is there a term for "triangulizing" a commutative diagram into a triangle?

Like going from CD 2 to CD 3?

@PM2Ring Yes. I only meant that the "beginning of the universe" is a consistent idea in GR, as in, it doesn't raise questions like "How can something be born from nothing?". Becuz it's the wrong question. This model is consistent but need not be factually correct. I think it's too naive in its view of time.

@SillyGoose not really, triangulating is something different

ah okay

also, your definitions are weird, e.g. your definition of the collection of objects in the undercategory doesn't really make sense

oh what would the definitions actulaly be like

if I didn't know what the undercategory was I don't think would've gotten what the objects are supposed to be

usually one defines the objects in the slice categories to be pairs $(f,x)$ such that $f: c\to x$ is a morphism in $C$ and $x$ is an object in $C$

oh not as the morphism itself

(morphism from the initial category C)

I mean, "morally" the object is the morphism but it's easier if you "attach" its target directly as the second element of the pair

i see i was thinking of abusing notation and writing the morphism as its target since the domain is always c

or labeling but i think that would actually be bad in drawing diagrams

the pair definition also avoid awkward turns of phrase like where you talk about the identity "of $f$" but then have to label it $1_x$

I see, okay maybe I will adopt this notation--it probably would get much hairier to try and use the notation i was using for this exercise in more complicated situations :P

also there's a bug in your definition of morphism where one of the two $h$s is supposed to be a $g$

oh whoopsies thank you

I also realized i didn't prove that these things obey the associativity law hehehe but i imagine that is not hard to prove here

the pair definition also allows you to state more easily how the morphisms work: For two objects $(f,x),(g,y)$ in the undercategory, a morphism $(f,x)\to (g,y)$ is given by a morphism $h\in\mathrm{Hom}_C(x,y)$ such that $hf = g$

@ACuriousMind what does the last $x$ refer to here? or is it supposed to be x is an object in $C$

oops, typo

ah okay cool

bleh off to write an essay i hope for more time to do category theory today :D

Can anyone say after whom the Carrolian limit is named in which we take the ultarelativistic $c\to0$ limit?

I think it is named after the author of the Narnia series Lewis Carroll @ManasDogra

The concept seems to have been introduced by Levy-Leblond who said:

In 1965, I published a paper, exhibiting a hitherto unknown limit of the Lorentz group, which I christened “Carroll group” because of its seemingly paradoxical physical contents. Since I saw it as more curious than relevant, I published it in French in a journal somewhat afar from the mainstream of theoretical physics at that time. It was most gratifying to witness the quite unexpected favour this paper started...

scipost.org/submissions/scipost_202212_00064v1

huh I didn't know lewis carroll also did some mathematics it seems

but anyway his works are characterized by "facility with word play, logic, and fantasy"

Does anyone know of work related to or similar to the work done by A. Doëring in their series of papers about topos in quantum foundations (inspirehep.net/authors/1218106)?

It seems like quite a grand idea and I was wondering if any fruits have been born from this work? Since it has been 10+ years since the original papers

@PM2Ring ill take a look thank you :)

Carroll group is named after Lewis Carroll because it is the Galilean group through the looking glass

Many kinematic groups

@Slereah Where is this from?

Don't remember

I have many papers

Why does (Sean) Carroll say that the $\omega\to\infty$ limit of Brans-Dicke theory gives back classical GR? I mean, it's not self-evident from the action $S_{BD}=\int d^4x \sqrt{-g}\left[\frac{\phi}{16\pi}R-\frac{\omega}{16\pi}g^{\mu\nu}\frac{\partial_\mu\phi\partial_\nu\phi}{\phi}\right]$ right?

Either he neglects the infinite term and posit $\phi\sim G_\text{Newton}$ or he omits the derivation that needs to pass through the EoM and possibly get the EFE in that limit (?)

