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00:00 - 13:0013:00 - 23:00

00:05
@SillyGoose You need to play through the counterfactual here if you don't understand what the text means: If the core electrons did participate in conduction, what orders of magnitude would you expect between the conductivity of those elements?
@ACuriousMind I will attempt this computation after i finish the section :)
@SillyGoose I didn't mean some fancy "computation" :P Just observe that Caesium has 20 times the atomic number of Lithium, but there's only a factor of two between their conductivities. What the text means is simply that the conductivities do not increase proportionally to the atomic number, so it's a good guess that there's not drastically more conduction electrons when the atomic number increases
hm but even in this table one out of six metals has anomalous behavior--isn't this also a cause for concern?
I am referring to the fact that the resistivity drops when going from lithium to sodium
the observation you're supposed to make is that the resistivities are all within the same order of magnitude
I'm not sure why you'd label the drop as "anomalous", that it can drop supports the text even more - you would expect a much larger increase at each step if the resistivity increased with rising atomic number because more than the valence electrons participated in conduction
well i think i would not take the data shown by this table as suggesting independence of resistivity on atomic number
i would agree that it suggests there is not a strong dependent on atomic number
00:20
@SillyGoose I think you're looking at this the wrong way around: You're not supposed to look at the table and go "wow, resistivity is independent of atomic number!". You're supposed to take the assumption that it is, look at the table and go "yup, no obvious contradiction there".
 
2 hours later…
02:00
Why is scattering assumed in classical Drude model? The Maxwell speed distribution directly follows from assuming that the free electron gas obeys the classical canonical ensemble (which need not assume scattering? I am not sure), which leads to the wanted specific heat capacity result.
Or maybe this just says that scattering is not necessary to explain the specific heat capacity given by the Drude model
Okay sorry ignore my question
(1) Canonical ensemble $\implies$ heat capacity result; (2) Canonical ensemble + scattering $\implies$ conductivity results
 
2 hours later…
04:29
Wow, the new Sonic movie was actually a top notch adaptation of one of my childhood favorite games
0
Q: Regarding recent infestation of new users resorting to gen AI targeting STEM communities

User1865345Of late, there has been a surge of new users who venture to various communities and answer at a pretty staggering rate with apparently good looking posts, majority of which would be long and heavy with mathjax formatted equations. The initial targets were: Cross Validated, Mathematics, Maths Over...

Made a post at Meta. Feel free to edit or add anything, if needed.
As usual, some user is saying flag and move on. At least read the post completely 🙂
I know now and then there will be some users who would use gen ai. But this is a coordinated surge by similar behaving users. I am reporting this incident.
👍🏻
What I wish is if one community bans the user in question, there should be some mechanism where that community's mods alert the others where the user is active.
That would make the detection easier.
For example, many of these users have banned at MO for months. Yet they are doing the same thing freely at other communities waiting to be recognized and flagged.
However, as I credited you folks there, let me 👏🏻 for you folks again to look into these nonsense and flag those.
Appreciate that.
As for mewoth, @naturallyInconsistent, I was already late and it was pretty hectic day for me and I even forgot the keys. Lol. I didn't even see the emails where two students said they would be writing a term paper. I had to hastily arrange that. 🙂
I would be going back after holidays again.
05:11
hi bestie
Hello, Allie.
my head hurts bad
m i a o ~ m i a o ~ a l l ~
05:15
meow
i dont know. possibly medication?
possibly anxiety
i dunno
Hmm.
@Allie you need meditation.
yah ive been trying
Darken the room. Light a candle. Stare at it.
its pretty hard a lot of times it straight up does not work. depending on where my head is at
and believe me i try very hard
Think about your favorite things.
05:18
its a little harder than that for me
could it be tension headache? Miao miao realised that a LOT of people have it; miao miao included, and massage to relax the shoulder and neck muscles have drastically improved quality of life.
dont worry, i got it
@naturallyInconsistent probably, i have EXTREMELY bad tension
@naturallyInconsistent hmm
But if it is anxiety, then maybe you will need psych help. They can definite do a lot.
i already do get said help
hence the medication
it is a slow process
i will tell myself today. i am capable
of doing this quantum chemistry
and surviving
but you definitely can do it
05:20
(what imminent fear is there? no idea)
allie has a headache. problem, be slain
@Allie you need a pet.
I have 2 cats
my dog actually died today.
🐱🐱🐱
05:21
meow
@Allie what??? Hmmm
Soo sad. Heaven got another angel.
woof in peace
Please don't feel so bad. It's good to cry. But have a moment enjoying the happy memories.
Mine died when I was away preparing my masters dissertation. I came to know months later.
oh my
i guess family didnt let you know since they knew you were stressed?
Yes.
Initially I was really angry. I mean how could they?
But then I understood their perspective. Still I was depressed for days. Spent late night in uni and going back only when the department had to be closed.
05:31
was just listening to youtuber explaining why Mozart's music was so good, and one part, he referenced the fact that a sad piece of music that Mozart made, was made when his mother died and he had to hide and postpone the news of her death so that his father would have time to prepare. That one night, he wrote a letter to his father saying that she was badly ill, but another letter to his friend to console his father because his mom actually died. Doggos are family, deserving of hiding death
Wow
In fact I dedicated my dissertation to my doggo.
Thanks to my guide who approved it.
Anyway Allie. Don't be sad so much. Attend your other two cats. Sometimes if one pet dies, they could impact the others. Check for any such signs.
 
