The h Bar

enumaris

12:00 AM

If you have very very large $\beta$ then you can approximate via Laplace's method

$\int_a^b h(x) e^{Mg(x)} dx \approx \sqrt{\frac{2\pi}{M | g''(x_0)|}} h(x_0) e^{Mg(x_0)}$

$x_0$ is the global max of $g(x)$

Sir Cumference

@psa The idea is that the difference between successive terms gets smaller as you make $\beta$ bigger

For large $\beta$ it very closely resembles a continuum

psa

1:02 AM

@JakeRose @SirCumference OK, so if that's the case, $\beta$ is inversely proportional to $T$ (I'm talking about thermodynamic $\beta$). We were told that this approximation is accurate in the classical limit, but doesn't the classical limit correspond to large $T$, small $\beta$?

Sorry, I meant $\sum_{j=0}^{\infty}$ in the infinite series, not $j=1.$

Jake Rose

1:13 AM

I've forgotten most of my thermo in preparation for the Part II maths cours I'm taking on it.

But I don't have any notion of my head of a classical temperature being high or low?

The thermodynamic temperature can't (usually) be below 0 but that's the only major restriction

Where does the integral come from?

psa

@JakeRose The integral is an approximation of the partition function for a rotating diatomic molecule.

The series is the exact form, but I don't think it's easy to solve (doubt there's any closed form solution).

The spectrum has degeneracy $\Omega = 2j+1$ and energy $E = j(j+1)\epsilon$

QM tells us we should only count every second $j$ for a diatomic molecule, but I'm ignoring that.

What I mean by high/low temperature is that the classical limit is valid assuming we have sufficiently high temperatures.

So high $T$ gives low $\beta$, and apparently that approximation is only useful in the classical limit.

So there's either something awry with my physics or I'm doing something wrong with the math.

it's weird, this seems accurate for low $\beta$ when I use matlab to calculate the integral and the series for $n = 100$

oops

I think I'm just tired, pretty sure it makes sense now

Sir Cumference

1:44 AM

@psa wait, right, i was thinking the other direction

$\beta$ is thermodynamic coldness so lowering it should make the series resemble the integral

psa

right, nice

the average energy should fall off like $\frac{1}{\beta}$ then I think?

hm wait no

Novalium Company

4:55 AM

I don't know if anyone has seen the news but universal cancer treatment might be coming. I hope it's not just unnecessary buzz

Johan Liebert

7:11 AM

Should a tag wiki excerpt describe what tag to use other than the given one. For example newtonian-mechanics.

Newtonian mechanics covers the discussion of the movement of classical bodies under the influence of forces by making use of Newton’s three laws. For more general discussion of energy, momentum conservation etc., use classical-mechanics, for Newton’s description of gravity, use newtonian-gravity.

And tag except of visible-light says "Questions related to the perception and measurement of light (primarily in the visible range), its mathematical description, the reproduction of colors by different means, color combinations, etc. Please use the tag [electromagnetic-radiation] if you want to refer to the general form of light." But I don't think questions related to the perception of light are answerable using physics (without residing to biology).

skullpatrol

7:43 AM

Roger Penrose: On gravity and quantum mechanics

Knight

9:13 AM

@skullpatrol I missed you pal

Secret

Composing music is very hard when you have a anti-motif bias

You end up with numerous chunks of completely distinct melodies and you struggle to glue them together into a song

Secret

9:27 AM

Knight

10:10 AM

My cousin is in Heidelberg Cement in Logistic department and he says that doing a job is a very difficult thing, there is a lot of pressure from upper officials and colleagues don’t exchange their shift duty no matter how sick you are (my cousin is in shift duty, means his duty time changes every 2 days)

Is doing a job really a difficult thing? I know do what you like rule, but I’m asking about the job in corporate sectors, is it really challenging?

John Rennie

10:32 AM

@Knight I've never found problems like that, but then I've always done jobs I like.

Knight

@JohnRennie Are you in corporate sector?

John Rennie

@Knight I worked for 12 years for Unilever, which is a huge multinational company. Then I worked for a number of small IT firms.

Knight

@JohnRennie Wow!

@JohnRennie Why do my cousins (almost everyone of them) feels so much pressure of the work? They say that if the someone from the other country who wants something from you (for job purpose, means if he wants some details or what not) then he generally calls at his day time (which is most of the time night in my cousins’ time zone)

How true are these things for a general public.

?

John Rennie

I don't know. I've always worked in skilled jobs i.e. first as a scientist then as a network engineer.

