The h Bar

12:04 AM

Any of you guys know what to study to learn about what happened in the first three minutes of the universe? When I look in cosmology books it's all about Lambda-CDM models and I don't see any QFT of the early universe in there?

Stan Shunpike

Nope.

At least, not me.

ACuriousMind

@bolbteppa Try non-equilibrium quantum field theory with inflaton models

0celo7

@ACuriousMind So I don't like scotch.

Also I don't like tequila.

ACuriousMind

@0celo7 Nobody likes tequila, that doesn't seem to keep anybody from drinking it :P

0celo7

Also sweet vermouth is kinda crappy

However, I do like Manhattans

We don't have any bourbon, sweet vermouth or cherries, so I can't make them

@ACuriousMind Book or article? Author?

ACuriousMind

12:11 AM

Oh, I thought as a general field, sorry

But I learned this from the guy who wrote it, and he seemed pretty convinced that it can model the early quantum universe

It's a young field, there isn't that much about it yet

bolbteppa

I was just looking at it there

0celo7

@ACuriousMind I have that DL'd

0

Q: Extra terms appear when deriving the Riemann curvature tensor, should they be there?

Curvature is often demostrated by parallel transporting a vector along a closed path and divide it by the area drawn around. I attempted to transport a vector $s$ along a tiny parallelogram given by $v$ and $w$ and factors of these vectors were the small $\epsilon$ and $\zeta$ respectively. So a...

So many terms...

bolbteppa

So it's not something that's standard in the books?

Weird

0celo7

@ACuriousMind Why is that article half blue

bolbteppa

I thought from Weinberg's book the first 3 minutes (which I read before I knew why triangles were involved in trigonometry) that they obviously had it sorted!?

ACuriousMind

12:13 AM

@0celo7 Lol, dunno, he likes colors

bolbteppa

In some sense anyway

ACuriousMind

@bolbteppa I'm not sure we have, quantumly, anything sorted there.

0celo7

@ACuriousMind Nothing is sorted quantumly

It will be sorted when we disprove Bell's inequalities

I had way too much to drink.

ACuriousMind

Lol...that's also preparation for college

0celo7

I keep clicking on the wrong bookmarks :D

I refuse to misspell anything, however.

I got my right click word correct thingie back btw

ACuriousMind

12:15 AM

@bolbteppa I think it's kinda sorted from the GR/cosmology perspective

But I don't really know

bolbteppa

Basically a book that explains this chronology http://en.wikipedia.org/wiki/Chronology_of_the_universe using as much math as is possible, I mean justifying sentences like
"In the first phase, the very earliest universe was so hot, or energetic, that initially no matter particles existed or could exist perhaps only fleetingly"
"In the second phase, this quark–gluon plasma universe then cooled further, the current fundamental forces we know take their present forms through further symmetry breaking – notably the breaking of electroweak symmetry – and the full range of complex and composite pa…

0celo7

@bolbteppa What makes you think it would be simple?

@ACuriousMind Is there really no way to reduce intoxication?

I have a whole night to learn more string theory

ACuriousMind

@0celo7 You mean, except sleeping it off? :P

0celo7

But I can't like this.

ACuriousMind

I don't know a way. If you find one, you'll get rich veeeery fast, I guess

bolbteppa

12:19 AM

Because Weinberg wrote a book called Cosmology and I thought this stuff would be in there, I guess it is in chapter 3 amazon.com/Cosmology-Steven-Weinberg/dp/0198526822 but I don't understand enough to know if that's 'the beginning'

That's why I think it's simple lol

ACuriousMind

lol:

Riding in a human is not as comfortable as riding in a car. — jinawee 4 hours ago

0celo7

@bolbteppa I have that book but it's unreadable

Multi-page calculations reduced to one line

bolbteppa

What I've found with his QFT & GR books is that the text is amazing and the equations are literally an unreadable mess, I'm expecting the same with cosmology lol

0celo7

@bolbteppa The first half of his GR book is OK

Mathematically simple, but OK

the whole "geometry is bullcrap" is offputting though

bolbteppa

I don't really get what he means by that, does he mean he's taking the equivalence principle as a guide and intoducing methods as they come along? Or does he mean he just doesn't care about starting from some Riemannian geometry postulate? I know it's ultimately motivated by the spin 2 argument, but in practice I don't know what that implies

Stan Shunpike

12:24 AM

In the Schrödinger equation, the wave function is not a vector correct?

bolbteppa

A function is a vector

Stan Shunpike

Right forgot

Duh

bolbteppa

The way I think about it is

0celo7

@StanShunpike Careful, there are different kinds of vectors.

