The h Bar - 2023-02-08 (page 1 of 3)

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12:17 AM

How would I design a practical for the following question: How does changing the string length and tension affect the standing waves on a string?

3 hours later…

Relativisticcucumber

3:41 AM

there is a quantity $\chi^\dagger \bf{\sigma} \chi$ in sakurai. he is stating here that, though it appears to be a vector, $\bf{\sigma}$ is not a vector, $\chi^\dagger \bf{\sigma} \chi$ actually obeys the transformation rule of vectors. but, i do not understand this quantity. what kind of product is being applied here? i thought $\chi$ is 2x1, and $\bf{\sigma}$ is 3x1 where each element is 2x2. what am i missing here ?

2 hours later…

6:05 AM

Sigma is a Pauli matrix, it's a rank 3 tensor

It maps two spinors to a vector

6:24 AM

tensor product is like inner product in that as concepts they are defined to satisfy particular criteria, right?

and so the kronecker product is a particular but not only choice of tensor product (as dot product is a particular but not only choice)

1 hour later…

7:46 AM

Those torsion guys in the Soviet Union had the right idea

Pretend your theory can be used to detect ICBMs

8:07 AM

@Relativisticcucumber they mean the vector where the i-th component is $\chi^\dagger \sigma^i \chi$,

If you add the spinor indices, the situation is $\chi^{\dot{A}} \sigma_{\dot{A} A}^\mu \psi^A$

@SillyGoose I would rather say that the Kronecker and dot product are representations in specific bases. Both the inner product and the tensor product structures are unique in the sense that all inner product spaces of the same dimension are isometrically isomorphic and everything that fulfills the universal property of the tensor product is likewise isomorphic to anything else that does so in that sense you actually don't have any choices here

8:28 AM

How's the coV recovery coming along @Slereah?

😷🤧🤒💉 ⚕️💊💪

Not very good

Going to the doctor tomorrow

MDs are hard to find these days.

Even the uni med schools are accelerating their training programs.

Relativisticcucumber

8:47 AM

@ACuriousMind ah okay thanks ;P

9:15 AM

oh interesting i did not know that thanks @ACuriousMind

9:59 AM

ncatlab.org/nlab/all_pages/category

the category of categories

3 hours later…

12:48 PM

Why is massless Klein Gordon (minimally coupled) not conformally invariant, anyway

What sets the scale in KG

@Slereah what do you mean here, minimally coupled to what? "Klein-Gordon" is to me just a free scalar field

$$\Box \phi + \xi R \phi = 0$$

Minimal coupling is $\xi = 0$

okay

The proper conformally invariant KG is $\xi$ being some dimension-dependent quantity

This is a conceptual question btw, I know that you get the appropriate result if you do the rescaling of the Laplace Beltrami operator

What makes this different from the EM case?

@Slereah that the $\square$ contains the metric

1:00 PM

Is there some fundamental length scale encoded in KG, though?

would there have to be?

What is that scale?

I mean yeah?

Not "fundamental" in a grand philosophical sense, but there has to be some scale defined there

the statement is that conformal invariance implies scale invariance, hence the absence of preferred length scales. I don't know why the negation would hold. Conformal non-invariance does not necessarily imply scale non-invariance, and in turn scale non-invariance does not necessarily imply the presence of a preferred length scale

Hm

Apparently all changes to the scalar curvature drop if the conformal factor is a constant

I guess maybe only the SCT part of it matters?

Is it invariant under the Weyl group?

Massless KG does seem to be invariant under dilation

I never rly know what SCT encodes in a theory

it's very special

1:10 PM

So it is

Although it's just the same thing as dilation except second order

It is probably not easy to find a simple case since in flat space, KG would also be invariant under SCT

1:29 PM

When does one use the WKB formulas with blowing up exponentials? I think I've only seen decreasing exponentials

More precisely, I only know the formulae in the first row of this table and the first row of the next, I wonder where I should use the second rows of each

2:16 PM

4

A: Why do we learn only two computations, cross sections and decay rates, in such a fundamental theory as QFT?

The small number of "conceptually independent types of processes and calculations" is exactly a symptom of the theory's being fundamental! Even in classical physics, all calculations could have been mathematically reduced to the calculation of the final state that evolves from an initial state (o...

