The h Bar - 2022-12-06

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Relativisticcucumber

3:24 AM

perhaps improper but bumping an unanswered question here in case anybody knows ! physics.stackexchange.com/questions/739277/…

@SillyGoose string theory & relevant physics

@SillyGoose for not unexpected but awesome @holography

1 hour later…

4:48 AM

Ugh; I tried to write a question on cosmic scale CP violation and I can't write it well

1 hour later…

5:55 AM

goodness i just realised you can save answers, has that always been there?

here i've been saving questions

6:50 AM

user image

How do we go from 2.24 to 2.25? if we divide both sides by dt it looks like a fundemental theorem of calculus-esque form

but i was reading from another set of notes that nigh copies sakurai's text which says 2.25 is achieved by taylor expanding the LHS of 2.24

7:13 AM

i feel like we can divide both sides by dt and then take the lim of both sides as dt -> 0. Then, we get a relationship between the time derivative of the unitary time evolution operator and $H \mathcal{U}(t,t_0)$. Since if we divide both sides in 2.24 by dt, the RHS has no dt dependence and is not affected by the limit taking

7:33 AM

You can certainly Taylor expand $f(t+dt)$ to get $f(t) + f'(t) dt$

7:53 AM

oh i see

and that would be from taylor expanding $\mathcal{U}(t+dt, t_0)$ around $t$?

Yes

cool tak!!

hm i think i am confusing myself about this operator formalist

formalism

so if we have $H(t, t_0)$ this is not a function of $t$, right? This is like $H$ the hamiltonian acting on parameter $t$?

user image

in particular, i am trying to figure out how to differentiate the expansion 2.29 term by term. also $H$ is independent of time

8:20 AM

H(t - t₀) just means H times (t - t₀) i.e. H times Δt

ah ah okay

but the unitary time evolution operator $\mathcal{U}(t,t_0)$ is actually more like a function of $t$?

Yes. It's an unfortunate confusion that the bracket indicates a function of time in one case and just a multiplication in the other.

dear god XD

this has been a large source of confusion. thank you.

:-)

4 hours later…

12:46 PM

Why time from the path integral works like inverse temperature from statistical mechanics? The path integral describes paths in space-time. Probability distributions cannot be spread out in time.

1:10 PM

@RyderRude The statistical partition function is the trace of $\mathrm{e}^{-\beta H}$. It's not hard to derive that you can express this trace as a path integral: We have that $\langle q'\vert \mathrm{e}^{-Ht}\vert q''\rangle = \int_{q(0) = q'}^{q(t) = q''} \mathrm{e}^{-S[q]}\mathcal{D}q$ for the "normal" path integral concerned with time evolution. If we set $q' = q''$ and integrate as a normal variable over $q'$, this gives the trace of $\mathrm{e}^{-Ht}$.

So $t=\beta$ gives the partition function.

there really isn't any deep significance to this, it's just that the thing $\mathrm{e}^{-\beta H}$ you want to trace over looks very much like a time evolution operator $\mathrm{e}^{\mathrm{i}Ht}$ so any expressions we have for that also work for this trace - the math doesn't care whether the $t$ is really a "time" or not

1:34 PM

Thanks. I was also thinking this isn't anything deep. I saw one answer describe some cutting edge Quantum Mechanics interpretation which takes this analogy literallu and interprets the quantum probabilities as a probability dostribution in spacetime, instead of as a probability distribution as a function of time

They said that this may solve the measurement problem. But they made it clear that it's unlikely

2:02 PM

@ACuriousMind I thinking reply is about quantum statistical physics, that is, about the energy probability distribution of a quantum ensemble at temeperature $T$. This can be calculated using imaginary time path integral

you* reply

your*

@ACuriousMind I saw one more analogy with classical stastical physics. That analogy interpreted the path integral of a one-dimensional quantum particle as describing the statistical physics of a 2-dimensional classical statistical system.

3 hours later…

5:03 PM

@ACuriousMind No, the planet at point 2 (perihelion) is faster than a planet in a circular orbit that passes through point 2. The circular orbit has $v^2=\mu/r$, the elliptical at perihelion has $r=a(1-e)$ and $v^2=(\mu/r)(1+e)$, where $a$ is the semi-major axis, $e$ is the eccentricity, and $\mu$ is the gravitational parameter.

