from a height. the glued body has more matter than both the constituent bodies. Therefore, it should fall faster

ACuriousMind

@RyderRude No, people didn't think that, Aristotle (who was essentially wrong about everything) thought that. Plenty of people understood Aristotle was wrong, they just weren't worshipped like him. Vitruvius already suggested in the 1st century CE that the gravity of objects did not depend on their weight, cf. reddit.com/r/AskHistorians/comments/2a60b9/comment/cis1w0q

qwerty

@ACuriousMind I think from a purely intuitive POV (I'll dig up the details later when I'm home) what we want is a measure of the parametrisation of the worldline or curve. in the threading formalism you follow along the curves (so the plus other terms that you wrote completes the squares iirc in the other sense; you follow the frame of the particle) so it makes sense it's just the einbein.

Ryder Rude

09:08

@ACuriousMind oh

qwerty

whereas I don't have that straightforward idea in the slicing view: the threading and slicing lapse functions definitely don't coincide.

123

@RyderRude yes but experiment shows acceleration remain the same

Slereah

@ACuriousMind But heavier things do fall faster!

Pretty unfair to judge Aristotle like that imo

qwerty

yes air resistance is dependent on mass iirc

Slereah

Yes

and Aristotle was very much talking about mechanics in a medium, he didn't even believe a vacuum was possible

Ryder Rude

09:11

@ACuriousMind interesting..

Slereah

He thought that objects in a vacuum would go at an infinite speed, which to be fair would mean that falling speed would be independent of mass :p

Ryder Rude

so Galileo only contributed that mass was irrelevant

@123 yes, but we will try to figure it out without experiment

qwerty

@Slereah I got into an argument with my high school physics teacher over this since he would never say 'in a vacuum' which is a very important condition imo

Slereah

Just ask him how he ended up being a high school teacher if he was so good at physics

qwerty

well, tbf he said it like once then decided it wasn't important

Ryder Rude

09:13

@123 if the two components of the glued body fall at different rates, then the smaller body would act as a parachute for the bigger body, cuz it will try to slow it down. this means the whole glued body must fall at a lower rate than its smaller constituent

ACuriousMind

@Slereah He can sue me if he thinks I'm being unfair to him

Slereah

He's gonna haunt your ass

123

okay

Ryder Rude

@123 so we have showed that fall rate cannot depend on amount of matter

qwerty

@Slereah lol I shouldn't knock him too hard. he was a substitute and definitely miles ahead of our main physics teacher who was a biologist by training

123

09:14

yes

Ryder Rude

@123 but it is mostly determined by experiments. i would say there are hidden assumptions in Galileo's armchair argument

so one must use experiments in the end

Slereah

If you use experiment you'd find that heavier objects go faster

also people didn't really have good time measurement for free fall experiments in olden times

Ryder Rude

@Slereah i meant experiments in a vacuum

@Slereah but one can just drop them at once?

Slereah

Galileo used objects falling on an inclined plane to simulate it going slower, which is questionable about whether this is the same case as freefall

Ryder Rude

i recently tried to demonstrate this experiment to a person, but I felt like i failed

i then had to say "they fall at the same time if air was negligible"

ACuriousMind

09:17

@Slereah I'm not afraid of a poltergeist who doesn't understand physics!

123

What i have concluded about mass , it is related to quantity of matter. Whether it is inertial mass, gravitational mass or in terms of density use in checmistry

Slereah

@ACuriousMind Ain't afraid of no ghost?

Ryder Rude

@Slereah i need some help if u have a minute...

