3:02 AM
@CaptainBohemian they are, yes

Anyone know a book for orbital mechanics with not much mathematics
?

1 hour later…
4:10 AM

@JackRod liked it too, thx for sharing! oh, they didnt say anything about fluid dynamics even though its very eminent... :o

4:56 AM
Hi Guys...

2 hours later…
6:49 AM
Someone online?

I guess

@RewCie listening to a good song

@JackRod which one?

I was thinking about entropy, is claimed that the universe entropy increases in irreversible process, but to say this is necessary to adopt the universe model as an isolate thermally universe?

$dS \geq 0$

I can relate it

3 hours later…
9:34 AM
Does total charge conserved?
In case if we charge two different capacitors separately at different voltages. And then attached to series/parallel combination.
What about specially series combination. It shows some problem in this case. Not showing same charge on each capacitor?
@JohnRennie sir, @ACuriousMind pls help me to figure out this above condition.

10:18 AM
Charges is not conserved in series combination. Why???

10:29 AM
I found one site of 'Trapped Charge" concept if charge before connect in series. But no detail there it is paper I don't have access.

@123 I have no idea what you mean when you say "charge is not conserved", or what it has to do with the series combination.

Two capacitors charge separately with batteries q1 = 10micro f, V1 = 600v and q2 = 20microf, V2 = 1000v. 1000v then disconnected. They are then joined in series.
Pls solve these @ACuriousMind it does not show that charge is conserved. It shows less than total charge. Which was before.
Total charge = 2.6x10^-2 C before placed in series. After series it shows Total charge = 2.1334x10^-2C
In question where I wrote problem q1 and q2 has capacitance C1 & C2 for charges

11:10 AM
@123 But the charge on a capacitor is never "conserved" if you just look at the charges of all capacitors in a circuit. If you just charge a capacitor from a voltage source, it starts at zero net charge and ends up at some finite charge
clearly, charge has changed (the additional charge in this case came from the voltage source/the wires, so the total charge of the universe is still conserved)

11:29 AM
But the same in parallel combination charge became conserved.

11:40 AM
so what?
capacitors behave differently in series than in parallel, like most other electrical components
it's not "charge conservation" that causes their behavior in parallel, but that putting them in parallel essentially is the same as just having one big capacitor with the capacitance of both, so there's no reason for the total charge on them to change

11:55 AM
Hi Physics people. I'm a mod on Aviation.SE and we occasionally get questions which are about wings - but not of the aircraft variety. It's a bit of an edge case for us. We might be able to answer it, but officially it is off topic. An example is here.
If this sort of question were migrated to Physics do you think it would be well received by your community, closed, or even migrated to Aviation as "looks like a wing, must be aviation related"?

I feel that it will not be well received by the community; but, you could try.

@Jamiec In principle questions about aerodynamics/hydrodynamics (or whatever else might be "wing-related") are on-topic here, but your particular example would be off-topic as engineering and/or homework-like, since it asks about a specific solution to a problem rather than about the physics behind it.

@NiharKarve what on earth are these mass eigenstates? Is there such an operator Mass Operator?

@ACuriousMind Thank you

12:14 PM
@Jamiec has the pandemic slowed the traffic on your site?

@skullpatrol yes

any change in this should be interesting

@CaptainBohemian have you seen this?

@NiharKarve not yet. let me read it then tell you my comment.

1 hour later…
1:34 PM
I have the impression of seeing the mass matrix in textbooks of classical mechanics but have never seen the term mass operator in quantum mechanics textooks. @NiharKarve

The mass operator in non-relativistic QM is just $m \hat{I}$
Since mass is just a constant

In QFT/Poincaré group representations the mass operator is $P_\mu P^\mu$
but I don't think that's really needed for the question above or to understand neutrino oscillations. That's just about the 3x3 mass matrix, the coefficients of the quadratic term in the Lagrangian. It's there at the classical level

Nihar already linked to the correct answer, it's where the mass matrix in the Lagrangian is diagonal, it has nothing to do with any operator.

yes

1:52 PM
calling the states corresponding to the creation/annihilation operators of the fields for the diagonal mass matrix "eigenstates" should probably be considered a bit of an abuse of terminology

2:47 PM
If we call an associated vector bundle $$(P\times_G\mathfrak g)/G\overset{\pi'}{\rightarrow}M$$ which is associated to the principal bundle $$P\overset{\pi}{\rightarrow}M$$ the "adjoint bundle", is there a common name given to the associated fibre bundle generated by $Ad:G\rightarrow \text{Diff}(G)$, $$(P\times_GG)/G\overset{\pi''}{\rightarrow}M?$$
Something like a group adjoint bundle?

