The h Bar

heather

19:07

@BernardoMeurer congrats!!

ACuriousMind

Is it just me or is the flood of no-effort one-liner questions that are either homework or completely unclear higher today than usual?

AccidentalFourierTransform

-2

Q: thermodynamics question on Legendre transforms

thermodynamics question and Legendre transforms

this one was great ^

John Rennie

Am i missing something here:

Sure they can be measured but there is no experiment that guarantees that c contributes very much. Like my poor analogy of the guitar string the energy is contained in the oscillating (frequency) of the photon and has little to do with its propagation. What experiment can prove it comes from c ? What experiment proves one idea over the other? There's already a flaw in one of the ideas considering A massless photon needs an elaborate explanations to explain its momentum. And it really doesn't even do that, it just uses a reverse calculation. — Bill Alsept 26 mins ago

You experimentally measure the photon momentum and get $p=h/\lambda$ and Bill Alsept still doesn't seem to believe it. Or am I misunderstanding what he's saying?

AccidentalFourierTransform

can we close comments as "unclear what you're asking"? :-P

John Rennie

He seems to be saying he doesn't believe photons are massless ...

AccidentalFourierTransform

19:20

tbh I'm not sure I believe photons are massless

ACuriousMind

@AccidentalFourierTransform That'd be "not constructive". I've moved the thread to chat. @JohnRennie Bill has some idiosyncratic views on light/photons (see the website linked in the profile), you're likely wasting your time.

@AccidentalFourierTransform Burn the heretic!

heather

@AccidentalFourierTransform but, but Einstein!

John Rennie

@ACuriousMind ah. My patience with such people is getting short these days.

Thanks for the heads up :-)

AccidentalFourierTransform

@heather Einstein banged his cousin

heather

@AccidentalFourierTransform that was when he was, like, 5. Cut him some slack.

ACuriousMind

19:25

@heather what?

AccidentalFourierTransform

@heather he was thirty-something

ACuriousMind

AFT is referring to Elsa Löwenthal, I believe.

AccidentalFourierTransform

no, Elsa of Arendelle

DanielSank

@heather Oh right. Forgot to update those.

Go ahead and close them out if you have a few minutes, otherwise it will be a couple days before I get to it.

AccidentalFourierTransform

1

Q: Regarding different representations of the Lorentz Group & its defining properties

Take $\Lambda$ to be a Lorentz matrix, it satisfying $\Lambda^T \eta \Lambda=\eta$. By writing $\Lambda=\exp[-\frac{i}{2}\omega_{\mu\nu}\mathcal J^{\mu\nu}]$, we find that the generators satisfy $$ [\mathcal{J}^{\mu\nu},\mathcal{J}^{\rho\sigma}]=i(\eta^{\mu\rho}\mathcal J^{\nu\sigma}+\cdots) \qqu...

quantum-field-theory special-relativity group-theory group-representations lorentz-symmetry

@ACuriousMind remember this ^?

ah, we were so young, so full of life

dbassett

19:32

@DanielSank, sorry to miss you earlier. I'm available to talk for the next few hours if you have time this afternoon.

ACuriousMind

@AccidentalFourierTransform No, my old brain does not remember every answer it wrote :/

'qftishard' was a nice username, though :P

AccidentalFourierTransform

@ACuriousMind I had forgotten about that question, but the other day someone downvoted it (and subsequently undid the downvote)

it was fun to re-read it

anonymous

@BernardoMeurer (::*Pats and Hugs*::) :'D Our hard work paid off !

Bernardo Meurer

19:49

@anonymous Yes it did :)

Thanks for the overwhelming help in solving all those integrals :P

Sir Cumference

20:11

@heather Here's an interesting way to think about it: remember when I talked about the scale factor? The ratio between a galaxy's distance at some time $t$ and its distance now? $a(t) = \frac{\text{distance}(t)}{\text{distance}_{\text{now}}}$

13.8 billion years ago, $a$ was equal to zero.

Every single distance in the universe was zero. However, when the Big Bang happened, $a$ began increasing. Space started to be created between matter.

