The h Bar

7:19 AM

Hi everyone! Is there any term associated with the rotational analogue of the centre of mass? Something like 'centre of moment of inertia'? I understand it would not be a single point but a line or a plane, which remains fixed even though the individual components of the object rotate under the absence of external torque.

For example, the combined centre of mass of a man walking on a boat on still water remains at a fixed position due to the absence of external horizontal force (neglecting viscosity of water). Here, the corresponding term is 'centre of mass'.

In the same way, when a reaction wheel in a spacecraft rotates in one direction, the spacecraft rotates in opposite direction. What is the name of the quantity which remains fixed?

user434058

@GuruVishnu There's radius of gyration, which is somewhat like the root mean square distance of all the partickes from the axis.

user434058

@GuruVishnu Well, in this case, the momentum of system doesn't change is a more general statement. Similarly, we can say that the anular momentum of the system doesn't change. I don't really see the need of anything being "stationary".

John Rennie

7:35 AM

@GuruVishnu it's a combination of the centre of mass and the axis of rotation.

That is, for a free mass the axis of the rotation always passes through the centre of mass.

The axis of rotation is the invariant line in a rotation.

JingleBells

We know that companies can give out some of their profits to stockholders but does that mean that the stockholders receive cash? If I buy 1 share of McDonald's and the company decides to give 20% of this years' profits to stockholders, will I get like 10$ of cash or something? Or the only way to make money of a stock is to sell the stock at a higher price than you bought it

Faded Giant

@JingleBells The dividend of MCD is about 2.56 %; you would get 5.00 $ per share.

JingleBells

@FadedGiant Lol I was still close, it was a complete guess. But that's how stocks work right?

Faded Giant

Dividend

A dividend is a distribution of profits by a corporation to its shareholders. When a corporation earns a profit or surplus, it is able to pay a proportion of the profit as a dividend to shareholders. Any amount not distributed is taken to be re-invested in the business (called retained earnings). The current year profit as well as the retained earnings of previous years are available for distribution; a corporation usually is prohibited from paying a dividend out of its capital. Distribution to shareholders may be in cash (usually a deposit into a bank account) or, if the corporation has a dividend...

JingleBells

7:50 AM

lol thx

Guru Vishnu

8:17 AM

@FakeMod Thank you for your reply! I was thinking of simplifying few things using this new quantity as we do by using the centre of mass in linear motion. Other than that, I can understand that both linear and angular momenta are conserved in the absence of external force and torque, and hence in the examples mentioned.

Guru Vishnu

8:28 AM

@JohnRennie Thank you for your reply, sir! I can understand your point. But to make things simpler, $\frac{1}{\sum m_i}\sum m_i v_i$ gives the velocity of COM. In the same way, what is the term for particle(s) having an angular velocity $\frac{1}{\sum I_i}\sum I_i \omega_i$? The reason I'm looking for the specific term is for Googling purposes.

Charlie

11:57 AM

@rob Ah I see that makes sense thank you :)

Slereah

12:39 PM

This paper has $\mathfrak{Op}$ and $\mathfrak{Vec}$

Easy on the fraktur

they barely look like letters

Exercise 1. Spend a little time meditating and convincing yourself that $L$ gives a sheaf of vector spaces over $X$.

@ACuriousMind how do I meditate

ACuriousMind

drugs, probably

Slereah

brb doing drugs

Dunois

12:54 PM

I am watching this video: youtube.com/watch?v=jlEovwE1oHI . At 10:30-ish in the video, the presenter states that the quantum fields only accept discrete amounts of energy, and that (say) if 2x 0.511 MeV of energy is added to the electron field, then two electrons will be created. I'm a bit confused because I have heard of "high energy" electrons, which I presume have n-times the 0.511 MeV of energy a "basic" electron would have. Could someone please help me understand this?

ACuriousMind

@Dunois First, the language of quantum fields "accepting" energy or having energy "added" to them is pop-sci phrasing that doesn't reflect what the formalism does - quantum fields are quantum operators, not some kind of weird energy storage. Second, 0.511 MeV is the energy-equivalent of the rest mass of an electron. you can add an arbitrary amount of kinetic energy on top of that by accelerating the electron, this is what "high-energy" particles are - very fast particles

Note that nothing requires the kinetic energy to be a multiple of 0.511 MeV or any other quantity - it's continuous.

