@imbAF $\vec E=\hat{\vec x}f(y-ct)$ is a perfectly valid EM wave that is pointing in the x direction but propagating in the y direction.

is it okay to talk about infinite dimensional complex projective spaces?

@SillyGoose it would certainly not be the first discussion of nonsense (if it is nonsense) that occurs in this chat smirk

hehe oh i just meant like does such a thing even exist without nuance

because i am thinking okay there is $\mathbb{C}P^n$ for the state space of finite dimensional systems, but i am not sure what could go wrong in the passage to infinite dimensions. since ACM had mentioned before that this geometric picture of things only works for finite dimensional systems really

Myow wording makes it clear that miao miao hath no idea either.

im trying to revise my quantum notes from the beginning >:D

@SillyGoose English: Axioms are stuff that you can fully prove to be true (e.g. group axioms) or have to accept to even begin discussion (e.g. Euclidean axioms). Physics deals with postulates, because those are choices of assumptions that can, at any future date, be refuted by experiment.

ah thatt is a good change

@SillyGoose: The infinite dimensional complex projective space ${\cal CP}^\infty$ is the classifying space for complex line bundles. It comes up all the time.

How do they conclude that $(2.2.39)$ implies $(2.2.35)$?

Since this is ST, I'll ping @ACuriousMind and @bolbteppa :P

The notation should already be self-explanatory but just in case: $L_m$ are the Virasoro operators and $a$ is a real number arising due to ordering ambiguity in the quantization of $L_0$

WillO: thanks

when we talk about transition probabilities in quantum mechanics, do we always mean performing clever measurements whose probability of occuring is equivalent to computing a transition probability?

more details in my write up above

OT: That figure is mesmerizing

what is OT :0

probably means off-topic or on-topic

Your wave for $\phi$ seems to not be a momentum eigenstate, but dont mind meow

@Mr.Feynman hehe yay

@naturallyInconsistent oh yeah im not sure if the "waves" are faithful to looking like actual gaussian waves. but they're meant to symbolically stand for close-to-momentum-eigenstates

@SillyGoose I have no idea what you mean by clever: it can be incredibly silly, but yes, we often intend to simply obtain the transition probabilities. We can often also obtain phases up to the overall phase freedom, by doing interference measurements

@SillyGoose oh, you misunderstand what miao miao is trying to convey. It looks to meow like fixed position eigenstates, e.g. stationary atomic states, rather than a momentum eigenstate. But of course, technically nobody can tell, since we have relativity, even in the Galilean case.

i guess i mean all this time i had thought about computing transition probabilities, but all we talk about in the postulates of quantum mechanics is born's rule, so i was thinking why would born's rule necessarily have to do with transition probabilities. and what i could come up with is that transition probabilities don't come from nothing, it is really a computation related to performing a measurement

The picture looks nice tho

@naturallyInconsistent ooh i see

and by clever i mean that in a particle scattering experiment if we are to compute $\langle k' \lvert k \rangle$, then really we should be performing a measurement using a detector that can only detect $\lvert k' \rangle$ states

@SillyGoose The Born rule is ostensibly worded about probabilities of measurement, but if you have them, you can convert that to transition probabilities if you so wish.

@SillyGoose How is that clever...

well it seems conceivably hard to create such a detector :P

or construct such an experiment

but maybe anything experimental would seem clever to me :P

@SillyGoose That is quite funny. There are canonically 2 ways to do a momentum measurement: Either do an experiment where you know the timing, so then you know the position difference between interaction region and detector, and you know the timing, of when the initial wave leaves the preparation box and finally reaches the interaction region, and then the time it reaches the detector.

Or where you have the detector, you swap it for a diffraction grating, so that then the different momenta will bend to different directions, and then you place detectors to measure the position of the newly deflected thing. This, you dont need to know the timings.

Feynman Hibbs uses the timing method to define the momentum everything, wavefunction and all.

The diffraction grating method is usually better: even back in the day the pioneers used prisms upon prisms to measure wavelengths to incredible precision. i.e. the ability to daisy chain and thus amplify the differences lead to much better results.

not to mention that you can simply blast with a strong initial beam, as opposed to having to control the timing of a short pulse.