AccidentalFourierTransform

20:34

Heisenburg, et al.

obe

@BernardoMeurer I bought it.

Bernardo Meurer

@obe Sweet, what did you go for?

obe

are you willing to skype me through the process with my webcam?

150 cad

Bernardo Meurer

Yep, I was about to suggest that

obe

ok im on the bus right now

ill be home in 30 mins

btw the guy there said I'll probably want to get an adapter for it since it's 1 inch smaller than a hdd but its not necessary if i dont move it around a lot.

what do you think?

@BernardoMeurer sorry i read this wrong, i went for a samsung 850 evo 250gb

Bernardo Meurer

20:50

Yes, HDD's usually come in 3.5" formats, and SSDs in 2.5", you want an adaptor, although it will work without. Get one when you can

@obe An absolutely fine SSD, you'll be happy

If you have space you might get away with having both the SSD and the HDD in

obe

will I be able to install windows from a usb?

i dont have a dvd drive

Bernardo Meurer

Yes

There's a process though

You need an 8GB USB Drive

I thin 4GB might work

heather

@ACuriousMind "banged" his cousin...i thought i read somewhere he hit his younger cousin or something when she was born. am i misunderstanding something?

Bernardo Meurer

@heather Some people take "banging" and hitting awfully close

obe

lmao

AccidentalFourierTransform

20:56

@heather nevermind. I sometimes forget youre 14 :-P

heather

does banging have a different meaning than slamming your door or hitting something then?

Bernardo Meurer

@heather Ask your father

I want no part in this

heather

@BernardoMeurer that sounds like a really bad idea.

AccidentalFourierTransform

lol

Bernardo Meurer

banging is slang for "to have sex"

obe

20:57

@heather look at the urban-dictionary definition of banging

heather

i retract all prior comments about einstein at age five.

obe

LOL

heather

for the record, @AccidentalFourierTransform started it.

Bernardo Meurer

Hahahahahaha

Oh heather

AccidentalFourierTransform

oh my, Im laughing out loud rn

heather

20:58

oh gosh, don't star that

AccidentalFourierTransform

i wish I could star it twice

Bernardo Meurer

We have to enjoy while you're still young and innocent :P

heather

lol, fair enough.

well, now I understand why ACM was so surprised.

ACuriousMind

I had my doubts you had heard that about five-year-old Einstein, yes :)

Bernardo Meurer

Man that was so funny

heather

21:01

i shouldn't have assumed that AFT was just using bad grammar.

with him, i should've known it was something a little less appropriate =P

obe

ugh the bus keeps stopping at every bus stop

don't they know i need to install my ssd -_-

ACuriousMind

@obe that's...kinda what it's supposed to do :P

Bernardo Meurer

@obe I have a facetime with my Grandfather somewhere in the next hour, after that I'm available again

obe

oh ok then

Bernardo Meurer

That is assuming he did not fall asleep again

obe

21:04

@ACuriousMind well if there is nobody at the stop and if nobody is getting off then it will skip it.

sometimes when im lucky it skips like 3-5 in a row

it's ok I'm getting off now

Sir Cumference

21:20

@heather Welp, now you see one of the reasons why I hate the name "Big Bang". All the immature kids keep laughing about it. :P

obe

I've never heard anyone laugh about that

Sir Cumference

In seriousness, though, it's just a misleading name

obe

unless they're 7

Sir Cumference

@obe I worked at the museum of natural history. Too many times have I heard people laughing when I said "Big Bang" or "Uranus"

obe

lol

btw it's too cold so im stuck in the bus stop until someone picks me up

rip installing ssd

Bernardo Meurer

21:24

Why are you stuck?

Sir Cumference

@heather If it makes you feel any better, we've all had embarrassing messages starred :)

Jaime Gallego

@obe To kill some time: how do they call very beautiful atoms?

AccidentalFourierTransform

OBE WAS HERE

5

obe

lol wow

@BernardoMeurer cold

Bernardo Meurer

@obe What teh fuck kind of bus you have that can't stand cold?

obe

21:29

didnt dress well and it suddenly dropped like 5 degrees

Bernardo Meurer

Ah

obe

@BernardoMeurer no i mean i cant walk home

im at the bus stop

Bernardo Meurer

@obe How far is it?

obe

3 km :)

Bernardo Meurer

Run!