Sir Cumference

@Slereah don't do crystal math

well i'll attribute my lame joke to sleep deprivation

JingleBells

If a company issues stocks (to gain capital for expansion) and the company succeeds but refuses to give out dividends (regular payments to the shareholders), what happens then?

Slereah

Sheaves have quite a tragic story, it turns out

Dunois

@ACuriousMind I'm not going to pretend I know what a "quantum operator" is, but I will roll with that. If I may ask--and this is as a complete layperson--if "particles" are "excitations" in a "field" (all of which I can somehow imagine), what does it even mean to impart kinetic energy to a particle?

Also, if that pop-sci approach is bad (and I concede it most likely is), could you recommend alternatives that are more rigorous but nevertheless approachable for a layperson?

ACuriousMind

1:05 PM

@Dunois While a quantum particle isn't a little ball that flits around, it still has energy and momentum, and it's kinetic energy is $\frac{1}{2}mp^2$, just like for classical particles. In terms of "excitations", think of a wave that travels (on a string or on water) - the velocity with which it travels is proportional to its momentum

Dunois

So a quantum particle is a localized excitation in a field that can have (definite?) trajectories?

Slereah

Bad news

ACuriousMind

@Dunois I don't believe that you can really usefully understand QFT without actually studying it (i.e. by taking a university course on it or by working through a university-level textbook). Anything that doesn't do the actual math necessarily only presents you analogies that make you feel like you've understood something but which necessarily break down somewhere.

Good analogies break down later than the bad ones, but none of them can really capture how QFT (or QM, for that matter) works because the analogies are necessarily analogies to classical things but the whole point of quantum mechanics is that the world is not classical.

Slereah

If it's localized, it doesn't have a well-defined momentum :p

ACuriousMind

@Dunois No, the momentum, like all quantum observables, is uncertain. Due to the uncertainty principle, a fully localized state has fully uncertain momentum, and vice versa.

JingleBells

1:09 PM

Wow! Is this a joke. I pay (dollar sign)194 for 1 share of stock in McDonald's and they yield a (dollar sign)5 dividend per stock annually. I mean, it's gonna take me 38 years to pay that (dollar sign)194 and start making a profit of (dollar sign)5 per year... you get the idea. How am I supposed to make money out of stock dividends?

Charlie

Is the point not that you sell your stocks eventually and make an actual profit?

Dunois

@ACuriousMind I see. That is foreboding for the future of public scientific temperament then. If I wanted to learn QFT, where would you suggest I start? I presume there is no way to "learn" it without being exposed to the math? Which means I'd probably have to begin by learning the math first?

ACuriousMind

Please don't use dollar signs for currency here, it messes up the MathJax renderer :P

Charlie

@Dunois what kind of experience in maths/physics do you have currently?

Dunois

@ACuriousMind so a quantum particle can have momentum, you can add or remove momentum from it, it is localized, but you just don't have any certain measurements for any of its observables?

JingleBells

1:11 PM

@Charlie Why give out dividends if the only way anyone can profit is by selling the stock at a higher price?

Dunois

@Charlie basically high-school math and physics? My background is in biology.

Slereah

@Dunois You're gonna need a lot more than that

Charlie

@JingleBells I'm not a stock market-y person, maybe ask on economics SE or something

ACuriousMind

@Dunois You would have to start learning quantum mechanics without fields properly first. I've heard Q is for Quantum by Terry Rudolph is pretty good for an introduction for non-mathy people, but you'd have to work through at least one of the standard textbooks like Shankar, Ballentine, etc. before even thinking about going to QFT

Charlie

+1 from me for shankar, it does a nice introduction on vectors before continuing

ACuriousMind

1:13 PM

@Dunois Uncertainty is not about measurements, and particles aren't really localized. The world is very complicated.

Also there is no good notion of position in a quantum relativistic theory :P

Dunois

Thank you for the textbook recommendations. I'd stand no chance of handling these books without some preparatory math, I presume?

Slereah

How much analysis do you know?

Dunois

I currently stand at "WTF is analysis".

Charlie

tbh you could probably get away with high-school math/physics with shankar, I can't speak for other textbooks but my degree is in chemistry (i.e. minimal maths) and I've been able to fairly comfortably cover it

JingleBells

So some companies do not give out dividends and if that's the case, then when buying a stock, the only way a person can make a profit is by trying to sell it to a person at a higher price, who hopes he/she will be able to sell it to the next person at an even higher price etc... isn't that like cryptocurrency?

