The h Bar

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

2:17 AM

^

7 hours ago, by Secret

:D

dmckee

2:34 AM

Don't you hate it when there is a question on the site that, though basic and homeworky, is fun to solve?

I've got a cute and compact answer to

0

Q: How to solve this problem without using energy conservation

I believe most of you probably solved the following problem using energy conservation as shown here. It states a block of mass m sliding on a sphere of radius R. I've be trying to solve this problem using only Newton's laws without energy conservation. I would like to know if it is possible and,...

but it's too much like homework for me to feel comfrotable answering.

Only I want to show off how clever I've gotten at solving undergraduate stuff now that I've been out of school for more than a decade and teaching for roughly four years.

yuggib

you can always show off here ;-P

or in a dedicated chat room

dmckee

2:48 AM

The clever bit is using $\alpha = \dfrac{\mathrm{d}\omega}{\mathrm{d}t} = \dfrac{\mathrm{d}\omega}{\mathrm{d}\theta} \dfrac{\mathrm{d}\theta}{\mathrm{d}t} = \omega \dfrac{\mathrm{d}\omega}{\mathrm{d}\theta}$ to integrate $\alpha = (g/R) \sin\theta$.

0celo7

@dmckee wrt. what?

dmckee

@0celo7 We're working in angular coordinates so $\alpha = \dot{\omega} = \ddot{\theta}$. So $\alpha = (g/R) \sin \theta$ is a differential equation. By applying the above identity you can find $\omega = \omega(\theta)$ and the rest is clear sailing.

0celo7

@dmckee Hmm, you pulled an ACM on me

dmckee

Clearly I can't type latex with any proficiency.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

@yuggib what would be the title of such a room?

"I can prove that in one less line" ;-D

dmckee

3:01 AM

I like it.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

thnx

user116211

WTH is that.... 50 people died ;\

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

Where?

dmckee

Orlando. But I don't want to talk about it.

Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

:(

user116211

3:08 AM

@dmckee: Actually one of the user's wife at Agents of Nothing was present at the Pulse that night; he was the first to report that at the chatroom; we were reluctant about that first; but how we knew such thing would culminate....

user116211

Lately I've been thinking about heat engines a while.... what about reversible engines that operate between more then two temperatures? What would be their efficiency? Would that still be less than Carnot's? Actually Carnot operates between two temperatures....

user116211

I have not got any literature dealing with that ;(

dmckee

Well, it is easy to show that the overall efficiency of (hot)--engine 1--(warm)--engine 2--(cold) is at most the same as a Carnot engine between the hot and cold reservoirs. Beyond that I don't know.

user116211

@dmckee Ah! yeh; it's an usual homework where we have to show that the efficiency is equal to that of an reversible engine which operates between hot and cold....

user116211

@yuggib: morning.

yuggib

3:16 AM

morning

dmckee

That's a straight ahead calculate and reduce problem.

yuggib

@Sᴋᴜʟʟᴘᴇᴛʀᴏʟ why not :D

user116211

But the point is there may be a reversible engine which operates between different temperature and not like that above @dmckee showed; suppose instead of adiabatic transformations, we could have a transformation between another heat reservoir i.e., the engine works between more than two temperature.

user116211

I searched some old books in the library and also read Fermi; but of no avail. They only consider engines which operate between two temperatures and if more then those sort of that dmckee showed; not the type I'm conjuring up in my mind.

user116211

I one saw WetSavanna talking on that a bit; but then of course it was minuscule and too superficial T__T

user116211

3:25 AM

> However, there are many other possibilities for the interface to the outside World. The engine could make contact with many more than two different temperature reservoirs during a cycle, or heat could be added at constant volume (e.g. from detonation of a chemical reaction inside a rigid vessel, as approximately happens during a Diesel cycle).

user116211

Let me leave a comment in his post; let's see whether he responds......

0celo7

@dmckee What???

I need to see this proof

user116211

@0celo7 whhhat?

user116211

wait......

0celo7

I've never seen the Carnot proof

user116211

3:31 AM

@0celo7 aether.lbl.gov/www/classes/p10/heat-engine.html

0celo7

In my intro class they just said "you can find it in books"

dmckee

@0celo7 The proof that the Carnot efficiency represents the limiting maximum? In the usual form it is more tedious than enlightening, and it relies on either the Kelvin or the Clausius version of the 2nd law which are at their heart statements of observational fact until you get statistical mechanics to motivate them.

But you can find a version of it in Zemansky & Dittman if you insist.

user116211

Also, the classic Fermi lectures.

0celo7

@dmckee I don't insist

I'm not a physicist

dmckee

@0celo7 You keep saying that, but you are being seduced by the dark side.

user116211

3:36 AM

He ends many of his discussion saying that ;/

John Rennie

@DavidZ it can be awfully hard to resist the urge to be helpful, but note that my comment does include the phrase learn the chain rule - the key word being learn.

user116211

I really don't want to help who doesn't show a minuscule of effort ;(

John Rennie

5:20 AM

@dmckee I would post the answer. Although, yes, it's a homework like question the OP is clearly just having fun with physics and I see no harm in encouraging that.