If you work in an unskilled job where you could be easily replaced then I guess you would feel a lot more pressure.

Knight

10:52 AM

Sir I think they are semi-skilled . assistant manager in logistic department, software engineer class 2 , officer in HR department.

John Rennie

I think it depends on the company, and on your immediate manager.

I wouldn't immediately jump to the conclusion that the whole of your working life will be hell :-)

Knight

So, in general what can we conclude? Or is it not possible to conclude anything?

John Rennie

I don't think it's possible to conclude anything.

Most of the people I know are happy with their jobs. That's in the UK of course, and it might be different in other countries.

Knight

Are you saying this only to keep me happy about the future ? 😀

@JohnRennie Are you angry?

John Rennie

No, that was meant to be a joke - obviously not a very good joke :-(

Knight

11:00 AM

Oh God!

Please don’t do that again, it just blew me off.

🥶

My GOD! I thought I lost you.

John Rennie

deleted

Knight

Sir I almost became ...

As ACM always say that chat is a very hard thing to keep up, you made a joke and here it struck me like a gold bullet in my brain.

John Rennie

@Knight sorry :-(

Knight

Don’t say sorry, I’m a subset of yours.

Teachers never say sorry to their good students (lol)

John Rennie

@Knight they are bad teachers then.

Knight

11:08 AM

@JohnRennie Sir what do these symbols mean in music?

bing.com/images/…

Yesterday there came a advertisement on TV where Star Trek Discovery music was shown an composer showed his notebook which was full of those symbols 🎶

John Rennie

You need to read an introduction to musical notation.

Knight

🎵

John Rennie

Something like this

Knight

It’s very hard to learn from beginning (especially without a teacher)

John Rennie

That link seems a pretty good introduction.

I wonder is there is a web site where you can put notes on the stave and hear what they sound like.

Knight

11:15 AM

Yes it was a very nice. But I don’t even know what does bass, beam means.

Have you ever read T.S. Eliot? Your countrymen poet?

John Rennie

@Knight No, T. S. Eliot is hard work to read.

Knight

@JohnRennie I thought you could explain me few of the references that Eliot make in his poems.

John Rennie

You'll have to Google for those. Entire academic careers have been made form trying to figure out what T. S. Eliot meant.

Knight

Wow! I don’t why whenever I read him my inner self says to me “ he is trying to say something but you’re too materialistic man to understand it”

John Rennie

Or of course he could just be talking nonsense then laughing about how seriously everyone is taking it.

2

Knight

11:25 AM

Yes, and it’s philosophy to differentiate.

What’s the truth

Slereah

12:12 PM

hey hey

Yuvraj Singh...

12:23 PM

Can any moderator can help me in viewing my deleted question please!

@ACuriousMind @DavidZ @rob

I ping you because you are moderators!

dsm

1:01 PM

@ACuriousMind Makes so much sense, thanks! My hold up was on interpreting $\text{ad}_X$ as a matrix, but of course that makes sense, as it's just a linear map $\mathfrak{g}\rightarrow\mathfrak{g}$. Cheers :)

Emilio Pisanty

1:13 PM

@YuvrajSingh... if you go to your user profile and in there you go to the list of questions, then at the bottom there should be a link that says "deleted recent questions"

for you, it should be physics.stackexchange.com/users/recently-deleted-questions/…

@JohanLiebert in general, on this site, the answer to "should the tag wiki (/excerpt) for tag X be improved?" is always "yes"

the answer to "... and who's willing to put in the work to improve said tag wiki?", on the other hand, has proved rather more elusive over the years

but if you're willing to jump in, by all means do so

@SirCumference that answer plays a bit fast and loose with AC. Given AC, yes, every vector space admits a Hamel basis. But without it, no.

50

Q: Is the non-triviality of the algebraic dual of an infinite-dimensional vector space equivalent to the axiom of choice?

If $V$ is given to be a vector space that is not finite-dimensional, it doesn't seem to be possible to exhibit an explicit non-zero linear functional on $V$ without further information about $V$. The existence of a non-zero linear functional can be shown by taking a basis of $V$ and specifying th...

... is at least one relevant thread.

I'm not sure whether that one has a proof that the axiom "every vector space has a basis" is equivalent to AC, but I'm fairly sure there's one in MO

Martin Sleziak

1:39 PM

That result is due to Andreas Blass, a reference is also given in the Wikipedia article: Basis (linear algebra).

