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8:59 AM
Looking up how point particles react in a gauge theory and I am seeing the word "electrogeodesic"
although it seems to not be a standard word
 
9:21 AM
Is there a name for the gauge theory with the Lorentz group as a gauge group that isn't soldered to the manifold, btw
If I just have some $SO(3,1)$ gauge theory, what is it called
 
that's what we call a "bad theory" :P
gauge theories of Yang-Mills type with non-compact gauge groups are pretty annoying (and I'm not even sure they're well-defined)
 
Classically I mean
 
No need to worry about QFTs
Just trying to get a better grasp on how important soldering is by making fake GR
 
I didn't say anything about QFT
 
9:26 AM
GR also has unbounded action :p
So obviously not a particularly new obstacle
As you well know globally defined Lagrangians are of the devil anyway
I don't even know why the action being negative is bad classically
 
I mean sure, you can probably have a classical gauge theory with random SO(p,q)s as their gauge group
but why would there be a special name for that if it's useless? :P
 
@ACuriousMind For pedagogical purpose
If there is no such theory I shall call it "fake GR"
 
I don't think I've seen a single reference about GR's nature as a gauge theory I'd describe as "pedagogical" :P
 
@ACuriousMind And look at how confused everyone is
 
all the "pedagogical" stuff waves its hands and babbles about diffeomorphisms!
@Slereah I mean, the difference is larger than just "the theory isn't soldered" - you have to use a different Lagrangian, perhaps YM type, so I'm not sure this is as illuminating as you hope because you can't separate out what's different because of the missing soldering and what's different because it's a completely different theory
 
9:35 AM
@ACuriousMind It is a pedagogical inquiry of many steps
 
like, you can also have Chern-Simons and Yang-Mills theories with the same gauge group but there isn't a lot of direct connections between them
 
9:50 AM
What is even the Lorentz force
Does it have anything to do with the gauge theory or is it just straight up from a Lagrangian
Seems weird that it would depend on a parameter if a gauge thing
 
@Slereah you get it from the worldline Lagrangian of a particle coupled to the field
nothing inherently gauge about it, I think that works the same way if the vector field is massive
 
Yet another way in which gravity differs I guess
I guess it makes sense because geodesics specifically work because the momentum is an associated bundle to the gauge
 
10:26 AM
Though you can couple a scalar field to EM by making it an associated bundle, otoh
And in some limit, that should reduce to the case of a point particle, no?
though the dynamics is still from a Lagrangian here so I guess it doesn't matter
Might be worth looking into what the Lorentz force looks like in KK
 
11:08 AM
Hello :3
I'm about to ask a controversial and strange question but I'm just curious about what the possible answers might be. So you know how 1% of the population are genetic psychopaths, what if we don't allow psychopaths to reproduce so as to get rid of that gene in the pool? P.S. I'm not suggesting it should or can be done!!!
That's called eugenics as far as I know
I should probably read the Wikipedia of it
 
@Slereah you do have that the "lorentz force trajectories" are geodesics of the higher-dimensional KK theory
 
I'm interested in it more of an effectiveness/results side rather than a moral/ethical side. If the psychopathic gene is clearly hurtful and damaging to society, if our goal is to make sure there's less damage in future generations, isn't the logical thing to do to get rid of the gene?
 
@ACuriousMind How does it work with respect to charge, though?
there's no "geodesic charge"
 
@Slereah the charge is the associated bundle/representation the particle transforms in
 
Hm
 
11:21 AM
nlab suggests David Bleecker, Gauge theory and variational principles, Dover publications, 1981. as a resource for this :P
 
That doesn't allow for arbitrary charge value though, does it?
And I assume it's only for complex reps and their conjugate
Like what kind of rep can a point particle have?
 
@JingleBells Saying you're not interested in morality and then immediately asking a moral question isn't exactly an inspiring start for any discussion. Stop hiding moral claims under the guise of "logic"!
@Slereah you have to identify the U(1) charge with the momentum in the compact dimension
 
@ACuriousMind I'm not asking a moral question, which one is it?
 
@ACuriousMind Ah nice
 
@JingleBells Classifying things as "hurtful", saying our goal is "less damage" - these are moral judgements about what is hurtful and what counts as damage
 
11:25 AM
Are negative charges literally going backward in time in that formalism 🤔
 
uhhh...since the compact dimension isn't timelike, why would they?
 
