The h Bar

@Slereah, @Semiclassical, @bolbteppa, @ACuriousMind - just eavesdropping on your string discussion...you all seem very broadely read. if i ever manage to get to grad level physics is this kind of general understanding i might expect, or are you reading much more broadely from personal interest?

bolbteppa

7:43 AM

Hopefully you'll know all the stuff we don't :p

antimony

haha here's hoping

Slereah

I don't know much about string theory tbh

I mean I know more about string theory than most people on earth, and more than most physicists I guess, but that's a pretty low bar

Emilio Pisanty

3

Q: What is the risk from radiation on imported food from Japan?

I'm currently resident in Hong Kong a country which appars to import heavily from Japan. Last saturday 7th May I went to a restaurant: http://www.openrice.com/english/restaurant/sr2.htm?shopid=39760 which I later discovered is themed after a popular Japanese coffee brand. I had one of those Fri...

That's an awfully clickbaity title

Any takers for how it can be edited to show the question in a more neutral light?

Particularly to show the timeframe in which the question was asked

Ratman

9:06 AM

Hi all, does anyone have any suggestion on where I can study quantum spin models in 1-d? For now I am mostly interested in XX and XY quantum Heisenberg models. I am looking to understand the concepts of quantum phase transition, spontaneous symmetry breaking in QM with infinite dof ( and why it doesn't arise in the finite dof limit) and the emergence of Dirac fermions in XX model, with using as prototype XX and XY models, the focus is on rigorous result.

bolbteppa

Lieb–Liniger model

The Lieb–Liniger model describes a gas of particles moving in one dimension and satisfying Bose–Einstein statistics. == Introduction == A model of a gas of particles moving in one dimension and satisfying Bose–Einstein statistics was introduced in 1963 in order to study whether the available approximate theories of such gases, specifically Bogoliubov's theory, would conform to the actual properties of the model gas. The model is based on a well defined Schrödinger Hamiltonian for particles interacting with each other via a two-body potential, and all the eigenfunctions and eigenvalues of this...

That's often a starting point in these discussions

Slereah

10:00 AM

Is there any source that discusses the limit of relativistic string to point particles in a non-off hand way

Like actually talk about deformation retract or something

Nakshatra Gangopadhay

I have a follow-up question regarding a question that I posted here a few days ago. If I have u=g(x), and some wavefunction \psi(u). Now, I replace all u's in this wavefunction by g(x) and get \psi(u)=\psi(g(x))=\phi(x)

Then \psi(u)=<u|psi>

and we can say |u>=|g(x)>

so, psi(g(x))=<g(x)|psi>=<u|psi>

Can I write <g(x)|psi> as some <x|phi> where |phi> is some other state

bolbteppa

Barbashov is maybe the only one I have seen that starts from the point particle and uses it to go to the string

The usual way is better, they are basically just doing it backwards anyway, and what happens when you go above strings, the usual way is immediate and it's a direct analog of SR thinking

Nakshatra Gangopadhay

Slereah

10:18 AM

I kind of want to see like a proper math version

Like "If you do a deformation retract of a brane along a Cauchy foliation of the target manifold, the $p$-brane reduces to a $0$-brane action"

or something like that

Does such a thing exist

maybe mapping the mapping space of $p$-branes to smaller branes

shit like that

bolbteppa

Does an area integral reduce to a line integral just by taking limits

Slereah

@bolbteppa Maybe it does in some sense!

samuel-lereah.com/articles/Physics/worldline-formalism

My best attempt at the idea so far

ACuriousMind

@antimony No, this definitely isn't "general understanding" - I pretty much specialized in QFT and string theory during my studies and read a lot of papers about that beyond the standard syllabus, I know far less about many other subfields (e.g. I know almost nothing about fluid dynamics).

Slereah

But it's all very coordinaty

It doesn't work unless I throw in an additional factor, though

It doesn't change the dynamic, but still

ACuriousMind

@Slereah ...are you talking about compactification?

Slereah

10:22 AM

@ACuriousMind I don't think so?