Jaime Gallego

21:30

He uses metric, praise the lord

obe

ok ill try, brb 30 mins or less

@JaimeGallego lol xD

Bernardo Meurer

30 minutes to run 3KM?

Sir Cumference

I really appreciate papers like this that are merely meant to explain complicated concepts in an easy way

Jaime Gallego

The answer to the question I posed before is "atomic models".

obe

@BernardoMeurer i cant run because its like -15 and i dont have a scarf

Bernardo Meurer

21:35

That's colder than my freezer!

(I've measured)

obe

are you sure you want to come to canada then?

Bernardo Meurer

@obe I don't leave home

And when I do I dress properly

I'm a man of preparedness

obe

i ended up running

im basically home now

@BernardoMeurer let me charge my phone and I'll video call you in 15 mins

if that's ok

@JaimeGallego ha-ha

Jaime Gallego

@obe Yes, I know it's lame. :D

Bernardo Meurer

@obe Sure thing, I'm on Skype

Jaime Gallego

21:52

On a serious note, I'd never thought of having a Skype conversation with SE users. Not today (time is 22:52 here), but might do it someday.

AccidentalFourierTransform

every "ooh wee" that mr.poopy butthole ever said [SPOILERS]

►

Jaime Gallego

That way you shall laugh at my apology for English speaking.

obe

I think my hdd might actually be 2.5in.

no adapter then huh

since when i place the ssd over where the hdd is it's the same size.

@BernardoMeurer is that possible?

Bernardo Meurer

Yep, it is, you there are 2.5" HDDs, they're just usually found in laptops, not desktops

heather

does gravity affect any other massless particles (other than photons)?

Bernardo Meurer

22:01

@heather Yes, your mom

See, I did an inverse "yo momma so fat" joke

AccidentalFourierTransform

@heather presumably, yes. But we don't really know for sure

we don't have a theory of quantum gravity

heather

@BernardoMeurer $\frac{1}{\text{yo momma so fat}}=$...

Bernardo Meurer

Exactly :P

You momma so massless

heather

@AccidentalFourierTransform reworded: have we detected any such affects like we have with photons?

@BernardoMeurer yo momma is a photon

AccidentalFourierTransform

@heather nope

Jaime Gallego

22:03

Yo momma so fat she is used to capture neutrinos!

ACuriousMind

@heather Can you name a massless particle other than a photon that we can observE?

heather

@AccidentalFourierTransform oh.

Bernardo Meurer

@ACuriousMind Your mom

AccidentalFourierTransform

AND THE PHOTON IS NOT MASSLESS

heather

@ACuriousMind the gluon?

AccidentalFourierTransform

22:04

"massless particle" is an oxymoron

obe

@BernardoMeurer uh oh

Bernardo Meurer

@obe What?

obe

I installed it myself somehow while waiting for my phone to charge but when I booted it up it says this

AccidentalFourierTransform

@BernardoMeurer uh oh

heather

@AccidentalFourierTransform wat?

obe

22:05

PXE-e61 media test failure, check cable

and pxe-m0f exiting pxe rom

no boot device found

press any key to reboot

Bernardo Meurer

There's no boot device

obe

what's a boot device?

Bernardo Meurer

PXE is a boot over network protocol

AccidentalFourierTransform

3 hours ago, by AccidentalFourierTransform

tbh I'm not sure I believe photons are massless

obe

ok so what do I do? :O

heather

22:06

@obe something you put on your foot?

=P

obe

xD

Bernardo Meurer

@obe Make a boot USB drive

obe

oh

with windows 10?

Bernardo Meurer

Let me get you a link

Get a USB drive

Yes

heather

@AccidentalFourierTransform and then we got into Einstein... but seriously, why not?

obe

22:06

okay I have one

Bernardo Meurer

microsoft.com/pt-pt/software-download/windows10

obe

16gb

AccidentalFourierTransform

2 mins ago, by AccidentalFourierTransform

"massless particle" is an oxymoron

heather

@AccidentalFourierTransform how so?