@ACuriousMind Oh right, just one component
I should look into it
I wonder if there is some manner of G-structure for KK
IIRC it is a very structured spacetime
 
@JingleBells also you need to stop blindly believing these eugenicist claims about what's genetic and what isn't. There's no "psychopathic gene", see - as usual - Wiki. "This behavior appears somewhat heritable and here's a bunch of genes linked to it" is a much weaker statement than "1% percent of people carry a gene and it inevitably produces a certain behavior"
@Slereah what do you mean? Usual KK is just a random 4d spacetime with a circle in the 5th, isn't it?
 
Don't they have constraints on their metric.
Maybe I'm confusing with another theory
 
ah, sure - the metric should split cleanly between the 4d and the 1d part
no cross terms
 
11:32 AM
Sounds like a G structure yeah
 
@ACuriousMind I should have specified what I mean by those words, when talking about this eugenics crap, I'm looking at it from a perspective of which decision leads to an increase in a certain metric. In my case, I used "less damage" as a metric but never specified what it is. If I used "dopamine maximization" instead of "less damage" would it still be a moral question to you?
 
Although I'm not sure how the theory change if you change that structure
If you want to maximize dopamine you can just try amphetamines
 
@ACuriousMind Sure, I haven't believed anything, I come here just to learn what you think, senpai
 
But you'll find out that happiness and dopamine aren't as well correlated as you'd hope
 
I don't know what happiness is
 
11:38 AM
@JingleBells then the moral part is in the "isn't the logical thing to do" part of your question - why would it be logical to increase whatever metric you're looking at? (You have to establish at least two moral truths there: That we should follow utilitarianism and that we should use that particular metric as a utility function)
 
What if...we insert Neuralink into psychopaths to simulate empathy? :O
 
@JingleBells "So you know how 1% of the population are genetic psychopaths[...]" sure sounds to me as if you believed this to be true when you wrote it :P
@Slereah I mean, KK isn't really that mysterious - the fifth dimension is literally a U(1) principal bundle over the 4d spacetime
 
If you want to learn more about morality there is no lack of books on the topic
Moral ontology if u want to know if it is an object 🤔
@ACuriousMind yeah I'm guessing the G structure is likely just gonna be basically like a bundle
Except a little different since it's geometric
Natural EM bundle
 
@Slereah sure it is, I buy a fresh pound of morality every week from my local morality dealer
sadly that's illegal so I get cognitive dissonance when I buy some Kantian deontology
 
@ACuriousMind Let's pick technological and scientific advancement as a metric to maximize (hypothetically). If we can prove genetic psychopaths lead to a significant decrease in overall technological and scientific advancement, isn't it logical to try to get rid of the psychopathic gene (if such a gene even exists)?
@ACuriousMind But...but...Jordan Peterson told me so :( (maybe without the genetic part)
 
11:48 AM
@JingleBells Now you've completely eliminated the question: Yes, if our only goal is to increase X, and if action Y increases X, then it is logical to take action Y. That's...just how decision-making works.
 
In metaphilosophy and ethics, meta-ethics is the study of the nature, scope, and meaning of moral judgment. It is one of the three branches of ethics generally studied by philosophers, the others being normative ethics (questions of how one ought to be and act) and applied ethics (practical questions of right behavior in given, usually contentious, situations). While normative ethics addresses such questions as "What should I do?", evaluating specific practices and principles of action, meta-ethics addresses questions such as "What is goodness?" and "How can we tell what is good from what is bad...
Tag yourself
 
@ACuriousMind Nice, I guess going about doing and proving and agreeing on definitions and metrics is where the hard part comes. By that I mean all the questions you'll ask me if I tried to turn it into a practical idea rather than a simplified hypothetical
What about Neuralink to simulate (or stimulate the weak) empathy in antisocial people?
 
@Slereah oh, great, there a meta-meta-ethic debate over whether relativism is cognitivist
 
Seems like a better solution
 
How meta
 
11:53 AM
mark zuckerberg enters the chat
 
@JingleBells no need to wait for the future, just feed them mdma
 
@Slereah Neuralink > mdma?
 