Slereah

1:16 PM

Might want to brush up a bit, then

I believe in high school it may be more called "calculus"

Charlie

it might also depend how long ago you did high-school math/physics, might be surprised at how much you've forgotten although you could probably get it back easily enough

Dunois

Fair enough. And since you all recommend this Shankar et al. book, may I ask for its proper title?

Slereah

@Dunois springer.com/gp/book/9780306447907

Charlie

to be clear I only recommend shankar because it's the textbook I'm currently using, there may be other better textbooks for beginners

Dunois

Well, I have all the concepts still kicking around, but I doubt I remember the formulae and the little tips and tricks, and all that.

Slereah

1:17 PM

It's a good idea to get some calculus in before tackling physics

Charlie

but if you don't want super hand-wavey conceptual stuff and want to actually learn to use QM I can testify shankar

Faded Giant

@JingleBells If you have to ask such basic questions, you probably shouldn't invest real money in the stock market.

The less common, even worse outcome: "3: [everyone in the financial system] WOW, where did all my money just go?"

Charlie

lol

Dunois

Hmm I think I have the Tom Apostol calculus books somewhere. I have no idea why I got them, but they're two huge volumes. Would those help?

JingleBells

@FadedGiant I'm not planning to invest in the stock market.

Dunois

1:18 PM

@Slereah thank you for the link btw.

Charlie

the calculus involved in (at least basic enough) QM isn't super involved, at least that's what I've found

Dunois

Hmm I'd actually like to walk away from the hand-waving. I think I've followed physics for so long as a layperson and kept looking only for "intuition" that I just haven't learned anything at all.

JingleBells

Quantum Stock Market - You invest, but the share price is at a superposition until you observe it

Slereah

You should at least have enough to deal with classical mechanics :p

Dunois

I see that both of you are suggesting a certain bar to clear, I just don't know what that bar entails. But I'll figure it out.

Charlie

1:20 PM

ideally you'd be reasonably comfortable with the maths beforehand, otherwise you'll be constantly looking things up and it might be a bit disheartening

Dunois

@Charlie you've just described, pretty much, the entirety of my learning process.

JingleBells

@Dunois mine too, i learn by looking things up multiple times, that way I learn only what I really need

Slereah

You can check out Feynman's books on physics for a good introduction

Charlie

I mean I can only speak from experience. But the bridge to cross between "ooh this animated video on youtube is pretty" and "I can actually use what I've learned to solve problems" is large, but rewarding once you're over it

ronak jain

Hi everyone

Charlie

1:22 PM

hello

Slereah

Hello

JingleBells

hello

Dunois

@JingleBells basically, but it appears this method is extremely slow (as I'm experiencing first hand). That said, even if I did learn linearly, I'd not remember much later anyway, so this is what works for me.

I'll also try the Feynman books then, but I doubt I have the time anymore to work through that much material. If I recall correctly, that's three entire volumes.

JingleBells

@Dunois meh, I learned programming by just googling how to do things multiple times until I finally memorize (though I still google)

Dunois

But I'll try all the same.

Slereah

1:24 PM

I'm afraid learning QFT isn't gonna be easy if you're pressed for time

Dunois

@JingleBells same here.

@Slereah I believe so too. But that's no reason to give up.

Charlie

I've opened the first few pages of peskin and schroeder a few times thinking I'd just make a start and got scared and gone back to my qm book :C

JingleBells

Learning to program by reading a book on programming and then turning on the computer, IMO is a bad way to do it. (I haven't tried it but it doesn't sound right to me)

Slereah

I'm not even sure it's a good idea learning QFT from QM directly

You may want to start with classical field theory

ronak jain

I am having a problem in single slit diffraction . Will someone help ?

Slereah

1:25 PM

also maybe RQM

Charlie

RQM is covered at the end of shankar, I'll get there eventually

Dunois

And I think therein lies my problem. I am mostly a "learn by doing" person. I am lost trying to approach all this more abstract stuff outside of small thought experiments.

Charlie

I've heard the term classical field theory used a few times but I don't really know where it lies inbetween QM and QFT

Slereah

@Charlie Classical field theory + QM = QFT

Dunois

Anyway, thank you all very much for your inputs. I'll try following up on the suggestions I've received here, and see where that takes me.

