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15:00
Which is the same as what our general solutiopn is
So it doesnt matter
Whats ansatz?
Well, not quite.
And what are the rigorous ways?
Suppose you wrote your general solution as Ae^(bt+ict)+Be^(bt-ict) with A,B being complex
would that necessarily be real?
15:01
(Sorry if Im being stupid/difficult here)
So the point is that, at the end of the day, you are not really interested in the full general solution
you're only interested in real-valued signals, which correspond to the subset of general solutions for which A,B are complex conjugate
but you can get that just as well by picking just one of your complex solutions and taking its real part
Anonymous
@JakeRose Check out the textbook by Hirsch-Smale. You'd also find it in any normal ODE textbook like the one by Murray, but Hirsch-Smale's approach is more qualitative.
Anonymous
I could tell you the full method, but I'm in a bit of hurry now :P
I very likely wont have access to the book until I get back to uni
WOuld it be posible next time you're online if youre free you could give it a go?
Or I can pass you my email and whenevrr you get a free spot you could?
@Semiclassical I think i understand it now
15:05
That makes a lot of sense
Thank you!
So nice to have somebody to talk stuff through
@JakeRose just out of curiousity why did you ask for a Cambridge graduate?
SHM is taught at other universities :-)
Ive found quite often when trying to talk to somebody about confusions with my lecture notes it takes quite a lot of time to bring them up to speed on what the notation is and such
So its often a bit easier to talk to somebody who has seen it in a fairly similiar way
Other universities will teach it fine (if not better) but the time spent talking about notation can often be a bit consuming
Anonymous
@JakeRose You'll get it on libgen. This is the book
15:08
Is libgen not the russian one?
Anonymous
Ah, wait. The PDF is freely available online: math.upatras.gr/~bountis/files/def-eq.pdf
Anonymous
There you go
Anonymous
@JakeRose Yes
15:53
Hee hee, I've got two answers on the hot network questions list. Feel those rep points flooding in! :-)
Anonymous
Doesn't getting more rep at 240k+ become boring? :P I guess not
> Hee hee, I've got two answers on the hot network questions list. Feel those <s>rep points</s>endorphins flooding in!
Gamification works.
@Blue I just gave away 1,000 rep points as bounties!!
@dmckee oi! :-) One of those answers is a technical one about general relativity! What it's doing on the HNQ is anyone's guess ...
Anonymous
@JohnRennie Oh, nice. Which questions?
Though I have to concede the other answer is rather less technical :-)
5
Q: Blueshift near the Schwarzschild BH horizon

Alex V.After having worked for a while with the Schwarzschild geometry, I have realized something I hadn't seen before and that I found slightly disturbing. Consider the 4-dimensional Schwarzschild metric: $$ ds^2 = -\left(1- \frac{2M}{r}\right)dt^2 + \left(1- \frac{2M}{r}\right)^{-1}dr^2 + r^2 d\Omega...

Anonymous
16:05
@JohnRennie I don't see a bounty there (?)
@Blue ah you meant which question had the bounties. This one:
106
Q: Does someone falling into a black hole see the end of the universe?

John RennieThis question was prompted by Can matter really fall through an event horizon?. Notoriously, if you calculate the Schwarzschild coordinate time for anything, matter or light, to reach the event horizon the result is infinite. This implies that the universe ages by an infinite time before someone ...

On Rob Jeffries and Pulsar's answers. They are just frackin' awesome answers and a good example of how amazing this site can be!
Anonymous
@JohnRennie Oh, you showed that few days ago. It indeed has some great answers :)
You know you're really good when the man himself @JohnRennie labels you or your work as "frackin' awesome".
Anonymous
I need to learn GR soon! Feels bad to be not able to understand all those nice answers
@Tanuj :-)
@Blue if I try to teach you GR you'll get only a partial understanding. That's why I've backed away.