Cross sections and decay rates do not strike me as the theory being fundamental

It's more the emphasis on asymptotics

If you work out $|S_{fi}|^2$ for different numbers of incoming particles, you find more and more volume elements due to the normalization of your wave functions, so we need to get rid of them. For one particle it goes away, for two particles we are 'lucky' that we can re-write it in terms of an invariant cross section by introducing the crazy Moller flux factor $I = \sqrt{(p_1 . p_2)^2 - m_1^2 m_2^2}$, for three incoming particles I have no idea what to do with those extra volume elements

Is LQG not covariant because space is discretized but time is continuous?

2:31 PM

What does covariance mean if space is discretized

"covariant" is one of these words I will always ask people to define because it's used so vaguely for so many things :P

What does diffeo- mean if it's discrete

What topology are we using

28

A: Why is Standard Model + Loop Quantum Gravity usually not listed as a theory of everything

One can pinpoint the technical error in LQG explicitly: To recall, the starting point of LQG is to encode the Riemannian metric in terms of the parallel transport of the affine connection that it induces. This parallel transport is an assignment to each smooth curve in the manifold between point...

oh yeah, it's not well well defined. sorry

Loop quantum dustification

2:40 PM

I guess there is probably some equivalent group in that case, but it will not quite be diffeomorphisms

i am thinking that this theory is wrong because it treats space and time differently. The correct theory should allow for arbitrary topologies of the time dimension. LQG treats time as a boring unitary evolution parameter

Also the covariance thing in GR is sort of related to how you can put coordinates on a spacetime, idk how that works if you use a cloud of points

idk any strict meaning of covariance beyond "there should be at least one re-formation of the theory where space and time on the same footing in the equations"

Classical mechanics can be made covariant and it doesn't

doesn't have them on the same footing?

yeah, there are two separate metrics

i am thinking that a correct theory of gravity would make unitary evolution postulate of QM more interesting, by allowing for interesting time

Do you know any attempts at allowing time loops for quantum theories?

2:51 PM

you can check this amazing question :

29

Q: Do any quantum gravity theories deal with closed timelike curves?

As far as I'm aware, there are no quantum gravity theories that deal directly with closed timelike curves. Some of them (like canonical quantum gravity, causal dynamical triangulation and loop quantum gravity) forbid them outright, others merely seem to not discuss the topic. I've found quite a v...

general-relativity quantum-gravity closed-timelike-curve

all answers trash tho

oh

you had asked this :)

thanks

@RyderRude why though

while GR theoretically might allow for weird spacetimes, to date no observation indicates anything worse than a few blackholes exist

it is perfectly possible that GR is far more general than it needs to be in what kinds of spacetimes it admits

I mean it is even certain

Our universe can't have every topology

it only has one

It's like a philosophical motivation for me

for a quantum theory can allow for every topology

cuz they involve all configuration

having dynamic topology in QG is an even worse minefield

3:00 PM

I doubt the 'unitary time evolution' thing in LQG is an issue

i think our universe doesn't strictly have a space like surface which ADM assumes

because of black holes

Black holes don't typically break spacelike hypersurfaces

why would black holes imply that?

especially boring stellar black holes

idk

they may imply it

but either way, the quantum theory can allow for arbitrary topologies

because of the path integral

3:01 PM

you can't say something is "because of black holes" and then say "idk" when someone asks you what hte causal connection is! :P

sorry :P

i don't have a profound understanding of GR

probably a good idea before looking at QG

i read it in one of Andrew's answers that the hypersurface assumption is good enough but not strictly true

yea, i've been trying to learn GR

Unless we find something really weird it is probably true enough

@RyderRude why would the path integral imply that?