@naturallyInconsistent yeah, off topic

sagecell.sagemath.org/…

Ooh! We now have the new image uploader in Chat!

@PM2Ring I'm using mobile rn, what's different?

shweeeeg

time to properly learn some differential geometry >:D

hi

hi

@Mr.Feynman I'm also using mobile. But mobile browsers usually have a 'Desktop Site' option. It's not great for reading Chat, but it gives you the Send, Upload, and Fixed Font buttons.

when they give you a distribution on the unitary matrices that is slightly not uniform

The uploader UI looks the same, but it now stores the image file on the new i.sstatic.net domain, not imgur. The old Stack Exchange imgur uploaders became a bit buggy a few years ago, and stopped allowing direct uploads from Wikipedia.

They also stopped accepting URLs from SageMathCell. So for the last couple of years I've had to download stuff to my computer (or phone) and then upload it from there to Stack Exchange. The new uploaders don't have that problem.

@PM2Ring Yeah, I do use that when I need to upload.

@PM2Ring Oh, ok. That is the answer :P

Wait, in my question this morning I didn't read the page properly lol

Sorry for pinging you ACM and Bolbteppa

Now, that is a dilemma. They are offline and the only way to have them read my apology for pinging them is to ping them again

@Mr.Feynman I solved your dilemma by starring the apology, I hope you don't mind.

@uhoh Are you saying that it's just x,y,z coords at which you evaluate the wavefunctions ?

anyone is invited to trace my reply to @uhoh back, if you know anything about DFT

@Mr.Feynman You can be forgiven since it is in reference to a ST topic

@bolbteppa are we string buddies now

@user70432 thanks pal

@MahNeh Yes, I assume so. The Python package is a "...Toolbox for Cross-Platform Post-Processing of Quantum Chemical Wavefunction Data" The solutions from DFT-like calculations are it's input, and human-readable information is it's output (like images of election densities, etc.) Go to Matter Modeling SE chat, most users there are DFT literate.

How can the discontinuity be deduced by going clockwise (as opposed to anticlockwise) from $\epsilon<0$ to $\epsilon>0$, and why is the $e^{-2 \pi i}$ inside the square root?

I understand that it is inside the square root because the branch point singularity arises because of the square root, but still if I want to explicitly see that e.g. the exponential factor doesn't contribute to the discontinuity, what can I do?

@Sanjana by magic. There must be some complex analysis magic at play, but it is so malformed that it is difficult to even discern what the author is trying to say.

😂

@Sanjana but you can definitely screw this argument and actually work out the proper arguments exactly if you simply do a few variable substitutions. First of all, substitute $q=im+k$ to convert the singularity from $im$ to the origin. This way, you will have something much more amenable to the standard complex analysis reasoning.

@naturallyInconsistent What to do after that? I am facing problem due to the exponential factor.

If I am given a simple log function and the cut is along the negative $x$ axis and I have to calculate the discontinuity in jumping from the 3rd to the 2nd quadrant, I just write $z_2=|z|e^{i(\pi-\delta)}$ and $z_3=|z|e^{i(-\pi+\delta)}$ and put these in the definition of complex log, take the difference and take $\delta \to 0$

I get $2 \pi i$ as a result

Here I have to find the jump from 1st to 2nd quadrant and the cut goes along the positive $Y$ axis!

So $z_2=|z|e^{i(\pi/2-\delta)}$ and $z_3=|z|e^{i(-3 \pi /2+\delta)}$

Sigh, this is sickening enough that imma have to actually work it out before I can properly reply

Yes, putting these in the exponential and the square root downstairs is scary...

the manned lunar landings are fake

@MahNeh then how did the lunar retroreflectors get onto the Moon?

How does that make it true necessarily?

i.e other missions did the same and were unmanned

It is you that made the claim that the manned missions are fake. I am not making that claim. The burden of proof is not on meow. If you think that the unmanned missions are real whereas the manned missions are fake, then you have to account for the lunar retroreflectors that are put there by the manned missions, that are not put there by the unmanned ones.

it's not fake becuz Buzz Aldrin punched someone for calling it fake

To me there are way too many objections to the pictures that have been published by Apollo missions plus the fact that we never repeated it after the Apollo missions

he wudnt hav reacted strongly if he was a paid actor

@MahNeh State your objections.