If you're serious about it you should do it properly. Get a copy of Carroll maybe. That seems to be a popular starters book.
Anonymous
16:12
Yeah, I understand. I started working on the Differential Geometry part. I developed a somewhat okay understanding of tensors and forms. Waiting for the summer holidays to come up (which would be around 2 and half months long). Learning at least basic Differential Geometry, GR and QC properly is in the bucket list
I think one of the worst explained part of GR is observers
Fortunately it's in MTW
somewhere
hartshorne is a really hard book right?
along with everything else
Anonymous
@JohnRennie Slereah had suggested me Callahan. I read the first few pages and it looks good. Haven't tried Carroll yet. Will try :)
Callahan is nice for an undergrad intro
it's fairly detailed on basic differential geometry
16:15
@Blue I'm not familiar with that book. From the blurb it looks good though.
and it uses a lot of embedded manifolds as examples, which makes things a bit easier to go down
Understanding that GR is a geometrical theory is the key to GR nirvana.
and then you find out it was strings all along
Not everyone who purports to know GR understands this of course - not that I'm going to name names :-)
"The Reference Frame Comment Policy

Avoid attempts to silence the discussion; spam and promotion of other pages and products; too frequent misconceptions."
16:21
Boom! Rep limit! Thank you HNQ :-)
@JohnRennie yes I know what capillary action is, but it seems a contradiction with communicating vessels in that case
@Curio I only skimmed the video but it all looked straightforward to me ...
Shouldn't all the tubes reach the same high?
@Curio no
What about here then? goo.gl/images/hjmnHN
16:34
@Curio I guess those tubes are too wide for the capillary effect to make much difference
You have to get down to a mm or so for the effect to be noticable.
@JohnRennie In $y=A\sin(kx-\omega t )$ , what are the velocities of wave and velocity of particle respectively ? $V_{particle}=\omega/k$ , right ?
Didn't we discuss this recently? Or was it someone else?
@JohnRennie : re "Not everyone who purports to know GR understands this of course - not that I'm going to name names ". Sadly some people who purport to understand GR say things which are badly out of kilter with the Einstein digital papers. Sometimes what they say flatly contradicts Einstein, sometimes whilst appealing to his authority. Sometimes what they say is flat out wrong.
[Random] Thinking about some weird delocalised notion of space for a scifi
Oh, wait a minute, I think that was with Abcd.
16:43
@JohnRennie velocity of wave would be $dy/dt$ ?
@EmilioPisanty It appears OP did not recover the ability to post answers.
The wave vector $k$ is $2\pi/\lambda$ and the angular frequency is $\omega = 2\pi f$. The velocity is just $v = \lambda f$.
If $k$ and $\omega$ are constants then the group and phase velocities are the same. For example this is the case for light in a vacuum.
@JohnRennie nice accent ina bacuum
anyways @JohnRennie so $v=\omega/k$ is particle velocity right ?
16:46
I think that's the phase velocity
The particle velocity is the group velocity.
@JohnRennie what is that ?
The group velocity of a wave is the velocity with which the overall shape of the waves' amplitudes—known as the modulation or envelope of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, a circular pattern of waves with a quiescent center appears in the water, also known as a capillary wave. The expanding ring of waves is the wave group, within which one can discern individual wavelets of differing wavelengths traveling at different speeds. The shorter waves travel faster than the group as a whole, but their amplitudes diminish as th...
@JohnRennie okay there are two velocities , one with which every particle of SHM vibrates and one with which wave moves forward . I'm calling the former as particle velocity
@Tanuj No.
Okay , so it's the latter
16:48
I'm not talking about the lateral velocity, just the velocity in the direction the wave is moving.