3:02 PM

i asked this related question about classical probabilites on a closed loop : physics.stackexchange.com/questions/230629/…

If you sum over all topologies in QG you get very very bad divergences

@ACuriousMind Because it's a sum over all metrics. metric is correlated to topology

like unheard of divergences

double exponential

@RyderRude that's not how it works - I can fix a manifold $M$ and then path-integrate over all isometry classes of metrics on it

i don't think it's a naive topology sum but it's some unknown math that modifies boring unitary evolution

3:04 PM

since I fixed $M$ this can't change the topology at all

yeah, that's what i don't want to assume. that we fix the manifold

the topology of a quantum theory should be uncertain

for philosophical reasons :P

in fact it is much more unclear to me how to write down a path integral over different topologies, since in contrast to the worldsheet integral in QM where I can sum over the genera of 2d manifolds, 4d manifolds have no simple enumerations

@ACuriousMind People who do such things usually use a 2D model

Or they don't sum over every topology

charlatans :P

They will just do like surgery theory stuff

3:06 PM

in fact, it is impossible for a neat enumeration of 4d manifolds to exist, cf mathoverflow.net/a/230407/157071

since i asked the question about classical probabilities on a time loop, i realised its solution : a classical probability distribution on a time-loop is a probability distribution over classical field solutions on the time loop

Also like

If your theory isn't too pathological

because in the classical path integral, delta probability distributions map to delta probability distributions

Topology change is likely not gonna be 4D manifold stuff

It's gonna be cobordisms

but this isn't true in the quantum path integral, because delta distributions diffuse

3:08 PM

idk if you can classify cobordisms between 3D manifolds

i don't think it's a naive sum over 4d topologies

it's some unknown math. trust me :P

@Slereah my understanding is that 4d cobordisms are similarly poorly understood in general :P

@ACuriousMind That's why they never tried shape theory

Relativisticcucumber

is there a reason we expect something with spin to behave interestingly in a magnetic field? why cant we apply any type of force? is it just that magnetic forces are much stronger than, say, gravitational forces?

@Relativisticcucumber something with spin and charge behaves interestingly because charged objects with angular momentum have magnetic moments

3:11 PM

Objects with spins have fancy interactions with many things

it's just that we have mostly the EM field in general

And in the EM case, only the magnetic part

but it's also true with all other interactions

in order to get gravitational effects you probably would have to claim that there's some quantum version of frame dragging, which I don't think is plausible to ever detect with realistic measurements

I mean maybe it's involved in like neutron star physics

and other than gravity and EM, which forces are there, really?

the other two :p

Relativisticcucumber

okay i see - so it's about spin and charge being together, not about spin in and of itself that allows us to observe things conveniently?

3:13 PM

we all know the strong and weak force are only part of the line-up for unclear reasons :P

@Relativisticcucumber spin and charge is the reason you can do observations via magnetic fields

Relativisticcucumber

hm why is spin precession interesting

that doesn't mean there aren't non-magnetic phenomena involving spin

Relativisticcucumber

interesting i see

e.g. when a particle with spin is absorbed by something it will transfer that as angular momentum to the absorber

Spin precession isn't interesting but it is a phenomenon, yes

3:16 PM

e.g. spin angular momentum of light is "real" in that you can do experiments to measure it but photons aren't charged, so don't start thinking that spin and charge/magnetism are instrinically linked

sciencedirect.com/science/article/abs/pii/0003491666902739

There is also spin precession of light in gravitational fields

The gravitational Hall effect

Relativisticcucumber

ah wow

Spin is just an extra degree of freedom for particles

Like all other such d.o.f., it can be affected by many things

Relativisticcucumber

i see, thank you

i think a sum over all topologies would simply lead to something like a bunch non-interacting quantum theories, one on each topology

there's no way to combine them as a single theory

like, a spherical topology can't be fitted on a flat one

this theory is definitely not what i want

so definitely not a naive sum over all topologies

3:24 PM

that's why Slereah mentioned cobordisms

yeah i didn't know the word but i got the feeling it was this issue :P

i've thought about this

it's a very uninteresting theory, yeah

in effect you would want to "sum" over all reasonable cobordisms between reasonable spatial slices (hold them fixed? maybe, maybe not), but still that "sum" is far too large in more than 2d

i think the global topology of the universe should simply be undefined instead of a bunch of well defined topologies

that was basically Wheeler's idea with the quantum foam

because the latter in an extremely uninteresting theory

quantum foam... never heard of it

is it like spin-foam but it treats space and time covariantly?