Charlie

1:28 PM

@Dunois You can ask questions in this chat if you need to, people are friendly

@Slereah ah I see, well I'll get there one day

Slereah

Basically it's all the Klein Gordon business sans the quantum deal

ronak jain

Can someone tell me that in single slit experiment does light get diffracted to all directions ?

Slereah

Depends on the hole, but it should, yes

ronak jain

@Slereah look at the diagram I am posting.....

@Slereah if light gets diffracted in all directions than should not I expect the intensity extended in all direction ?

Slereah

Extended?

JingleBells

1:35 PM

Why do banks sell mortgages? I mean, if I'm a bank and I loan out 300,000 euros to someone to buy a house, I simply have a piece of paper called a mortgage. I can wait until the borrower pays me the principal with interest or it's very likely I sell it to some other bank. But why is that? I cannot sell it for 310,000 euros to make a profit, so why do I (and many banks) sell mortgages?

ronak jain

@Slereah yes extended in all directions

Dunois

@Charlie thank you, I'll keep that in mind. Just one more follow up question: the math I'd need to know to learn QM (and then QFT, I guess). What would that entail? Linear algebra? Calculus?

Slereah

@Dunois Those are both good to have, yes

Dunois

Any thing else other than that?

Charlie

Not massively

Slereah

1:38 PM

If you're doing basic QM stuff, that will do

Dunois

Because if I were to triage and focus on learning something, those are the two math topics I'm interested in, have some familiarity with, and would use outside of this pursuit.

Charlie

Again I am barely clawing my way out of "beginner" status, but linear algebra and calculus up to partial derivatives seems to be the bulk of what's been covered so far

Slereah

yes pretty much

Dunois

Hmm fair enough. I think that's a decent yardstick for me, considering you stated you come from a chemistry background @Charlie.

Slereah

Basically all of math can be used in QM, but that's not really for a beginner's course

ronak jain

1:40 PM

@Slereah what happened ?

Charlie

Don't get hasty and try to attack QFT early, it's no joke, there is plenty of interesting stuff in QM :)

Slereah

also just

classical mechanics

Charlie

yis

Slereah

Learn about classical mechanics, particles in potentials, lagrangian mechanics, hamiltonian mechanics, etc etc

Dunois

I guess getting to a beginner's level of understanding will already be a monumental task for me. And as you're both pointing out, I'll attempt classical mechanics and QM first.

Slereah

1:41 PM

I mean you can do QM without classical mechanics, but I wouldn't recommend it

You'd just learn formulas and not really have any idea what they mean

Dunois

Damn. Any book suggestions for those? I guess they're covered in Fenyman's books, for instance?

Slereah

Feynman's an alright introduction to basic physics, yes

Charlie

the feynman lectures definitely cover classical mechanics

ronak jain

@Slereah hi :-) did you look at my problem

Dunois

No, I'd actually like to understand stuff, so no shortcuts.

Charlie

1:42 PM

that's the spirit

Dunois

Thank you both for your help, once again. Let's see how this goes!

I wish you a pleasant weekend ahead.

Charlie

good luck :)

oh that reminds me, how do you pronounce "Szekeres" in "Kruskal-Szekeres"? As "Zuh-Care-Ess"?

ronak jain

@Slereah are you still around ?

Anyone here to response back ?

@Charlie can you solve my query of physics ?

Charlie

not sure sorry

ronak jain

@Charlie can you tell me about someone in the room who can ?

Charlie

1:54 PM

maybe try asking on the main site physics.stackexchange.com

ronak jain

@Charlie by I want a long discussion . Do you know someone ?

ACuriousMind

@ronakjain Please don't ping random people to answer your questions; if someone here can answer and wants to, they will

2

Charlie

no, if someone is willing to answer they will, the only advice I can give is to ask on the main site if you want more people to see your question

ronak jain

@ACuriousMind but I thought none had looked at my question ? Can you

ACuriousMind

I didn't really understand it at first glance but I'm not really interested in discussing diffraction right now anyway

ronak jain

1:56 PM

Ok

If you want than I can explain

If you are interested to answer

JingleBells

y banks sel mortgages

c'mon guys, every physicist knows this

Charlie

2:13 PM

Interest is how banks make money from you, that's like asking why banks give loans

Mad Spaces

3:54 PM

In a normal plate capacitor.. if we increase the distance.. we do arbeit against the attractive Coloumbforces. But where does our arbeit go into ? like should the potential energy of the system increase? if so this is not the case when we consider the energy to be 0.5 * E^2 ( E is electric feld ) since E feld becomes smaller

JingleBells

6:22 PM

@Charlie Why banks sell mortgages to other banks? I mean, they can't possibly sell it at a higher price, right? That would mean that the person who's paying out the mortgage will have to pay more in total without agreeing to any of this.