ACuriousMind

@Slereah the marshmallow man is pretty scary

Ryder Rude

have I said anything wrong in this answer physics.stackexchange.com/a/830870/156987 @Slereah

Slereah

09:19

I wouldn't call Aristotle Marshmallow-shaped

qwerty

@RyderRude you can do it with a piece of paper the same size as a thick book, on top of the thick book

ACuriousMind

I didn't mean Aristotle was the marshmallow man, I'm just saying there are ghosts I'm afraid of :P

qwerty

@ACuriousMind what is the marshmallow man?

it this like some German ghost? :p

ACuriousMind

have you never seen the original Ghostbusters :P

Ryder Rude

@qwerty thanks. That's genius

@qwerty i will use this demonstration the next time

123

09:22

How to tag own comment?

qwerty

@RyderRude the high school teacher I knocked wasn't completely useless haha

Slereah

@ACuriousMind Gee, feeling like an old man now

Ryder Rude

@123 i haven't found a way

qwerty

@ACuriousMind I think I might have but completely forgotten it xD my apologies

123

@RyderRude What about my above comment in explaining mass?

Ryder Rude

09:23

I'm not entirely confident about that answer because I haven't studied this in detail

ACuriousMind

@qwerty how could you forget the marshmallow man!

Ryder Rude

@123 yeah.. it depends on quantity and type

123

Let explain. 1. Quantity of matter increases which increase resistance in motion change. 2. Quantity of matter increases which increases force of gravity 3. Quantity of matter increases density of material increases.

@RyderRude Yes quantity of material and type of material.

Ryder Rude

@123 the third one is wrong. Can u tell why

123

@RyderRude If size/volume increases then density can remain the same.

Ryder Rude

09:26

@123 yes

123

But problem is that, we don't exactly know what actual is. We know only from related quantities.

Ryder Rude

@Slereah i thought he used this to demonstrate law of inertia

123

@RyderRude Yes i have a plan to make a youtube video for students. Because still there is no video which fully explain newton's laws of motion.

Ryder Rude

@123 u can maybe use Galileo's inclined plane for the first law

123

I was confused about N3L and N2L. Then i found in N3L our system contains two particles system with no external force for law of momentum. And in N2L we take one particle as system and other as external

@RyderRude Yes i have made the presentation and simulation for it.

But N3L and N2L required mass to explain and understand fully.

Ryder Rude

09:32

great

123

Because normally people understand mass as quantity of matter. But what i found mass in reality is not quantity of matter rather mass is related to quantity of matter. It just give us sense of mass not actual idea of mass

Am i correct

Ryder Rude

yes. the mass of an electron or any other fundamental particle is not related to the quantity of matter

123

@RyderRude One more idea of mass in sense of people using apparent weight. More quantity of matter feels heavier , but feeling heavy is force not mass.

In chemistry people also relate mass with quantity of matter.

Ryder Rude

yes. e.g. far away in outer space or in a free fall elevator, u won't feel the weight of anything u hold

but they still have mass

123

All of these idea of mass is true because in actual mass is related to quantity of matter.

Mr. Feynman

09:35

I see, so high school physics/math teachers having insane ego is international

qwerty

@ACuriousMind did you follow what I wrote at all? if not I can explain what I mean by complete the square

123

@RyderRude Yes that's why i called they have feeling of apparent weight not mass.

Ryder Rude

@123 right

naturallyInconsistent

@qwerty slice the thread

123

Even we don't feel force on us like motion in free fall we don't feel any force of gravity. Until force produce some pressure or stress in our body

qwerty

09:38

@Mr.Feynman lel. the one I was talking about tonight was a substitute and wasn't that bad at all. my main physicd teacher in HS was a biologist. she couldn't answer a q I had on ohms law/transformers and so I asked an ex electrical engineer maths teacher and she got mad

@naturallyInconsistent we slice the bread kitty!