3:27 PM

Not really

Outside of being foamy

oh

foam sounds very cool, yeah

a foam should be like a generalised manifold, on which topologies should only exist locally

I'm not quite sure you know the words you are saying

i don't either

the wiki article on the quantum foam is very short

it says spacetime is allowed to quantum fluctuate

as a treat

"quantum fluctuation", much like "covariant", is one of these words that doesn't really mean anything :P

3:38 PM

I mean it has a meaning, but probably not as interesting as people imagine

yes, the unambiguous technical meaning can't support all the weird statements people make about quantum fluctuations

It is as interesting as the non-quantum fluctuations

If you think temperature fluctuations are cool

You're in good hands

temperature fluctuations are probably sometimes cool and sometimes hot

3:53 PM

the article doesn't define quantum fluctuations, so i went to the article on fluctuations. It's defined as energy time uncertainty principle and creation of virtual particles :P

this is not the rigorous meaning, right?

this article says virtual particles are directly undetectable. this article shouldn't be allowed

4:20 PM

no, the rigorous meaning is just that some variances of some operators don't vanish :P

the energy-time uncertainty principle in the form it is often presented in doesn't exist and has nothing to do with virtual particles, which are their own rabbit hole

yeah, this is so crackpot lol

back when i knew zero physics, i thought wikipedia was phd level accurate

unfortunately, both these notions would be at home within mainstream physics :P

but they have this article about virtual particle creation due to vacuum fluctuation lol

Wikipedia hasn't pulled this from thin air, this is how actual physicists talk about this stuff sometimes

yeah

4:22 PM

sometimes it's because they're doing pop-sci and they think it's a good idea to simplify it in this way (I disagree), sometimes it's because they've just read these phrases in another explanation and haven't really stopped to think about them carefully

it sounds cool but it's straight up a lie

i read one book which stressed a lot on this interpretation

the energy-time uncertainty principle is a particularly popular offender because it just feels as if it should be true

yeah

everyone knows that energy is to time as momentum is to position (which is true), so of course you must have an uncertainty principle for them that's like the one with momentum and position

soo many reputable physicists say that high energy particles can get created for a short time

yeah

4:24 PM

and the virtual particles idea is so popular because, well, that's what Feynman diagrams look like

in a way, these diagrams are too good

also, the vacuum bubble diagrams do play a role in vacuum energy calculation, i think

they make scattering amplitudes so easy that people think the pictures are the process

so everyone interprets them as actual particles

that's the idea i bought 2 years ago. that the physical processes look like those pictures

but a pop video did explain that i was just integrals

some pop videos are making an effort to clear this up

so while I point out these kinds of errors whenever I see them, I really wouldn't want to call the people talking like that "crackpots". It's very understandable how they arrived at that idea and usually it doesn't cause a lot of harm - after all, lots of physicists keep saying this stuff because it has no (or at least no negative) impact on their ability to do correct physics most of the time

i think can lead students into rabbit holes though

4:28 PM

but it is a particularly ripe source of confusion for the layman or student who knows enough to realize these popular pictures are wrong but not enough to see how else to interpret them

it can

and since physics.SE's main asker population is people confused about physics we have to engage with this kind of confusion far more often than most other physicists

too many questions asked about this

indeed, many of the people who use that language probably would say something like "oh, don't take it too literally, I just like the picture" when you'd ask them. But if you've just seen the statement in a lecture or read it in an article, you can't do that as such and physics.SE ends up with a lot of these questions

there's also the weekly question that confuses quantum fields with classical fields and thinks that particles are bumps in the field

i have had this confusion in the past. i thought QFT resolved the wave particle duality because a particle is just a bump in a classical field according to QFT

i think some physicists are genuinely coming up with theories involving virtual particles being physical

they write these ideas in books and articles

but i don't think that that confusion can be attributed to popular videos. The official phrase "particles are excitations of quantum field" misleads non physicists into thinking that particles are bumps in a classical field

4:42 PM

the issue is a bit more subtle than that

I think the people who use this phrase earnestly understand the phrase "the particle is an excitation" differently

see the discussions at physics.stackexchange.com/q/127141/50583 and physics.stackexchange.com/q/154391/50583, for instance

it's related to an issue with "physical intuition" more broadly: I think people who think this is an useful thing to say have trained their intuition to work with this in a way that doesn't mislead them

I'm looking for a color that stands out well against black. I'm working on revisions to a manuscript and I need the revisions to easily stand out for my collaborators. Most of the colors on this page overleaf.com/learn/latex/Using_colours_in_LaTeX are very "mat" and I'm looking for something a little more "glossy".

and they think it is useful to talk like this so that other people can develop the same kind of intuition, but it is very hard to communicate "intuition" except by way of example

yeah, any physics student who uses this phrase likely knows about operators

@ZeroTheHero do you mean a text color that stands out against black text color on a white background?

yes.