1 hour later…
06:58
sometimes it's good to have a break. i've been feeling mildly burnt out lately. i had a long walk at the beach :)
07:54
Apparently all infinitesimal spaces have entirely boring lattices
Literally nothing spatially to differentiate them from a point
Only their spaces of probes differ
at least within the context of topos theory
No non-trivial subregions for infinitesimal points
Non-standard analysis does have it but it doesn't admit any obvious parallels to formal synthetic geometry
Nilpotent elements seem to basically contribute zilch
08:40
@Slereah intuitively it makes a lot of sense
@qwerty walk, walk~
hi besties
guess what
im going to start reading Ashcroft
i did NOT expect to get this into physics but it just happened naturally
so excited for all the books i have to read
i want to know WHAT THE HELL A PHONON IS
08:59
@HerrFeinmann I'm not sure it does :p
It works though I don't think it's intuitive
Like it's a very algebraic way to do it
@Allie Do you know what the normal modes of an oscillation are?
yes
its that for electrons in a crystal?
Things get extra bad for stupider spaces like supersymmetric spaces
which I'm not sure if they have any good interpretation
@Slereah sounds cool though.
meow
09:02
Well it only does because physicists just add the word "super" everywhere
@Allie hm. So physics have got all the cool names. I see.
@Slereah lol
im in a good mood
this is not normal....
@Allie medication working
i was just gonna say it must be the chemicals modulating my brain activity...
Hello @JohnRennie (only you were the one I didn't interact here)
09:03
because usually my brain says "everything bad you should be sad and nothing matters"
Apparently in the topos way a supersymmetric space is basically just a slightly different version of a space with infinitesimals, but only in the sense that it's a non-trivial space with only a point???
@Allie brain is a trickster.
@Allie In a crystal you have many atoms all vibrating as if they are all connected with tiny springs. In principle we can analyse the normal modes for this oscillating system. In practice there are 10^(large number) of these modes, but in principle it could be done.
but right now.... i am just excited to learn and read
@Allie great!!
@qwerty 👍🏻👍🏻
09:04
@Allie And each of those modes is a phonon.
@JohnRennie i see
I will still be reading this book to get the full picture :)
@Slereah you read Goldblatt's book on Topoi?
I did not
I'm not sure I'll ever really get supersymmetry outside of "it no commute"
I see
Anyway whenever you are done with this @Slereah, may I suggest you do probability?
Hell no
09:08
@Allie They behave like particles because they scatter off each other i.e. one mode can exchange energy with another mode.
I'm no big fan of stats :p
plotting to convert one physicist to statistician
@Slereah never say never.
You will be loving Kolmogorov. He was a cool guy.
This is like the a phonon being annihilated as the energy of its mode decreases, and a new phonon being created as the energy of the new mode increases.
@User1865345 Didn't, I just said hell nah :p
thank you bestie i am excited to learn about this
althought tbh my brain is pretty fried rn its 4 am
09:10
@User1865345 most evil thing
I advice every newbie to begin with Kolmogorov's landmark Grundbegriffe der Wahrscheinlichkeitsrechnung.
but that makes sense how it acts like a particle
i was always confused by that
@Slereah you need exorcism. I will show you the beauty of probability world. It's magical.
It's ruled by law of large numbers. What a beauty.
lol
Monkeys can write Shakespeare owing to this.
09:11
meow
they can also write my entire chat history
...
Law of Large Numbers is like God card. It can do anything.
can it buy me a new car
i didnt think so
smile
We are beyond materialistic possessions. We only deal with probability.
09:14
i joke
i will hopefully move to the city where i will never have to drive again next year
just pray I get into one of those phd programs!!!!
@Allie although there were some nerd guys who apparently didn't like law of large numbers and revolted against it.
@Slereah you've been posting lots about topos theory lately - what interests you about it, in relation to physics?
The original version (from Gut's Probability text):
Still no love for probability? 🤔
@Allie you will.
Have faith.
@qwerty pretty much
also just generally an interesting notion
pretty much...?
09:21
meow.
i will tell everyone here as soon as i get my first acceptance
09:33
M E O W ~
@Slereah I mean what's the connection to physics?
@qwerty It's a generic setting for mathematics, much like set theory
You can basically deal with any type of theory in them
But you can also choose specifically some type of properties you find important in there
So it can make some rather complex statements very compactly
oh cool
