The h Bar

Obliv

02:26

can some1 help me with $\mathcal{L}\{\sin(2t)\}$

If i integrate it twice I'm getting $\mathcal{L}\{\sin(2t)\} = \frac{-1}{s} - \frac{1}{s}\mathcal{L}\{\sin(2t)\}$

Silly Goose

03:37

how does anyone ever learn string theory :P

nickbros123

05:40

@ACuriousMind , if it is no hassle, is it possible for you to link me to a source that shows that the divergence of coloumb force field is the dirac delta function, derived from the theory of distributions?

bolbteppa

06:49

@nickbros123 Do you know/appreciate the standard one given in EM books like Griffiths

Physics Meta

07:03

0

Q: Is the voting format of SE which confuses "like" with "correct" appropriate for physics

I will give an example of a negative vote I just got. My problem with this vote is that I do not think anything is wrong in the physics of my answer. I accept that the reader does not "like" my answer as appropriate to the question, which is a popularity vote, but I also accept that I may have a...

discussion

ACuriousMind

11:23

@nickbros123 math.stackexchange.com/a/1335781/143136 provides a rigorous proof without going deep into the theory

Mr. Feynman

GR is so elegant

I wish QFT were as elegant as GR

Avantgarde

11:40

QFT has virtual particles. GR doesn't have such magical properties. So QFT>GR

Mr. Feynman

12:31

Elegance>Magic :P

Ryder Rude

12:50

I think both r very magical theories

I can't pick one becuz i love quantum gravity

It wud b like picking between sons or daughters

Leaky Nun

how can energy be transferred via vacuum? (yes, i know this is exactly how photons work)

ACuriousMind

13:05

@LeakyNun then what are you asking :P

Leaky Nun

more like, it doesn't make sense to me that energy can be transmitted without a medium

but i suppose mass can, and e=mc^2, so it all works out??

ACuriousMind

ah, an aether theorist

Leaky Nun

@ACuriousMind bruh

ACuriousMind

you're not alone, physicists had a hard time accepting that, too!

Leaky Nun

like at least it's unintuitive right

Physics Meta

13:07

-1

Q: What type of questions can you even ask in physics stack exchange

So physics stack exchange is being a little bitch. I just posted a normal ordinary high school level question and it got closed down within the next 2 minutes. The question did not: Ask to find the answer of a homework problem Ask what is mathematically incorrect about my solution what it did a...

discussion

ACuriousMind

but Michelson-Morley laid the aether to rest for all but the most determined believers

Leaky Nun

and also if energy can just transmit through vacuum, then why doesn't a circuit leak energy everywhere

ACuriousMind

@LeakyNun some circuits do, we call them "antennas"

Leaky Nun

@ACuriousMind yeah but how do you wrap your head around it

ACuriousMind

I mean, it's just the way the world works? What even is this "energy" you're so concerned about travelling through vacuum?

I try not to attach too much ontology to my physics :P

Leaky Nun

13:10

i see, a fellow "shut up and calculate" enjoyer

@ACuriousMind does it make sense to say that actually particles are just excitations of a field so particles travelling through vacuum are actually all just energy travelling through vacuum

ACuriousMind

eh

I don't like the "excitation" language

yesterday, by ACuriousMind

@DIRAC1930 see https://physics.stackexchange.com/a/154393/50583, https://physics.stackexchange.com/a/127147/50583 for some old takes of mine on the issue of "excitations"

Leaky Nun

@ACuriousMind ok, so what is an electron?

Ryder Rude

U can think of spacetime as the medium

ACuriousMind

@LeakyNun some sort of quantum state :P

Leaky Nun

@RyderRude Leibniz has something to say about that

Mr. Feynman

13:22

What's wrong with defining particles as 1-particle states of the Fock space of a field?

Ryder Rude

It's becuz that stuff only exists in the non interacting theory

ACuriousMind

@Mr.Feynman nothing, I just wouldn't apply the name "excitation" to the results of that

Mr. Feynman

Oh, ok so it's about jargon :P

ACuriousMind

(also the issue is more subtle for non-Abelian gauge theories, but since there are no non-confined non-Abelian bosons after EW symmetry breaking that's not relevant in practice)

Ryder Rude

@LeakyNun wut does Leibnitz say about this

Leaky Nun

13:25

@RyderRude spacetime doesn't exist, it's just the relative positions between stuff

Ryder Rude

Ooh that's just false now becuz of GR

I used to love this idea tho

Mr. Feynman

@ACuriousMind are you familiar with P&S? What do you think of their introduction of Feynman diagrams?