@Charlie I'm pretty sure you just constructed a principal bundle :P

:o

although I'm not quite sure what you mean by the $\mathrm{Diff}(G)$ in the $\mathrm{Ad}$. Don't you just mean the adjoint action of the group on itself?

yeah I mean the action of $G$ on itself as a manifold
not as a Lie group

ah, sure

2:57 PM
I'm actually not 100% sure what I'm doing, it was just out of curiosity, nice to have names for things :P

then yes, I think you just constructed a principal bundle - it has fibers isomorphic to $G$ and the adjoint action acts freely and transitively on the fibers.

ok then that's fine, ty

I haven't tried to show it in detail since I'm working but I'm pretty sure it's really just isomorphic to $P$
(which one would expect from the notation alone - $(X\times Y) / Y \cong X$ is true for most notions of product, quotients and subspaces)

3:47 PM
Hello World

4:12 PM
Hello friend. That's lame, maybe I should give you a name.
Wollpapper

2 hours later…
5:46 PM
@ACuriousMind can you come to the princeton gravity seminar to translate what the physicists are saying

Hi Guys...

hello

What is conservation of charge about..?
What features is tell us and applications/purposes?

What do you mean what is it "about"?
The conservation of charge means that in a closed system the net electric charge remains constant in time.

6:12 PM
that won't take too long

uh quick question, I see people use the phrase "relativistic quantum field theory" sometimes and wonder why the qualifier "relativistic" is necessary, is non-relativistic qft a thing?
wait nvm

@RyanUnger this or his book are the friendliest you're going to get
Yes non-relativistic qft is a thing, c.f. second quantization

wait second quanization is non relativistic?

and by friendly I mean skimming courses in GR, supersymmetry, supergravity, string theory, superstring theory, conformal field theory,

am I missing the point

6:27 PM
For multi-particle quantum mechanics of identical particles, you can't tell which particle arrives at which place when you evolve a system, so doing normal QM with such systems requires symmetrizing or anti-symmetrizing the wave functions (fermions vs bosons), this is super redundant, a more useful set of variables arises from realizing all particles are the same so their stationary states are the same so the particles are just jumping between stationary states
Now what matters is the number of particles in a given stationary state, this is the occupation number representation, and it's natural to define operators which create or destroy particles in a given stationary state and to work with these instead. This is second quantization. Haven't brought in relativity yet. Now you're looking for the probability of finding a given set of occupation numbers...
@RyanUnger all the cool people do GR via ads-cft

oh I thought second quantisation was just this business of finding lorentz/poincare algebra representations

Have a look in chapter 9 of L&L on this

Is everything in modern physics like the standard model formulated as a gauge theory? I really like learning the differential geometry for it so far and from what we've done so far in QFT in my classes, "second quantisation" where we "promote" fields to operators seems really, really messy and unsatisfying

Does current increase when “passing” a (positive) current source, just like voltage increases when “passing” a (positive) voltage source?

uh, maybe, $V=IR$ means that an increase in voltage must be accompanied by an increase in current or resistance right?

6:32 PM
Promoting wave functions to operators is just re-writing wave functions in terms of creation and annihilation operators since it's more natural to care about whether a particle exists in a given stationary state or not when you're dealing with multi-particle systems of identical particles

that being said a wise person would not trust my knowledge of electrical circuits lol

Non-relativistically, particle number is conserved. You can prove this. Relativistically, particle number is not conserved, particles can pop into and out of existence, so it's almost silly not to work in a second quantization formalism in QFT

first quantisation is considered a relatively hacky recipe for obtaining quantum from classical physics though, I assumed at a certain point we drop the attempts at "crossing the bridge" between classical and quantum field theory
As in, learning QM without any reference to classical mechanics in terms of hilbert spaces was way more satisfying than the "and now we promote position to an operator" kind of approach that felt really contrived
then again I get that qft isn't in a finished state the way qm is

If you do QM without reference to classical mechanics you're playing a game of pretend, at the end of the day everything has to be related to classical mechanics while realizing CM is a limit of QM, this is what all those QM debates were trying to say, but this promoting wave functions to operators thing can be justified very concretely, e.g. the chapter I referenced above, I mean it's unavoidable
It takes ages to get this tbh, qft is a complete nightmare

I mean, recognising that they must be relating in some limit is unavoidable I guess, but trying to use familiar notions from classical mechanics in ungodly ways just to make quantum mechanics feel less abstract isn't unavoidable
lol yeah

6:47 PM
@schn Currents aren't quite the same as potentials. A voltage source has a potential difference across it, so voltage increases across the voltage source. Currents don't decrease as they go around the loop though, so a current source doesn't really have any reason to increase the current. It just supplies energy so that current remains the same across it in the circuit.

7:06 PM
@JMac Alright, thanks. How about a circuit in which a voltage source (kind of) counteracts the current source? Like this one
Could one expect the current just before and after the current source not to be the same?
Or, what I meant to ask was, could one expect that the current through the current source isn’t $I_S$, since the voltage source also supplies a current that can’t dissapear?

7:42 PM
If we charge two capacitors with batteries separately than disconnect batteries and joined in series combination. In ideal condition does this system is isolated or not???

@schn As far as I can tell that doesn't prevent that loop from having a current $I_S$. The ideal current source is just a circuit element that always has the same current going through it regardless of voltage, while conversely an ideal voltage source has the same voltage across it regardless of current.

8:25 PM
@RyanUnger yo

8:35 PM
@bolbteppa lol?
@BalarkaSen yo

9:24 PM
@JMac Makes sense. Thanks for the reply.

9:59 PM
@RyanUnger unfortunately, they probably speak the GR dialect of physics in which I'm not fluent :P

10:11 PM
"dialect"?
have i been learning a slang version of GR?