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7:07 PM
@BernardoMeurer congrats!!
 
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?
 
this one was great ^
 
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?
 
can we close comments as "unclear what you're asking"? :-P
 
He seems to be saying he doesn't believe photons are massless ...
 
7:20 PM
tbh I'm not sure I believe photons are massless
 
@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!
 
@AccidentalFourierTransform but, but Einstein!
 
@ACuriousMind ah. My patience with such people is getting short these days.
Thanks for the heads up :-)
 
@heather Einstein banged his cousin
 
@AccidentalFourierTransform that was when he was, like, 5. Cut him some slack.
 
7:25 PM
@heather what?
 
@heather he was thirty-something
 
AFT is referring to Elsa Löwenthal, I believe.
 
@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.
 
1
Q: Regarding different representations of the Lorentz Group & its defining properties

AccidentalFourierTransformTake $\Lambda$ 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...

@ACuriousMind remember this ^?
ah, we were so young, so full of life
 
7:32 PM
@DanielSank, sorry to miss you earlier. I'm available to talk for the next few hours if you have time this afternoon.
 
@AccidentalFourierTransform No, my old brain does not remember every answer it wrote :/
'qftishard' was a nice username, though :P
 
@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
 
@BernardoMeurer (::*Pats and Hugs*::) :'D Our hard work paid off !
 
7:49 PM
@anonymous Yes it did :)
Thanks for the overwhelming help in solving all those integrals :P
 
8:11 PM
@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.
 
8:34 PM
Heisenburg, et al.
 
obe
@BernardoMeurer I bought it.
 
@obe Sweet, what did you go for?
 
obe
are you willing to skype me through the process with my webcam?
150 cad
 
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
 
8:50 PM
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
 
Yes
There's a process though
You need an 8GB USB Drive
I thin 4GB might work
 
@ACuriousMind "banged" his cousin...i thought i read somewhere he hit his younger cousin or something when she was born. am i misunderstanding something?
 
@heather Some people take "banging" and hitting awfully close
 
obe
lmao
 
8:56 PM
@heather nevermind. I sometimes forget youre 14 :-P
 
does banging have a different meaning than slamming your door or hitting something then?
 
@heather Ask your father
I want no part in this
 
@BernardoMeurer that sounds like a really bad idea.
 
banging is slang for "to have sex"
 
obe
8:57 PM
@heather look at the urban-dictionary definition of banging
 
i retract all prior comments about einstein at age five.
 
obe
LOL
 
for the record, @AccidentalFourierTransform started it.
 
Hahahahahaha
Oh heather
 
oh my, Im laughing out loud rn
 
8:58 PM
oh gosh, don't star that
 
i wish I could star it twice
 
We have to enjoy while you're still young and innocent :P
 
lol, fair enough.
well, now I understand why ACM was so surprised.
 
I had my doubts you had heard that about five-year-old Einstein, yes :)
 
Man that was so funny
 
9:01 PM
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 -_-
 
@obe that's...kinda what it's supposed to do :P
 
@obe I have a facetime with my Grandfather somewhere in the next hour, after that I'm available again
 
obe
oh ok then
 
That is assuming he did not fall asleep again
 
obe
9:04 PM
@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
 
9:20 PM
@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
 
In seriousness, though, it's just a misleading name
 
obe
unless they're 7
 
@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
 
9:24 PM
Why are you stuck?
 
@heather If it makes you feel any better, we've all had embarrassing messages starred :)
 
@obe To kill some time: how do they call very beautiful atoms?
 
obe
lol wow
@BernardoMeurer cold
 
@obe What teh fuck kind of bus you have that can't stand cold?
 
obe
9:29 PM
didnt dress well and it suddenly dropped like 5 degrees
 
obe
@BernardoMeurer no i mean i cant walk home
im at the bus stop
 
@obe How far is it?
 
obe
3 km :)
 
9:30 PM
He uses metric, praise the lord
 
obe
ok ill try, brb 30 mins or less
@JaimeGallego lol xD
 
30 minutes to run 3KM?
 