Stan Shunpike

@0celo7 yeah exactly, how do I know when a function is or is not a vector? Or are all functions vectors?

ACuriousMind

12:28 AM

@StanShunpike All functions into vector spaces are themselves vectors.

bolbteppa

The whole theory derives from the notion of "expected value", i.e. measurement/born rule, that's all you need, so you can do probability on a normal function space (Schrodinger waves) or you can do probability using Hilbert spaces (there are books that do it this way) or you can use some weird forms of probability (forget the book!)

0celo7

@ACuriousMind This. Functions just aren't vectors in the sense of arrows, @StanShunpike .

bolbteppa

You can think of a function as an infinite-dimensional vector

0celo7

Does a period right after the name still work or do you have to put a space?

bolbteppa

I think...

0celo7

12:29 AM

@bolbteppa Yes, I think so.

ACuriousMind

@0celo7 I think punctuation works

0celo7

@ACuriousMind.

ACuriousMind

Yep

0celo7

Did that work?

Noice

GG H-bar

@bolbteppa Einstein derived his equations before we even knew what spin was

ACuriousMind

@bolbteppa Well, only functions from an infinite set into a vector space will be an infinite-dimensional vector space ;)

bolbteppa

12:31 AM

There might be some nonsense special cases, but basically you can think of a function as the vector (f(1),f(2),...) only at a continuously infinite number of points, and then (I think) you can think of the polynomials 1 = (1,0,0,...), x = (0,1,0,...), x^2 = (0,0,1,0,...) as a countable basis (when the space is separable or something)

0celo7

@ACuriousMind Infinite set?

ACuriousMind

@0celo7 Like functions on $\mathbb{R}$

bolbteppa

You know the only spaces that exist are $\mathbb{R}$ and $\mathbb{C}$ lol

0celo7

Is an interval of R an infinte set?

bolbteppa

Yeah

0celo7

12:31 AM

I think math clears the mind...

ACuriousMind

Functions $\{0,1\}\to\mathbb{R}$, for example, are not an infinite vector space, they are just $\mathbb{R}^2$

0celo7

@bolbteppa What?

ACuriousMind

@bolbteppa Ahh, damn physicist :P

0celo7

I'm tipsy, but that's definitely wrong

@Qmechanic You need to take over the world with your $\approx$ notation!

bolbteppa

An interval of $\mathbb{R}$ is an uncountably infinite set unless it's an interval containing one point, because you can subdivide and subdivide with rationals, and in between any of those two points there'll always be a real number you can't put in any list you try to make

Qmechanic

12:34 AM

@0celo7 : Ha-ha. Thanks.

Stan Shunpike

@ACuriousMind So not all functions are vectors? I didn't follow your point. Could you elaborate?

0celo7

@Qmechanic String theory texts are very confusing. One moment they say $T_{\alpha\beta}=0$ and then they do random crap with $T_{\alpha\beta}\ne0$.

@ACuriousMind WTH I can't paste into chat anymore.

Stan Shunpike

I understand its only a vector in the axiomatic sense not the arrow sense.

bolbteppa

@ACuriousMind if those functions map to every point of $\mathbb{R}^2$ then you've set up an isomorphism between the set of (arrow) vectors in $\mathbb{R}^2$ so they definitely form a vector space, more generally any set of functions forms a vector space, but in this special case you mentioned we can literally represent them as arrows lol

Well, I should be more clear, the functions have to satisfy the axioms of a vector space, which means the functions have to map between spaces that allow you to write things like $\sqrt{2} f(\vec{v}) + e^{i \pi}g(\vec{w})$, so it depends on the underlying fields (but in physics you basically ignore this)

Stan Shunpike

@bolbteppa How do we know the wave function has this property?

bolbteppa

12:40 AM

@StanShunpike I found Apostol very confusing tbh, the linear algebra section really confused me tbh (as did every linear algebra book), I recommend reading Gel'fand's little linear algebra book and using my answer here math.stackexchange.com/a/1077144/82615 to interpret it, then look back at Apostol and see how messed up it is :( I really liked Apostol too!

Wave functions are always complex valued, this is the expected value calculation I was talking about i.stack.imgur.com/iTIPS.png (Parthasarathry's Quantum Stochastic Calculus P. 1 if interested)

You see there the wave function is a vector with n values, but there's no reason why we need to stop at n or even a countable number of values right?

@0celo7 I will buy Cosmology off you cheap if you're interested? ;)

Stan Shunpike

Right, that makes sense. Okay, so what does the $\frac{\partial d}{\partial dt }$ map to for the time dependent Schrödinger equation?

An operator maps from between vector spaces

So does this just map from t= 0 to some later t?

