The h Bar

3:19 AM

@FadedGiant so if we have to make a conclusion, nothing on Earth can generate several gigaelectronvolt gamma rays? Not even the most powerful thermonuclear weapons or most powerful accelerators?

@FadedGiant what are some of theoretical methods to generate gigaelectronvolt gamma rays on Earth if not by thermonuclear weapons or accelerators?

Azmuth

Morning

Later

6:38 AM

As many people are interested in online collaboration, the room Find your physics partner has been created to connect people having common physics interests with each other. Please first read the guideline of the room. If you have any question, request, suggestion, criticism, ... about this room, please send your messages in Later's Room.

John Rennie

@MohamedObeidallah I imagine the LHC can generate photons that energetic, though at vanishingly low intensities.

Azmuth

7:00 AM

Welp, check this out: twitter.com/WineandHair/status/1305520867162677252?s=20

That's how new family members are welcomed....

But, everyone else is looking so intrigued...?

Mithrandir24601

10:24 AM

@JohnRennie The LHC can operate at >10 TeV, so should be possible

Færd

3

ACuriousMind

12:23 PM

@Mithrandir24601 It's probably pretty unlikely to get such highly energetic photons from an LHC collision because there's enough going on there to create other new particles from that photons energy

I don't know how unlikely but I wouldn't be surprised if statistically it hasn't happened even once during the operation of the LHC so far

Mithrandir24601

1:12 PM

@ACuriousMind Oh sure, I don't think you'll get much of a chance to measure them either :P

Azmuth

1:48 PM

@ACuriousMind Hello! You told you know String Theory? Right?

ACuriousMind

@Azmuth sure, why?

Charlie

2:20 PM

When we build the gauge potential $A_\mu$ from the gauge field and generators $A_\mu=A_\mu^aT^a$, what are we actually doing? Is the gauge field a tensor field?

Apparently the gauge potential is "lie algebra valued"

I'm not really sure I know what I'm asking, maybe nvm

ACuriousMind

@Charlie That's what I yesterday talked about with "tensoring" the representations and the field having two indices

Charlie

oh

ACuriousMind

The field $A$ takes values in $\mathfrak{g}\otimes V_\Lambda$, where the latter is the ordinary vector rep of the Lorentz group.

Charlie

do we do this in QED too?

so $\mathfrak g=\mathfrak u(1)$?

ACuriousMind

17 hours ago, by ACuriousMind

well, $\mathrm{U}(1)$ is special

Charlie

2:24 PM

ah

how do you quote messages like that btw?

I feel like i've tried posting the permalink before and it just shows the link

3 mins ago, by Charlie

do we do this in QED too?

oh

...

ACuriousMind

It does it only if the link is the only thing in the message

Charlie

ahh i see

Slereah

Lie algebras are tensors in some sense, yes

The algebra of a Lie group is roughly vectors of the underlying Lie manifold

Charlie

2:44 PM

is gauge theory a lot more differential geometry intensive than GR?

ACuriousMind

depends on how you do it, just like GR :P

Charlie

:c

ACuriousMind

but it's a different part of differential geometry for sure

Charlie

oh ok

I saw $A_\mu$ referred to as a connection so i was just curious

ACuriousMind

@Charlie I just mean that there are very non-rigorous approaches to both that don't care much about the formal differential geometry and very rigorous approaches that care deeply.

Charlie

2:46 PM

ok that's fair

ACuriousMind

if you want to be very abstract you can cast gauge theory so generically that it subsumes GR just as a special kind but the action of GR and the special relationship between its connection and the metric mean that GR in practice typically employs very different methods from generic gauge theories

Charlie

ah yeah in what I briefly read on pse it was mentioned that gr can be a gauge theory

I kind of skimmed the part of schutz that talked about the linearized equations and gauges, it seemed fairly involved

apparently the lecture notes for the qft course this year are handwritten so my day is already ruined

Superfast Jellyfish

@Charlie speaking of handwritten lecture notes, one of our prof casts and teaches off of his handwritten notes :o

His handwriting is hideous

Charlie

It should seriously be a violation of the geneva convention to use handwritten notes imo

I had lectures notes last year written in felt pen

I kid you not

Superfast Jellyfish

On the other hand, my friend had to sit and latex a set of lecture notes for his prof

@Charlie what even xD

Charlie

3:02 PM

ACuriousMind

The use of handwritten notes usually tells you one of three things: 1. The lecturer is overloaded and hasn't got the resources to produce typeset notes. 2. The lecturer doesn't really care about the quality and accessibility of their notes. 3. The lecturer is from an older generation and actively refuses to go with the times.