I really appreciate papers like this that are merely meant to explain complicated concepts in an easy way
 
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
 
9:35 PM
That's colder than my freezer!
(I've measured)
 
obe
are you sure you want to come to canada then?
 
@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
 
@obe Yes, I know it's lame. :D
 
@obe Sure thing, I'm on Skype
 
9:52 PM
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.
 
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?
 
Yep, it is, you there are 2.5" HDDs, they're just usually found in laptops, not desktops
 
does gravity affect any other massless particles (other than photons)?
 
10:01 PM
@heather Yes, your mom
See, I did an inverse "yo momma so fat" joke
 
@heather presumably, yes. But we don't really know for sure
we don't have a theory of quantum gravity
 
@BernardoMeurer $\frac{1}{\text{yo momma so fat}}=$...
 
Exactly :P
You momma so massless
 
@AccidentalFourierTransform reworded: have we detected any such affects like we have with photons?
@BernardoMeurer yo momma is a photon
 
@heather nope
 
10:03 PM
Yo momma so fat she is used to capture neutrinos!
 
@heather Can you name a massless particle other than a photon that we can observE?
 
@AccidentalFourierTransform oh.
 
@ACuriousMind Your mom
 
AND THE PHOTON IS NOT MASSLESS
 
@ACuriousMind the gluon?
 
10:04 PM
"massless particle" is an oxymoron
 
obe
@BernardoMeurer uh oh
 
@obe What?
 
obe
I installed it myself somehow while waiting for my phone to charge but when I booted it up it says this
 
@BernardoMeurer uh oh
 
@AccidentalFourierTransform wat?
 
obe
10:05 PM
PXE-e61 media test failure, check cable
and pxe-m0f exiting pxe rom
no boot device found
press any key to reboot
 
There's no boot device
 
obe
what's a boot device?
 
PXE is a boot over network protocol
 
3 hours ago, by AccidentalFourierTransform
tbh I'm not sure I believe photons are massless
 
obe
ok so what do I do? :O
 
10:06 PM
@obe something you put on your foot?
=P
 
obe
xD
 
@obe Make a boot USB drive
 
obe
oh
with windows 10?
 
Let me get you a link
Get a USB drive
Yes
 
@AccidentalFourierTransform and then we got into Einstein... but seriously, why not?
 
obe
10:06 PM
okay I have one
 
obe
16gb
 
2 mins ago, by AccidentalFourierTransform
"massless particle" is an oxymoron
 
@AccidentalFourierTransform how so?
 
@obe Download the tool
 
10:07 PM
@heather its very complicated to define what a "particle" is
and the formal definition assumes that $m\neq 0$
 
@ACuriousMind was I wrong about the gluon? Have we observed gravity affect it?
 
so the standard definition of particle does not include things with $m=0$
 
but photons m=0 so are photons not a particle?
 
one may extend the concept of particle to include things with $m=0$, but it doesn't really work
at least, in my opinion
 
why can't you say that a photon is not a particle?
 
10:08 PM
@heather we don't really know if $m_\gamma=0$ or not
all we know is that $m_\gamma< 10^{-18}\ \mathrm{eV}$
 
um, yeah we do. at least i thought so.
 
we could have $m_\gamma\neq 0$
 
@AccidentalFourierTransform that's by experiment, but by theory....
 
@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
 
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.
 
10:10 PM
Well, we don't really know if "the photon can go the speed of light"
 
@AccidentalFourierTransform what formal definition is that?
 
all we know is that it goes very fast
 
@AccidentalFourierTransform But if the photon were massive, would it vary its velocity when moving through gravitational fields or the like? Honest question.
 
well, i mean, by definition it goes the speed of light.
because its light.
 
Oh. I just remembered light does bend when near a black hole.
 