ACuriousMind

@StanShunpike Given a vector space $V$ (over $\mathbb{R}$), you can, for any two functions $f,g: X\to V$, write $(f+g)(x) := f(x)+g(x)$ and $(r\cdot f)(x) = r\cdot(f(x))$, so functions into a vector space are vectors

bolbteppa

Derivative as a linear map: the-idea-shop.com/article/225/…

ACuriousMind

If you do not restrict the kind of functions, the vector space of functions $X\to V$ has its dimension as the size of the set $X$

Stan Shunpike

@bolbteppa wow that's really cool! I follow all that, so what does that tell me about the time derivative operator?

bolbteppa

12:58 AM

Since wave functions usually have something of the form $\Psi(t,\vec{x}) = \Phi(\vec{x})e^{-\tfrac{i}{\hbar}t}$ you can just write $e$ as a Taylor series and view derivatives of it the exact same way as in that link

ACuriousMind

Careful, that's a stationary wavefunction. Do not think all wavefunctions can be written that way, I've seen people assume that too many times

(All wavefunctions are sums of these, though)

bolbteppa

I'm just giving an example to get the thinking across ;)

I was gonna quote the line at the end about integration being linear to make that point with a Fourier transform lol

But more fundamentally, and this is what literally motivated Dirac, the time derivative of the wave function (is linear and it) results in a linear operator acting on $\Phi$, namely writing $\Phi$ in it's quasi-classical approximation $\Phi = e^{\frac{i}{\hbar}S}$ and taking the time derivative gives $\frac{\partial \Phi}{\partial t} = - \frac{i}{\hbar} H \Phi$ which is the Schrodinger equation.

Stan Shunpike

@ACuriousMind what do you mean by stationary states?

ACuriousMind

@StanShunpike Those that do not change in time. States whose time evolution is just a phase $\mathrm{e}^{\mathrm{i}Et}$ stay the same state the whole time.

Stan Shunpike

So what is different in the non-stationary case?

ACuriousMind

1:08 AM

@StanShunpike They are a sum of these states. The formal idea is that the spectral theorem gives you that the stationary states span the space of states, and you can then express every state as a sum of these stationary energy eigenstates.

In case your space of states is infinite-dimensional, there are some subtleties, but they are mostly swept under the rug until you are forced to face them.

Stan Shunpike

So the non stationary states can be written using stationary eigenstates?

ACuriousMind

@StanShunpike Yep

bolbteppa

It looks like Susskind's 2013 lectures actually follow Weinberg pretty closely, the last 4 being close to chapter's 3 & 4 of Weinberg!

Stan Shunpike

Which set of lectures

bolbteppa

theoreticalminimum.com/courses

Sean

3:16 AM

So, if I knew nothing (beyond a little that I read on Wikipedia) and I wanted to know more, what would be a good book or resource to read?

About gauge theory

Stan Shunpike

3:59 AM

An excellent question. Hear hear.

I have the same one.

What is a good intro book? Furthermore, can anyone think of a better name than gauge theory that more accurately captures what it is?

I read somewhere that Weyl named it after gauge wire fences but has nothing to do with that

David Z

6:11 AM

Gauge wire fences? Never heard that... it's called gauge theory because it arises from gauge invariance, which is the idea that you can change the values of certain variables (gauge degrees of freedom) without changing the physics.

I'm not sure why gauge degrees of freedom have that name. According to this paper, the first person to use the name was Hermann Weyl in 1929.

Stan Shunpike

6:42 AM

@DavidZ Source: Quantum Field Theory for the Gifted Amateur page 126. "Einstein's general relativity showed that space-time geometry has a dynamical role and Herman Weyl wondered if the scale of length could itself be dynamical, varying through spacetime.

In this picture, one could make a choice of gauge which would be a choice of scale-length: metal wire comes in different thicknesses or gauges, so the term seemed entirely appropriate.

End quote

Stan Shunpike

8:30 AM

@ACuriousMind So for Lagrangian densities, one of the easiest ones I have worked with so far is the Massive Scalar Field where I have a Lagrangian and when I plug it into the Euler-Lagrange equations out pops Klein Gordon equation

@ACuriousMind Can you give me a similarly easy example for the Hamiltonian density that I could try out? I wanna have a case for each that I am very familiar with so I can always go through them if need be.

In other words, I want a Hamiltonian density equation that I can plug into the density form of Hamilton's equations of motion.

infinitesimal

8:57 AM

:-O

Stan Shunpike

9:30 AM

Hey, anybody got ideas for something cool science imagery thing I could put on the cover of my third album? I've seen a bunch of people running simulations and doing all sorts of cool stuff, so if anyone has anything they think might make a good album cover, let me know.

