The h Bar

DanielSank

00:04

@ACuriousMind I voted to close that.

I don't know what he's asking, and it's probably too broad.

ACuriousMind

I'm inclined to agree

DanielSank

The broadness aside, I don't understand the question.

ACuriousMind

That's why I asked what the user means with "carry" - unfortunately, they ignored that part of my comment. The second paragraph is also very...confused

0celo7

@Huy never trust the catering staff

user54412

00:58

6

Q: Interstellar communcation with FTL

I am designing a world where humans have achieved FTL by means of the Alcubierre warp drive and are colonizing the stars. Originally I had communication pegged as being done with quantum entanglement and the like, but I recently heard of the no-communication theorem that, seemingly, prevents thi...

user54412

Why is it that 99.999% of everything the public "knows" about faster-than-light anything is just plain wrong?

user54412

Pretty much every single answer and comment there is irretrievably flawed :(

ACuriousMind

lol, it's tagged "science-based", and the tag description is "For questions that require answers based in hard science, not magic or pseudo-science. "

0celo7

no magnets???

ACuriousMind

I have a feeling I don't want to click on other questions tagged "science-based"

user54412

01:07

Isn't @HDE226868 interested in preserving the integrity of the science-based tag? @HDE226868 You should politely inform everyone that (1) dark energy does not have negative density, (2) there is no exception to no-communication, (3) FTL travel is equivalent to time travel, always, and (4) wormholes and Alcubierre are the sorts of science fiction that isn't published in reputable journals.

user54412

What I really don't understand is people's insistence on finding justification for their fantasy in hard science. How good or bad a story is is independent of how scientifically justified its premises are.

ACuriousMind

I completely agree, but others apperently don't

0celo7

@ChrisWhite sci-fi? cds.cern.ch/record/358132/files/9806096.pdf

user54412

Sci-fi was never about science. The "science" it references is the "magic" cf. Arthur C. Clarke -- a means to explore human nature in an otherwise unattainable setting. This is why sci-fi and fantasy are inextricably linked.

0celo7

arxiv.org/abs/0705.2768

wormholes are not strictly sci-fi

user54412

01:10

They are jointly a genre about broad-brushstrokes human nature, rather than individual vs. individual or individual vs. society storylines.

0celo7

Unless Arkani-Hamed and Polchinski are sci-fi people...

user54412

@0celo7 I can write "wormhole" on the blackboard too. That doesn't make it physical.

0celo7

> wormholes and Alcubierre are the sorts of science fiction that isn't published in reputable journals

user54412

I stand by my claim.

0celo7

You're telling me I can't find anything on wormholes in Class. Quant. Gravity?

user54412

01:13

There are other ways to interpret my claim.

0celo7

ELI5 please

user54412

I said reputable, and I implied physics journals. Any journal that just manipulates symbols with no reference to physical reality is either math or disreputable. Take your pick.

0celo7

Is Witten a reputable physicist?

ACuriousMind

Sometimes

user54412

I thought he was a journalist or something ;)

user54412

01:19

The fact is, being able to write down equations (even self-consistent ones, thought this low bar is often not met) does in no way oblige nature to obey them. You can't say "wormholes should exist because I wrote down a definition in mathematical symbols" any more than you will an organism into existence by describing its biology.

0celo7

I'm not saying wormholes exist because of that, but by your definition you'd have to exclude a lot of "physicists" from the profession of physicist.

user54412

People don't believe in black holes because Schwarzschild and Kerr found solutions to Einstein's equation. People believe in them because we see their effects quite dramatically, and have a mountain of evidence for them. (And we'll have pictures of them in a few years at most!)

ACuriousMind

@ChrisWhite Well, for a question such as the one on worldbuilding, it would suffice to describe the biology and show it does not contradict the currently known laws of biology, no?

0celo7

@ChrisWhite So string theorists are not physicists?

user54412

@0celo7 You don't get to be a physicist just by calling yourself one. There are a fair number of mathematicians who for whatever reason think that empirical science is the only worthwhile endeavor, and so they contort themselves into pretending to do it, which is insulting both to pure mathematics and to empirical science.

user54412

01:23

Also, those are few in number. The vast majority of physicists have never glanced at a single equation from e.g. string theory. They are only influential among young enthusiasts such as yourself.

obe

@0celo7 How much of QM is contained in this chapter?