Bernardo Meurer

@obe Download the tool

AccidentalFourierTransform

22:07

@heather its very complicated to define what a "particle" is

and the formal definition assumes that $m\neq 0$

heather

@ACuriousMind was I wrong about the gluon? Have we observed gravity affect it?

AccidentalFourierTransform

so the standard definition of particle does not include things with $m=0$

heather

but photons m=0 so are photons not a particle?

AccidentalFourierTransform

one may extend the concept of particle to include things with $m=0$, but it doesn't really work

at least, in my opinion

heather

why can't you say that a photon is not a particle?

AccidentalFourierTransform

22:08

@heather we don't really know if $m_\gamma=0$ or not

all we know is that $m_\gamma< 10^{-18}\ \mathrm{eV}$

heather

um, yeah we do. at least i thought so.

AccidentalFourierTransform

we could have $m_\gamma\neq 0$

heather

@AccidentalFourierTransform that's by experiment, but by theory....

AccidentalFourierTransform

@heather but the "theory" is constructed to match up the experiments

if we find that $m_\gamma\neq 0$ we have to modify the theory

heather

no, no, Einstein's theories.

the idea that objects with mass cannot reach the speed of light because they gain mass and therefore slow down as they approach it in a vicious cycle. the photon can go the speed of light, therefore it doesn't have mass.

AccidentalFourierTransform

22:10

Well, we don't really know if "the photon can go the speed of light"

David Z

@AccidentalFourierTransform what formal definition is that?

AccidentalFourierTransform

all we know is that it goes very fast

Jaime Gallego

@AccidentalFourierTransform But if the photon were massive, would it vary its velocity when moving through gravitational fields or the like? Honest question.

heather

well, i mean, by definition it goes the speed of light.

because its light.

Jaime Gallego

Oh. I just remembered light does bend when near a black hole.

David Z

22:12

@heather BTW: energy. Not mass. (If one wants to be pedantic about it)

AccidentalFourierTransform

@DavidZ an eigenvector of $H^2-\boldsymbol P^2$, where $H$ is the Hamiltonian and $\boldsymbol P$ is the momentum operator

heather

@DavidZ to be further pedantic, E=mc^2, so they're the same (ish)

AccidentalFourierTransform

an eigenvector with isolated eigenvalue

that is, not in a continuum

David Z

@heather oh goodness no

Don't tell me they got to you too :-(

lol

AccidentalFourierTransform

@JaimeGallego massive or massless, the trajectory of photons is affected by gravitational fields. This has been measured

@JaimeGallego ah, yeah

heather

22:13

@DavidZ have i been tricked?

pop sci books, you have failed me! =/

AccidentalFourierTransform

@heather hmm not really. $c$ is the speed of causality, which in standard electrodynamics happens to coincide with the speed of light

David Z

@AccidentalFourierTransform hm, well, I'm not as familiar with that one as I would like, but I would be wary of any definition of particle that prohibits having zero mass

@heather a good lesson to keep in mind ;-)

Bernardo Meurer

Now all I have to pass in Real Analysis II and Complex Analysis

This course has a lot of maths, jesus

David Z

The full equation is $E^2 = m^2c^4 + p^2 c^2$

heather

wait, i think i've seen that

AccidentalFourierTransform

22:15

@DavidZ not really actually. Massless particles are as pathological as it gets

obe

@BernardoMeurer I did.

AccidentalFourierTransform

@DavidZ QFT with massless particles simply makes no sense

Bernardo Meurer

@obe Did what exactly?

heather

if you assume $p$ is 0 and then solve for E you get E=mc^2

AccidentalFourierTransform

we never actually take $m_\gamma=0$ in actual computations beyond tree level

because of IR divergences

heather

22:16

what is $p$ again?

obe

@BernardoMeurer I'm downloading windows 10 from the link in my e-mail they sent me when I bought it.

Jaime Gallego

Momentum

obe

iso

is that the right one?

heather

@JaimeGallego oh, okay. thanks!