@Slereah are there particularly well known examples of this?
@qwerty mostly fairly abstruse statements about gauge theory :p
09:38
xD
@User1865345 oh thanks. @Slereah have you read/seen this paper too?
Yeah
Unfortunately all the most important part of topos theory for physics involved $\infty$-topos which are extra shitty to deal with
10:03
interesting that a mathematical physics paper makes so much reference to philosophy
it's a popular thing to do in that sort of domain :p
interesting. on an unrelated note @Slereah I saw your comment from earlier about all Bayesians being losers or libertarians :p I know what you mean but it's not exactly true, as there are some disciplines which use Bayesian stats more than others
I know, I'm just being a bit silly
Just groups who have turned some scientific idea into a trend
Not the first time this happened
cough
Clinical trials and epidemiology are all Bayesian. If you survived covid, leave a note of appreciation for Bayesians.
I know
I mean more
Those types
10:18
yeah me and pm 2ring brought it up the other day chat.stackexchange.com/transcript/message/66847191#66847191
thanks rationalist bros /s
Just a fact: Bayes himself is not too much responsible for what we know as Bayesian statistics.
Dude is enjoying in his grave all the credit in his name.
It was actually Sir Harold Jeffreys who popularized objective Bayes, the thing we use.
And surprise....
Sir Harold Jeffreys was a physicist.
ahh we should give Jeffreys the prior credit
2
B)
🤣
Right
Btw this is not a one off example. There were many statisticians of the golden age who were initially physicists.
So Physicists love probability. 🥱
it makes sense. a lot of fields of physics only really make sense if you're strong in statistics
No idea but I loved what you said.
My primitive memory reminds of Maxwell distribution curve.
10:32
Bayes was more about divine providence than statistics
That is true.
Dude wasn't thinking about statistics.
It is only after de Finetti formalized the existence of priors based on conditional independence and exchangeability.
The paradigm should be named after them, not Bayes. He has got undue credits.
Saw that in Wikipedia:
> De Finetti held different social and political beliefs through his life: following fascism during his youth, then moving to Christian socialism and finally adhering to the Radical Party.
Some radical changes indeed.
10:58
there are too many things named wrongly
it aint an egregious case, like stolen credits
True. Bayes should be given credit for developing a rather special case of what is today's Bayes' theorem. But he was nowhere near any form of interpretation of the same.
I think it was actually Laplace who did the heavy lifting.
Finally people like I mentioned above formalized the subjectivity.
there are many such instances elsewhere too. Generalisations of a theorem tends to still take on the name of the original
I see.
Stigler's law of eponymy, proposed by University of Chicago statistics professor Stephen Stigler in his 1980 publication "Stigler's law of eponymy", states that no scientific discovery is named after its original discoverer. Examples include Hubble's law, which was derived by Georges Lemaître two years before Edwin Hubble; the Pythagorean theorem, which was known to Babylonian mathematicians before Pythagoras; and Halley's Comet, which was observed by astronomers since at least 240 BC (although its official designation is due to the first ever mathematical prediction of such astronomical phenomenon...
2
Even this was also not named after the original guy. Lol.
BTW Stigler is a renowned statistics historian.
His PhD work was some hard core asymptotic results. But later he turned to history.
11:14
on a reverse(?) tangent. that paper on topos theory is really interesting, as it's poking at something I've mentioned before on chat. about how we only measure real numbers; but actually even that is not strict enough.
What's everyones favourite era of physics?
We typically only count things or look at intersections for the most part
@DIRAC1930 paleolithic
yup
@DIRAC1930 when Maxwell developed his equations.
Don't ask me why. I watched a video of a girl who said that.
Probably she was talking about Feynman; I didn't complete it.
@User1865345 Kathy?
11:22
Maxwells, Diracs, Schrodingers and Einsteins equations are the only ones I care about
Wait. Let me watch my history. I didn't remember the name.
@Slereah the Mesolithic was more fun
I really don't care because I can't assess her opinions. I still don't know why these physics vids come to my feed, although I do occasionally click.
Paleolithic had many great physicists rly
Ug
Grugg
Hey @qwerty, also found this thread while googling.
11:24
Throg
9
Q: In the topos-theoretic interpretation of Physics by Isham & Doering what role does intuitionistic logic play?