Just "the limit of a string is a point" sort of thing

ACuriousMind

if you have a p-brane and compactify d of its dimensions, the effective theory has a p-d brane

Slereah

Well that could certainly be part of it, yes

but I meant more leaving the target space intact

And just shrinking the brane

Along a particular foliation

ACuriousMind

I don't understand what sort of limit you're imagining there

Slereah

is that a thing that exists

Well, take your target manifold $M$, a foliation by spacelike hypersurfaces $\Sigma_t$, some $2$-manifold uuuuuh (I'm running out of good letters) $S$ and a string $X : S \to M$

ACuriousMind

@EmilioPisanty maybe just add a "after the Fukushima incident" or something like that to the title?

Slereah

10:25 AM

And now imagine some map that will send $X$ to a... I guess it will be a traintrack 1-manifold, generally, such that for $X$ on $\Sigma_t$, the string is reduced to a point

(Yes I know that the resulting lines will depend on the foliation because there's no localized vertex in strings)

ACuriousMind

but what process does that correspond to?

what's physically happening there?

Slereah

Well physically nothing I guess, just trying to figure out how one can get the limit to a point particle generally

[please note that I'm talking classically here]

ACuriousMind

as I said the idea of "the additional dimension shrinks so much we can effectively ignore it" is already modeled by compactification

Slereah

[just relativistic strings going to relativistic points]

ACuriousMind

oh, you still think classical strings are somehow relevant :P

Slereah

10:28 AM

Well, I don't know about "relevant"

bolbteppa

If $\mathbf{r}$ is independent of $\sigma$, their derivation of the string from the point particle stops at the first step

Slereah

But I don't need to justify myself in studying topics :p

bolbteppa

Is it really consistent to do that working backwards I'm not sure, but at least going the other way it seems to make sense

Slereah

String theory is also useless yet I don't see you justify yourself!

ACuriousMind

sorry, when someone is talking about "strings" I always think they're trying to do string theory. If you're just interested in classical strings for reasons unrelated to string theory, sure, go for it

Slereah

10:31 AM

@ACuriousMind If it makes you feel better just pretend I'm talking about domain walls

or just plain old geometry

Although I think cosmic strings are infinite, so idk if those are very good to treat as point particles

Open ones, at least

Or maybe I am tuning my relativistic guitar

bolbteppa

All you're really doing is looking at Minkowski space and saying a surface is parametrized by two parameters and that the surface has one time-like and one space-like direction, why do you need to do that and then restrict to the case of a curve when you can just do the curve directly

Slereah

Well, the thing is that in some cases, you won't get a curve!

You'll get a graph!

ACuriousMind

why would you get a graph?

Slereah

Train track (mathematics)

In the mathematical area of topology, a train track is a family of curves embedded on a surface, meeting the following conditions: The curves meet at a finite set of vertices called switches. Away from the switches, the curves are smooth and do not touch each other. At each switch, three curves meet with the same tangent line, with two curves entering from one direction and one from the other.The main application of train tracks in mathematics is to study laminations of surfaces, that is, partitions of closed subsets of surfaces into unions of smooth curves. Train tracks have also been used in...

You'll get one of these

@ACuriousMind idk, consider the pair of pants worldsheet

ACuriousMind

@Slereah but how are your "classical" strings merging?

Slereah

10:36 AM

what would be the contraction of that to a point

ACuriousMind

that's not a very classical behaviour

Slereah

@ACuriousMind Hence why it's also a good idea to maybe consider it as more of a geometry problem

Although Wu totally talks about curves like that in GR

I suspect that such a limit would be highly non-unique tho, so idk

but I would still be interested to find out if something on the topic has been done

Ratman

@bolbteppa thanks for the suggestion, I have found some notes looking for Lieb-Liniger model that could help.

Slereah

like your string could contract to any point on that string at a given time, and if the string is closed, it's even worse!

An open string can contract to a point it contains, but a closed string can't get contracted without moving the string itself!

ACuriousMind

@Slereah ...what do you do if the string is wrapped around a hole (it's not null-homotopic) :P

Slereah

10:39 AM

@ACuriousMind Yet another issue!

What if my string is tied through a network of wormholes!

and it's tied into knot

And I don't have my cosmic string scissors

I guess maybe it's doable in some very specific set of circumstances

Like the one Barbashov does

Open string in a topologically simple space

Ratman

@ACuriousMind As a professor told me one time when discussing in which field I could specialize in the master thesis , "either you are Landau or you got to specialize in some subfield".