ACuriousMind

I haven't read P&S

Mr. Feynman

Ok nvm

Leaky Nun

@RyderRude i thought GR just replaces "positions" with 4-vectors or something

like, i don't think physics makes any claims on ontology

Ryder Rude

13:27

No, SR does that. GR makes spacetime dynamical

Leaky Nun

hmm...

ACuriousMind

No, it doesn't

Ryder Rude

Ooh and plus spacetime can hav a non-trivial topology

ACuriousMind

the metric is dynamical, not "spacetime"

Ryder Rude

So spacetime is definitely its own thing

@ACuriousMind oh yeah, but the spacetime has topology at least

ACuriousMind

13:28

and in fact string theory has a "split ontology" about whether or not spacetime is emergent or fundamental, cf. this answer of mine

Ryder Rude

Ooh but we discusswd that stuff on chat. We arrived at the conclusion that the emergent view is misguided becuz it takes feynman diagrams as fundamental

The conformal field theory ultimately only defines the Feynman diagrams

And Feynman diagrams are def not part of ontology

ACuriousMind

you have a habit of claiming we've reached "conclusions" with which I do not agree :P

Ryder Rude

Lol

nickbros123

@ACuriousMind thank you @ACuriousMind !!! this i appreciate very much. very elegant proof

my mind is very much at ease now compared to 2 -3 days back about the dirac delta function usage

Ryder Rude

Idk we just concluded that the non-perburbative string theory is fundamental instead of the worldsheet stuff

Worldsheet is only a tool for amplitude calculations. Worldsheets cant exist in the ontology, i think

geocalc33

13:34

is non perturbative theory just the absence of using perturbative techniques?

Ryder Rude

No, it explains more stuff. Perturbative expansion can b derived from it

E.g. in QFT, non-perturbatibe stuff is instantons

Leaky Nun

is spacetime more fundamental or is gravity more fundamental?

ACuriousMind

@geocalc33 more-or-less: yes, but in this context the problem is that string theory is currently only defined "perturbatively", i.e. the perturbation series is not some approximation or expansion of some quantity, it is its definition

Ryder Rude

Here's the order : first comes topology. On top of that, a bunch of interacting fields r defined

ACuriousMind

@LeakyNun if only we knew :)

Ryder Rude

13:37

One of those fields is the metric field, which is gravity

But the topology is the underlying stuff

Leaky Nun

topology of what exactly

Ryder Rude

Topology can hav measurable effects

Topology of spacetime

ACuriousMind

@LeakyNun This is the physics usage of "topology", they really mean the structure of spacetime as a smooth manifold

Ryder Rude

For e.g. space may not b infinite. It may b the surface of a 4D sphere

Leaky Nun

@ACuriousMind a smooth manifold of what

ACuriousMind

13:38

@LeakyNun ::shrug::

Leaky Nun

yeah this is my problem with the ontological claim that spacetime exists

Ryder Rude

Topology has measurable effects. Lemme explain

ACuriousMind

I think the careful claim here is that spacetime is a manifold of "indices" that allows us to separate objects and events from one another

Ryder Rude

A spherical topology wud mean when u go around the universe and keep going, u come back to the original point. How do u explain this phenomenon using "relative distances between objects"? @LeakyNun

ACuriousMind

whether this endows "spacetime itself" with any sort of ontological weight is a matter of debate

geocalc33

13:40

spacetime exists as a model that packages space and time together as a (3+1) lorentzian manifold

Leaky Nun

@RyderRude A and B has small distance, B and C has small distance, ..., Z and A has small distance

Ryder Rude

What

Leaky Nun

what

Ryder Rude

Idk :P

Leaky Nun

@ACuriousMind how does anything move at all

@RyderRude have you seen stuff arranged in a circle

you don't need a continuous circular "medium" to exist for that

Ryder Rude

13:43

Idk what that means. Very vague idea

Topplogy is the structure of spacetime itself. It does not refer to an arrangement of objects

geocalc33

I'm disappointed that my weird free schrodinger equation in 1D didn't work out

ACuriousMind

@LeakyNun nothing can ever move, Zeno already figured that one out :P

Leaky Nun

@RyderRude well you never observe spacetime, you only ever observe the objects

Ryder Rude

@LeakyNun Plus u shud also note that that the metric field is on an equal footing as electromagnetic field or klein gordon field. So there is no good way to reduce the metric field into "relative measurements between objects"

Leaky Nun

i suppose

Ryder Rude

13:47

@LeakyNun if u cudnt see light, wud u deny electromagnetic field too?