@JingleBells why "Neuralink"?
I do not know of a single demonstrated useful application of that thing
how would it possibly "simulate empathy"?
you're just using "Neuralink" as a stand-in for "magic"
 
As Slereah said, wait for the future
 
@ACuriousMind monkey torture
 
11:54 AM
it's currently being developed still
@ACuriousMind I'm not
 
Also stimulating people's brain directly isn't a new thing
It has been done since at least the 70's
Deep brain stimulation (DBS) is a neurosurgical procedure involving the placement of a medical device called a neurostimulator, which sends electrical impulses, through implanted electrodes, to specific targets in the brain (the brain nucleus) for the treatment of movement disorders, including Parkinson's disease, essential tremor, dystonia, and other conditions such as obsessive-compulsive disorder (OCD) and epilepsy. While its underlying principles and mechanisms are not fully understood, DBS directly changes brain activity in a controlled manner.DBS has been approved by the Food and Drug...
 
@ACuriousMind You're a very interesting person to chat with
(in a good way)
I like it when someone points flaws in my thinking
@ACuriousMind Why are you accusing me of this?
I sometimes feel like you're putting words in my mouth
 
fqq
"If we can prove genetic psychopaths lead to a significant decrease in overall technological and scientific advancement"
first of all you would need to define a precise quantitative measure of technological and scientific advancement (and this is IMO already more or less impossible without a lot of ideology/moral values), then you would have to prove that, which is most likely false given that I suspect scientist are more likely to be psychopaths
and this not even talking about the fact that you are basing all of this on 1% of the population having a particular gene leading to a certain behaviour, and that that's accurately measurable
(than you talk about Neuralink, and I will not comment on how likely it is that at least one of its founders is a psychopath)
 
Jinglebell's plan :
 
12:19 PM
@Slereah XDDD
works better than expected tbh
needs some tweaking though
maybe an upgraded module
it needs a no rudeness module
 
I guess conservation of charge in KK is due to the "charge" direction being a Killing vector field
 
@fqq @ACuriousMind This is what I mean by "all the questions you'll ask me if I tried to make it practical/a reality"
 
@Slereah yes - the 5th momentum is conserved
@JingleBells I'm describing what I perceive you as doing: You imagine this meaninglessly hyped technology to have capabilities without any evidence and without any proposed mechanism of action ("do stuff with the brain" is not a mechanism of action). To me that is wishful thinking, a belief in magic, not science.
 
That is an old tradition
 
@JingleBells but the point is that these are all the hard and important questions
 
12:32 PM
I have recently read those old declassified MKULTRA documents and boy did they have high hopes
a lot of research on hypnotism
Hypnotize those dreaded soviet spies
 
@ACuriousMind I never argued against that
 
the hypothetical of "If X is the sole good and Y leads to X then we should do Y" is so trivially correct there is nothing to debate about; the only reason I can see anyone would want to debate it for specific values of X and Y is by hoping for some sort of semantic poisoning that will get people to stop questioning whether X is really good
@JingleBells but then what is your point?
if you don't want to debate the actual morality here, what is the question?
 
@ACuriousMind As I said at the start, I'm interested in hearing what y'all think, what potential problem it might have, etc. I'm not debating on that issue, I'm learning more
@ACuriousMind I think you're getting unnecessarily deep, all I wanted to do is learn more and hear your opinions, there's no evil semantic poisoning plot here
 
Me I am in favour of good things and staunchly opposed to bad things
 
@ACuriousMind You're accusing me of what you perceive I'm doing, maybe you should ask more questions before rushing to conclusions because in some situations your perception lies, it's not what I'm actually thinking and I feel like my views are being twisted
 
12:41 PM
I think misrepresenting the intent of @JingleBells is morally good
Keep doing it @ACuriousMind
 
I think a pigeon invaded my house
 
I closed that window for good, no pigeons detected
 
I feel like I'm constantly being attacked here
 
I once got a bat in my bedroom and I can assure that wasn't as enjoyable as you might think
 
12:43 PM
Yup, goodbye guys, thanks ACM for the discussions but honestly I always feel bad afterward when I come here
Or maybe I'm overreacting rn
I've learned my lesson to run when I smell toxicity, and right now my gut is telling to close this chatroom and don't join again
So I'll do that
There are other smart people to chat with on the internet
 
@JingleBells You should accept that communication via chats is not a direct as IRL. People might misunderstand you or you might misunderstand them
 
@Feynman_00 I've accepted that but it doesn't change the fact that it feels toxic
 
I have to disagree about that, this chat is not toxic at all. As far as I'm concerned people discussing with you have always been polite and respectful. A message may be blunt but that's not what toxic means.
That said, if this chat makes you feel uncomfortable, you can leave as soon as you want as you shouldn't do something that you don't like, should you?
 