@Mr.Feynman yes, you need to use the e.o.m., cf. Weinberg

@SillyGoose Depends on what you mean by "related" - there are two parts here, the categorical part and the idea of considering "quantum logic" as the foundational prinicple in the first place. For the categorical ideas, cf. Bohr topos on nLab;

the "non-topos" part here of considering "quantum logic" as the non-distributive lattice of projectors is an old idea going back to von Neumann and is still an active niche of research (e.g. asking what lattice structures force a lattice to be equivalent to the lattice of projectors on a complex Hilbert space, explaining the "emergence" of complex Hilbert spaces from the logical structure alone)

I thought Streater called quantum logic a lost cause

@Slereah the main significant result that "revived" it to some extent was Solèr's theorem in 1995, while Streater seems to have been only aware of an older theorem by Piron

also, I think Streater is more saying that it's a "lost cause" to try to use the "quantum logic" approach to argue that one might not necessarily need complex Hilbert space - he's talking about people attempting to use p-adic Hilbert spaces or whatever, while I had the opposite direction in mind: Trying to pin down the exact properties of quantum logic that make complex Hilbert spaces inevitable

hello, i have another question about words ;P i am wondering what the phrase "locally inertial coordinates" means.

wait i think this is a reiteration of "what are coordinates"

i retreat

@ACuriousMind oof

@Relativisticcucumber You can choose your coordinates in such a way that the metric tensor at a point is the Minkwoski metric $\eta$. Such coordinates are called "locally inertial"

It is important to stress that you're operating in the tangent space of a single point, not in a neighbourhood thereof

@Relativisticcucumber geometers call them normal coordinates if you're trying to find them in the math literature

@Mr.Feynman "oof"?

ok i think what i am confused about is why this means the coordinates are inertial -- because i thought that for any physical situation you can describe it with any coordinates so any spacetime, flat or not, can be described by any type of coordinates and the only thing we can call flat/inertial is the manifold and the metric?

@Relativisticcucumber they're called locally inertial because at a point (=locally) they look like Minkowski space (="inertial" space)

but what does this mean "the coordinates look like Minkowski space"? because isn't Minkowski space defined by the manifold and has nothing to do with the coordinates ? i think this is wrong but im not sure why.

@ACuriousMind That "oof" represents how I feel about it because I had checked Weinberg and apparently he and Carroll use slightly different conventions as I tried to work the EoM from Carroll and the terms are somehow different (?). I guess it's no topic to delve into right now since it was just a brief 2-page discussion on Carroll

@Relativisticcucumber we mean that at that point, in those coordinates, the metric is numerically equal to the Minkowski metric diag(-1,1,1,1)

(and also the terms making it unequal to the Minkowski metric away from that point are at least of order $\mathcal{O}(x^2)$ in the coordinates)

@Relativisticcucumber The most remarkable thing is that you can work as if you were in Minkowski space, i.e. the laws of Physics take that very form they take in Minkowski space and then it's only about changing coordinates

@ACuriousMind ok ok i see

@SillyGoose man i'm with ya ab precise wording

strangely i only recently started to encounter this issue of tripping up on words so much

i dont know how to avoid it D,:

what is the language of a cucumber

I'm at a worse stage. I'm starting to forget how to speak Italian and I speak an idiosyncratic mixture of Italian and English

I can't trip up on words I don't remember :P

@Mr.Feynman italinglish will be the official language of the cucumber

funnily enough i had a nightmare about you recently @Mr.Feynman

lol

In the dream i had a really important physics task to do. im not sure what it was or why but i remember it was urgent. so i was confused about part of it and i asked something on here.

then

you said

"i know the answer but im busy ill reply when i can"

and i kept waiting. then i kept pinging you, but i kept getting "still busy but ill let you know when i can"

and that happened until i woke up and i never got an answer

and that's a nightmare?

i think the dream was like i would die if i didnt finish the task -- it was something very urgent like that