AccidentalFourierTransform

@DavidZ also, most formal theorems in QFT (Källén–Lehmann, LSZ, Coleman-Mandula, etc) only work if there are no massless states in the theory

Bernardo Meurer

22:16

@obe Ah, yes, then you don't need that tool. Download the ISO and use this

obe

ok

ACuriousMind

@heather Gluons are color charged and thus confined; no one has ever detected a free gluon.

Bernardo Meurer

I'm a free Gluon

AccidentalFourierTransform

I'm a free Gluten

heather

@ACuriousMind oh.

David Z

22:19

@AccidentalFourierTransform Oh, you mean as a renormalization parameter? Well, I see your point, but I still don't really agree with it. I think the evidence suggests that a proper theory should be able to handle massless particles, and a theory which is incapable of doing so is only useful as an approximate description of reality, unless we find experimental evidence indicating otherwise.

Jaime Gallego

@AccidentalFourierTransform But still, if the photon were massive and decreased its potential energy, wouldn't that increase its speed, so $c$ wouldn't be constant anymore?

As work is being done on it

ACuriousMind

@AccidentalFourierTransform Not exactly true, E.g. Coleman-Mandula fails only when there is no massive particle, and I don't really know why LSZ would need mass off the top of my head, either

David Z

In other words, if our theories are not compatible with massless particles, I place the blame on the theories rather than on the definition of particle. While recognizing that we don't really know which is the proper resolution.

@heather yeah, but remember $p \neq 0$ for photons

AccidentalFourierTransform

@DavidZ call it a renormalization parameter, call it a real mass. But it is there, in the theory. You cannot take $m\equiv 0$ without running into all sorts of wild divergences

and IR divergences cannot be reabsorbed into counter-terms

they are "real life divergences" so to speak

David Z

Sure, but still, I consider that a failure of the theory rather than a failure of reality

AccidentalFourierTransform

22:22

they are reflecting a real life phenomenon: massless particles are an ill-defined concept

@DavidZ what is a failure of reality anyway?

Im only speaking about mathematics

David Z

@AccidentalFourierTransform See, that's the crux of it. I don't believe that's a real life phenomenon

@AccidentalFourierTransform Well I'm talking about physics ;-)

ACuriousMind

@AccidentalFourierTransform What are you talking about? If you're going so formal, then a massless particle is just a state transforming in the massless representation of the Poincaré group. Weinberg's theorem proves that all massless vector bosons are gauge bosons and therefore are protected from acquiring any mass, so renormalization is irrelevant unless the gauge symmetry is anomalous

AccidentalFourierTransform

@ACuriousMind hmm I have to disagree there. CM explicitly assumes that there are no massless states (and a finite number of massive states below any finite energy). And LSZ fails in theories with massless particles

both from the theoretical POV and the practical POV

obe

@BernardoMeurer 64 bit right?

David Z

To put this in other words: if I understand correctly, you observe that QFT can't describe massless particles and conclude that massless particles can't exist, whereas I observe that QFT can't describe massless particles and conclude that QFT is likely not to be a proper description of reality

In any case fundamental QFT is not my area of expertise so I can't challenge you on the mathematical arguments

AccidentalFourierTransform

22:24

the formal treatment of the LSZ formalism (Haag-Ruelle and frieds) explicitly assumes that $m\neq 0$

Bernardo Meurer

@obe Yep

AccidentalFourierTransform

and it hasn't been extended to handle massless states

not because they don't know how to extend it

it simply cannot be done because a theory with massless states is deeply ill-defined

ACuriousMind

@AccidentalFourierTransform Explain the success of QED and gauge theories, then. I'll concede they are probably rigorously undefined, but that applies to all but the most trivial or low-dimensional QFTs, so it's a red herring.