Slereah

Landau didn't know every field!

Where's Landau's book on vulcanology

or meteorology

Lev Landau

What is that on the board

bolbteppa

10:57 AM

Is it a gamma matrix

bolbteppa

11:10 AM

@Slereah In Polyakov it seems more reasonable to just set $X^{\mu}(\tau,\sigma) = X^{\mu}(\tau)$ and $h^{\alpha \beta}$ only having $h^{11}$ non-trivial to do the transition

Slereah

So basically the motion of the endpoint?

but then that's only in a coordinate patch!!!

What if the sheet splits

bolbteppa

It's the point particle case no

Slereah

11:30 AM

how does one specify that a worldsheet never split in a coordinate invariant way

a worldsheet that splits still has the topology $\mathbb{R}^2$

Convexity would do it, but you could have non-splitting worldsheets that aren't convex

ACuriousMind

@Slereah for an open string? number of connected components of the boundary

Slereah

Well yes, but that's assuming a foliation, no?

ACuriousMind

an open worldsheet that doesn't split has just two - a "right" and a "left" boundary, but one that splits somewhere will have more

Slereah

Although... I guess if you have a worldsheet that doesn't split, the boundary is two copies of R

and if it splits there are three

ACuriousMind

that's what I mean, yes

Slereah

11:38 AM

What is the Hilbert space of string theory anyway

I know that for quantizing a single bosonic string it's like a regular particle Hilbert space $\otimes$ some Fock space for string excitations

what is the full one like?

Or is there no full one that people consider in the perturbative version

ACuriousMind

I don't know what you mean by "full"

Slereah

I mean that's like the Hilbert space for a single string, but the "real" string theory is a sum over however many strings

ACuriousMind

eh

Slereah

I assume you need a Hilbert space to accomodate arbitrarily many strings

and their excitations

ACuriousMind

that's the part where it gets muddy

Slereah

11:40 AM

Is that one of those string field theory only business

ACuriousMind

string theory is not the theory of "a bunch of strings floating around but quantized "

Slereah

or M theory or whatever

ACuriousMind

string theory is a framework for specific theories just like QFT

asking what the Hilbert space of string theory is is about as meaningful as asking for "the" Hilbert space of QFT

Slereah

Well what is perturbative QFT if not a bunch of little particle collision diagrams :p

@ACuriousMind Well I'd be satisfied with any string theory Hilbert space

You know how cognition works

prototype v. exemplar v. formula

ACuriousMind

and it's also not a quantum theory where we'd have a time evolution operator or anything

it only has "Hilbert spaces" associated to the strings at the outer (infinite past/future) boundaries of a worldsheet

Slereah

11:42 AM

I mean I know that the perturbative one is only for scattering yes

hence why it is BAD

ACuriousMind

there is nothing else

Slereah

what of the M theory

ACuriousMind

string theory is defined by the sum over worldsheets

@Slereah no one knows how the quantum theory of that one is

Slereah

Shouldn't M theory have an actual theory that can do things, at least hopefully

@ACuriousMind Do they not know, or do some people think they know but nobody agrees

ACuriousMind

"M theory" is just the name of a concept that should exist and correspond to 11d SUGRA, just like the five different ways of doing string theory correspond to the five different 10d SUGRAs

Slereah

11:44 AM

^this is how cognition works

it involves a lot of dogs

in this case, replace the dogs on the left by examples of Hilbert spaces in a string theory, and on the right it's a "canonical" Hilbert space for a string theory

ACuriousMind

@Slereah I'm sure some people think they know

but I'm also sure no one really has anything that really works

as much as string theory dresses itself in "this is just a classical theory quantized", it is not a QFT

Slereah

Well I'm sure we would have heard of it otherwise

ACuriousMind

there's no interaction picture or anything, you just have the in/out Hilbert spaces associated to the Fock spaces of the strings at the edges of the worldsheets and a prescription for how to compute scattering amplitudes

Slereah

I know, but I also know that plenty of people are not satisfied with that state of affair :p

ACuriousMind

that's fine

Slereah

11:47 AM

I'm sure there's a bunch of proposals

ACuriousMind

the problem is a bit that proposals for that are even less "testable" than the string theory we already have

the scattering prescription suffices to take the "low-energy" limit and get an effective QFT

and the effective QFT is what we are comfortable to work with to see beta function, particle content and whatnot

Slereah

$$\mathcal{H} = L^2(\text{sheaves of differential cohomology on the $\infty$-topos BV-BRST of smooth $p$-branes with orbifold twist})$$

Something like that

@ACuriousMind Psh who cares about testability

What are we, engineers?