Physics Meta

0

Q: Why are my 6-months old questions suddenly being getting downvoted?

My reputation earlier today was 2007. Suddenly it became 1997. 10 reputation losses within an hour. Why? I checked & found that my old questions that were greatly appreciated are simultaneously being downvoted. My old questions are suddenly continuously getting downvoted for no reason. No comments

discussion

Gowtham

10:12 AM

@infinitesimal these 2 meta posts !

infinitesimal

I see.

0celo7

10:39 AM

@ACuriousMind No way quantumly is a word.

ACuriousMind

@0celo7 I don't care. It's shorter than saying "in the quantum theory" everytime :P

@StanShunpike Can't you, uh, just Legendre transform the Lagrangian and derive the KG again? ;)

Gowtham

11:10 AM

@ACuriousMind some user thought his profile was offensive as he quoted Goebbels and hence the downvotes i think

ACuriousMind

@Gowtham I know. This doesn't change the answer I gave, though. Frankly, my sympathy is non-existent.

Gowtham

@ACuriousMind i thought he will delete the question when he saw the now-deleted meta post

ACuriousMind

Since I can see the meta post and the reason for its deletion, I think it is better to not discuss this matter in chat for now.

Sean

11:46 AM

What are the rules for deletion of meta posts? In general

Stan Shunpike

1:48 PM

@ACuriousMind here's the thing about that tho: can I always Legendre transform a Lagrangian to find a valid Hamiltonian? I thought there were some cases that you couldn't put into the Hamiltonian formulation. Otherwise, I would have known to do that of course.

@ACuriousMind So I am confused how I am supposed to know whether or not a Hamiltonian version exists for any given Lagtangian.

David Z

2:26 PM

@Sean I don't think they're explicitly spelled out anywhere. We don't really delete meta posts very much. Authors are of course free to delete their own meta posts under the same conditions that apply to main-site posts. (Zero or negative score and no upvoted answers, or something like that)

Nick

3:26 PM

Gosh, I have 22 chapters to revise in 15 hours. I'm panicking. Could someone give me some advice.

Nick

3:39 PM

I just spent the last four hours drawing a compound microscope and astronomical telescope. I've met eighth graders effortlessly do what I've failed to do in the past four hours.

dmckee

@Nick Triage. First the stuff that is both important and attainable.

Nick

@dmckee Well, It's always nice to enrich oneself with common sense. Still, Triage! is now my motto.

@dmckee Um, do you now some simple optics?

I got a refracting telescope here, I don't get how the final image is formed.

Physics Meta

0

Q: Why in the world (not US) did this suggested edit get rejected?

The edit in question. Fixing 3 different spelling mistakes and added some italics to make the post a bit easier to read and tried to clean up where the author was using quotation marks to refer to "see" as a word and where he used them to put special emphasis on the word (might have gotten one wr...

support suggested-edits

Nick

I get that lenses can be though as being consisting of prisms but how do I know those rays that bend towards the observer make a final virtual image? It seems so random.

Ugh, it's okay if you can't help. Venting my difficulties somehow relaxes me.

dmckee

3:54 PM

@Nick The lens law tells you where images form, and the sign conventions that go with it tell you if they are real or virtual.

Lens law: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$.

But to understand simple optics, you also need to pay attention to the human eye.

Nick

@dmckee Ok, ok, I know that. I have to reproduce the exact diagram and in most of my attempts the diagram got all wacky and final image ended up at infinity.

dmckee

Where is the near point? What set the distinguishability limit (ans: angular resolution given by the receptor cell size and the diameter of the organ). That sort of thing.

Nick

Um, I feel you're right. I should really correlate my theory here to make it perfect.

@dmckee oh. I actually didn't know that. Thanks for telling me :D

dmckee

I find the design of two-lens optics very hard to explain clearly. It's probably the most difficult lecture for me in the 2nd semester intro class.

Nick

@dmckee Gosh, not to mention analytically, the confusion in sign convention when there are two lenses.

Heck, I'm confused when it comes to singular lens/mirror sign conventions.

dmckee

4:00 PM

Ah .. for the multiple lens bit I say "the image from the first is the object for the second".

Nick

I know that... OH, lightbulb, we apply signs wrt to the lens in question. It makes things easier. kay

But when I derive the formulae for mirror/lens equations, I apply cartesian sign convention. And when I use the formulae, I apply cartesian sign convention. In the end, I feel, there was no use for the conventions in the first place.

eh, maybe I'm just naive.

I'm surely naive.

It must not be double-entry of signs as I think it is.

It's just in most expected solutions in optics, the minus signs seem counter-intuitive (for me atleast)

*Sigh* Does anyone have a pencil I can borrow?