Mozibur UllahIsham & Doering have written a series of papers exploring how to ground physics in topoi. Now the internal logic of topoi is higher order typed intuitionistic logic. In their theory what role is played by intuitionistic logic? What are the types in their theory? I've also asked this question on ...

Maybe you find that relevant.
Her videos are too long
@Slereah remind me about Ug's law and his rival Grugg
Early GR model
"thing fall down"
no surely that was Throg
11:26
Does anyone have any information about Schrodingers beliefs regarding quantum field theory
> If you push something hard enough, it will fall over — Fudd's First Law of Opposition.
Legit law.
11:47
if the field is continuous how can the energy transfer be discrete??
which field and what energy transfer
EM field and photons
Well, first you could explain what you mean with continuous field :P
every point in space has a value
even if you keep zooming in
Same way that non-relativistic QM works even though position is continuous
Your wavefunctions aren't "sharp" configurations of the EM field
11:56
i.e. it just works?
it's a probability distribution over the space of all EM fields
There's no fundamental contradiction here
so if we keep tuning down the energy eventually the EM field is not continuous anymore?
What do you mean by not continuous exactly
the real EM field, not the probability distribution
like what situation do you have in mind where that's an issue
11:59
let's say i have a single photon, which we know is a wave in the EM field, so it distributes across space, and then its energy is transferred to a point; where did the energy in the other points of space go?
Well, first issue : there are no single photon states
what do you mean by "and then its energy is transferred to a point"?
an electron absorbed the energy of the photon
electron is the point
And typically in experiments where we have a "photon", we don't have a photon (eigenstate of the number operator), we have some wavepacket
hmm that's a good point
so it's never a single photon?
because a single photon would continue through the entirety of space and time?
12:03
Single photons aren't actually states
like even "behind the laser beam"
They're not normalizable
@LeakyNun are electrons points?
i guess all the scipop videos that say "photon" is wrong then
12:03
Also like typically in QFT settings, we look at asymptotic states, so we don't really see the "real" process
We don't see the unitary evolution of the EM wavefunction
As it is not tractable
@naturallyInconsistent depends on the, uh, "Copenhagen interpretation"
QFT is still a quantum theory, given some time parameter your wavefunction evolves continuously as $\psi(t)$
And the "real field" is gonna be measurements you can do on that wavefunctions
which would be continuous as a result
But nobody does it because it's not a solvable problem so far
@LeakyNun it is good that you understand that it depends
can free electrons (not bound to an atom) receive a photon?
Sure
12:06
@Slereah so if "single photons" don't exist, how did the absorption lines form?
Although with the caveat of what I said, in QFT you don't really have "individual electrons" receiving "individual photons"
That's an approximation we do
@LeakyNun you should check that the bare interaction is forbidden.
by failure to conserve energy-momentum
what do you mean?
It is a standard example problem that professors would set students to do
but Slereah said "Sure" to that
ok i want to understand this from another angle
let's say i shoot two electrons towards each other
and then they are deflected and they travel an approximately hyperbolic path
12:10
@LeakyNun that's the thing, you cannot prove that the path is approximately hyperbolic
would i be correct to say that one electron actually transfered "one photon" to the other, and then the "photon" is actually the energy difference between the two electrons across the whole time (so it doesn't have say one frequency and one energy across time)?
@naturallyInconsistent uh... this is messing with my brain lol
do we just not have this problem in the classical setting because there are a lot of electrons?
@LeakyNun Slereah definitely knows that a universe with only just one free electron in a vacuum and a photon, then the conservation of energy and momentum leads to triviality. The issue is that there are many other scenarios.
@LeakyNun once you step into quantum realm, things are horrible like that.
(anyway, gtg, sorry)