The key reason we don't answer homework questions is so we don't encourage homework questions. However I see no problem in encouraging recreational physics.

user54412

@JohnRennie what's confusing me is that you wrote that answer after marking the Q as a dupe

John Rennie

@ChrisWhite I VTC'd the question as a duplicate, but the OP responded by editing it in a way that I thought made a plausible argument for it not being a duplicate. I then posted an answer but forgot to withdraw my VTC. Oh well :-)

user116211

0

Q: Some questions about the Kitaev Chain Model

In the paper,'Unpaired Majorana Fermions in Quantum Wires', Kitaev shows that unpaired Majorana Modes can be found at the end of a Quantum Wire for certain conditions. In the special case(b), the two ground states $\psi _0$ and $\psi _1$ can be shown to be of even and odd parity indicating non-...

quantum-mechanics quantum-field-theory condensed-matter

user116211

Too many questions in a single post - too broad?

user54412

yes I think so

John Rennie

5:36 AM

Although given my close votes generally run out two thirds of the way through the day I'd be inclined to save them for the truly awful questions. That one is at least a genuine question about physics.

user116211

-1

A: 3 Stage Resolution to Fermi's Paradox?

I just want to add my two cents, too large for a comment. Based on Ray kurzweil idea, there is another explanation for the lack of communication from far advanced civilizations. The cosmic orgasm hypothesis (you will not find it on wikipedia). The idea is that as civilizations approach the techno...

user116211

The comments below the post are reallllly odd ;(

user54412

@MAFIA36790 You seem to notice CO's comments a lot. Then again, I guess they are everywhere

user54412

also, wat is that answer saying

user116211

I really don't know what to say about CuriousOne.... he is .... well, he was suspended for his odd comments once; and then DS gave a valuable lecture on how to add constructive comments; but yeh....

user54412

5:39 AM

too bad people didn't like the question -- there actually is an objective, but subtle, problem with the OP's reasoning

user54412

it's a case of false dichotomy (trichotomy?)

user54412

his three cases don't include the far more likely scenarios of there being a spread in the distribution of technological progress

user54412

also, it is definitely not philosophy

user54412

my heart breaks for philosophy sometimes -- physicists and mathematicians keep claiming it's all junk, and then they throw unwanted junk at it, and then they point to the new junk as reaffirming their suspicions

John Rennie

It's the sort of thing we've all discussed in the bar late at night, but that doesn't make it the sort of thing well suited for discussion here. That was my reasoning for my VTC.

user54412

5:44 AM

the background perhaps, but his problem is with a well-defined logical fallacy

user54412

not that I'm inclined to vote to reopen on my own

John Rennie

My general rule is that if I can't, at least in principle, answer a question with a mathematical model then it isn't physics.

user54412

a model? like the Drake equation? :p

user54412

honestly, I don't know why everyone thinks the life and intelligent life terms are so common -- it's clear that no interesting chemistry happens in most exoplanet environments, and it's clear that intelligent life developed once in a third the age of the universe here, given perfect conditions for life

user116211

@ChrisWhite Drake? The SETI dude?

user54412

5:50 AM

was he?

user54412

I just know his "equation"

user116211

An astronomer from Cornell, aha!

user116211

What does SETI actually do? Did they so far discover something?

user54412

alas, back in the day writing down a general high-school-level stoichiometry ansatz made you famous

user54412

@MAFIA36790 you probably would hear about it if they had ;)

user54412

5:53 AM

most astronomers think SETI is a waste of resources (Contact captured this pretty well)

user116211

To me, Anti-Life equation (which I doubt ACM knows) is more valuable than the Drake Equation ;P

user54412

(I'm not really against it myself, since they ask important questions and hardly cost anything, though they do tend to attract some more fringe people)

John Rennie

@ChrisWhite yes, the Drake equation is a perfectly respectable mathematical model, though it doesn't address the Fermi paradox. If you have an answer that uses some similar plausibly rigorous reasoning then I'm happy to vote to reopen the question so you can post it.

user116211

nods

user54412

@JohnRennie well, I'd argue there is no paradox if you put our best guesses rather than wishful thinking into the Drake equation, but again I'm not committed to the question

user54412

5:57 AM

I'm just taking the opportunity to have some virtual beer and discuss these sorts of things :p

Secret

philosophy with donuts

user116211

Related: curious.astro.cornell.edu/about-us/130-observational-astronomy/…

John Rennie

> supporters of SETI and other programs note that the amount of taxpayer money that goes into these programs is less than one military helicopter per year

That puts it in perspective :-)

Secret

6:30 AM

quantamagazine.org/20160607-new-boson-claim-faces-scrutiny

albanydailystar.com/science/…

New Fundamental Particle Discovered?? + Challenge Winners! | Space Time | PBS Digital Studios

►

a good summary of the latest

yuggib

it's amazing how many people thinks that $\aleph_1$ is the cardinality of the real numbers

@_@

Secret

$\aleph_1$ is cardinality of $2^{\mathbb{N}}$, right? which is bigger than the reals (assuming continuum hypothesis)

yuggib

T__T a lot of confusion

Continuum Hypothesis (CH): $\aleph_1=2^{\aleph_0}$

where $\aleph_0=\#\mathbb{N}$

however, the continuum hypothesis is non-provable and non-disprovable in ZFC

but in ZFC, $\#\mathbb{R}=2^{\aleph_0}$

Secret

6:45 AM

do the power set of the naturals actually well defined, or only $2^{\aleph_0}$ is?