0celo7

@obe Define "amount of QM"

ACuriousMind

@ChrisWhite: It sounds to me as if you are excluding "showing something is compatible with the currently known laws of nature" from physics, but keep "showing something has evidence for it". But the first step is essentially for the second - for the observations to be interpreted as evidence for something, you must first have a coherent description of in within the theoretical framework.

obe

@0celo7 % of shankar, idk what we measure by.

0celo7

That seems way compressed.

ACuriousMind

01:25

Did Schwarzschild and Kerr first see the evidence and then decide to derive the BH solutions? If they derived them without motivating evidence, does that make their work pure math that retroactively becomes physics when evidence is discovered?

0celo7

I can't imagine the HUP being covered in 1-2 pages.

user54412

@ACuriousMind Is it possible for the physics/non-physics nature of investigation to be indeterminate until afterward? Can we physics retroactively assimilate math?

ACuriousMind

@ChrisWhite Ah, I see you have seen the consequence. Yes, I'm fine with stuff being math until evidence makes it physics.

obe

@0celo7 Sorry, HUP?

0celo7

Heisenberg UP

user54412

01:27

@obe My guess: ~60% of a Shankar.

obe

It seems to be a lot.

ACuriousMind

So 600 Millishankar?

0celo7

It is way compressed.

user54412

Yeah, my 60% is assuming everything is fully covered, in which case you're missing a bit more with Dirac equation, some extra path integral stuff, and pretty much all of perturbation and scattering theory.

obe

That's only one chapter.

ACuriousMind

01:29

@0celo7 Why not? Deriving the general uncertaintly relation does not need more space, at least at the physicists' level of rigor, and what else is there to do? ;)

0celo7

Angular momentum...

obe

@0celo7 @ACuriousMind Here is HUP.

Is it good enough for me? (Learning it formally first time)

0celo7

@ACuriousMind How is quantum mechanics well defined if the uncertainty principle means everything is uncertain :)

user54412

@ACuriousMind Less space might even be better. Then we wouldn't be elevating a property of Fourier transforms to some sort of physical law handed down from on high.

0celo7

@obe Sure. You should just get something and read it, you're wasting time.

ACuriousMind

01:32

@ChrisWhite It holds more generally than for Fourier related quantities, but it's a simple consequence of the Cauchy-Schwarz inequality for Hilbert spaces, so I agree with the thing about the physical law.

obe

@0celo7 Right, I dropped the lecture notes because they didn't include some important things.

ACuriousMind

Actually always acting as if "uncertainty relation" means some relation between position and momentum is detrimental - all non-commuting operators fulfill an uncertainty relation

obe

This book is supposed to be advanced, though I find it simpler than shankar.

Weird.

0celo7

Speaking of QM, @ACuriousMind I'm going to re-read Weinberg with Weigand alongside and really try to absorb it. Please excuse the inevitable dumb questions.

user54412

I suppose it does hold more generally, but all my QM background was in infinite-dimensional Hilbert space. The year after me actually started with spin spaces, which in hindsight I've come to think is a good idea.

obe

01:33

I need to ask dumb questions as well.

In fact I have some.

0celo7

yours are dumber than mine ;)

obe

Of course.

ACuriousMind

@0celo7 Not sure if I can answer stuff about Weinberg (don't ask me about cluster decomposition!), but I'll try

0celo7

@ACuriousMind QFT in general, I really did not learn it well.

I have no clue how RG works.

I barely have a clue how renormalization in general works.

obe

Can someone walk me through this.

It is the first part of the math chapter, I finished the rest though I didn't get the first part.

0celo7

01:36

Doing things

obe

@ACuriousMind Do you have time to help?

0celo7

the Meister will have to do it

ACuriousMind

@ChrisWhite Yes, I very much think starting QM in finite-dimensional spaces is a very good idea, especially because physicists always ignore the subtleties of infinitely many dimensions, so one should begin QM in a setting where these subtleties are absent.