@MahNeh they announced that they r going to do it again. they didnt need to announce if it was a lie that they wanted buried

I just wonder if more people here are skeptical of it or most believe the landing

What is there to wonder about it? There is no qubbling about it from the scientific establishment. There is a lot of connections between science and NASA, say, that if there is any sensible doubt, it would long have been documented in the scientific literature.

i'm pretty firmly of the belief that, with the state of 1960s tech, it'd have been harder to convincingly fake the moon landing than to actually do it

what

this intro is so good

@Semiclassical I'm just saying that politicians use propaganda very well when they need it

and you illustrated that by comparing the moon landing to the Holocaust

hence, "what"

@MahNeh That is not even any where near a similar thing. Are you even attempting to make a coherent argument or not?

@MahNeh yes, but u can look up the opinions of rivals.

Soviet scientists seem to hav thought it was legit

Okay my fault to put my finger in a beehive

en.m.wikipedia.org/wiki/Apollo_11_missing_tapes

there is a rule of thumb that historians use to filter: if people wrote things that make them look bad, then theyre true things

@MahNeh what do you mean by this?

@MahNeh what do you mean by linking to this?

but this rule has to b used carefully.. e.g. u may think that some writing makes people look bad, but they may hav thought that it made them look good

the rule cant be applies here and these documentations can still be lies

given exactly how much documentation there is of Apollo 11, i'd be more surprised if some of it hadn't gone missing

@Semiclassical I think that the lord's propaganda (pun intended) could still cover for the lack of technology for simulating or faking the moon landings

no

just going to leave this here

e.g. past armies boast about murdering countless people in their writings, exaggerating the numbers becuz they think it makes them look good

Okay you disagree but that is what I meant anyways

Thanks for the video though I'll take a look

@MahNeh Again, what do you mean by this? Can you for goodness's sake write a statement that is clear as to what you even mean by all these random statements?

i like the "who cares" section at the end the most tbh

XD

@Semiclassical if ya werent bringing this up, miao miao would too.

True

I agree with that sentence but not with conspiracy very much since I believe questioning things is always useful

I would say that one of the most interesting things to observe from "conspiracists" is opposite reaction from people that know as much or less than them

well, that's also a point the video makes. that it's not as if conspiracies don't exist, but that it's silly to focus on the moon landing when there's already a lot of actually existing conspiracies

in the sense of people with power wanting to hold on to that power

@MahNeh do you question whether we have measured the mass of electron correctly?

@naturallyInconsistent at which energy scale? :P

What do you mean by " electrons "

@Semiclassical That is not actually a suitable quibble. There is this entity that at the low energy limit is what corresponds to an electron, and the mass at the low energy limit is well-established. Just like how the running coupling has the low energy limit of being precisely the fine structure constant and nothing else.

@MahNeh whatever standard physics thinks it should be.

To very many people Tempora surveillance program or the NSA surveillance program would be conspiracies

Are they not?

yeah, and the difference is that those conspiracies are 1) real and 2) represent actual power

The only point I'm making is that there isn't always a clear cut line bw them even when there is a main narrative

(honestly if you want to go down a conspiracy rabbit hole i'd look up Operation Gladio)

I don't I'm more interested in the reaction of people to them than learning new ones

there r many realistic conspiracies

Gladio is a funny one b/c there's a lot that has been confirmed

but at the same time you get to stuff which is more speculative

A much more sensible point to make is that, no matter which side you pick on the 9/11 thingy, the only explanation is a conspiracy. Either you accept the USA government's evidence that it is a conspiracy by bin Laden, or you accept one of a gazillion conspiracies that had been cooked up.

for a conspiracy to be considered, it doesnt just hav to be realistic, it also has to be important

It is not that people are ignoring that conspiracies exist. It is that you have to be much more useful / informative than just asserting this or that.