And of course, the same reference can be found in many other places. Mathematics: Vector Spaces and AC, MathOverflow: Axiom of choice and bases of vector spaces over a fixed field.

Blass, Andreas (1984), "Existence of bases implies the axiom of choice", Axiomatic set theory, Contemporary Mathematics volume 31, Providence, R.I.: American Mathematical Society, pp. 31–33

Yuvraj Singh...

1:54 PM

@EmilioPisanty thanks sir but it only provide recent question link!

quallenjäger

Can someone explain what anti-de sitter space and de sitter space are?

Are they simply landscape and swampland?

Jim

2:12 PM

@quallenjäger landscape and swampland? I'm not even going to begin to figure out that metaphor. No, they are exponentially contracting and expanding universes respectively

JMac

@Jim Apparently it's an actual thing en.wikipedia.org/wiki/Swampland_(physics) I googled it because I thought they were using a very weird metaphor or translation.

Jim

@JMac like almost everything else about string theory, that metaphor makes little sense, is overcomplicated, and probably is based on something stupid

JMac

@Jim I don't think it's a metaphor, is my only real point. It's a terminology that string theorists use. If it makes sense to use in this context, or if people should really care at all, is another question entirely.

Jim

it must be a metaphor unless they are talking about literal swampland. Since that would be ridiculous, I'll lean towards it being a metaphor

JMac

@Jim Not really, in my opinion. They are talking about a physical concept that people refer to as "swampland". Although there are probably metaphors that led to that naming convention, it doesn't really imply that using that terminology is itself a metaphor. They aren't trying to compare it to actual swamps, they are trying to ask about "swamplands" as defined in the string theory context.

Jim

2:27 PM

you're saying that although the etymology may have been a metaphor, it is now a separate term that has its own definition and no longer is a metaphor?

I can get on board with what you're saying, but I'd probably still personally rather lump it in as a metaphor, if only under my own internal definition

JMac

@Jim Yes. It's not being used as a metaphor, so it's not a metaphor in this case, even if it's etymological origin is metaphoric, the way I see it. I guess my point is that the person using the term "swampland" is not themselves (necessarily) trying to connect the concept with actual swamplands; they are just using terminology which would be understood. To me, the difference is in the intention.

Jim

@JMac Yeah, I see what you mean. Although any newcomer would initially see it as a metaphor because they don't know better, someone needing to use the term would not do so with any intent of comparing the two concepts. In that case, I change my stance to criticizing the etymological origin, rather than the standard usage

JMac

@Jim Yeah, that's really what I was getting at. We can blame the people who made the convention; but once the crappy metaphor becomes incorporated into the terminology, it doesn't seem fair to assume that everyone is actually using it metaphorically.

Jim

I completely agree. The people that made the terms were to blame. It's awful

quallenjäger

2:49 PM

Well people get bored at work. I used to give stuff very weird names to make these dry written papers bit interesting.

But yeah, in string theory, landscape and swampland are actually classifications of physical theories, whether it is compatible with string theory.

Semiclassical

3:12 PM

I feel like I should know this, but...

If I consider entangled pure states of 2 electrons, then the only spherically-symmetric state is the singlet. If I allow for 3 electrons, then there aren't any spherically-symmetric states because the total spin must be 1/2 or 3/2. But if I allow for 4 electrons once more, then there should be a spin-0 state.

Which, I guess one would still call a singlet?

Yuvraj Singh...

A good song is always a good song!

Any Body Can Dance -Bezubaan (ABCD) Full Video Song HD

►

One who watch it please share his view what they feel!

Semiclassical

I guess the point is more-or-less this: If I entangle two electrons to get a singlet, and then tensor that with another singlet, then the result is still spin zero. But I could also achieve spin zero by first entangling two pairs of electrons as two-electron triplets and then entangling these.

But then I don't expect to get nice symmetries across all four particles.

Secret

3:47 PM

those are very different states, right?

they don't evaluate to the same density matrix

Semiclassical

yeah, by singlet I just mean "has total spin zero" since the only possible Sz is zero.

I think this comes down to saying that, if you want to insist on having spherical symmetry for a state with at least three particles, then you're going to have to give up on some other nice symmetry considerations.

Novalium Company

helo mai frends

velcam

Semiclassical

velkommen

...and that exhausts my knowledge of norweigian

Novalium Company

Здравстуй.

Emilio Pisanty

4:03 PM

@YuvrajSingh... how old is this deleted question?

and why do you want to see it?