4:46 PM

the traditional choice would be red, wouldn't it?

bright enough red so that it's still recognizable as a difference in greyscale, ideally

I was hoping to find some palette of colors that's a little more glossy. That red is very "flat".

maybe I just need to slightly change the font of the revisions along with a color.

the xcolor documentation linked there has a lot more color palettes/series/whatever in the Examples section

I'm not sure I get what you mean by glossy but if you don't find it there you're perhaps trying to create an effect that isn't related to the actual color (I'd use "glossy" to describe how something reflects light but there's usually no light source in text documents ;) )

right but some colors come out as very "shiny" on a document (on the screen or printed) so text in this color is difficult to read.

on the other hand the xcolors are very "mat" (at least the ones listed on that link) are too flat.

I think the solution is just to use red and change the font slightly.

the double contrast will work better.

yeah I did it using \textsf and then red.

It's simpler than messing around with colors.

so the combo
\newcommand\revision[1]{{\color{OrangeRed} \textsf{ #1 }}}
works well.

5:06 PM

@ZeroTheHero Now here's a heretical question: Why do you need to visually mark revisions at all? :P

that's what version control systems are for

5:36 PM

@ACuriousMind that one's easy: you are a professional programmer and I am not (or at least nowhere near your level). My student does all this fancy version control using Git but my collaborator and I prefer to do revisions using the "token" method. For now I have the token, so I'm in charge of making revisions until the next iteration where someone else will have the token.

5:54 PM

@ACuriousMind is this new avatar anything close to your likelyhood?

No, not really, it's still Disco Elysium characters

though it's arguably closer than the one before, at least I have a beard, too :P

6:06 PM

He looks like an average musician from the 60's

are equivalence classes of a particular object $T$ denoted by $[T]$ in short hand?

yes

ah danke

too bad that ZA/UM fucking collapsed

Probably won't get another game like Disco Elysium now

I just want another game with writing as good as DE

doesn't have to be a sequel

6:18 PM

Did you try the Blackwell games

They're not bad

Let $\mathcal{H}$ be a Hilbert space. Let $T$ be an isomorphism (unitary map) defined by $T: \mathcal{H} \rightarrow \otimes_{i=1}^n \mathcal{H}_i$. Let $H$ be a hamiltonian $H: \mathcal{H} \rightarrow \mathcal{H}$. I am wondering about intuition about why the first sentence of the following picture is true. What I am thinking right now is that $THT^{-1}$ is still a unitary transformation of $H$. Thus, inner products are preserved. Thus, for each eigenvector $|\psi\rangle$ of the hamiltonian $H$

the inner product $\langle \psi | H \psi \rangle = \lambda$ is preserved, so the spectrum is preserved?

user image

but i feel my reasoning might not be sound because in like textbook qm when you are performing a unitary transform, say the rotation operator, you are still mapping vectors from $\mathcal{H}$ to $\mathcal{H}$, not from the space to a factorization of the space?

@Slereah this is the first time I'm hearing of them

@ACuriousMind I've decided to stop proof by baseball bat for a while

:p

@SillyGoose for every eigenvector $v_\lambda$ with $Hv_\lambda = \lambda v_\lambda$ you have that $THT^{-1}(Tv_\lambda) = THv_\lambda = \lambda Tv_\lambda$, so $Tv_\lambda$ is an eigenvector of $THT^{-1}$ with the same eigenvalue, so the spectra of $H$ and $THT^{-1}$ are the same

6:34 PM

how do I see that $THT^{-1}$ has no additional eigenvalues to the spectrum of $H$?

because $T$ is an isomorphism and the argument works in the other direction as well - for every eigenvector $v'_\lambda$ of $THT^{-1}$, $T^{-1}v'_\lambda$ is one of $H$

user image

ah i see

i.e. this is a bijection between eigenvectors

I gotta sleep

but feel free to enlighten me @ACuriousMind

6:37 PM

I have no idea what you mean

and why is that a screenshot instead of a link to the comment?

can one also make a preservation of inner product argument?