The hell is a gismo
 
Oh bundles again :(
 
12:51 PM
Do they mean gizmo and if so that's a pretty casual term
 
Considering the context it seems so, that is just an intuitive definition of connection
 
@Feynman_00 ...wait, why would anyone think a bat in the bedroom to be enjoyable?
I mean, I can come up with some explanations for that, but...uh...
 
Also why would you swing a bat at a pigeon you monster
 
I could see that question coming and yet I decided to leave the phrasing unchanged :P
@Slereah Because I have a grudge against pigeons
 
Have you never read Moby Dick
This will not end well
 
12:55 PM
Have you ever lived in an attic, hearing pigeons during the mating season every morning? :P
 
city pigeons are tragic really - descendants of once widely cared-for domestic animals that have been kicked out of their ancestors' homes by technological progress and are now universally hated by the descendants of their former masters
3
@Feynman_00 I have lived in an attic, but there were no pigeons
 
Well said, city pigeons
 
I won't comments on general mating season sounds :P
 
I live in a rural area
 
Are they more uncouth and conservative
 
12:58 PM
@Feynman_00 they're mostly former domesticated pigeons, too
truly wild pigeons mostly live in cliff faces and other mountainous features
 
I see
@Slereah lol
In fact these pigeons are quite fearful in constrast to city pigeons that walk among people
Imagine someone joining the chat and seeing the last three starred message talking about pigeons
 
honestly, your first message had perfect comedic timing
 
The rural ones are probably more likely to get snacked on
 
yeah, not a lot of pigeon-eaters in cities
 
Well, cats
 
fqq
1:03 PM
do foxes hunt pigeons?
 
I mean, it's possible but do cats really kill that many pigeons? I've seen cats bring back smaller birds but never a pigeon
 
@ACuriousMind I believe
 
Alright, this reminds me of my cat bringing a pigeon corpse in my terrace
 
@Feynman_00 You're right that most of the conversations I've had here have been respectful and even though sometimes blunt, not toxic. "I think misrepresenting the intent of @JingleBells is morally good, Keep doing it @ACuriousMind" This is the message that really pissed me off for some reason (combined with previous feelings from this room), and it's my problem for acting so impulsively and I should learn to deal better with rude behavior, especially online. This is an insight for improvement.
 
googling "do cats hunt pigeons" is a ride, from "no, most cats won't harm a pigeon" to "help cats are SLAUGHTERING my pigeons" there's a full spectrum
 
1:07 PM
Also, cats do some weird noises to deceive birds
I've heard my cat doing that sometimes
 
Yes, that's it
my lil ball of fur is a ferocious killer :(
 
There is quite a lot of heated discourse on letting cats kill animals
since you basically can't stop them short of confining them inside
 
I mean, I eat meat every week. I would be a hypocrite if I stopped my cat
Sometimes my cat will bring me some dead animal's head as a prize, though :P
 
you're probably not eating the local songbird population, though
 
1:12 PM
You don't know me
 
What if Slereah is a cat
 
The cat is just fulfilling the ancestral pact of protecting us from vermin
 
@Feynman_00 does your cat at least the corpse in plain sight?
one of my friends has a cat who always hides dead mice in shoes
if it's not a shoe you wear often this results in a much worse surprise down the line
 
@ACuriousMind Yep, she (forgive me for using non neutral pronouns for a cat) calls me to show it off :P
But yes, some cat do that as well
The bat I mentioned before had been caught by my cat while sitting on the windows of my bedroom. I saved it from death and my reward was my room being haunted for 15 minutes with that thing moving on a circular path
 
I mean...if the bat had died it would've just haunted the room as a ghost bat
 
1:20 PM
Just in time for Halloween
 
Ordinary bat are already difficult to deal with
If you have a bat inside your room, open the window and then GET OUT
 