Leaky Nun

EM field is a good way to preserve locality

@RyderRude well we can see gravitational waves so i don't know why you make the first part

i guess it's similar to the thing that in QM things are wavefunctions, and we don't ask what it is a wave of

Ryder Rude

We dont "see" gravitational waves directly. We only notice the movement of apparatus

Leaky Nun

@RyderRude ok you also don't see light, you just notice the change in energy of your cells in your eyes

Ryder Rude

Then u wud need to deny the existence of objects too

It's all in ur head in the end

As feelings

Leaky Nun

s o l i p s i s m

bolbteppa

13:52

@Mr.Feynman It's a mess, their cross section section is a mess, etc...

The cover is very cool though

Mr. Feynman

@bolbteppa Oh my, that's a relief because I'm really struggling to understand their point

bolbteppa

Look at how they deal with electromagnetism in this book, you have to wait until chapter 9 on path integrals to justify some things iirc

Even their discussion on KG is incredibly confusing if you think about it

geocalc33

$$ix \hbar \frac{\partial^2}{\partial x^2}\Psi(t,x)=\frac{t\hbar ^2}{2m} \frac{\partial}{\partial t}\Psi(t,x)$$

I fixed it!

Wow it was that easy

If this is not "physical" then I give up

Mr. Feynman

14:09

@bolbteppa Yeah, they avoid the canonical quantization of the EM field but I'm fine with it

On the other hand, I'm struggling to see the big picture in the Feynman diagrams chapter (chapter 4)

user223626865

@SirCumference fine, thanks 👍

geocalc33

there are reasons why a body stays in motion

but at the moment only demons come to mind

bolbteppa

These notes based off it might say something that will help

Mr. Feynman

14:28

I'll check them

Otherwise I'll use some other book like Weinberg for this part

Ryder Rude

@geocalc33 r u trying to re-discover Schrodinger eqn on ur own?

geocalc33

@RyderRude I'm trying to understand a few related things

@RyderRude I can give you a brief summary. I derived the equation from looking at a Killing vector field in a space isometric to (1+1) minkowski space and using the induced metric from regular minkowski space (in null coordinates) the flow lines of said killing vector field now satisfy a "heat-like" equation.

I should say that $\Psi(t,x)$ satisfies a heat like equation...and respectively $\Psi_t(x)$ satisfies the killing field $\vec X= \langle x \log x, -y\log y \rangle$

note $\vec X$ is killing w.r.t. $g=\frac{dxdy}{xy}$

which is isometric to minkowski (1+1) in null coordinates

So it's almost as if embedding $(M,g)$ into null minkowki i.e. $(\Bbb R^{1,1},h)$ where $h=dxdy$ yields this heat like equation. i.e. forming the pair $(M,h)$ where we assume the measure induced by the metric $h$ by means of the volume form

$(M,h)$ is quite a strange object though

so I'm sort of wrestling with these facts

bolbteppa

15:12

@Mr.Feynman Welcome to the QFT book rabbit hole, it's not going to end at Weinberg

Ryder Rude

15:25

@geocalc33 Thanks 4 the summary. I have yet to study this stuff :P. So i don't exactly understand what you r doing

geocalc33

@RyderRude This is a very nonstandard derivation that you won't see in any textbook and it's because I did some self learning.

Ryder Rude

Good luck on ur further research :)

geocalc33

thanks :)

Mr. Feynman

15:48

@bolbteppa I mean, I like using several books. What I don't like is that I feel like I don't understand things...

Slereah

Is there a way in some sense that the measures on manifold defined by the density bundle are the only measures compatible with the manifold structure

like what set of properties of a measure will define them to be uniquely those

ACuriousMind

@Slereah cf. mathoverflow.net/q/219002

Slereah

So just being a Borel measure is enough?

no other Borel measure on a manifold?