0celo7

4:18 PM

@ACuriousMind Does anyone actually do the analytic continuation of the zeta function? I've read four string theory resources that all say "it can be done".

Nick

@0celo7 Are you talking about the riemann zeta?

0celo7

@Nick Yes.

Nick

6

Q: What is the analytic continuation of the Riemann Zeta Function

I am told that when computing the zeroes one does not use the normal definition of the rieman zeta function but an altogether different one that obeys the same functional relation. What is this other function that they use explicitly given? Also if I were to take one of these non trivial zeroes ...

complex-analysis analytic-number-theory riemann-zeta riemann-hypothesis

0celo7

@Nick Ok, you can use the functional equation.

@Nick Do you just plug in $s<1$ into the functional equation?

Nick

@frogeyedpeas If you evaluate the series $\displaystyle \sum_{k=1}^{\infty }\dfrac1{k^s}$ for $\text{Real}(s) \leq 1$, you will get the answer not to converge. So you cannot evaluate the series at any of the zeros, let alone non-trivial zeros. — user17762 Jul 7 '13 at 3:42

0celo7

4:26 PM

@Nick I mean do we just plug in $s=-1$ into $$\zeta(s)=2^{s}\pi^{s-1}\sin\Bigl(\frac{\pi s}{2}\Bigr)\Gamma(1-s)\zeta(1-s)$$

I'll try it, see what happens.

Nick

Did you get $-1/12$?

0celo7

Yup.

Cool, now where is that derived?

Rudin? Ahlfors?

Nick

You mean the analytical continuation of the zeta function ? I think you can find one on MSE if you search hard enough.

0celo7

@Nick I'll look.

Nick

But I'm pretty sure I saw it somewhere in a Numberphile video regarding the sum of all natural numbers being $\zeta(-1)$

0celo7

4:31 PM

@Nick Well that's not analytic continuation.

Series magic isn't very interesting.

Nick

@0celo7 No, it's a cheap parlour trick that astounds 2nd semester highschoolers.

0celo7

@Nick Exactly.

ams.org/journals/proc/2001-129-07/S0002-9939-01-06033-6/…

Nick

This was the video I was reffering to, I think:

Riemann Hypothesis - Numberphile

►

0celo7

@Nick I watched that during a Numberphile binge once.

I stopped watching those videos when I learned some math. I don't like being treated like an idiot.

Nick

@0celo7 God, I'm relieved I'm not the only person who binge watches youtube.

@0celo7 Well, good luck. Hope @ACuriousMind can satisy your curious mind.

0celo7

4:37 PM

@Nick That paper I linked explains it.

I just don't want to work through it :P

It will be saved for a later date.

Nick

It's taking time to load.

0celo7

Knowing that it can be done and knowing where it is done is half the battle.

Nick

@0celo7 Did you know that $\displaystyle \zeta(-s) = -\frac{B_{s+1}}{s+1}$?

0celo7

@Nick Is that used in the paper?

Nick

I didn't see the paper yet. My nets very slow. Maybe 100 years later. But I found it elsewhere, B is a Bernoulli number. Look that up. I think it could be useful for you.

0celo7

4:42 PM

@Nick I did know that, but it's not used in this paper. (Know but can't prove.)

Nick

@0celo7 Gosh, (referring to the paper) that's the easy proof!? Something tells me I'm not going to major in math.

0celo7

@Nick Ha, I read that title, looked that the first page and thought: "OK, this will be simple," but that was naive.

I could have sworn there was a simpler proof using contour integrals.

Nick

I think there's an entire book just about this.

0celo7

So You Want to Get a PhD in Mathematics?

►

Just major in double and triple integrals.

Nick

... I can major in singing the C Major to an army major.

Wait I heard contour and zeta something something over at MSE

12

Q: Zeta function zeros and analytic continuation

I'm learning about the zeta function and already discovered the intuitive proof of the Euler product and the Basel problem proof. I want to learn how to calculate the first zero of the Riemman Zeta function, but I know first that I will have to learn about analytic continuation and other things....

complex-analysis riemann-zeta

Seriously, when people aren't around here go to the Math room. They're very friendly.

They don't bite.

... actually some do but the regulars don't.

0celo7

4:54 PM

@Nick Reading right now.

Nick

@0celo7 Yeah, it's gonna take a lot of reading. I'm going to go read a big fat book now. Hope I'll be alive l8r.... Nah, I'll surely be alive :D

bolbteppa

5:56 PM

piddly double and triple integrals...