Fortunately I seem to live in some kind of cursed land
There are almost no life ever in my flat
Few bugs even
 
Speaking of bundles, I realized vector/tensor bundles are not enough for my purposes. G-principal bundles are needed D:
 
What do you need
Also really there's only one vector principal G-bundle really :p
Well, one per dimension
Although it's pretty rarely used because translation G-bundles tend to be a bit weird
Although I occasionally see people talk about the R-bundle of time
But it's only a principal bundle if the spacetime is static
 
At the moment I don't need anything specific, I just want to know what I'm dealing with when I start studying gauge theories
 
1:32 PM
Principal bundles are gonna be useful for that, certainly
 
And read carefully the message ACM linked some weeks ago
 
Although I guess technically, you can use $\mathbb{R}$ as a gauge group for EM
As long as you're not quantizing anything it mostly works IIRC
But you still need a group action
 
My only solace is that I can now understand Arnold :P
 
I figured this chatroom overall doesn't have the right atmosphere for me so I won't be joining again (I've scheduled my profile for deletion to further prevent that). I'd like to thank all people who've helped me and who've had discussions with me here throughout the years, especially ACM. Slereah, most times you've been funny and interesting so I won't judge you on just a single rude comment. Maybe I'm being too dramatic here but I don't feel liked by the few people with whom I interact here.
This is my last message, wish you all the best y'all.
 
1:40 PM
Goodbye.
 
1:50 PM
@Slereah yes, outside of quantization you can't decide between U(1) and R
 
Presumably it could even be the long line 🤔
Long EM
Perform the long gauge transformation
 
is the long line a Lie group?
 
I'm guessing no
Also there are no nowhere vanishing vector fields on it, so I don't think the connection would even make sense there
1
Q: 1-point compactification of long line (long circle)?

Carla_The long line is locally compact and Hausdorff so it has a 1-point compactification. What can be said about it? Is it anything new? Searching internet for "long circle" returns no results, which seems strange since this seems like a pretty simple space to consider.

the long circle isn't a manifold apparently
Long line is fun and all but really you basically can't do anything with it
It supports basically no interesting structure
 
Long circle?
 
One-point compactification of the long line
Since the group operations have to be smooth on a Lie group I'm guessing that will fail for the long line because it is very badly behaved for continuity
Since any continuous function on the long line has to eventually be a constant, the function $f(x) = x + a$ will eventually be a constant for every value of $a$, so that they have no inverse for $x$ large enough, I think?
If we assume + continuous
 
3:00 PM
I'm afraid I'm not familiar with such topological concepts, sorry
 
3:11 PM
As you should
It has no use in physics at all
 
3:26 PM
I like pure Math too but let's say topology is not my priority right now :P
Actually I should decide what I should do next to improve my Math background: a) Topology b) PDEs c) Rigorous distribution theory d) functional analysis e) learn more about calculus of variations
I think b) and c) are the most important at the moment but I'm scared of terribly technical lemmas in b), those are the worst part for real
 
::has flashbacks to Sobolev spaces::
 
fqq
3:42 PM
yeah I wish I'd known more proper PDE theory but I also don't really regret not going too much into it :P
 
@ACuriousMind Measure theory too now that you mention it but that will happen in a far far future
@fqq Yeah there is this sort of barrier with PDEs
 
in some cases, ignorance really is bliss :P
 
Oh, and then Lie theory and representation theory but I'm quite excited to learn it
 
Lie theory is fun
 
Well, differential geometry is fun so I guess it really is
As long as I don't have to deal with technical lemmas, I really hate those
Like reading a Math book and finding an extremely specific property proved with an extremely specific guess that comes out of the blue
*triggered*
 
3:53 PM
I mean, that's just how proofs are written
 
Lol
 
lThere's an entire book written to show the proof process of the Euler formula step by step
 
Some theorem have nice proofs where you follow a logical path and come to a conclusion, on the other hand there are result that are proved using a specific ansatz (on which a Mathematician sweat blood) and proving it serves the purpose
Of course that's not a criticism to Math, it's just frustrating to study some things that really come out of the blue
 
 
4 hours later…
8:02 PM
how does this follow?
 
8:30 PM
WHich definition of covariant derivative?
 

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