Ryder Rude

@123 right

naturallyInconsistent

@qwerty claws out

qwerty

@naturallyInconsistent backs off uhh nice kitty :( pls don't hurt me

Ryder Rude

@qwerty do u prefer self learning or lectures

qwerty

@RyderRude self

123

09:40

@RyderRude Thanks

Ryder Rude

@qwerty same. it is efficient and u get more information

ACuriousMind

@qwerty I don't really have anything to say except to observe that "the curve" is the entire spacetime in 1d, so there isn't really any intuitive difference to me between this threading and slicing in 1d

qwerty

@ACuriousMind well, maybe that's the case in string theory? I'm not sure what you mean. we are "usually" slicing or threading up 4d, and the curve followed by a particle is a thread or 1D submanifold

ACuriousMind

@qwerty it has nothing to do with string theory - the relativistic particle action is purely classical

formally it's an action on a 1d spacetime - the "real" spacetime is the target space of the fields

Ryder Rude

also see time reparametrisation invariance. the configuration space of this action includes time while the "time" parameter is a gauge parameter

ACuriousMind

09:46

so when you try to "thread" that 1d spacetime, you just get one thread, and that's already the entire space time

qwerty

but that's fine?

ACuriousMind

I'm not saying it isn't fine

qwerty

I'm not sure I follow your point

ACuriousMind

I'm just saying this oddity might explain why two things that are in general different coincide in this case

qwerty

hmm

1

Q: Is the einbein the same thing as or related to the threading lapse function?

If I understand correctly the einbein can be understood as the component of a one-dimensional metric, along a particle worldline. I'm not so sure of writing it out explicitly, but this seems like it might be: $$-c^2 d\tau^2 = - c^2 e^2 dt^2 \ .$$ To me this seems mathematically and conceptually c...

general-relativity classical-mechanics lagrangian-formalism string-theory

123

09:49

If i have two blocks of same masses connected with a spring , placed on a horizontal frictionless surface.

qwerty

I suppose itsa yes after all.

but how it fits in with the adm one I guess I'll have to trust you ACM

123

We defined this system in terms of center of mass (COM). Is it also possible two define the system position of individual particles like take a coordinates $\Large{(x_1,y_1,z_1,x_2,y_2,z_2,t)}$

naturallyInconsistent

@qwerty attacks both the threads and the bread

qwerty

@naturallyInconsistent please don't slice up my skin kitty D:

actually ACM you are close to convincing me but I can visualise the threading scenario easier

I just don't have a picture of the einbein when you have the slicing

naturallyInconsistent

@qwerty are you made of either?

qwerty

10:04

@naturallyInconsistent they say you are what you eat, and I do consume bread...

naturallyInconsistent

@qwerty licks

qwerty

@naturallyInconsistent boredpanda.com/why-cats-eat-bread-explained is this you

naturallyInconsistent

maybe

Sorry for the ping: @ACuriousMind a cursory Google of "einbein QFT" seems to keep turning up worldline formalism; they integrate out the fermion degrees of freedom and then use Schwinger's trick to convert to fermion loop integrals. These seem to be mostly written by string ppl too. Is there a standard QFT using einbein without eliminating the fermion degrees of freedom?

ACuriousMind

10:22

Aug 18, 2023 at 15:43, by ACuriousMind

@Sanjana the worldline formalism is pretty much fiction, no one thinks about QFT in that way

You can of course quantize the non-fermionic theory of the free relativistic particle, but it's not a particularly interesting quantum theory

Slereah

I'd say it's a very interesting theory

naturallyInconsistent

10:43

@ACuriousMind Well, IIRC, there was some duality such that, if we can work out all the vacuum diagrams, then it will also contain the solution to any standard QFT. That is, when in the standard formalism we ignore all the vacuum bubble diagrams because the denominator will cancel them off, if we had instead ignored all the connected diagrams and just focused upon getting the vacuum bubbles, a duality exists to get us the usual fare in terms of that. Did I remember correctly?

qwerty

@ACuriousMind may I ask what the worldline formalism is or should I google it?

naturallyInconsistent

@qwerty I just described it~

qwerty

@naturallyInconsistent oh, I see. yeap it's beyond me :)

naturallyInconsistent

@ACuriousMind But that's precisely the opposite of what I wanted. I wanted to see if there is a QFT more in the normal sense except that it had time reparametrisation invariance as in einbeins.