I really need to resist responding to Zee. @ACuriousMind
@Tanuj ah OK, I misunderstood what you mean by particle velocity
Consider a region of space where it looks visually like a pile of sand (because pockets of spaces are being translocated from their original positions, thus result it to look scrambled despite internally, each bit is connected normally as if it is never scrambled (i.e. the topology is retained). Now passing a cube object through it will give you a swarm like appearance:
@JohnRennie got it , the wave velocity is $v=\omega/k$ , what is the velocity of particle executing SHM ? $dv/dt$ ?
Anonymous
16:49
@Semiclassical Zee?
MSE chat room user.
Nothing here.
@Tanuj you mean, for example, if the wave is on a string how fast is a point on the string moving sideways?
one can then imagine while the cube is within this region, and hence look like a swarm as seen from the outside, a ball then hit the swarm and thus the bits of the cube become scattered despite maintaining connectivity
Anonymous
@Semiclassical Ah. We have our fair share of such users here. :P
Thus locally at every point of the cube, space looks normal, but seen from the outside, the cube look like a scrambled mess
16:50
@JohnRennie yea , sideways or up and down . Like if we just focus our attention on one particle , it will be in an SHM , right ? I was asking about the velocity of that particle , not the velocity with which the wave propagates.
@Tanuj We usually use "the wave velocity" when talking about a pure signal. When you combine them you really have to say "group velocity" and "phase velocity".
For an idea on what I am talking about, refer to this video:
here, the playfield is scrambled, but the connectivity is not, thus it is like a region of space packed with wormholes in all directions
@dmckee Okay
@Tanuj OK. If $y = A\sin(kx - \omega t)$ then imagine sitting at the point $x=0$ watching the particle moving up and down. It's position is then $y(t) = A\sin(-\omega t)$
16:52
@JohnRennie yea
And the transverse velocity is indeed just $dy/dt = -A\omega\cos(-\omega t)$
Now, for non-dispersive wave the group velocity and the wave velocity are the same, but that is a special case.
@JohnRennie okay cool.
Now, we can go one step further, by having object collisions actually result in the change in the connectivity of each piece. Then if the aforementioned scrambled cube get hit by a rolling ball, it is "shattered" because space is rearranged thus trying to take the cube out of the region and one will found the cube is altered in some way
@JohnRennie when we use $v=\sqrt{\dfrac{T}{\mu}}$ , $v$ is velocity of wave , right ? (The longitudinal wave) , or the velocity of its propagation ?
16:55
Yes
Got it . Thanks.
@EricSilva this conversation hurts me inside
Me too me too
Then...just drop it?
Anonymous
Doesn't really help to feed the trolls. :)
17:02
I knoooow.
But ugh, it's just so asinine
@ACuriousMind Ive tried but the dude honestly constantly belittles people while putting his ignorance on full display and after a while it just becomes hard to deal with I guess
@Blue Since when is trolling equivalent to hitting your foot with an axe, pulling your pants down in the public and saying "oops! I pooped myself"?
Were I an owner of that room Zee would be enjoying a break from it ...
That's what's Zee monologues are like
Anonymous
@BalarkaSen That's a type of attention seeking aka trolling.
17:06
Have you tried speaking to the room owners?
Anonymous
Just tell one of the mods to suspend them for a day or so
Anonymous
If (s)he is annoying you people
@EricSilva 1. I don't really encourage using this room to have a meta conversation about another user/room 2. Since this behaviour is not currently a blatant violation of Be Nice, I hesitate to take action as a non-RO/non-math mod. Have you tried talking to your room owners/mods?
I don't think there's anything per se suspension-worthy about that guy
@BalarkaSen if one person is annoying everyone else it's perfectly OK to ask them to stop or leave.
17:08
For the most part, I agree that "ignore" is probably the right approach
Anonymous
@BalarkaSen Then just put them on ignore. I know it is hard to ignore such people, but it's worth it to save your sanity.