ACuriousMind

so I don't think it's clear how one would even tell what the "correct" non-perturbative formulation of string theory is because it is unclear what sort of effect that would even have

@Slereah I put that into quotes because I'm not thinking about experiments here, really

I'm saying I wouldn't even know how to assess the theoretical physical significance of the non-scattering part

Slereah

Well, you know what I always say

When in doubt, do the hydrogen atom

ACuriousMind

easy, just take the low-energy effective QFT and do whatever you do in QFT for the hydrogen atom

Slereah

11:52 AM

if your theory can't do the hydrogen atom without going back to QFT, is it really good for anything!

ACuriousMind

the problem is that the "low-energy" threshold here is so high that it's unclear what sort of situations one should think about in order to see truly "stringy" effects

@Slereah my point is more that any deviations from the QFT hydrogen atom in prediction has to be so miniscule that it's not a practical way of assessing a "true" string theory

Slereah

Well I'm not saying it should be, but I'm saying you should be able to compute it from the theory

ACuriousMind

if the person who designed the theory isn't a complete idiot it will be such a tiny correction (if any) that that's not a criterion you can usefully apply

Slereah

Not a lot of difference between the Pauli equation hydrogen atom and the Dirac equation hydrogen atom, but it's good that we can do both

It's the completeness requirement for a theory thing

The theory should be able to predict everything within its domain of discourse

and since string theory is a theory of everything that's a pretty large domain

ACuriousMind

@Slereah but that's the thing - via the effective QFT, it already "predicts everything"

Slereah

11:57 AM

well yeah but that's like saying "GR can predict orbits by going to the Newtonian limit!"

ACuriousMind

we do not know any actual phenomenon that you would need string theory (or any other beyond-QFT) to explain

Slereah

True, but lame

ACuriousMind

so there's no starting point for the theory

Slereah

if your theory of everything only works in its already known limits, then it's not a very impressive one!

ACuriousMind

I'm not saying you're wrong philosophically, I'm explaining why I think we don't have a good angle on how to get the "full" string theory/M-theory whatever

@Slereah well, yes...that's kinda what the opponents of string theory say!

Slereah

11:58 AM

Maybe I am a string hater

Boo string theory

Do better you hacks

ACuriousMind

but it's a very general problem for the QG theories, I think

Slereah

I'd try to read more string field theory but then when they start talking about the superorthosympletic group my soul starts leaving my body

Well some of them are very easy for that

covariant QG and canonical QG and euclidian gravity do it very easily, it's just that they otherwise don't work

ACuriousMind

they're all just motivated by us being aesthetically displeased with QFT and GR not playing nice, not by actual phenomena we obviously need a new theory to explain

and so you don't know what sort of "fundamental mechanics" to look for because all you want to do is get a theory that has both QFT and GR as its limits, but we don't really have data on what else it should be

Slereah

Like you can do the hydrogen atom in covariant QG, it is super easy

just too bad that it's not renormalizable!

ACuriousMind

If all we knew about QFT was that it should reduce to both classical EM and quantum mechanics in some limits, how would we ever have arrived at QED?

Slereah

12:02 PM

@ACuriousMind Whatever people were doing in the 20's with it!