@obe I'm reasonably free. What's your question about it?

obe

I don't get from 4-5.

0celo7

the only subtlety I see is $$\sum\to\int$$

ACuriousMind

01:39

@obe 5 is the defintion of the LHS

obe

And I don't see how the volume of the configuration space is 3N.

0celo7

3 space coordinates for N particles

=3N directions

ACuriousMind

@obe Well, what is the length of the interval $[-0.5L,0.5L]$?

obe

Ok.

fail.

Thanks, though I have more questions.

ACuriousMind

@0celo7 Ahahahaha...by far not the only one, but that's a tricky one, too

Think about this fun statement, for example: Every Banach space (and thus every Hilbert space) is either finite-dimensional or of uncountable dimension. Yet, we always give countable "eigenbases".

obe

01:42

It says the $\hbar$ in 6 defines the dimension of the momentum and $p$ and gives $p/\hbar$ an inverse length.

0celo7

@ACuriousMind what

user54412

@ACuriousMind something something seperable L^2 something :P

0celo7

I can't into analysis

say that again in 4 years

maybe 2 if my undergrad analysis is really good

obe

@0celo7 Though you don't do functional analysis in analysis I and II.

ACuriousMind

@obe The exponent has to be a dimensionless number. So, if $q$ is length, it has to be multiplied by something of inverse length to give something you can write in an exponent.

@ChrisWhite Yeah, separability plays a role (only for the separable spaces we have such bases), but the point that is glossed over is that the "eigenbasis" is not a basis in the usual sense of linear algebra, since infinite sums over the basis vectors are allowed (and one should ask which of these sums are allowed!)

@0celo7 The proof of the dimensionality statement follows from Baire's category theorem (which has nothing to do with categories). That we write down countable eigenbases you should know from e.g. the harmonic oscillator.

obe

01:47

@ACuriousMind why is 8 defined that way in here.

0celo7

@ACuriousMind stop saying that word countable like I know what it means :(

@obe I should learn what a Banach space is in analysis

obe

@0celo7 Idk, is it in rudin?

0celo7

when I take functional analysis I can understand @ACuriousMind although by then he'll probably only converse in sheaf cohomology

ACuriousMind

@0celo7 Oh, why didn't you say that earlier! A set is countable if there is a bijection from it to the natural numbers (i.e. it has "as many elements as there are natural numbers")

0celo7

@ACuriousMind because I need to clean my room and this is very distracting :P

@obe I'm prety sure you need that to define the Lebesgue measure but I'm not sure

in any case I'll have the experience and intuition to learn ahead

maybe

user54412

01:51

@0celo7 Here's an exercise for you: Write down the 10-15 axioms of a separable Hilbert space. Now start with a set, and add the axioms one by one, starting with associative addition. Name each algebraic/analytic object along the way (the first one is a semigroup). You now have an outline for a nonnegligible chunk of an undergrad math curriculum.

obe

@ACuriousMind Did you see my other question?

ACuriousMind

@obe Hm, what do you mean "why"? They want to have symbols (the LHS and the middle) for the plane waves on the RHS, and we are interested in the plane waves because they are a basis of the space (modulo some subtleties I will not pester you with now).

obe

@ACuriousMind By why, I mean how or what for.

To confirm LHS = linear hilbert space? RHS = real hilbert space or am I dumb?

ACuriousMind

@obe Knowing several bases of a space is very useful in applications - some operators (matrices) are diagonal in some bases, but not in others

@obe Left Hand Side and Right Hand Side

0celo7

@ACuriousMind so the quantum numbers are the bijection?

ACuriousMind

01:53

(of the equations)

obe

Wow dumb.

;)

ACuriousMind

@0celo7 Yes, exactly

0celo7

@obe serious question: how have you made it to QM without knowing that

obe

@0celo7 LHS/RHS is from grade 7.

0celo7

@ChrisWhite IDK what any of that is

obe

01:55

I didn't know it was used in advanced math.