2 is unfortunately very common

Charlie

afaik it was eventually delegated to one of the teaching assistants and we did get typed notes towards the end of the year

Superfast Jellyfish

I legit thought that that “why” was some $wh^{l}_{g}$

bolbteppa

3:34 PM

It's not an easy question about the sense in which GR is a gauge theory

Azmuth

@Charlie Do you prescribe medicines too?

Lecturer was actually a doctor and he used to prescribe medicines first

then he came to physics and started teaching GR

Slereah

3:58 PM

@bolbteppa You know damn well

It's not rocket science

bolbteppa

That's a 22nd century math my 21's century pea brain isn't ready for

Slereah

nlab is a bit frustrating bc you spend ten years learning about differential geometry and then that site just uses whole new math

Jack Rod

@ACuriousMind are you working for a software firm as part time?

bolbteppa

You can't really know diff geom if you don't see it as the $n=0$ case of $\infty$-diff geom

Slereah

@bolbteppa I can't even tell if you're joking or if that's a real category

bolbteppa

4:04 PM

Neither can I :(

Slereah

Differential geometry is probably one of those $(\infty, 1)$-topos

ACuriousMind

@JackRod I have a full-time job, why?

bolbteppa

32

Q: What is an $(\infty,1)$-topos, and why is this a good setting for doing differential geometry?

In this post on the n-Category Café, Urs Schreiber says that, "The theory of G-principal bundles makes sense in any $(\infty,1)$-topos." I followed the link to the nLab and tried to chase definitions, but I found too quickly my head spinning. What is an $(\infty,1)$-topos, and why is this an app...

"The idea that this is "the appropriate setting for the study of principal bundles, i.e., doing differential geometry" is ridiculous"

bolbteppa

4:17 PM

I think people view this nlab stuff as the analogue of doing calculus etc over finite fields etc... yeah it's a 'generalization' but who cares (obviously some people do)

Slereah

@bolbteppa It is intriguing

Jake Rose

5:02 PM

Is this what they mean by reparametrisation invariant?

bolbteppa

Yeah

Jake Rose

So it’s just a transformation such that the form of the equation is the same

If it wasn’t, it wouldn’t mean the action changes value would it? It just means we have tk work it out with a different equation each time?

It’s just a fancy way of saying, no matter how you’re keeping track of it, can write this equation

bolbteppa

If $\tau' = 2 \tau$ then $\frac{L}{-mc} = d \tau' \sqrt{(\frac{dx}{d \tau'})^2} = d (2 \tau) \sqrt{(\frac{dx}{d 2 \tau})^2} = d \tau 2 \frac{1}{\sqrt{4}} \sqrt{(\frac{dx}{d \tau})^2} = d \tau \sqrt{(\frac{dx}{d \tau})^2}$

The action is the same whether proper time runs twice as fast, 3 times as fast, or whether you choose some other parameter like time some specific coordinate system i.e. it is independent of the parameter you use, yeah the fact that the action is invariant under the transformations means you can always write it that way

Remember this is just an arc length in space-time, basically like an arc length in 3D space, e.g. the length of an arc on a circle is what it is, it doesn't matter if you computed it's value by integrating with respect to say the x axis or the angular coordinate $\theta$ at the end you just expect the same geometric quantity

Superfast Jellyfish

5:21 PM

@JakeRose ooh! Is that the new notability update?

Jake Rose

5:32 PM

@SuperfastJellyfish it is indeed. I’m on the 2017 iPad Pro (so home button and Apple Pencil 1) and I love it. I’ve always stuck with notability hoping for an update and this does it perfectly.

Still some consistent bugs left over, but it mostly works great for physics

I’m debating upgrading for a newer iPad Pro. New pencil is amazing and it just feels so good. And my current iPad has an annoying hotspot issue

Ahhh I see

I have a hard time seeing “the result stays the same” from “the equation stays the same”

But the key thing is that the parameter is a dummy variable so it doesn’t matter

Ergo number has to be the same

Slereah

Well

The result isn't the same

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