Anonymous
I've recently had a similar experience on the classical channel chat
@Blue I am not annoyed by him per se
the problem with that attitude is that it leaves such people in a position to confuse people who wander in and aren't aware of it
I just think it's cringe
Anonymous
17:11
Anyhow, I think the math SE chat lacks active ROs
I'm just gonna leave him on permanent ignore and be done with it
Anyone can volunteer to be a room owner. If you spend a lot of time in a room and think you could help improve it then ping a mod and ask to be a room owner.
Anonymous
I guess SemiC and Balarka should volunteer
Anonymous
That room seriously needs some
Anonymous
That said, Zee is out for 30 mins at least
17:19
0
Q: In what sense is a separable potential maximally non-local?

Logan MA (rank-one) separable potential is an operator $V$ with the coordinate representation $$ \langle \mathbf r' | V | \mathbf r \rangle = - A u(r) u(r')$$ where $u(r)$ is a real-valued function. It is clear that this is not a local potential as it is not proportional to $\delta(\mathbf r - \mathbf ...

Initially I was thinking: What on earth is a gold atom doing in there
@Blue I pass to SemiC and declare myself an overlord of the math chat without any direct responsibilities
My question about whether someone falling into a black hole sees the end of the universe has some wonderful answers that show a deep understanding of the mathematics involved and give a rigorous treatment that any competent physicist could follow without too much pain.
Also can I take a moment to say this is so fucking great
John Duffield best answer
17:22
I shall comment no further.
Anonymous
lololol
Except to say that unlike Rob and Pulsar's answers I won't be awarding it a bounty.
All of your questions are trivia that are addressed in the margins of Einstein's digital papers
learn to READ PLEBIANS
Anonymous
@BalarkaSen SemiC is too sweet. You need someone mean ;)
@JohnRennie : I have answered your old black hole question. Note the Einstein quote, and remember what you said in this answer.
@JohnRennie : re "I shall comment no further". You should however think it through.
17:27
You can spot a Duffield answer because it always starts with a quote of the post to which he replies "no"
Anonymous
@Slereah :'D
@Slereah : Sometimes I like to answer each element of the a question step by step, with a definitive reply.
OK time for tea. But remember this: sometimes for a "wonderful" answer to be right, Einstein has to be wrong.
@JohnDuffield when you get back, what is your opinion of the Laplace-Runge-Lenz vector?
In classical mechanics, the Laplace–Runge–Lenz vector (or simply the LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another, such as a planet revolving around a star. For two bodies interacting by Newtonian gravity, the LRL vector is a constant of motion, meaning that it is the same no matter where it is calculated on the orbit; equivalently, the LRL vector is said to be conserved. More generally, the LRL vector is conserved in all problems in which two bodies interact by a central force that varies as the inverse square of...
I used to hate this thing, until like yesterday
Anonymous
@JohnDuffield I don't understand what you try to achieve by posting non-mainstream answers, and trying to teach random people on the Internet your theories and conclusions. If you really feel they're good enough just publish them in real journals, so the the whole wide world benefits from your knowledge. Otherwise, they will just get buried under the debris on the Internet in due course of time and your contributions to physics will go unrecognized.
Ah but you're forgetting the big conspiracy, Lagrangian's are a lie used to convince you not to feel shame at night, but there is a secret reality purposely being stymied by big Lagrangian
Or so I've heard...
There is place welcoming alternative theories, vixra.org/ e.g. these vixra.org/author/william_o_straub are okay but then you get the craziness e.g. here vixra.org/qgst
One gets to feel important, feel they published, feel they are engaging like those in the 1800's did, and still let everyone else know to safely ignore as well
17:41
@bolbteppa main place I know about LRL vector is that it can be used to explain the otherwise accidental degeneracy of the hydrogen atom
Though I don't think I've ever sat down and worked through the details of that.