10:12 PM
@heather BTW: energy. Not mass. (If one wants to be pedantic about it)
 
@DavidZ an eigenvector of $H^2-\boldsymbol P^2$, where $H$ is the Hamiltonian and $\boldsymbol P$ is the momentum operator
 
@DavidZ to be further pedantic, E=mc^2, so they're the same (ish)
 
an eigenvector with isolated eigenvalue
that is, not in a continuum
 
@heather oh goodness no
Don't tell me they got to you too :-(
lol
 
@JaimeGallego massive or massless, the trajectory of photons is affected by gravitational fields. This has been measured
@JaimeGallego ah, yeah
 
10:13 PM
@DavidZ have i been tricked?
pop sci books, you have failed me! =/
 
@heather hmm not really. $c$ is the speed of causality, which in standard electrodynamics happens to coincide with the speed of light
 
@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 ;-)
 
Now all I have to pass in Real Analysis II and Complex Analysis
This course has a lot of maths, jesus
 
The full equation is $E^2 = m^2c^4 + p^2 c^2$
 
wait, i think i've seen that
 
10:15 PM
@DavidZ not really actually. Massless particles are as pathological as it gets
 
obe
@BernardoMeurer I did.
 
@DavidZ QFT with massless particles simply makes no sense
 
@obe Did what exactly?
 
if you assume $p$ is 0 and then solve for E you get E=mc^2
 
we never actually take $m_\gamma=0$ in actual computations beyond tree level
because of IR divergences
 
10:16 PM
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.
 
Momentum
 
obe
iso
is that the right one?
 
@JaimeGallego oh, okay. thanks!
 
@DavidZ also, most formal theorems in QFT (Källén–Lehmann, LSZ, Coleman-Mandula, etc) only work if there are no massless states in the theory
 
10:16 PM
@obe Ah, yes, then you don't need that tool. Download the ISO and use this
 
obe
ok
 
@heather Gluons are color charged and thus confined; no one has ever detected a free gluon.
 
I'm a free Gluon
 
I'm a free Gluten
 
@ACuriousMind oh.
 
10:19 PM
@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.
 
@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
 
@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
 
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
 
@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
 
Sure, but still, I consider that a failure of the theory rather than a failure of reality
 
10:22 PM
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
 
@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 ;-)
 
@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
 
@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?
 
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
 
10:24 PM
the formal treatment of the LSZ formalism (Haag-Ruelle and frieds) explicitly assumes that $m\neq 0$
 
@obe Yep
 
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
 
@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.
 
@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
 
Then don't compute in tree levels! That's a failure of the perturbative formalism, not a fundamental failure of the QFT
 
10:28 PM
@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"
 
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
 
@DavidZ I don't know what a photon really is. All I know is its mathematical description
 
the sad moment where i realize i'm wasting time on productivity stack exchange.
 
@DavidZ and my POV is that it is a mathematically ill-defined concept.
I don't know if they really exist
 
@AccidentalFourierTransform gotcha. No arguments there.
 
10:30 PM
@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
 
@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.
 
@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
 
Why would the massive longitudinal states have negative norm? A massive vector field has positive norm longitudinal excitations
 
By longitudinal I mean the scalar state
not the $\sigma=0$ polarisation
 
10:45 PM
Ah, yes, sure, you have to get rid of the scalar part for all vector fields, that's not the problem.
 
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
 
But what happens to the $\sigma=0$ massive polarization?
 
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
 
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
 
by longitudinal you mean the $\sigma=0$ state, right?
because to me the longitudinal state is the scalar :-P
 
10:48 PM
Yes, I call the $\sigma = 0$ state "longitudinal"
 
@ACuriousMind well so what? if they decouple you cannot measure them
if you cannot interact with something
not even in principle
 
@AccidentalFourierTransform You can't measure your diverging self-energy either, so what's the problem?
 
@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
 
@AccidentalFourierTransform Do you have a reference for that?
 
@ACuriousMind no, but I guess it's true
 

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