@TejasDahake You should take a look at the vis-viva equation. I have some info at physics.stackexchange.com/a/676872/123208 & physics.stackexchange.com/a/675868/123208

oops, you're right

If I had a dollar for every sign error I've made in celestial mechanics, I'd have... a lot of dollars. :)

5:22 PM

We probably should have discussion about ChatGPT on Physics.meta.

62

Q: Ban ChatGPT network-wide

Use of ChatGPT generated text for posts on Stack Overflow is temporarily banned. However, the reasons for the ban really apply to much or all of the network, and certainly for sites that are similar in nature to Stack Overflow. I suggest (temporarily) banning ChatGPT network-wide. It turns out th...

discussion status-review answers policy

We have begun internal discussions to identify options for addressing this issue. We’re also reading what folks write about the topic on their individual sites, as one piece of assessing the overall impact. While we evaluate, we hope that folks on network sites feel comfortable establishing per-site policies responsive to their communities’ needs. — Slate ♦ 21 hours ago

I suspect that it's already been used on Physics.SE, but not to the same extent as on SO.

@PM2Ring I am confused about what it would mean to "ban ChatGPT". If the output is good enough to pass as a meaningful answer, how are we detecting that the answer was generated by a machine learning algorithm? If the output isn't good enough to pass, it should get downvoted and/or deleted anyway.

The problem is that ChatGPT output looks good on the surface, but it may be totally incorrect.

oh, I'm not confused about why we might not want GPT-generated answers. I'm confused about how people think we can enforce this ban

Ah, right

"answer that looks good on the surface but is actually nonsense" describes the contributions of various humans on this site, too :P

are we supposed to train a classifier and if it says your content is GPT-generated above a certain threshold we ban you?

5:38 PM

Yes. The problem is that it takes a lot more work to detect than obvious crap. There are some tell-tale phrases that indicate that it's a ChatGPT answer, but I think the main way it's currently being detected on other sites is purely from the sheer volume: people posting multiple answers in an hour.

oh, sure, but if their posting volume is high and the answers are garbage we can already suspend people for "consistent low-quality contributions"

I don't really want to have to make an argument whether the content is generated or not in that case

True, but we (community & / or mods) still have to do the work of evaluating that the answers are garbage. And they can post faster than we can evaluate, especially if they don't bother evaluating the stuff themselves.

@PM2Ring yes but how are we proving they're posting generated content? Maybe it's just a weird person that drafts a bunch of answers and then posts them all at once :P

and we already have various rate-limiting mechanisms on SE, just tune one of those globally to prevent actual floods

Oh, I agree it's not easy, and difficult to police properly.

in principle someone could be employing humans to write garbage answers instead of an AI - that wouldn't be any better in terms of content, right?

I feel the reflex "ban ChatGPT" doesn't actually ban the behavior we care about here

5:48 PM

When the text is sufficiently large it tends to be noticeable that there's no underlying sense to it. "The lights are on, but nobody's home". Or as one commenter put it, it looks like a cake, the frosting looks enticing, but the cake's actually made of styrofoam.

Of course, it's the content that counts, not how it was produced.

In principle, I have no objection to people using AI to assist them to produce answers. It would be great if such tools could improve the quality of the grammar and phrasing in answers & questions.

And what about all the people who won't be able to join the community because they're terrible at making helpful and constructive co-- ... oh.

2 hours later…

Relativisticcucumber

7:44 PM

hi ! i am thinking about how a superposition of states can represent a probability of measuring a state in two different outcomes each with different probabilities. the thing that is bothering me is if a state is in said superposition, i do not get what it means to say it spends "more time" in one state than the other. isn't it just always in both..? i am thinking about this [...]

[...]because i am trying to convince myself of the idea that there truly are no hidden variables and what this means for the nature of the wave function. in the many worlds theory when it says that a measurement is a collapse into that state and branches off into a system where that happened, my understanding is that the probability comes into play here by saying there is a much [...]

[...] larger chance it would go into "world one" as opposed to "world two" if the probability for the outcome corresponding to world one is larger than that for world two. is this correct?