I don't know what you mean about 9/11

One of the things I have heard this there isn't any proof that humans can get through the Van Allen radiation belt although I know that Wikipedia says you would be fine

@MahNeh Are you doubting that we have real humans up in the ISS right now?

i'm thinking back to the guy on campus carrying a sign saying "satellites do not exist"

e.g. if the war on Iraq was for profits, that would be an important thing for people to know

I think it orbits on the very edges of it whereas the rockets should have gone right through the center

this is a realistic and an important conspiracy theory

@MahNeh Radiation is not something that just disappears. Your "very edges" actually means that for the long times that the astronauts would be exposed to whatever diminished radiation, it would be a lot more potent than the short time that the rockets would have endured.

@MahNeh look, those of us outside of USA can agree with you on this, but you are not even attempting to make a coherent argument when you just throw random shit like this

What do you mean by random s***? have you ever read noam Chomsky?

I'm not talking to you anymore though thank you.

@MahNeh Yes. I was very sad to learn that Chomsky would sometimes exaggerate USA atrocities. Not that there is any lack of that; Kissinger is very vile indeed, but Chomsky already made great observations on, say, manufacturing consent and other work, and really did not need to veer into weird things.

Just read about Project Condor, the vietnam war, and the aid to Israel, etc...

He tells you what it is.

@MahNeh Why do you think that other people would be ignorant of these things?

In fact, most of what he says it has been only corroborated in research

Well, at least I am not the one so ignorant as to not know the fact that the video technology of the time disallowed the faking of the moon landing, or how 9/11 and the Iraq war happened, or tried to link the moon landing to the Holocaust.

I could ask you a few facts about the history of Singapore where I live and maybe you will know much about them

Yes. On a barely related note, I served NS. I lived through when Mahathir was always quarrelling with LKY.

At the entry to link the moon landing to the Holocaust but I tried to show that the power of propaganda is easy to underestimate.

@MahNeh You might want to fix the front half of the statement. As it currently stands, it is not even well-formed.

I meant that the link between one and the other was just potentially the effect of propaganda

And when you first proposed that, you received a "what". I am not the one to send you that, but it should not be a big stretch to assert that it is both an invitation for you to substantiate that argument, and an exclamation at the level of ignorance one is detecting from that. You could have easily made the conversation much more fruitful, but you have not yet done so.

In fact, there is indeed some good arguments you could have made, if you wanted to highlight the importance of propaganda in both situations.

There is legitimately some possible good conversation to be had.

u can read the opinion of rivals

there is also conspiracies about aliens which r realistic and kind of important

pass

oh, he sees that you would like to pass, so he will pass your pass so that you can be passed that he passed your pass. He has never paid attention to having been passed.

@naturallyInconsistent i would try to parse that, but see above

@Semiclassical lol. dun pass miao~

@Sanjana where is this from? I have tried to work it out in various ways for so long, that I have simply given up and tried to work out what it would be if I summed the contribution from both contours. If the relation it worked out is correct, then I ought to be able to show that it has to be zero, but I can get something manifestly positive, after some casting, so I really think this is nonsense.

@MahNeh Interesting

Haven't seen someone else in Singapore here

It shouldnt be surprising. SG punches above weight class in sciences.

is it bad notation to use E# instead of $\times 10^{\#}$

like $4.26\text{E9}$ instead of $4.26\cdot 10^9$

I tend to use a small capital e since it seems more compact and clean

@RyderRude guilt obviously :p

in what sort of course does one learn about manifolds?

i have started to work through the loring tu diffeg book from the beginning, and I guess I was surprised to see that knowledge of manifolds is a prerequisite

A course like 'Advanced Calculus' or 'Calculus on manifolds' or 'Differential Geometry' or 'Manifolds'

hm interesting. at my consortium, there is a course and seminar for diffeg. the course is "Description: Curves and surfaces, Gauss curvature; isometries, tensor analy­sis, covariant differentiation with application to physics and geometry (intended for majors in physics or mathematics).".

the seminar is "Description: Selected topics in Riemannian geometry, low dimensional manifold theory, elementary Lie groups and Lie algebra, and contemporary applications in mathematics and physics".

i guess i should jhust read the provided appendix

@MahNeh how do you know you are not fake?