ACuriousMind

I'm pretty sure they already knew about phenomena you can't explain with ordinary QM

Slereah

I'm not a picky man

I'm not asking that it works in experiments, that it predicts anything new, or even that you can physically calculate anything

Just try something idk

go wild

bolbteppa

What's wrong with Barbashov's version of the limit from strings to particles in (2.23)

Slereah

It's one of those things where people get super partisan for some weird reason

I don't care that much about who wins the quantum gravity race

@bolbteppa Well it only works in a very limited number of cases and also you kind of have to add weird terms to the action to make sense?

bolbteppa

I think it's a general derivation in (2.23) and they don't add anything

Slereah

12:11 PM

Well yeah but then obviously they're cheating because they're using specific coordinates

bolbteppa

They're not using specific coordinates, and why they write the overall constant as energy per unit length is also something you can show by looking at the non-relativistic limit

Slereah

The sheet is already $\mathbb{R} \times \mathbb{R}$ and $\sigma$ is purely timelike and everything has the appropriate number of boundaries

This wouldn't work if you considered an arbitrary worldsheet in an arbitrary spacetime

Also I think it wouldn't work for a closed string?

bolbteppa

I don't know what that means :p But for $S = - T \int \sqrt{(\dot{x} \cdot x')^2 - \dot{x}^2 x'^2} d \tau d \sigma$ it works

Slereah

It certainly does!

There is actually a better demonstration of it in one of Nambu's papers

bolbteppa

You mean the Goto paper where he basically does this backwards

Slereah

12:14 PM

Err Goto

yes

academic.oup.com/ptp/article/46/5/1560/1862902

a cool paper

bolbteppa

Yeah it's the same idea

They even reference it for this

Slereah

I know

It's how I found it :p

bolbteppa

I know you know I just seen your question :p

Slereah

Well, the question says I don't know!

bolbteppa

I think this is the best one can expect

Slereah

12:15 PM

Or at least I don't know everything

I'm pretty sure you can't consider every string as a point particle in some limit, but there is probably a class of them that you can

I'm just not sure how wide that class would be

like if you had a string that tied all the way around the two mouths of a wormhole, it would be a stretch to consider it as a point particle

bolbteppa

Well the big thing is appreciating that $\gamma = m_0 c/l_0$ is actually the string tension and it's given as energy per unit length. You can see this has to be the case from the non-relativistic limit where you get the non-relativistic action for a string letting one interpret the coefficient in that way. The Becker book does it explicitly

Slereah

It would be a literal stretch

bolbteppa

This means we can take this $l_0 \to 0$ limit and the $L \to 0$ limit simultaneously. That the integral thing in (2.23) is actually the length we can just give the Goto argument if we need to justify it's interpretation

Slereah

yeah that part is fine, mostly

Since if you add the length of the string in the action like that, it doesn't change the EoM

So it's probably fine on a formal level

Ratman

@Slereah Well you can be sure only that these books weren't published, but yet Landau could have wrote it

bolbteppa

12:20 PM

So I mean I don't know what the issue is except vague arguments that we can't even write $\sqrt{(\dot{x} \cdot x')^2 - \dot{x}^2 x'^2} d \tau d \sigma$ because it's sullied by using coordinates even though it's covariant

Slereah

@Ratman I'm not sure I trust someone who looks so much like Kramer

@bolbteppa Well as I said, it's a very specific case

bolbteppa

It's not a specific case it's everything the free bosonic string claims to describe

How do you argue $S = - \alpha \int ds$ reduces to the free non-relativistic action without using $ds = \sqrt{1-(v/c)^2} c dt$

Slereah

there's something going on there

bolbteppa

We'd never get anywhere if we didn't just accept arguments on this level and move on, there's nothing wrong with it

Slereah

I didn't say I had the solution in mind!

bolbteppa

12:26 PM

Is pulling $\sqrt{\dot{x}^{2}(\tau,\sigma^*)}$ past the integral without using some $...$ terms okay

Slereah

@bolbteppa Also really if you're gonna use coordinates for the NG action, why use such a vulgar one

No that's fine

I'm just not sure what's gonna happen for like

a closed string

bolbteppa

The whole thing is covariant so it doesn't matter that we use them in this form

Slereah

or anything else with a weirder shape

bolbteppa

It works for a closed string too

It's just shrinking down to a dot

Slereah

Yeah but then that's not the same process, is it?

If you do it by shrinking the $\sigma$ parameter, a closed string isn't gonna contract

bolbteppa

12:28 PM

All boundary conditions are built into the action as it's written in (2.23)

Slereah

I'm not 100% sure there

bolbteppa

They even have a paragraph on string fields later on

Slereah

I think in $2.23$, no matter what shrinking you do to the parameters, the string is never gonna go to places it wasn't before, so to speak

Which works for shrinking an open string, but not so much for a closed one

bolbteppa

The action just describes the surface generated by a string moving through space-time, it makes no different what type of string it is, you're just looking at the surface it generates as it evolves for any type of string

Slereah

I think you need to contract the brane itself and not play around with the parameters here

I mean I guess maybe mathematically you'll end up with the same action, but it feels a little weird you know?