@Relativisticcucumber who says superposition is about "spending more time in one state than the other"

I think this is an extremely weird thing to say :P

@ACuriousMind I don't know any details but it's quite likely that it was already trained to evade such classifiers

a policy of banning chatGPT might have some effect even if it cannot be enforced, some users will respect it I guess

Relativisticcucumber

@ACuriousMind my professor :/// god

why do i even go to university

okay how would i understand this notion of superposition then? my confusion is how these different probabilities do not contradiction the notion of no hidden variables

I'm not exactly sure what the question is

the Born rule says that for any observable $A$ with eigenvectors $\lvert \psi_i\rangle$ for eigenvalues $a_i$ the probability to measure the outcome $a_i$ for some state $\lvert \psi\rangle$ is $\lvert \langle \psi_i\vert \psi\rangle\rvert^2$

"superposition" is just the observation that you can think about this also in the way of writing the state as a sum (or "superposition") of the eigenstates, viz. $\lvert \psi\rangle = \sum_i c_i \lvert \psi_i\rangle$

and then the $\lvert c_i\rvert^2$ are the probabilities from above

there is no temporal component here - $\lvert \psi\rangle$ doesn't "spend time" anywhere, for all we know it is a stationary state that doesn't change with time

@fqq just train a larger classifier!

("just make it larger" seems to be the accepted process in ML generally - if we get better GPTs by making it larger, we obviously just need to train larger GPT-hunters :P)

8:17 PM

@ACuriousMind Tell that to people trying to carve out handwavy analogies between QM and CM

I'm not new to that kind of statement either

Relativisticcucumber

8:33 PM

@ACuriousMind but what does it mean that it is "more probable" so in other contexts this means there are more ways to achieve something, but i dont know how to interpret this qmech-ically

@Relativisticcucumber the probabilities here are just frequentist claims: If you repeat this measurement on an identically prepared state infinitely often, then these probabilities correspond to the frequency of the respective $a_i$ in the results

the formalism itself does not explain where these probabilities come from or what they "mean"

Relativisticcucumber

got it hm that is interesting - are there theories on this - like specifically how the probability is encoded

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

Relativisticcucumber

where the probabilities come from i guess - like exactly how something has the probability it does (but not what results from this - i know there are many theories about that)

what exactly this weird probabilistic instruction for how measurements in QM work means is known as the measurement problem and the "solutions" people keep coming up with are quantum interpretations

Relativisticcucumber

8:40 PM

yeah this is not what i am interested in though i dont think? hmmm

well i should think about my question more and come back

i am not articulating well

okay so like in normal probability the probability is given by the number of ways to get something / total possibilities and this has the implication that you mgiht be more likely to find this thing. for instance 3 red balls out of 10 balls then you have 3/10 chance of choosing it

what i want to know is not that this means you have 3/10ths chance of pulling red

i want the analog of the explanation "3/10 probability means 3 of the 10 possibilities are red"

maybe that is more clear

to be the stuff you linked only explains the interpretation/implication

yes, but that's not how all classical probabilities work, either

Relativisticcucumber

oh?

if I have a weighted dice, it has non-uniform probabilities to land on its sides, right?

I don't see how that kind of probability is related to the "number of ways to get something"

@Relativisticcucumber IIRC there should be a footnote in Griffiths page 21 (third edition) that will help you

Let me check if the page is correct

Relativisticcucumber

i just think in that case, there is a "hidden variable"

which is my entire issue with this probability notion

there is an explanation that underlies that probability

for the dice

8:45 PM

the "number of ways to get something" is when you have a uniform probability measure on the event space - then the probability for a certain subset to happen is just the number of events in the subset divided by the total number of events

Here it is "If you like, instead of photos of one system at random times, picture an ensemble of such systems, all with the same
energy but with random starting positions, and photograph them all at the same time. The analysis is identical, but
this interpretation is closer to the quantum notion of indeterminacy."

but even though people usually love to assume uniform probabilities as the "natural" meaning of "random", there isn't really a convincing argument to do that in general

Relativisticcucumber

Hm i do remember this - so is there really just many ensembles that exist and so greater probability for one case because more ensembles exist that relate to that case? doesnt this contradict what ACM is saying?