AccidentalFourierTransform

@ACuriousMind the fact that almost every computation beyond tree level is IR divergent means that you cannot set $m\equiv 0$

you just cant

you have to keep the mass finite and only take $m\to 0$ at the very end

after all the crazy IR cancellations

ACuriousMind

Then don't compute in tree levels! That's a failure of the perturbative formalism, not a fundamental failure of the QFT

AccidentalFourierTransform

22:28

@DavidZ more or less. When I said that there are no massless particles I meant that they are not well defined mathematically. I would never venture to claim anything about "reality"

ACuriousMind

The "keeping mass finite and then sending it to 0" is just another renormalization scheme, I don't see why that should be more disturbing than all the other divergences we have to control in perturbative renormalization

AccidentalFourierTransform

@DavidZ I don't know what a photon really is. All I know is its mathematical description

heather

the sad moment where i realize i'm wasting time on productivity stack exchange.

AccidentalFourierTransform

@DavidZ and my POV is that it is a mathematically ill-defined concept.

I don't know if they really exist

David Z

@AccidentalFourierTransform gotcha. No arguments there.

AccidentalFourierTransform

22:30

@ACuriousMind you can work with massive QED, and take $m\to 0$ at the very end

that is what it is actually done in real computations anyway

try to calculate the electron self-energy in massless QED

it diverges. The theory is ill-defined

@ACuriousMind no no no no, not at all. Keeping $m\neq 0$ is fundamentally different from keeping $\Lambda<\infty$. IR divergences and UV divergences have nothing to do

using a massive photon is not a renormalisation scheme

not at all

ACuriousMind

@AccidentalFourierTransform And how is that formally consistent regarding the construction of the space of states? You need something equivalent to Gupta-Bleuler quantization (BRST quantization) to get the correct states for the massless theory, and taking the limit of the massive theory does not induces the necessary quotients. Making the massless particle massive completely fails for non-Abelian theories because the decoupling of the longitudinal mode in the amplitudes is more subtle.

AccidentalFourierTransform

@ACuriousMind you can have massive QED with longitudinal states, and these have negative norm. And you have to construct the space of states. It is more complicated than in the massless case but it is in principle the same procedure. You can use the Stückelberg method to restore the gauge invariance of the massive theory, and everything else works similarly to the massless case

As of today, the Stückelberg method is the most general way to give gauge bosons mass

ACuriousMind

Why would the massive longitudinal states have negative norm? A massive vector field has positive norm longitudinal excitations

AccidentalFourierTransform

By longitudinal I mean the scalar state

not the $\sigma=0$ polarisation

ACuriousMind

22:45

Ah, yes, sure, you have to get rid of the scalar part for all vector fields, that's not the problem.

AccidentalFourierTransform

I call it longitudinal because its polarisation vector is $\varepsilon^\mu\propto k^\mu$

@ACuriousMind well, you get rid of it by the same method as in the massless case

ACuriousMind

But what happens to the $\sigma=0$ massive polarization?

AccidentalFourierTransform

as long as $m\neq 0$, its there

together with the other two polarisations

but it decouples too in the massless limit

because $\varepsilon^\mu_0\to k^\mu$ in the massless limit

ACuriousMind

I already said it decouples :P

If you're going to make formal complaints about divergences, I'm complaining about the state space of your $m\to 0$ theory begin formally wrong because it still includes those states, even if they decouple

AccidentalFourierTransform

by longitudinal you mean the $\sigma=0$ state, right?

because to me the longitudinal state is the scalar :-P

ACuriousMind

22:48

Yes, I call the $\sigma = 0$ state "longitudinal"

AccidentalFourierTransform

@ACuriousMind well so what? if they decouple you cannot measure them

if you cannot interact with something

not even in principle

ACuriousMind

@AccidentalFourierTransform You can't measure your diverging self-energy either, so what's the problem?

AccidentalFourierTransform

@ACuriousMind its different+

because they are decoupled even if $m\neq 0$

as long as the current $j^\mu$ in $\mathcal L_\mathrm{int}\sim j^\mu A_\mu$ is conserved, the scalars are free

also, there are other IR divergent objects besides the electron self energy

heck, not even the concept of "electron" is well defined if $m_\gamma\equiv 0$

if you have true massless states in your theory, you cannot have discrete eigenvalues of $P^2=H^2-\vec P^2$. So there are no particles at all

I don't like massless particles

ACuriousMind

@AccidentalFourierTransform Do you have a reference for that?

AccidentalFourierTransform

@ACuriousMind no, but I guess it's true

Transcript for