Yeah I kind of am in the middle of that (going on for about 3 years now :\ )
lol
I know a math prof on campus who says that's the wrong way to understand that degeneracy though
Yesterday I finally seen where it comes from, separation of variables in parabolic coordinates, you get the beast from nothing!
lemme find it
There's a few things going on, that whole Bertrand closed orbits thing, as well as action angle variables theory leading the energy to depend on two action angle variables apparently explaining the degeneracy, somehow linked to the closed orbits thing, a big mess right now
17:46
yeah, here's the long paper where he writes about it: arxiv.org/pdf/1309.2694.pdf
@JohnDuffield I think you're missing out on all the vixra fun, you can publish your own theories there, read other authors attempts at explaining all of physics without math, just words, and then write counterveiling correspondences published on there disputing their theories, like Newton etc did in the 1600's, so you get that feeling, and can convert followers sympathetic to your theories
Will resume thinking about scattering in QED today, then return to math related stuff later. I have some time now that I have completed a trivial Django project and an even more trivial android app thingy hehe
The wiki talks about superintegrability of LRL like this paper does, that's another level for me right now heh
Btw, in case anyone ever wanted to know what I sound like, here you go
hehe
@Cows did you get Compton scattering?
17:49
oh nice
you know it's nick Compton and his collars stay scattered
@bolbteppa yeah, I will be working on Compton scattering today. I had read it , but I am going to try to sit down and do it book closed today.
I will be very proud of myself once I do it
@Cows it's a mountain to climb to get to Compton scattering from nothing in QFT tbh, a whole course worth of work really
If you really got it that's awesome
Yes, I will be making a video of me doing in using QFT
I really wish I had read Relativistic Quantum Mechanics before QFT, life would have been immensely easier
17:53
yes one starts by using einsteins relations and the resolving schrodingers eq, and gets dirac et all methodology
it's hard to type fast enough, but i get what you are saying
yes, i love qft
@Semiclassical any idea where in that paper, or what he was getting at, by saying it's the wrong way to think about degeneracy? (It's alright if not, just curious)
That St$\"{a}$ckel stuff is really cool, really hard to make sense of
(a with dots over it)
not finding it right now myself. maybe I'm remembering what he said wrong
Then there's the whole SO(4) aspect of this stuff, another mountain
I vaguely think the more fundamental thing is that the problem is separable in more than one coordinate system, which is why you get the LRL vector, by using one coordinate system as your coordinates, and using an invariant coming from the separation constant in the other coordinate system, you get the LRL vector. I think this itself maybe more fundamentally due to action angle variables being constrained. Maybe this is all a consequence though
18:02
well, I suspect the statement from Miller would be that the problem is not merely integrable but superintegrable
but I don't know what exactly that implies, so that's a slogan not a statement
do check out pages 28-29 though
The reason I mention it is because the whole separability thing is linked to that St$\ddot{a}$ckel stuff he's going on about, I think you use this St$\ddot{a}$ckel stuff to prove the problem is separable in some coordinate system, let alone more than one system
But idk about the super-ness
Landau says "The specific property of the Coulomb and oscillator fields in quantum mechanics (presence of accidental degeneracy) is in correspondence with the fact that in classical mechanics closed particle trajectories exist in these (and only these) fields", so idk which turtle is most fundamental yet
the biggest turtle
Riddle me this : is the Moebius strip spacetime obtained by twisting and identifying two spacelike hypersurfaces a FRW universe?
On one hand, it is foliated by homogeneous and isotropic Cauchy surfaces
on the other hand, I don't think there's a spacelike Killing vector field for this that spans the entire spacetime
Due to the lack of orientability
I'm fairly sure it qualifies, but that means I'll have to treat the issue more delicately
18:20
Maybe only if you allow for inflation runs
The exact geometry isn't really important here :p
Making a fun little page for my site on the FRW solutions~
Nice for a refresher
I don't remember much cosmology
18:39
I'm simply unable to watch those Susskind cosmology lectures, I just know it will confuse me more than enlighten me, but they look good
Im ngl
Susskind is a fairly boring lecturer and writer to me
I cant bring myself to read or watch hist stuff
Has an air of 'everybody is below me' about him
His popular black hole book is great tbh
Anyone here who works with Mathematica?