im not sure if that linked. it was meant to respond to feynman's post

@Relativisticcucumber yes, the classical dice (weighted or not) has as its hidden variable various parameters of the throw - classical mechanics would in principle predict the result of the throw perfectly, it's just that that's very tedious to compute and it's hard to measure the parameters of a human throw, so we just assume some sort of uniform distribution over the parameters and that results in the end in the distribution for the dice results

@Relativisticcucumber That footnote relates that probability over time interpretation to something closer to a statistical ensemble, which makes it closer to the standard interpretation of QM

Relativisticcucumber

8:50 PM

i think i just cannot accept no hidden variables conceptually. ive seen the bell inequality argument but : PPPP

the claim that QM has no hidden variables, i.e. Bell's theorem, is precisely that no such theory can explain the kind of probabilities you get from quantum mechanics

yes, this is counter-intuitive

Relativisticcucumber

fjdfskjfdklsjlk it doesnt make any sense

well the derivation is sensible but

i cannot see it

no one claims it isn't weird - you have been trained to think about physics as a mechanistic and deterministic exercise and now QM tells you you've been lied to

2

But the simple brutal facts are: QM works, and Bell's theorem is sound

Relativisticcucumber

oh no

@Relativisticcucumber you say that because you've lived all your life in a classical world :P

A quantum human would strongly disagree :P

8:54 PM

I prefer to think of this not with dread but with wonder - the world is much weirder than I ever thought before I learned about QM

that's fascinating

Relativisticcucumber

oh god but if there is no reason for things

how to do science

one experiment at a time? :P

Relativisticcucumber

ahhh okay thanks for the insights @Feynman_00 @ACuriousMind

you are my heros

science predicts the results of experiments, you can still do that, you just can't predict the result of a single measurement

Maybe I had the right Professors but accepting QM was never a problem for me, I find it as "natural" as CM is (in the sense I consider natural neither :P)

Relativisticcucumber

8:57 PM

i agree cm is not natural

this bell inequality topic has really thrown me though

i think i alwasy accepted quantum but had a hope that there was still explanations so i was in pseudo quantum land

My point is nothing is really natural

Relativisticcucumber

now i have made the full trip

@Relativisticcucumber I would like to stress that this is not an unusual reaction :P

Relativisticcucumber

:,)

And this goes for several other topics in Physics

8:59 PM

much like relativity, quantum mechanics takes the world view classical physics built and just...demolishes it

I'm still looking for a counter argument for the EFT discussion of the other day, I find that the hardest part to accept (not understand) in all of Physics

Relativisticcucumber

@Feynman_00 what was this about ?

This is an example of someone not accepting something @Relativisticcucumber

the problem is that we have a tendency to teach classical physics as The Truth, and physics courses rarely bother discussing epistemology or philosophy of science at all

yesterday, by Feynman_00

The only thing that makes me sad about QFT is the "effective field theory" stuff

Read from here on @Relativisticcucumber

9:02 PM

so students are taught a particular way to reason about the world and then we just pull the rug out under that way of reasoning. It is understandably disorienting if you haven't discussed the limitations and fallibility of scientific theories before, or the idea that science is a model, not a Truth

@ACuriousMind I think accepting something you have is not the truth is not a big deal as you only need to have a contradiction in the experiments to speak for you. What is unconceivable for the (or rather for my) human mind is to accept the possibility of non-existence of such truth

@Feynman_00 if you accept that we can never have Truth, why does its existence matter?

Well, I want to stress I might understand but not accept it right now. Of course if I just accepted it would be no different from e.g. free will, which is pointless to even discuss about

Relativisticcucumber

@Feynman_00 i am trying to figure out what effective field theory is ;P

the usefulness of a scientific theory lies in us using it to predict experimental results or design new technology, not in how close it lies to some "ideal truth"

of course if you think such a Truth exists then a theory is more useful the closer it is to the Truth because being closer to the Truth by definition will increase accuracy, but the existence of Truth is not required for science to work

9:07 PM

"but the existence of Truth is not required for science to work" I completely agree with this and I think no on should ever deny this statement

Although I'm on this boat "if you think such a Truth exists then a theory is more useful the closer it is to the Truth because being closer to the Truth by definition will increase accuracy"

@Feynman_00 and so it doesn't matter whether it exists or not :)

I'm less saying "you should believe there is no Truth" and more "you shouldn't care"

Relativisticcucumber

dont you think a "Truth" can reveal both how and why

and even if there is no answer to "why"

there must be to "how"

i mean things do happen

@Relativisticcucumber why?