ACuriousMind

6:36 PM

@0celo7 Umm...no, I don't think anyone ever explicitly shows that :D

Everyone just always links to Terry Tao :P

@StanShunpike Well, if the Legrendre transform succeeds, you get a Hamiltonian. It can happen that you incur "constraints" though, so that the Hamiltonian doesn't contain all the information of the system on its own

0celo7

@ACuriousMind Yuck how can anyone like number theory...

ACuriousMind

I can't recall whether I've ever really done classical mechanics with Hamiltonians by actually solving Hamilton's equations

@0celo7 Well, I also am content with the fact that Terry Tao has done it for me :D

0celo7

@ACuriousMind Speaking of Hamiltonians, how are phase space diagrams made?

Are they just the integral cuves of the Hamiltonian vector?

ACuriousMind

Yeah, I think so

They just show you the allowed trajectories, which are the integral curves, yes

0celo7

@ACuriousMind So you've seen the numeric solutions.

ACuriousMind

6:40 PM

Yes, I've seen them

0celo7

Just no one does them analytically

ACuriousMind

I've never done them, though

0celo7

Yeah

ACuriousMind

I think if you do chaotic systems and stuff you do Hamiltonian mechanics all the time

But my main experience with Hamiltonians is quantum

0celo7

@ACuriousMind So what are tachyons? They're just negative mass squared, right?

ACuriousMind

6:41 PM

@0celo7 The string tachyons? Yes

0celo7

@ACuriousMind And we've just decided that tachyons are unphysical?

Does negative mass squared always imply FTL?

ACuriousMind

@0celo7 Nope

I think there was this question which Leandro and Qmechanic answered about that

0celo7

@ACuriousMind So why is there a confusion then?

ACuriousMind

@0celo7 Because you can do naive computations where they are FTL, and because "Negative mass!!!!111!!!"

8

Q: Do tachyons move faster than light?

I am trying to understand whether or not tachyons travel faster than light. The linked Wikipedia page shows some seemingly contradictory statements, and they are confusing. For instance, the first sentence states that tachyons "always travel faster than the speed of light" whereas, in a later se...

special-relativity faster-than-light tachyon

0celo7

@ACuriousMind Maybe I'm dumb, but from $p^2=\mp m^2$, doesn't it follow that negative mass squared gives spacelike momentum? Does that not imply anything about the velocity then?

ACuriousMind

6:44 PM

@0celo7 Read the post. Essentially, tachyons cause non-zero VEV in many cases instead of being FTL

For example the Higgs is a tachyon field :D

Nobody ever tells you that unless you ask, though^^

0celo7

@ACuriousMind So why do we consider the string vacuum unphysical then?

Maybe it's just unstable and could slip into another, stable, ground state.

ACuriousMind

@0celo7 Yeah. But an unstable vacuum is...unphysical, or we would have to think that the universe around us is likely to collapse any minute

It's not that likely we would have made it 13.7 billion years in an unstable state

0celo7

@ACuriousMind You said something about that the other day though.

ACuriousMind

Oh, but that was metastable, not unstable

The tachyon does not sit in a local minimum, it's truly unstable, I think

But don't take my word for it

0celo7

@ACuriousMind In Qmechanic's post, shouldn't he have a $\approx$ in (1)?

ACuriousMind

6:48 PM

@0celo7 Yes, but I don't think any equation there is off-shell

0celo7

@ACuriousMind Oh yeah. No one ever says that though. They just casually brush $\mu^2<0$ under the table.

ACuriousMind

@0celo7 Exactly. I was a bit troubled by that, but most just shrug when you point it out. Another indication that tachyons are not really that bad

0celo7

@ACuriousMind Our favorite user commented on Qmechanic's answer

Also he has two "new" answers. You might have already seen them.

ACuriousMind

@0celo7 I saw

I'm honestly a bit more disturbed by some other users currently, though (no I won't tell who :P )

0celo7

@ACuriousMind I heard about the Goebbels guy.

ACuriousMind

6:59 PM

Well, as I already said, I'm not sure this should be discussed here, but let me just say that I am truly amazed at the utter lack of awareness and empathy it takes to quote the Nazi minister of propaganda approvingly on the topic of truth and call him a martyr.

But it's not just that, 12232 is really one of the crackpots I'm not that hostile towards. At least they are civil.

Why would anyone name a planet Roddo?!

Physics Meta

0

Q: inviting people to answer questions

Suppose I have a question and I am in dire need for the answer to that question . Let's say that question fails to attract answers or attentions. But there are some users who I believe can answer that question . Is there any way by which I can request them to post an answer ?

support feature-request

0celo7

@ACuriousMind :urbandictonaries:

Hmm.

Wut?

ACuriousMind

7:16 PM

@0celo7 lol

That doesn't answer my question :D

0celo7

@ACuriousMind I'll address it in my Nobel speech.