@ACuriousMind was on the phone and swapped to laptop

@SillyGoose $\langle v, Hv\rangle = \lambda$ does not imply that $v$ is an eigenvector of $H$

Am I the only one who thinks some dubious jumps have been made? Like we start with a classification system and end up with a prediction system which in some sense predicts that metaphysics is meaningless. However, using empirical probability betting against metaphysics is a bad idea as it has been an aid historically. — More Anonymous 2 hours ago

Can you tell which part is unclear?

I don't know what "classification system" or "prediction system" you're talking about

I also don't know what it means to "predict" metaphysics is meaningless

I also don't know where "empirical probability" comes into this

in short: everything is unclear to me :P

6:41 PM

Ah ... So I'm replying to this comment

Where do you think Carnap got the idea that anything not empirically verifiable, like metaphysics, is meaningless (hint: TLP 6.53)? But TLP is not dispositive because Wittgenstein repudiated much of it in the late period. His late philosophical therapy is arguably even more limiting, it denies philosophy its own subject or method, and sets aside many traditional philosophical problems as pseudo-problems stemming from linguistic confusion. Equivalence principle would not be philosophy to Wittgenstein, it is science's business. — Conifold 3 hours ago

Yes, I realize that

this does not make me understand what you said any better

So here's my personal philosophy. I start out with a symbols as an attempt to describe a system. This is a classification system. For example for an ideal gas I describe the number of molecules N. Okay so far so good. Now I get lucky and find 2 classifications systems which are not equivalent (like N =N) to describe the same system.

I use a symbol to describe this

ANd then I have symbolically moved from a classification system to a predictive/falsifiable system

how do you expect anyone to understand you if you just start your personal theory by using words in an idiosyncratic way?

@ACuriousMind By me explaining

@MoreAnonymous yes, but you just posted that comment as if everyone should be aware of what you mean by e.g. "classification system"

if there is literally only one person in the world that knows (you), what's the point of the comment

you're communicating nothing, effectively

Also your explanation jumps so quickly to things like "for example for an ideal gas" without having given any kind of definition of what you're doing

you can't define things by example

what's a "symbol", what's a "system", what is even the question this personal philosophy is trying to answer?

6:48 PM

Now a predictive system can be falsified. So when I say Carnap starts with a system which is a classification I dont see how he ever gets to make the claim it is falsifyable

@ACuriousMind At some point Im going to give examples and say its possible use words without defining them axiomatically

@ACuriousMind is this like a generalization of matrix similarity?

there's a reason actual philosophical texts doing epistemology spend a lot of time carefully explaining their starting points

@ACuriousMind Very well ...

symbol are swiggles that humans use to point to ideas

@SillyGoose sure

@MoreAnonymous what if I don't write my ideas down

system is any phenomena the human can experience and describe

@ACuriousMind I'm replying aint I

6:51 PM

?

terrence deacon is the go to dude for my thoughts on what a symbol is

Like, why does the symbol have to be a "swiggle". If I acoustically talk to someone, am I communicating an idea in a meaningfully different way than writing it down?

See here:

20 secs ago, by More Anonymous

terrence deacon is the go to dude for my thoughts on what a symbol is

usually we use the word "symbol" for anything that represents an idea

Fair. But heres how Im using it

Origins of Life, Consciousness, and Entropy

6:55 PM

I'm not watching a 3h video to understand what you mean by "symbol"

@ACuriousMind Good lets make do with examples

no, I don't really think this will be an enjoyable discussion for me, sorry

@ACuriousMind Ah okay :(

@ACuriousMind Would you be willing to participate if I can find a shorter textual version of his symbol ideas?

no because that's just one aspect of what I didn't understand about what you said

Was this lacking too

8 mins ago, by More Anonymous

system is any phenomena the human can experience and describe

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