Relativisticcucumber

well is things happen there has to be a way by which they happen

right?

why?

9:10 PM

Let me phrase it like this: does it matter for the progress of science? I don't think so. Does it matter to me as a human being? Yes

So in that sense it matters :P

Relativisticcucumber

@Feynman_00 how did you learn about effective field theory

i am rather confused about it

@Feynman_00 but what changes? What is the actual difference between a world in which the Truth you want exists and one where it doesn't?

@Relativisticcucumber if you don't know QFT yet I think the "effective field theory" discussion isn't really for you

Relativisticcucumber

i just want to know what it is

but indeed QFT is my next priority, right now im working through sakurai first !

In a nutshell it's just saying that theories are effective in the sense that they are only valid in some specific range of parameters, e.g. below a certain energy of the particles involved

Relativisticcucumber

got it

9:15 PM

@ACuriousMind It's not about making an actual difference in something. I really enjoy Physics and maybe I would study it regardless (or I would study Math, who knows), but my relationship with science is also about finding "the truth" (This makes it sound like a sect lol)

I generally try not to care about things that make no difference ;)

I understand that mindset of yours but I disagree, I would consider myself as the opposite

you only care about things that make no difference? :P

I would edit my message to correct the meaning but posterity wouldn't understand this reply, so I'll just leave it like that :P

@Relativisticcucumber Sorry for ghosting the message above, I was really focused :P

In the physicist convention $\mathfrak{su}(2)$ is made up of hermitian matrices, isn't it?

yes

9:21 PM

So it's not anymore $T_{I}SU(2)=$Anti-hermitian matrices

I mean, up to an $i$ factor

that depends on what exactly you mean by that :P

The tangent space to the manifold is made up of the antihermitian matrices, to the Lie algebra in the physicist convention is not really the tangent space in the identity

no, the matrices $\mathrm{i}\cdot\mathfrak{su}(2)\subset\mathbb{C}^{2\times 2}$ are not the tangent space to the submanfold $\mathrm{SU}(2)\subset \mathbb{C}^{2\times 2}$

Even worse D:

but of course you have $\mathrm{i}\cdot \mathfrak{su}(2)\cong \mathfrak{su}(2)$ as real Lie algebras and so this is "the Lie algebra" of "the Lie group" $\mathrm{SU}(2)$

9:26 PM

Yes it's all played on isomorphisms

almost all "the"s in math are up to isomorphism

isomorphic objects are not really distinct objects

Isomorphisms are evil though, sometimes you need to have a canonical isomorphism (which is the case here), sometimes you don't

But in any case, I enjoy $e^{tX}$ convention more for the time being :P

Fun fact, I found out "spinor" is pronounced "speenor" only a week ago

Once again I've spent a year mispronouncing stuff, please tell me I'm not alone

no, the /i/ sound is short as in "kit", not long as in "glee"

but if you've pronounced spinor like spine before this you're definitely not alone

Yes, it's not actually a "ee" sound, but you understood what I meant

The fun thing is that speaking italian I pronounce it normally, so I pronounced this word as "spine" only speaking English. After the first time hearing the correct pronunciation I wondered that it made no sense that "spin" and "spinor" had different sounds

I consider this as the second greates betrayal right after "Lie", which still hurts after two years

10:39 PM

What is the forefront of textbook theoretical physics knowledge at this point in time?

Is it like string theory?