Like if I shrink the parameter a little bit on a closed string, then it will cease to be a closed string

since you no longer have $X(\sigma_1) = X(\sigma_2)$

bolbteppa

12:32 PM

Yeah but the weirdness is in that limit, what limit isn't weird when you think about it

Slereah

idk I think the process should be continuous at least

bolbteppa

$\lim_{x \to 2}\frac{x^2 - 4}{x-2} = 4$ is weird

Slereah

I want to see little retracts of the string

Like what Barbashov is doing here is essentially taking an open set of the sheet and shrinking its domain

It's not the string itself shrinking, so to speak

Doesn't matter that much I suppose, but I wonder if you could do it that way

bolbteppa

Right it's shrinking the area that the string spans in space-time down to a curve

Slereah

the same way you shrink a loop in homotopy theory

bolbteppa

12:36 PM

I'm sure you could do it with a retract but you'd probably end up doing what they do here at some intermediate step in some form

Slereah

Well yes, but I'd like to see it!

many things are equivalent, that doesn't mean we shouldn't do it!

I think it is of the utmost importance that someone do it bc I think it would be cool

fqq

@Slereah the problem is that apparently some other attempts at quantum gravity don't even have that

Slereah

Well I never said it was easy

but I think just saying "That's not the goal here!" is a bit of a cop out

If it doesn't exist yet that is fine, but pretending that the question itself is irrelevant is a bit weird

fqq

@Ratman I don't know what the best source would be, there are many books, e.g. Sachdev - Quantum phase transitions

bolbteppa

Retraction (topology)

In topology, a branch of mathematics, a retraction is a continuous mapping from a topological space into a subspace that preserves the position of all points in that subspace. The subspace is then called a retract of the original space. A deformation retraction is a mapping that captures the idea of continuously shrinking a space into a subspace. An absolute neighborhood retract (ANR) is a particularly well-behaved type of topological space. For example, every topological manifold is an ANR. Every ANR has the homotopy type of a very simple topological space, a CW complex. == Definitions == ��3...

The action written as (2.23) is probably the $F$ in the definition of a retract

Slereah

12:43 PM

I know what a retraction is, yes, that is the word I employed :p

I think it works as a retraction in the open case but not in the closed case

In the closed case I guess maybe you'd need to retract in some notion of "the middle", but that seems hard to define properly

bolbteppa

Where is the distinction of open vs closed written in the action?

Slereah

it works for both, but in the closed case that limit isn't a retraction

Since it doesn't preserve the loop

fqq

@Ratman Mussardo - Statistical field theory, Tsvelik - ¨ QFT in condensed matter" or something like that, Giamarchi - Quantum physics in one dimension

Slereah

the string just snaps open and goes down to a point like a dying Pacman

fqq

then there is more specifically all the Bethe Ansatz stuff, again I'm very rusty so I don't know the best resources, maybe these notes arxiv.org/abs/1609.02100

Slereah

12:50 PM

also if the topology goes slightly more complex than open or closed, then I think it all goes out the window

bolbteppa

The closed string doesn't need to snap open it's like a ring getting smaller until it collapses to a point!

Slereah

Is that what happens in Barbashov?

I think not

He only changes the parameters, the mapping $X$ doesn't change at all

bolbteppa

Because the length shrinks down to zero in the limit, what else can happen

Slereah

So it can't "shrink" in that sense

it can only be "less" of what it already is

which works for a line, but not for a circle

you can only have a subset of that circle, not a smaller circle

bolbteppa

The length literally shrinks to zero so that the line/circle collapses down to a literal point, it has to

Slereah

12:54 PM

well its length shrinks, yes, but only because you consider a receeding arc of the circle!

bolbteppa

The tension goes to infinity in the same limit, which is equivalent to $l_0 \to 0$

Slereah

Hm

bolbteppa

You'd be contradicting the meaning of a limit to say otherwise!