ACuriousMind

In other words: The notion of "set of zero measure" on a Riemannian manifold is independent of the metric chosen, and the densities are exactly the measures whose notion of "zero measure" agrees with that intrinsic notion

Slereah

Is it bc open sets on a manifold are diffeomorphic to Rn and therefore it has to map to some appropriate Borel measure on Rn too

idk how mappings of measures work

ACuriousMind

16:01

yes - the "intrinsic" sets of zero measure here are, in a coordinate chart, exactly the zero measure sets in the sense of the Lebesgue measure on $\mathbb{R}^n$

Slereah

Good if true

I'm trying to really separate how manifolds work in terms that are independent of each other

ie consider what pertains to spacetime regions independently of what pertains to curves in spacetime etc

ACuriousMind

meanwhile I've somehow cornered myself into doing extremely pedestrian geometry: map projections

Slereah

are you planning to sail to the americas

ACuriousMind

no, but I want to make several different maps of a fictional planet - at least two azimuthal maps as seen from the poles and a normal plate carrée and all of the software that exists for projections I've found either doesn't do exactly what I want or is so complex that I'm not sure how to do with it what I want

Silly Goose

There’s nothing to project if the planet is flat ;)

ACuriousMind

16:10

@SillyGoose it's actually a hollow world and the people live on the inside but so far I think that's not relevant to the maps

Slereah

what about a toroidal world rotating inside out

Silly Goose

Why are manifolds the darling space of physics

or is that not a true statement

Mr. Feynman

Define a darling space

Slereah

manifolds are basically what a "space" is

Silly Goose

Lol that is a good one @Mr.Feynman

Slereah

16:17

They're not the most general definition of a space but if you go broader you're probably go "Wait a minute that's a weird space"

ACuriousMind

@SillyGoose Physics experiments result in real numbers $\mathbb{R}^n$. Being locally homeomorphic to $\mathbb{R}^n$, manifolds are good models for "spaces of possible results for physics experiments"

Silly Goose

Hm so what is the essential bit that manifolds give us that we need concerning something being a space

Slereah

Being locally euclidian and being separable basically

ACuriousMind

@SillyGoose Essentially that they can be mapped by $\mathbb{R}^n$. "a space is something that has coordinates" is the idea here

Silly Goose

So are things like Lie groups of operators being manifolds not related to this benefit of space being a manifold

Slereah

16:21

I mean most transformations we consider are either parametrized by numbers or are discrete

ACuriousMind

@SillyGoose A Lie group is a continuous group of transformations, and if you unpack what exactly we mean by "continuous" you'll end up more or less with the idea that it's a map from the reals to the group, $t\mapsto g_t$

so indeed I would claim that Lie groups appear in physics precisely because we often have the situation of a group of transformations being indexed by real numbers

(there is actually a line of thought that takes this idea and runs with it far into category land, namely that the "correct" objects of study should not be manifolds but generalized smooth spaces, which include far weirder objects than manifolds but are built on this idea "a space is something that can be mapped by coordinates")

Silly Goose

So in theory we could index group trans formations by any uncountable set? And this would change our choice of using a manifold?

Non real uncountable set

ACuriousMind

@SillyGoose well, the reason you want to index it by real numbers is because you want to use the smooth structure of the reals to state things like "When $t$ is close to $0$, then $g_t$ is close to the identity"

i.e. the "indexing" here is not merely algebraic, it's topological - you want notions of "closeness" on both sides - and it's analytic - you want notions of derivatives to state things about "infinitesimal versions" about such transformations.

Silly Goose

Are the reals the unique “insert what structure they’re being used as” that do this?

ACuriousMind

depends on what you mean by that

there's an entire branch of mathematics that does "analysis" but with p-adic numbers instead of the reals

Mr. Feynman

16:28

@ACuriousMind Yeah, throw me right into a rabbit hole. It's always those you trusted that stab you in the back...

Jk, I'm still overwhelmed by P&S and diagrams to get interested :P

Slereah

I've seen people attempting to model physical space with finite fields

it is a little weird

Silly Goose

17:23

In the above screen shot, $V_i$ is the diagonalizer of $\rho_i$, the reduced density matrix with every subsystem but the ith one traced out. By diagonalizer, I mean that conjugating $\rho_i$ with $V$ diagonalizes $\rho_i$.

I am having some trouble discerning the meaning of $r_{\alpha_i, \beta_j}$.

It seems like given an n-qubit density matrix $\rho$, trace out of all but subsystem $i$ and $j$ and then take the $\alpha, \beta$ GGMM basis coefficient

Obliv

17:38

ugh idk why this isn't working. $$\mathcal{L}\{\sin(2t)\} = \int_0^{\infty}e^{-st}\sin(2t)dt = \frac{2}{s}\int e^{-st}\cos(2t)dt = \frac{-e^{-st}}{s} - \frac{2}{s}\mathcal{L}\{\sin(2t)\} , \mathcal{L}\{\sin(2t)\} = \frac{1}{s} - \frac{2}{s}\mathcal{L}\{\sin(2t)\}$$ rearranging I keep getting $\mathcal{L}\{\sin(2t)\} = \frac{s}{2s + s^2}$

I've tried using both terms as u, i've done it many times and I will never arrive at $\frac{2}{s^2 + 4}$ what am I doing wrong?