@SillyGoose define "forefront" :P

maybe like the most refined and most complete theory that attempts to explain all physical phenomena

ah, yet another reductionist :P

I mean the agreed upon boundary in that direction is QFT

what do you mean by reductionist here

everyone would like some sort of quantum gravity, and plenty of string theorists are of course betting on string theory but the boundary there is really rather broad

@SillyGoose Reductionism is the position that all phenomena should be reducible to some "fundamental" set of phenomena that explain all others. In this case by "reductionist" I mean that you obviously equate "progress" in physics mostly in terms of how well it achieves this reductionist goal

but there's lots of other progress - in fact most actual physicists, and not even most theorists, do not work on a theory of everything

so I am always hesitant to pretend that "the forefront" is quantum gravity. It is the forefront in the sense of the reductionist programme, but most physics that is done isn't actually in service of reductionism

10:49 PM

what is the alternative to deepening one's understanding of a phenomena than to attempt to figure out how that phenomena occurs?

Some people spend decades developing theoretical methods to deal with some very particular class of systems (classical, quantum, quantum statistical, whatever). They're not working towards generalization or grand frameworks, they just want to understand some particular complicated thing in every detail

oh i see, i am for that

Like, quantum mechanics doesn't help you to solve complicated classical mechanics problems

but there is still value in developing an understanding of complicated classical mechanics setups, e.g. for the statics of buildings

and in all these tiny subfields and research directions there is, of course, also a "forefront" of what the people currently working on it would like to understand but don't yet

that's why I'm careful to point out that saying quantum gravity or QFT or string theory or whatever is "the forefront" of research is very explicitly reductionist; this is why hep-th people have a reputation for arrogance :P

hm i see. well i don't think i'll be doing hep. i hope to be able to continue to do physics xD. i am more of a working out the details of something interesting than develop a theory of everything type of person xD

oh, there's plenty of details to work out left in QFT, I'm sure

10:57 PM

yeah i'd just like to be able to work with quantum theory every day and learn new math and physics along the way--i think i will be quite content with that

unless you're currently applying somewhere, you probably don't have to decide that right now

just go with the flow and see what you like

ill be applying next year : P too soon

im going to do my thesis on some quantum stuff so that will be a good way to gauge my actual interest i n such work i think

right, and you're probably in the US where you for some reason go straight from Bachelor to having to decide on a PhD direction

oh yes xD

I much prefer the European system where you first do a not-so-constrained master's degree before having to decide about a PhD

I know a lot of people who really only found the stuff they wanted to do during their master's

(or, like me, realized they didn't actually want to commit to a PhD - but at the end of my bachelor's I was absolutely convinced I'd become a professional scientist)

11:06 PM

ah mayn xD are there funded masters though

it's not structurally different from a bachelor's degree - you don't get money for being a student

people often work as TAs for undergrad courses or scientific assistants in research groups if they need to earn some money

Did you end up finishing a PhD? @ACuriousMind

@Obliv no, nor did I start one :P

yeah, interacting with this dimension in such a way might disturb the balance.

I remember someone posted your string theory notes on here and I took them because I thought maybe i'd need them down the line lol.

So I just assumed you did/were doing a phd of some kind

I think you probably just mean the notes from the string theory course I took?

11:15 PM

that's probably what it was..

ill see if I can find it.

Dude this cursive alone is illegible for me :P dropbox.com/sh/eyxqpt9addc7g84/AABkibP7z3nWD6ACYJDXtVXQa?dl=0

omg u think that is illegible xD

I haven't used cursive since like early grade school, and it took me until today to realize I've been doing my signature wrong :P

oh, that's the notes for the first lecture I took in a course on constructive fermionic field theory

user image

my cursive not actually cursive

like the T in cursive has that squiggly thing on the left you're supposed to strike through and connect to the next letter, i've just been letting it hang out

oof i'd prefer the doc scanner

11:27 PM

3

Q: Light or neutrinos graze or pass through the Sun and arrive at Earth - need an expression for Sun's gravitational effect on observation direction/time

Skyfield's Github has discussion Jupiter hiccup #815 which then links back to to Non-physical gravitational deflection corrections for Solar System bodies #734. The script and plot from #815 are shown below. The half amplitude of the 'hiccup' or wiggle in Jupiter's RA is about 0.0001 radians or 1...

observational-astronomy general-relativity space-time time skyfield

+100 bounty added now

user image

11:47 PM

@SillyGoose how can hand-writing possibly be so tidy?

XD

the handwriting award goes to @SillyGoose

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