@naturallyInconsistent as in, say i have two electrons A --- B, and then at time t=0, A moves leftwards and emits a photon rightwards, and then at time t=1, B receives the photon and moves rightwards, and then i can prove that energy and momentum are not conserved?
wait even the first step is problematic
i've created energy out of nothing
A was stationary, but then A and the photon both gained energy
i would have to assume that A was moving rightward at the beginning
(and then transfer to A's reference frame and derive the same contradiction)
@LeakyNun A free travelling electron cannot emit a photon
that is mind boggling
12:17
What is the problem you actually want to solve here?
you've said a lot of rather confused things that are a wild mixture of a classical, QM and QFT picture and the reason it doesn't make sense to you is because it doesn't - you're mixing wildly incommensurable viewpoints with each other
i mean i don't know what naturally meant by the scenario that would violate energy and momentum
You cannot have the scenario that a free electron absorbs (or emits) a photon and conserve both energy and momentum
that's why that kind of absorption/emission can't happen
it's a relatively straightforward exercise, you just write down the conservation equations and derive a contradiction
5 mins ago, by Leaky Nun
(and then transfer to A's reference frame and derive the same contradiction)
is it the same as what i did here?
not really, reference frames aren't really relevant here
as in, it was more of a shortcut
12:24
but yes, the contradiction is probably most obvious in the rest frame of the electron that is supposed to emit something
yeah
@ACuriousMind could i solve this problem by declaring that E=hf and p=h/λ are wrong because it wouldn't be one photon with one definite energy?
@ACuriousMind yeah i think i'm still digesting the idea that if you zoom in far enough things don't have definite paths
Solve which problem? That free electrons can't absorb/emit photons isn't a problem, that's perfectly in sync with the reality we observe
because i've seen too many drawings of single electrons
@ACuriousMind no, but electrons repel each other right?
@LeakyNun Yes. What does that have to do with photons?
any force transfer is a photon right
12:30
nope
well, not a real photon
many people insist on talking about "virtual" photons, but as the name says, they're not real
I explain the formal derivation of the Coulomb force from the QFT scattering here
if they're not real how did they repel each other
I don't know what that question means
well electron A lost energy and electron B gained energy
they did so via the EM field
the EM field carried the energy
What does "via" mean?
A delivered the energy to the EM field and then the EM field delivered the energy to B
12:33
What does "it carried the energy" mean?
like a mailman delivering a letter!
@LeakyNun I would suggest that there is absolutely nothing in the physical formalism that supports this story, as nice as it may be.
well how do EM waves exist without a medium then
what do EM waves have to do with electrons repelling?
they both use the EM field
12:34
So?
I'm not saying the EM field cannot carry energy
I'm saying trying to describe the interaction of two electrons in terms of them shooting packets of energy via the EM field at each other is doomed to fail if you poke at it hard enough
hmm
how do they interact then
12:54
@Slereah I was thinking that a discrete lattice is spanned by a (set of) discrete (finite) displacement vector(s) and an origin. If you imagine to apply this to the infinitesimal case, you have you origin but the infinitesimal displacement (or better arbitrary displacement) still map you to the same point. Not that I know anything about this. I'm doing heavy handwaving
@HerrFeinmann Wrong interpretation of the word "lattice" here
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet). An example is given by the power set of a set, partially ordered by inclusion, for which the supremum is the union and the infimum is the intersection. Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple...
@LeakyNun Magic.
i see, so a sufficiently advanced technology
That's only a slight exaggeration, there just is no good story for what the interacting time evolution actually does (essentially the only story we've come up with are those of the virtual particles but it has many problems). I rant about this e.g. in this answer
00:00 - 13:0013:00 - 23:00

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