Ryder Rude

@123 yes

123

10:48

Thanks

naturallyInconsistent

@qwerty It is surprisingly easy to understand. It is mostly a simple trick by Schwinger to convert the lawn into an integral $\mathrm dy/y$, and then convert that $1/y$ into yet another integral $e^{iyz}\mathrm dz$ and then swap the integrals and get rid of $y$. Then you can expand the resulting integral into classical particles moving around in loops. Sadly, ACM is somewhat implying that these trickery arent useful.

ACuriousMind

11:05

I'm mostly implying the main practical usage of this formalism is to justify the string perturbation series over worldsheets as its stringy analogue :P

@naturallyInconsistent I'm not exactly sure what that means, but if you turn a theory reparameterization invariant you then have to use BRST to quantize it as it becomes a gauge theory/the Hamiltonian becomes purely constraints, it's not exactly something you want to do to a theory if you can avoid it :P

Slereah

It's a good exercize for BRST quantization otoh

also the quantization of the relativistic point particle is so full of fucked up things that it's a pretty good tour to see the issues of relativistic quantum theory :p

although it certainly doesn't make it a good theory to use practically

naturallyInconsistent

11:20

@ACuriousMind I see, thanks. You have definitely found the correct set of words that is going to successfully spook the kitten away. Very Halloween.

qwerty

are we allowed to drop f bombs in the chat? no one else was doing it so I didn't wanna get banned for it lol

naturallyInconsistent

bomb

PM 2Ring

168

A: Are expletives (cursing, swear words or vulgar language) allowed on SE sites?

No. Using expletives is not acceptable behavior on any Stack Exchange site and is a violation of the Code of Conduct, even on Meta. There are a very small handful of exceptions (such as if you were talking about the word itself on a language site), but in general you should not use expletives any...

Things may be a little more relaxed in some chat rooms, though.

OTOH, a chat room can't have an official policy of permitting swearing. But the room owners etc may not be so strict about enforcing the Code of Conduct regarding swear words, especially when it's obvious to everyone involved that the words aren't being used to attack someone.

qwerty

@LuckyChouhan not to bring the current mood of the chat down too much, but I thought about what to say: my academic journey was a very long series of unfortunate events and a string of at least one abusive person - he was being academically/intellectually dishonest and gaslighting me on maths/results. I know some of these words overused as hyperbole right now but I don't use them lightly. there was over a year when I couldn't work or think about physics at all

not being able to do physics without blanking out was effing scary. sadly not everyone was shocked: apparently it's common for PhDs and I find that abhorrent.

I want to do something about it, so things arent just a roll of a die for students. but it's not clear what can be done.

I was also fortunate to have wonderful people in my personal life and also a mentor; I realise if I had to be financially self sufficient I would not have completed, let alone get feedback from an examiner that it was one of the best theses they had marked in decades. I only wish everyone had a more level playing field.

PM 2Ring

11:39

I rarely swear in Stack Exchange chat rooms, but sometimes it's appropriate...

In Connor's second thesis it is stated 'There is no fate but what we make for ourselves.' Does the routine destroy our creativity or do we lose creativity and fall into the routine? Anyway, who's up for a road trip!

2

qwerty

indeed

ACuriousMind

12:32

@qwerty I'm not banning anyone for saying "fuck" once unless it's in an insult like "fuck you", but if you use it every other sentence there's going to be problems :P

Slereah

@ACuriousMind How do you feel about using this paper

bpb-us-e2.wpmucdn.com/sites.uci.edu/dist/d/3128/files/2017/09/…

ACuriousMind

it's not wrong

Mr. Feynman

@qwerty I once had a physics teacher that had trouble telling $\sin$ and $\cos$ apart

Slereah

just remember that sin(x) ~ x

You can picture which one it is

it's the one that passes through 0!

Mr. Feynman

I'm talking about something worse, Slereah

I mean in a unit circumference, which is the sin and which is the cos

Ryder Rude

12:46

@Mr.Feynman maybe the teacher followed a strict rule where they don't memorise anything

but this one is so basic and widely used. it's like refusing to memorise multiplication tables

PM 2Ring

Maybe sine and cosine should have been named the other way around... But it's a bit too late to change them now, or to reverse the (x, y) convention for 2D coordinates.