You have to have that air to get into the strings club
I read some of his theoretical minimum books and they just werent for me tbh
True
Why cant everybody be a freeman dyson
Just an old polite man
18:44
Susskind's black hole information book? It's good.
Dirac was an old, polite man.
More so than Dyson I guess.
@Blue : Re "I don't understand what you try to achieve by posting non-mainstream answers, and trying to teach random people on the Internet your theories and conclusions". They aren't my theories. Note that I refer to Einstein a lot. And the evidence. And I give references. The key word is teach.
@bolbteppa : Re "I think you're missing out on all the vixra fun... convert followers sympathetic to your theories". I'm not fond of vixra, and they aren't my theories. They're Einstein's theories, and Maxwell's, et cetera. I'm here to try and educate you such that you do your own research and think for yourself, and stop believing in popscience trash.
@JohnDuffield vixra is the perfect place for your theories, they are most certainly not Einstein's, e.g. he believed in quantum mechanics and didn't think the electron was some classical thing like you do
Im just about to start a biography of driac
Heard a lot of stories about him from my supervisor
how many colors do holes have
(his dad was good friends with him)
18:52
there's black holes
white holes
blue holes
red holes
Specifically about swimming in the river cam a lot..
I think I've seen grey holes
You should go to the fireplace in Cambridge he sat at while writing up the Dirac equation, or something like that
Anonymous
@JohnDuffield Well, I have never seen anyone including myself, agreeing with your interpretations of Einstein's theories. If that's the case, even then it is worth publishing your conclusions if you think they're right. BTW pretty much everywhere on the net (Wiki, PSE, people's blogs) you have created a negative reputation for yourself. Not sure if you're fine with that, and how long you want to continue with this unfruitful endeavor of yours.
or the chairs Hardy sat at all the time
Touching that furniture gives one powers apparently
18:54
I wonder if its still around @bolbteppa
Im back in a couple of weeks so I'll have to have a good look for it
@bolbteppa : I've read the Einstein digital papers, and more. I know what Einstein believed. And that one thing he didn't believe was that elephants could go to the end of time and back, and be in two places at once. See Susskind's the elephant and the event horizon.
@Blue I dont know anything of the theories or their interpretations that he may have been posting. But is it not more correct to put your views out their and allow them to be scrutinised, than to scrutinise them based on the fact nobody else agrees with them?
Well, I'm prepared to admit that the received view of Einstein is a caricature of the real Einstein.
Just putting an opinion out there
@Blue : re "Well, I have never seen anyone including myself, agreeing with your interpretations of Einstein's theories". People do. You don't even agree with the mass deficit.
18:57
The history is a lot more complicated than what people tend to actually remember.
Can somebody do me a favour
If they have a scientific calculator about
I left mine at home
And need a quick number put in
What I'm not prepared to agree on is that said historical questions are decisive. They tell us what Einstein thought; that is not the same as what we 'should' necessarily think.
@Semiclassical : there are some massive differences between what Einstein said and what some modern physicists say.
The evidence is what's important.
Anonymous
@JohnDuffield Well, good luck with whatever you're trying to achieve, then. And yes, I do not agree with "electron's mass increases when you lift it up". Let's end it there.
18:59
$\sqrt{0.03*10^(-21)}$
Anonymous
By the way, as of now, I think I only found vzn agreeing with your
conclusions.
Would be greatl appreciated if somebody could tell me what that equals to like 3sf
@Blue : again, they aren't my theories.
@JohnDuffield Skipping all the equations means you'll completely misunderstand the points Einstein was making in all those papers, and Susskind is talking about Hawking radiation, something Einstein didn't know about, so why compare Susskind's statement to Einstein... Vixra is the place things for things like this to be nurtured
@Semiclassical : And everything you think you know about black hole physics is wrong.

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