ACuriousMind

I see you're still assuming that our economic system is somehow fair or optimal :P

2

JingleBells

So you're telling me that if I get a mortgage, the interest is not fixed? Meaning, without my agreement, the total amount of money I'll have to return gets higher because the bank has decided to pass me over to some other bank... wtf they are literally exploiting me for money. The profit they make, I have to pay

ACuriousMind

A mortgage is just a loan backed by a property. What value you assign to it is based on how likely it is the loan will be repaid, and what value you think the property backing it has. Whether or not the rate of interest can change over time depends on the contract of the loan, but it's not necessary that it can change at all.

JingleBells

@ACuriousMind Well, if mortgage interest rates are fixed, that means the bank can't sell it to some other bank at a higher price, right?

ACuriousMind

The lender might sell a loan because they need the money now, not when the loan is paid off, or because they think they're not going to get much from it but have managed to deceive (or "convince") someone else that it's a good bet for them to buy it.

@JingleBells I don't understand what you mean by "higher price". The value of a loan is not fixed, as I just explained it depends highly on how you value the various risks and backing properties involved

When the seller and the buyer both think they're getting a good deal, a sale happens.

JingleBells

6:30 PM

@ACuriousMind Bank pays me 300,000 euros so I can buy a house. I agree to pay them 310,000 euros for some time period. If the bank decides to sell the mortgage to some other bank, they can sell it for 320,000 euros (and they make a profit of 10,000 euros) but I'll have to pay 320,000 euros in the end, no? I'm confusion

ACuriousMind

E.g. one of the recent finanical crises was (very simplified) due to most buyers massively overvaluing the backing properties.

JingleBells

@ACuriousMind Yes, I've learned about that one, but I'm confused about how a bank can sell my mortgage at a higher price without me having to pay more eventually

ACuriousMind

@JingleBells As I just said, the loan isn't "worth 310,000", so you can't think about making a profit of 10,000 when selling it at 320,000

JingleBells

@ACuriousMind What is it worth then? It surely must be worth more than what the first bank paid for principal

ACuriousMind

A very simple model might go like this: I estimate that there's a 50% chance you stop paying back the loan in the near future, and I also estimate that the finished backing property is worth 200,000. Then I'd say I get 310,000 50% of the time, and 200,000 the other 50% of the time, so I'd model the value at the average, 255,000. Someone else might model it differently (think you're more able to pay, or think the property is worth more), and I manage to sell the loan for 260,000.

That's 5,000 profit!

(Note that in this model I've lost 45,000 by giving you the loan to begin with, so the rate of interest I demanded was too low if my estimates were already like this at the time the loan was created)

JingleBells

6:39 PM

@ACuriousMind Actually, you've given out 300,000, and you sold it at 260,000, so you've actually lost 40,000

ACuriousMind

In this model I'd have had to set the estimated payback at at least 400,000 to break even when giving you the loan.

which is 33% interest, but then again, 50% is a high estimation for failure, so it kinda works out :P

In reality there's complicated financial analysis behind the probability of defaulting and the modelling of the property price, as well as various other factors, but that doesn't change the basic idea that the value of a loan is very different from the total sum expected to have been paid back at its expiry date

JingleBells

So you give me 500,000 so I can buy a house. I agree to return 600,000. My property is worth 400,000. There's a 75% chance you get 600,000 and 25% chance you get 400,000. So (3*600,000 + 1*400,000) / 4 = 550,000. You sell it at 550,000 or higher and BAM, profits. Is that how it works?

ACuriousMind

yes, that's the basic idea

JingleBells

Got it, thanks :P

bolbteppa

7:30 PM

15

Q: Physical interpretations/meanings of the notion of a sheaf?

I fairly understand the fiber bundles, both the mathematical concept of fiber bundles and the physics use of fiber bundles. Because the fiber bundles are tightly connected to the gauge field theory in (quantum) field theory, and the general relativity in gravity theory. Here the gauge field theor...