@ACuriousMind What the hell is a twistor?

@ACuriousMind Was it at least a good quote?

ACuriousMind

@0celo7 No idea

@0celo7 Ugh, not particularly, just something about truth someday again triumphing over lies.

I mean, the context-free content isn't bad, but I'm sure you can find better persons who've said it better

0celo7

@ACuriousMind By "good quote" I meant would it have been a good quote had it not been a Goebbels quote.

ACuriousMind

@0celo7 If you manage to work roddo into your Nobel speech, I will applaud you

0celo7

@ACuriousMind Is the Urban Dictionary definition correct?

ACuriousMind

7:21 PM

@0celo7 No idea, I've never heard that before

0celo7

@ACuriousMind Wait, what do you think roddo means?

Stan Shunpike

@ACuriousMind good #timeofday! So about this Legendre transform, are u saying that I can always (or in almost all cases) apply it and get acHamiltonian. But that in some cases, it may have fewer degrees of freedom?

ACuriousMind

@0celo7 Well, my UD result says: "the act of tying up several chickens, locking them in a filing cabinet and disposing of them in a retirement home wheelie bin. "

DanielSank

To anyone who went to the APS March meeting: congrats on still being alive. Five days of 10 minute talks is an assault on the human brain :P

Stan Shunpike

@DanielSank Is it fun? Do they post YouTube videos of it?

0celo7

7:26 PM

@ACuriousMind Ok, I thought you meant UD has something different than what you knew.

Stan Shunpike

btw has anyone else seen the string theory vs LQG faceoff with Carlo Rovelli? It was quite funny m.youtube.com/watch?v=jEr038WOKFI

0celo7

I want an LQG book.

ACuriousMind

@StanShunpike It might, for example, happen that the momentum associated to something simply vanishes (as it does for (parts of) the electromagnetic field, for example), or that it is expressible in terms of the other momenta and positions. In that case, you can still Legendre transform, but the vanishing momentum, for example, is not really a free variable - the whole theory is constrained to the surface in phase space where that $p=0$.

You can still use the Hamiltonian for this, but you have to remember the relations among the momenta, which are called constraints

It gets ugly from there :P

Stan Shunpike

@ACuriousMind So the Hamiltonian then only becomes a valid description of the system under some circumstances?

ACuriousMind

@StanShunpike It is still a valid description of the system together with the constraints.

It is a valid description without constraints if the transform is uniquely invertible.

This can get messy, and often it is better to just forget about this and not really care for the constraints until you feel that you've got unphysical answers

Stan Shunpike

7:33 PM

Oh brother.

Yeah, that is quite complicated

0celo7

@ACuriousMind Why is the string landscape "the end of science"?

Stan Shunpike

People are over dramatic

ACuriousMind

@0celo7 How should I know?

0celo7

@ACuriousMind Lack of dumbness.

Idk, you said you can compactify on a circle. That's more ST than I know.

Sean

@DanielSank do you go to many of the APS meetings?

Meanwhile, I saw that @KyleKanos was throwing down with some guy on meta haha

ACuriousMind

7:51 PM

@0celo7 Yeah, but I don't have a full idea of what "the string landscape" is, nor what "the end of science" even means.

@Sean I don't understand why his explanation is downvoted. The rejection of that edit is perfectly reasonable, imo.

Sofia

@0celo7 I understand that you are very happy there in the bar. But, you with the gravitation, won't you want to solve the problem of some fellow that doubts that the time exists?

Sean

I agree. I suspect maybe the OP down voted and no one else voted. Changing scare quotes to italics is not really an improvement.

ACuriousMind

@Sean No, there are 2 downvotes and 1 upvote

(The upvote is mine)

Sean

Weird. Let me help fix that

Also those comments are getting progressively more amusing.

@Sofia so let them think time doesn't exist

Also I'm almost positive that time question is a duplicate

Hey, @ACuriousMind what do you know about gauge theory?

Sofia

8:26 PM

@Sean No, you don't have to despise people who ask naïve questions. The theory of relativity confuses many people (and some also seek sensational effects). But it's not to be despised. I saw once a question, why the time is 1dimensional and not 3D, and it seems to me quite legitimate. Anyway, @KyleKanos noticed that the question is a duplicate, and I also voted for close.

DanielSank

8:40 PM

@StanShunpike I don't think so. Folks in my group were taking about this though. It would make a lot of sense if APS would require slides to be submitted electronically before the meeting. This would avoid delays from A/V problems, laptop crashes, etc. and would make it easy for people (including those not at the meeting) to follow the slides. Recording video would be a good idea too.