Ryder Rude

long ago, i used to believe that a theory of everything would explain why the multiplication tables are the way they are :P

PM 2Ring

And to add to the confusion matrix indices are in row, column order.

The history of the word "sine" is a bit convoluted. It was originally from an Indian language, but came into Latin via Arabic. But IIRC there was a misprint / mistranslation involved. Let me check Wiki for details...

naturallyInconsistent

@PM2Ring there is actually a system explaining why which of each pair of those functions got the co- prefix. Sadly, that happened to be a pretty bad map onto the frequency of use.

@PM2Ring just use the Simon Clark's youtube video on it. He was overwhelmed by that video being his first meme

(and only. as of now.)

Sine of the Time

@PM2Ring I confirm. My history is convoluted

PM 2Ring

13:01

> The modern words "sine" and "cosine" are derived from the Latin word sinus via mistranslation from Arabic

See en.wikipedia.org/wiki/History_of_trigonometry#Etymology

From en.wikipedia.org/wiki/Sine_and_cosine#Etymology

> The word sine is derived, indirectly, from the Sanskrit word jyā 'bow-string' or more specifically its synonym jīvá (both adopted from Ancient Greek χορδή 'string'), due to visual similarity between the arc of a circle with its corresponding chord and a bow with its string (see jyā, koti-jyā and utkrama-jyā). This was transliterated in Arabic as jība, which is meaningless in that language and written as jb (جب).

> Since Arabic is written without short vowels, jb was interpreted as the homograph jayb (جيب), which means 'bosom', 'pocket', or 'fold'.

> When the Arabic texts of Al-Battani and al-Khwārizmī were translated into Medieval Latin in the 12th century by Gerard of Cremona, he used the Latin equivalent sinus (which also means 'bay' or 'fold', and more specifically 'the hanging fold of a toga over the breast').

@naturallyInconsistent Sine corresponds closely to the chords that were used by the ancient Indians, and by Ptolemy, etc. And obviously the names predate the discovery of $e^{i\theta}=\cos(\theta) + i\sin(\theta)$

naturallyInconsistent

@PM2Ring I know that. I'm referring to something else.

imbAF

13:48

When studying the case of an incoming particle towards a potential step or barrier, it seems to me that we equate the concepts of (reflection/transmission/incoming)probability current with the actually incoming/reflecting/transimitting particle current? Why is that? Does it mean that there is a 1 to 1 equivalence between probability current and actual physical current of some quantity ?

naturallyInconsistent

@imbAF yes. imagine you are in the pioneers' shoes, trying to make a new theory. Older theories already had such suggestive concepts. Isn't it the normal thing to try it out and see if the new theory accepts the old concept with little changes?

Mr. Feynman

Why is the GF it (zero-temperature) many-body temperature defined with a $N-particle$ "ground state", i.e. the Fermi sea?

I mean, why not with vacuum (0 particle state) like in relativistic QFT

ACuriousMind

@Mr.Feynman If it's a vacuum, where's the body (let alone many of them)?

imbAF

@naturallyInconsistent Ok I see, thanks

Mr. Feynman

@ACuriousMind I don't know :P

Then I guess it's just a matter of what is useful in this context

But I mean, you can have $N-1$ particle states

ACuriousMind

14:14

@Mr.Feynman What I mean is: If you have a condensed matter system like the free electrons in a conductor, then the ground state isn't "the vacuum", it's "all the electrons are in the lowest possible energy state"

If you phrase this in terms of c/a operators the ground state is the "absence of excitations" just like in hep-th QFT, but physically this "absence of excitations" does not mean the absence of particles in that case

Mr. Feynman

Alright, this much is clear. Now, I'm asking this because since we still work in a Fock space, on which c/a act, the vacuum *is* in the space of states, it's just unphysical (?)
I mean, destruction operators do not annihilate the fermi sea (at least those with suitable momenta)