0celo7

do you know what WLOG is

ACuriousMind

@obe It's used in chatting about advanced math and by lazy writers (so about all mathematicians :P)

obe

@ACuriousMind Your explanation now makes a lot more sense, I first thought what...

ACuriousMind

@0celo7 Of course you know a semigroup: $\mathbb{N}$! ;)

obe

@ACuriousMind Plane waves are the basis of the hilbert space?

ACuriousMind

01:57

@obe I see how that was confusing, then :D

obe

I don't get that, I though it had an orthonormal bases.

ACuriousMind

@obe It has, as every vector space has, many different orthonormal bases, and the plane waves are one of them

0celo7

@ACuriousMind all groups are semigroups so I know a lot more than that one

ACuriousMind

@obe Do you know and are you comfortable with different bases in linear algebra, and how to switch between them?

obe

@ACuriousMind Is that part of "infinite orthonormal basis"?

I guess.

ACuriousMind

01:59

In particular, can you tell me which matrices are the ones that switch between orthonormal bases?

because those are gonna be very important

0celo7

I know this one

::jeopardy music::

obe

@ACuriousMind I think.

ACuriousMind

@obe "infinite orthonormal basis" just means that there are infinitely many basis vectors

0celo7

@ACuriousMind $E_8\times E_8$

did I get it

ACuriousMind

@0celo7 what a heterotic failure ;)

obe

02:01

orthonormal matrix, though are there infinitely many orthonormal matrices?

0celo7

@ACuriousMind lol

obe

@ACuriousMind can you give an example of change of basis to plane wave?

I've not seen it.

ACuriousMind

@obe In the real case, they are orthogonal matrices. (and yes, there are infinitely many of these) In the complex case, they are the unitary matrices

user54412

@ACuriousMind Do you mean orthogonal in the "they should have called this orthonormal" sense?

obe

@ACuriousMind is the determinant of a unitary matrix 1 always?

and if you can, example of plane wave basis please.

brb

0celo7

02:04

@obe no that's a special unitary matrix

It's always a...phase? maybe

ACuriousMind

@obe Weeeeell, here's where I have to handwave/lie so that the infinite-dimensional subtleties doesn't don't break our neck. Also, change from which basis into it?

@ChrisWhite Yes, indeed :D

obe

orthonormal basis.

ACuriousMind

@obe But the plane waves are an orthonormal basis

You might want to revisit the notion of base changes in finite-dimensional linear algebra first

obe

yeah

ACuriousMind

@0celo7 Yep, it's always a phase because $A^\dagger A = 1$ forces $\det(A)^*\det(A) = 1$, so $\det(A)$ is on the unit circle.

obe

02:09

i don't see how the plane waves are an orthonormal basis.

like it never talked about that in the math part.

ACuriousMind

@obe Well, take the scalar product of two of them - what do you get?

0celo7

@ACuriousMind good to know I knew that

and...room is...sorta clean

oh well, leaving in two days

my poor books...all alone

poor Shankar, Zee, Carroll, Weinberg G&C, Weinberg C

Poor Java book I bought for a CS class and never used

ACuriousMind

@0celo7 Keep them somewhere where Einstein can read them ;)

Perhaps they'll not be lonely that way

0celo7

@ACuriousMind I'm taking the important ones: Wald, HIS, Straumann, QTF, BBS, BLT

and the holy iPad of the Caribbean

ACuriousMind

...I needed way too long to realize BLT is not a sandwich.

0celo7

02:16

lol

ACuriousMind

QTF is Weinberg's tQToF?

tQToF is a fitting abbreviation, it's almost as ugly as his notation :P

0celo7

QTF is Weinberg, yes

I also have some other stuff

See I have two options tomorrow while I'm at the hospital: read Weinberg or play Pokemon