@Sean I go to March meeting every year.

Sean

@Sofia who said anything about despising anyone? It was a bad question on a flawed premise, and a duplicate. That's all

Stan Shunpike

8:59 PM

@ACuriousMind What is the Schrödinger equation? Like, as I see it, Lagrangians and Hamiltonians allow us to describe the evolution of the system. So what is the Schrödinger equations purpose? If the Hamiltonians and Lagrangians give us the evolution, why is the Schrödinger equation needed?

0celo7

@Sofia I was busy with my siblings, sorry. I have no idea what that even means.

Stan Shunpike

@ACuriousMind although now that I think about it, the Lagrangian even for something simple like a spring or a pendulmn only yields equations of motion. That's not telling me how the system behaves from $t_i$ to $t_f$. Is that what the Schrödinger equation is for?

Sofia

@Sean Unfortunately, you'll see a lot more of questions in which the fellow who asks doesn't even understand clearly what he wants to ask, and it's us who have to crystalize his question. That's the situation many times.

bolbteppa

When you look at boiling water, the steam is made up of bubbles of water, and in those bubbles of water is steam, which is made up of bubbles of water, etc... this is an examples of a scale-invariant system. Using this, I'm supposed to motivate why someone would even think to look at angles, why in the world would someone notice this is an angle-preserving transformation as being fundamental!?

Sofia

9:15 PM

@KyleKanos I have a problem with a fellow who wants us to explain him an article. I feel some pity for him, but on the other side no wish to parse someone's article. Now, about the rules of our site, do we in general do such things? Get into articles and explain them to users? Isn't that an exaggerate expectation from us? What's our policy on such things?

user1667423

Anyone here familiar with perfectly matched layers (PML) for FDTD?

Sofia

@KyleKanos the question is here

bolbteppa

@StanShunpike the Lagrangian $\mathcal{L}$ is a function of paths $\gamma$, $\mathcal{L}(\gamma)$, yet the Heisenberg uncertainty principle says "there's no concept of the path of a particle", which means we don't even know the values of the position/velocity variables making up $\mathcal{L}$ at the same time. How does it make sense that quantum mechanics involves Lagrangian's and their associated Hamiltonian's when we can't even specify the variables?

ACuriousMind

9:37 PM

@StanShunpike The Schrödinger equation is none other than the statement that the Hamiltonian is the generator of time translations. It is the quantum analogue to the phase space equation $\partial_t f = \{H,f\}$.

@Sean Enough that I wrote my bachelor's thesis on two-dimensional gauge theories

(The analogue is clearer in the Heisenberg picture, where it is literally just replacing the Poisson bracket with the commutator)

@StanShunpike You should not mix the descriptions. Lagrangian and Hamiltonian mechanics are both equivalent ways of describing the classical world. There, the equations of motion tell you everything you need to know about a system - you give the initial positions and velocities (or momenta), and then it gives you the unique time evolution of the system - the trajectory

The Schrödinger equation is the "equation of motion" of the Schrödinger picture of quantum mechanics, where the world is not made up anymore out of things that have definite positions and momenta, and that refuse to let definite trajectories be associated to them.

Um...is asking us to explain a paper on-topic?

0celo7

9:52 PM

@ACuriousMind Surely you meant $ df/dt=\{H,f\}$, right?

ACuriousMind

@0celo7 Oh, yes, that's the total derivative there. Sorry

0celo7

@ACuriousMind Np

ACuriousMind

I guess I'm so used to never dealing with explicit time dependency that one forgets that there is a difference

0celo7

1:1 with Sapphire. The tonic is still too much. I'm afraid I'm not much of a gin & tonic person.

ACuriousMind

@0celo7 Heh, I'm not stopping anyone from drinking the stuff pure :D I wouldn't necessarily advise it, though.

0celo7

9:55 PM

@ACuriousMind I've heard that North American tonic is too sweet. That's what I don't like about G&T, it's too sweet.

ACuriousMind

If your tonic water is sweet, you are not drinking tonic water.

0celo7

@ACuriousMind Blame Canada Dry.

ACuriousMind

At least, sweet is not something I associate with it

::blames Canada Dry::

0celo7

This is actually really sweet, I'm drinking this too fast.

Stan Shunpike

@ACuriousMind (note: pardon if nothing I say makes sense) But just to clarify, the concept of equation of motion now carries a different meaning in quantum mechanics correct? Although we are trying to predict future probability amplitudes, we aren't describing those features of the classical world any more through our equations of motion now

When people ask if something is on topic, are they asking for opinions just from people with enough rep?

0celo7

9:59 PM

@StanShunpike The classical equations of motion hold quantumly when averaged.

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