Secret

7:07 AM

5 hours ago, by Sᴋᴜʟʟ ᴘᴇᴛʀᴏʟ

7 hours ago, by Secret

John Rennie

@Secret why do you keep mentioning this? It's not a new book, so why the sudden interest in it?

Secret

(Ack, cover blown!) The reason is obvious

It's a sacarsm

The EERIE Silence

user116211

John Rennie

What comic is that?

user116211

The MASK!

user116211

7:22 AM

Dark Horse Comics

Secret

Did not know that The MASK has a comic version

user116211

@Secret o.O

Secret

I am aware of the flim version, not so much of the comics

I rememebr I first watched that when I was around 6, and got scared by the scene that looks like a fire ring

John Rennie

Ha, out of 714 servers there were no, repeat no, backup errors last night!
Mind you, the Sunday night backups are not especially stressful :-)

Secret

@Secret Ok my memory is all muddled up again. There's no fire ring in the movie. I must have mixed up with something else

Danu

7:35 AM

Hey, remember that one time that nobody believed me that you can write $f\circ f^{-1}=\operatorname{id}$ and $f^{-1}\circ f=\operatorname{id}$ for injective/surjective but not necessarily bijective functions (looking at you, @0celo7 and @ACuriousMind). I happened to be looking at Spivak's textbook on calculus, and guess what I found...

(to be fair, he adds a caveat about the domain of the r.h.s. possibly being larger)

Secret

8:18 AM

@Secret This question has already been answered by friend, we can mark it off the list

yuggib

8:48 AM

@Secret the power set of naturals is $2^{\aleph_0}$

Secret

8:59 AM

Meanwhile I was almost planning to ask about the following question, but end up searcing MSE instead.

currently, it is still beyond my level thus I will leave this for later

6

Q: What is known about the power set of the real number line?

Cantor's theorem states that the cardinality of a set's powerset is strictly greater than that of the set itself. This clearly applies to the reals also; if I'm not mistaken, the cardinality of the power set of the reals would be $\beth_{2}$. Is there any literature on the powerset of the reals?...

elementary-set-theory cardinals

I do, however have a quantum conceptual question that I can ask you, but phrased in undergrad wavefunction collapse language as I still have not finsih reading von neumman yet

@yuggib
Suppose I have a set up containing one electron. 8 light minutes away I placed a detector B that can read the spin of the electron (and can flash red if spin up, green in spin down).

Suppose I have a friend Ann standing next to detector B.

Now I use another detector A next to the electron unit to measure my electron spin. Suppose my measurement collapse it to spin up. will I expect 8 minutes later, Ann will inform me her detector flashes red?

My guess is that when the electron state get projected to e.g. spin up eigenstate, that information will need to travel with an upper boun…

yuggib

@Danu this looks very close to an abuse of notation in my opinion

yuggib

9:20 AM

@Secret it depends on how your experimental setup is done

Secret

yuggib

the most effective way to think about it in my opinion is as two non-interacting apparati, that in addition have a localized in space interaction with the particle. Of course to give a precise mathematical meaning to all that could be rather hard, nevertheless it should in principle be possible

instead you may think of a time-dependence that models the switching "on/off" of the apparati

so you would have a dynamics that consists of five parts:

the three time-independent parts are the free (non interacting with the apparati) particle dynamics, the A free (switched off) dynamics, and the B free (switched off) dynamics

the two time-dependent parts are the interaction of the particle with A, taking e.g. place from $t=0$ to $t=t_A$, and the interaction of the particle with B, taking place from $t=t_A+8\text{min}$ to $t=t_B+t_A+8\text{min}$

this would give the dynamics of the whole system A+B+particle

and of course if the measurement apparati behave as they should, you would get that for $t_A \leq t< t_A+8\text{min}$, the reduced state of the particle alone would be that of spin up. Then, your apparatus B would measure spin up, and essentially leave the reduced state of the particle unchanged (but of course the reduced state of B changes, as the whole state of the system, according to the full dynamics)

2physics

@secret what is "Chat interview featuring guest speaker Slereah
tomorrow" who is slereah ? please can you tell me?

yuggib

9:36 AM

@2physics meta.physics.stackexchange.com/questions/7782/…

Secret

@ yuggib, I see
@2physics the link contains all the details you need to know. But in short, he is good at CTCs

2physics

9:48 AM

@yuggib@Secret I got it. Thanks.

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