FenderLesPaul

Weinberg G&C deserves to be alone

0celo7

:(

FenderLesPaul

that book is the shittiest physics book ever written

0celo7

02:22

you're right it's an assault on classical physics

@FenderLesPaul all kidding aside, that's not true

why do you hate it

FenderLesPaul

it takes everything nice about GR and throws it away

it's like he has a vendetta against geometrical methods

it's too field theoretic for my tastes

as far as GR goes

0celo7

I'm pretty sure he says "we only call it curved spacetime because of Einstein's obsession with geometry: there is nothing curved and there is no geometry"

only gravitons

and sgravitinos

FenderLesPaul

that's like insulting my mother

how dare he

HOW DARE HE

0celo7

@ACuriousMind is on amazon buying it right now

FenderLesPaul

noooooo

0celo7

02:28

@ACuriousMind he uses so many indices it hurts :D

FenderLesPaul

T_T

0celo7

he also says black holes probably don't exist and dying stars just explode

ACuriousMind

@0celo7 I would very much disagree with "there is no gemoetry"

I guess this might also be the reason I dislike his QFT style.

0celo7

@ACuriousMind yeah there's plenty of geometry :)

idk about gemoetry

gem poetry?

FenderLesPaul

geometry = gem poetry

ACuriousMind

02:32

Gem poetry sounds as if it has something to do with causal diamonds

0celo7

@ACuriousMind he seems to be very anti-math even though he is (very likely) very well versed

FenderLesPaul

anti-math is fine really

it isn't good

but it's bearable

0celo7

he is the editor of monographs in mathematical physics

FenderLesPaul

what I hate is how he just butchers the beauty of gR

GR*

e.g. by using coordinates for fucking everything

0celo7

and I know he did lectures on rigorous string topology and geometry

FenderLesPaul

02:33

it's a geometric theory of gravity Weinberg

jeebus christ

0celo7

no it's a theory of a symmetric tensor field on Minkowski space that some ~~German~~ Austrian thought looked like Riemannian geometry...what an idiot

FenderLesPaul

lmfao

cries

0celo7

don't you love how he introduces the Christoffel symbols

no mention of parallel transport

no mention of tangent bundle

> let's see what happens when we accelerate a world line in Minkowski space

FenderLesPaul

yeah

like what the fuck?

what is wrong with that guy?

I met someone here who liked Weinberg's GR book

I stopped talking to him thereafter because that tells me more than I need to know about him as a person :p

0celo7

I don't dislike it

FenderLesPaul

02:38

this person cherished it

when he said he thought it was better than Wald

I rage quit

0celo7

I think it's good for the person not wanting to go to Wald or Straumann level autism

although its age really shows

have you read his newer cosmo book?

FenderLesPaul

yeah

that's a lot better imo

0celo7

I have it, but won't take it to school

I have other things to read first

plus the bajillion books I have to read for school!

FenderLesPaul

Idk if it's something to read for fun though

it was definitely useful for research

but it's quite dry

0celo7

I have to sleep, I'm not like @ACuriousMind

I have to be up at the same time it is in Germany right now

night

ACuriousMind

02:43

g'night

obe

@ACuriousMind The integral of the scalar product you mean? isn't it 0?

@0celo7 For what?

ACuriousMind

@obe Nope. The scalar product on the space is $(\psi,\phi) := \int \phi^*(x)\psi(x)\mathrm{d}x$. Orthonormality means you should get deltas for the product of the basis vectors. Indeed, $\psi = \exp(\mathrm{i}p_1 x)$ and $\phi = \exp(\mathrm{i}p_2 x)$ gives $(\psi,\phi) = \delta(p_1 - p_2)$!

obe

@ACuriousMind Ok, sorry if this is dumb though I don't see how you got the last equation.

ACuriousMind

@obe Plug in $\psi$ and $\phi$ as given and write down where you're stuck

obe

@ACuriousMind Before that, is p the momentum and why is it there?

ACuriousMind

02:50

@obe Yes, $p_i$ are two different momenta (I'm not writing down the annoying $\hbar$, write $p_i/\hbar$ instead to compare to the book). They are there because you asked me to show that the plane waves are an orthonormal basis

obe

@ACuriousMind Right, I got it, it's just the definition of the dirac delta function for exponential.

ACuriousMind

@obe Yep!

obe

Ok, cool now I can move on to the next part.

Thanks a lot. ;)

Kyle Kanos

So it seems I might have to learn Pascal :/

ACuriousMind

@KyleKanos For your potential job?

Kyle Kanos