Slereah

I guess maybe I need to work it out explicitely to check

Like maybe consider a closed string with two circles on the boundaries and see what happens

bolbteppa

If anything stays finite then you still just have the string action

So the way they wrote it with that $\sigma^*$, I mean is there not some approximation there with $...$'s

Slereah

12:56 PM

The $\sigma^*$ I am fine with, that's just the mean value theorem :p

I'm trying to think of a way to write this proof in a coordinate invariant way :p

I guess you could use a length function $l(X)$

and then perform a retract on $X$

But then you need to define a foliation first I guess

But I guess that definition would work for any foliation

bolbteppa

So because $\sigma^* \in [\sigma_1(\tau),\sigma_2(\tau)]$ it's different for every $\tau$ so really there is no approximation

Slereah

so it is independent of the foliation in that sense

but I guess there is kind of a choice there

To which point do you contract it to

but I think you need to decide that by hand

maybe by considering the midpoint on the boundary condition idk

rb3652

1:14 PM

Hi everyone

Slereah

Hello

rb3652

I have a quick question

I created a riddle inspired by physics.stackexchange.com/questions/126919/…

41

A: Does time move slower at the equator?

The difference would indeed be measurable with state-of-the-art atomic clocks but it's not there: it cancels. The reasons actually boil down to the very first thought experiments that Einstein went through when he realized the importance of the equivalence principle for general relativity – it wa...

I'm trying to understand the answer (I'm only an first-year undergrad in Physics)

We expect time to tick slower at the equator because the earth spins fastest at the equator, and slowest at the poles (in fact, the poles technically don't rotate at all)

Thus, we expect time to dilate by an amount given by the gamma factor

Apparently this effect of time dilation cancels out because the equator is farther from the earth's center (due to the equatorial bulge), and so time ticks slightly faster than the poles, which are closer to the core?

Would that be correct? @Slereah

Slereah

I don't know if it cancels but yes, there are several effects at work

rb3652

David Hammen states "Yes. The flaw is that you are ignoring general relativity. The poles are closer to the center of the Earth and are thus deeper in the Earth's gravity well than is the equator. The combined effects of gravitational and special relativistic time mean that clocks at sea level tick at the same rate. More precisely, clocks at the surface of the geoid tick at the same rate."

13

A: Does time move slower at the equator?

Is there a flaw in my reasoning or have I simply not been reading the right journals? Yes. The flaw is that you are ignoring general relativity. The poles are closer to the center of the Earth and are thus deeper in the Earth's gravity well than is the equator. The combined effects of gravit...

Slereah

1:30 PM

Also check out this interesting tidbit from xkcd :

"It's common knowledge that Mt. Everest is the tallest mountain on Earth, measured from sea level. A somewhat more obscure piece of trivia is that the point on the Earth's surface farthest from its center is the summit of Mt. Chimborazo in Ecuador, due to the fact that the planet bulges out at the equator.
Even more obscure is the question of which point on the Earth's surface moves the fastest as the Earth spins, which is the same as asking which point is farthest from the Earth's axis. The answer isn't Chimborazo or Everest. The fastest point turns out to be the peak of Mt. Cayambe, a vol…

With these you could try to figure out which point of earth has the largest time dilation!

BannedUser

3:59 PM

hey

so i was thinking a projectile motion

i think at maximum height potential energy is 0

since when ball is going up gravity does negative work

and when ball goes down gravity does positive work

must be 0

at top

Ratman

@fqq thanks a lot, those are exactly the notes I found after bolbteppa suggestion. Giamarchi index seems to suite more what I should do. Thanks for the help again

Slereah

fqq

4:25 PM

@Ratman I've never read Giamarchi's book, keep in mind that it's relatively old and there's been a lot of activity in the field in the past 15 years

RewCie

What is the purpose of pain?

why I was born with a badluck!? Since the very beginning, nothing seemed to be going right.

Ratman

4:39 PM

@fqq I think it shouldn't be a problem, I intend to use it just for few parts, but thanks a lot for the warning. My problem is that the path followed in my course is quite particular (just in the sense that I am having hard time finding the literature that use the methods presented) so I am trying to fill some gaps for specific topics.

Semiclassical

5:48 PM

@antimony not sure why you pinged me on that. i don't know bubkis about strings :P

Transcript for