More Anonymous

18:01

So I know up to first order correction any metric can be coordinate transformed into the minkowski metric. How does this work in practice? Like can someone link me this for the flrw metric?

Slereah

@MoreAnonymous Riemann normal coordinates

More Anonymous

@Slereah ofcourse they are the same thing :P

Slereah

A way to construct them is to use the radiating geodesics from the point you consider

Or you can just find a coordinate transform where the first derivative is the matrix that diagonalize the metric

which could just be literally that matrix really

it will diagonalize it at one point but nowhere else

More Anonymous

@Slereah I havent heard of this method

can u elaborate or reference?

Slereah

Choquet-Bruhat uses it to construct the Riemann normal coordinates

have some set of orthonormal vectors at the center and then radiate them out via parallel transport

More Anonymous

18:08

Introduction to GR relativity and blackholes?

That book

Slereah

No

More Anonymous

then?

Slereah

Cauchy problem book

General relativity and the einstein field equations

it may be in other books too idk

More Anonymous

got it

Slereah

but basically just do the transform at one point by diagonalizing the matrix using typical matrix calculus stuff and then just extend it is the typical method

There's more than one such coordinate transform since you basically only need to have the first derivatives to be a certain way

and even then at one point

More Anonymous

18:19

alright

Mr. Feynman

19:32

Carroll too talks a bit about Riemann normal coordinates

DIRAC1930

Do dressed particles behave like free ones because $G(k)=\frac{1}{P^2 - M^2- \Sigma}$ satisfies the momentum space free field equations? The issue is that the above ignores all the multiparticle states from the KL spectral rep. It seems like we've fudged the top by defining a branch cut along where the multiparticle states are.

Silly Goose

20:03

It depends what they’re wearing. I imagine a particle in formal attire would behave less free than one in some comfy pajamas

Does anyone know some good review papers to get a sense of the field of quantum computation and quantum information? Like one that gives a brief historical recount as well as the significant developments and the major open problems?

Perhaps @glS you may know:)

or are textbooks like nielson and chuang actually appropriate for gaining this information

Mr. Feynman

20:20

@SillyGoose you took me off guard

Silly Goose

20:37

XD

ACuriousMind

I mean, the top quark obviously is named so because it wears a little top hat, soo...

Mr. Feynman

21:04

The charm quark is so elegant

glS

@SillyGoose uhm. What do you mean by "get a sense of" here? If you're talking introductions to the field, sure I can suggest stuff (N&C being a standard one). If you're talking some kind of historical intro, I'm less sure. I guess it depends the level of technicality you're looking for

like, you'll have things doing a "historical recount", others doing "(old, recent?) significant developments", and others doing "major open problems"

journals.aps.org/prxquantum/abstract/10.1103/… is a nice recent papers about some open problems

for historical stuff I really don't know much. Maybe this video by Shor discussing the development of his algorithm might be of interest? youtu.be/6qD9XElTpCE

but I think N&C also does a little bit of history. Though I've probably always just skipped those parts lol

DIRAC1930

21:27

On second thoughts, at $P^2$ near the pole, the nonsingular part of the GF is suppressed

I don't think this has much to do with it though

Maybe it's best just to look at the propagator in terms of there being a pole at each excitation of the system

DIRAC1930

21:47

On another note, maybe this Mandalstam-Tamm paper is the whole reason why particles can be regarded as free at asymptotic $t=+ \infty$ since in this limit, if the partlces started as eigenstates of the free Hamiltonian at $t=-\infty$, they will tend towards eigenstates of the free Hamiltonian at $t=+\infty$ since the system tends towards conservation of proper energy in this limit

Then we just have to justify the $t=-\infty$ limit

I don't know

bolbteppa

22:02

@DIRAC1930 that's what L&L are saying

DanielSank

22:30

New game:

Search a random Wikipedia article. This is your band name.
Search a random famous quote. This is your album name.
Search a random image. This is your album cover art.

Compose these things into joke albums.

Examples: drive.google.com/drive/folders/…

Clarification: for the quote, it is acceptable to use a substring.

DIRAC1930

22:48

@bolbteppa Where does L&L write about the reasons for asymptotic states being free?

DIRAC1930

23:51

What if I start with normalizable eigenstates of $\hat{H}_0$ in the Gellmann-Low theorem?

Localized wavepackets

Is this okay or does something bad happen

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