ACuriousMind

@Mr.Feynman You have to think about the c/a operators differently - as I said, this is about excitations. The creation operator in this many-body conductor context in my example above does not create an electron ex nihilo, it raises an electron from that sea of electrons in the ground state to a higher energy level

the mathematics is exactly the same - you have a ground state and a bunch of c/a operators acting on it - but the physical interpretation of the action of the c/a operators is different

it's why the Dirac sea was even possible as an idea - nothing in the math itself tells you that the ground state is "empty", only that none of the annihilation operators can lower it any further

Mr. Feynman

@ACuriousMind Ok, I think you probably mean the particle/hole transformation

that retains the algebra

Slereah

14:36

Just thought about it

Do parametrized point particles have retarded and advanced solutions

I guess they would just be the two orientations of curves

I guess there's no fundamental reason why you should pick $\tau = t$ and not $-t$ as a gauge fix

Silly Goose

Schweg

Ryder Rude

14:54

@Slereah but does orientation of the curve affect any predictions?

orientation is not an observable, i think

it is just choices of parameters for the curve

Mr. Feynman

15:11

I think we discussed this here, so I'll mention it again. Regarding the usual argument of QFT for e.g. the vacuum polarization that must have the form
$$\Pi^{\mu\nu}(q)=A(q^2)g^{\mu\nu}+B(q^2)q^{\mu}q^{\nu} \tag{1}$$
Is there any branch of math dealing with this kind of argument? I don't how to better phrase it.

For reference, I'm not asking to explain $(1)$, it's pretty obvious. Just, physics textbooks typically do that as a "guess". So is there any field doing this more systematically?

ACuriousMind

@Mr.Feynman It's representation theory - you look at the space of all polynomials/tensors in $g$ and $q$ and observe that the spin-2 subrep is spanned by $g$ itself and $q\otimes q$

Ryder Rude

15:32

22

Q: Hilbert, Gödel, and "God equations" - a 19th century lesson for 21st century physicists?

It seems there are a lot of respected physicists appearing on pop-sci programs (discovery channel, science channel, etc.) these days spreading the gospel of "we can know, we must know." Three examples, quickly: 1) Many programs feature Michio Kaku saying that he is on a quest to find an equation...

mathematics history theory-of-everything

Mr. Feynman

15:43

@ACuriousMind I'm sorry, spin 2?

ACuriousMind

@Mr.Feynman two Lorentz indices, that's the spin-2 rep

ah, well, not exactly, but it's the spin-2 + the trace part + ...

I'm pretty sure this argument can be made in these terms

Mr. Feynman

mhhh ok, well, you answered the question

It's one of those things one wants to know without delving too much into :P

user430580

16:08

A physicist, an engineer, and a statistician are hunting a deer. They see it in the distance. The physicist calculates a parabolic trajectory, pulls back the bowstring the calculated amount and fires. The arrow lands 3 meters too short. The engineer adds in a fudge factor for air resistance, pulls back the bowstring and fires. The arrow lands 3 meters too long. The statistician yells "we got him!"

Slereah

16:58

for my stupid page of every formalism for the point particle I'm trying to remember how screw theory works

The formalism that nobody has used outside of France in a century

idk why we love it so much

it wasn't even invented by a Frenchman

it's mostly terrible because most screw theory sources are meant for engineers

Slereah

17:13

Apparently because of that guy

Richard von Mises

Richard Martin Edler von Mises (German: [fɔn ˈmiːzəs]; 19 April 1883 – 14 July 1953) was an Austrian scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of Gordon McKay Professor of Aerodynamics and Applied Mathematics at Harvard University. He described his work in his own words shortly before his death as: practical analysis, integral and differential equations, mechanics, hydrodynamics and aerodynamics, constructive geometry, probability calculus, statistics and philosophy. Although best...

Silly Goose

19:30

i am wondering where one would get the idea of introducing an einbein into an action?

Slereah

19:59

Why not, it's an integral on the line

The volume form is the einbein

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