I'd take that any day over the "unidentified monster is chasing me through various locations until I wake up after jumping out a window" nightmares I usually have

well my biggest fear is like anticipatory waiting

so its a nightmare for me XD

in any case "I need the answer to this question or I'll die - I know, I'll ask in the h bar" is a sound strategy ;)

desperate times

@Relativisticcucumber Of all things why a nightmare...? :P

In contrast to real life I'm pretty playful here

@Relativisticcucumber That sounds like a couple of weeks ago about the Dirac equation though

It's very peculiar how the internet lets people you don't really know from all around the world enter your dreams. I once had a dream about the chat too

In that dream there was someone purchasing books using my Amazon account and I couldn't find out their identity. Then I noticed the books were in German and about philosophy, so I opened the chat and tagged @ACuriousMind to know if he was using my account to buy books, but he denied

lol

And refused to prove me wrong or collaborate. My concerns didn't weaken but then I woke up

LOL

If you really want to work in the neighbourhood, normal coordinates are basically such that the metric is $g = \eta + \mathcal{O}(x^2)$

plot: @ACuriousMind figures out i have a fear of anticipation. acm steals @Mr.Feynman's identity and amazon info to incite chaos. then acm hits me with a question i cant possibly answer threatening to murder every pigeon on earth if i dont answer. everytime @Mr.Feynman opens hbar acm does something else to escalate the identity crisis so that all @Mr.Feynman can do is say "ill answer soon" and this is how ACM annihilates every pigeon on earth while simultaneously torturing hbar engagers

@Slereah i see

that's what GR people mean when they say "locally minkowski"

If you look at the various quantities you can get, they will all be some variation of $\mathcal{O}(x^n)$ in normal coordinates

So that very close to your point, there will be no measurable difference

@Relativisticcucumber Heh...and halfway through the plot we flash-back to a pigeon killing my parents, revealing my tragic backstory and motivations

but then there's more

ah, you have to leave something for the sequel

we find out @SillyGoose trained the pigeon to kill ur parents knowing this is how you'd react

because they want geese supremacy

If the definition of DOS the following is said: " the number of states of that system per unit energy, expressed as a function of energy.". I have a question about this. Does the density of states takes into consideration states of same energy? Or only the fact that states with this energy value exist. And it only counts the different energy values that can be occupied and belong to an interval but not the multiplicity

@Relativisticcucumber Now, this is starting to sound like my average dreams

@ACuriousMind that sounds like an ornithophobic Batman origin story

Hi

Hi

I also hav these monster chasing me dreams. I can jump really far into the mountains in those dreams, but the monster is even faster

So they r very depressing and tense. But I always hav this jumping power

After thinking so much about ontology philosophy, i feel back on square one

I dont think philosophy of ontology helps with physics at all

It's like I learned nothing

Before i started doing philosophy, I had this vague idea about a universe that is conscious everywhere

But even now, I feel that idea remains just as vague. I've made no progress in understanding it

I also hav lots of helicopter crash dreams

They hav very pretty scenery. But they crash

Is there any physics model which employs panpsychism?

These days I feel like I am drifting closer and closer to philosophy :P

Protect the pigeons !!! @Relativisticcucumber

Is it not a problem that the accepted answers to some questions on stack become irrelevant or incorrect as years pass?

Not because the answerer was wrong at the time but because the years have brought in new information

accepted answers in general are a problem :P

fyi: we currently display the top-voted answer above any accepted answers, but it was a narrow decision (see physics.meta.stackexchange.com/q/13811/50583(

When we are describing a single particle, at what point does this become in the realm of RQM compared to QFT?

I think you may have answered this before. I remember you stating that asymptotic states of QFT are the states of RQM

Is there a correlation between the density of states and the multiplicity of a macro state, for a given arbitrary system?

Is there a reason why we consider the time independent schroedinger eq. when we deal with the problem of a particle in a box?

@RyderRude I sometimes have monsters chasing me but the causality in my dreams is so messed up I never end up killed or I'm watching 3rd person myself or someone else which would be me in the dream. Recently I've survived by killing them

Someone proposed the theory that if you make sure to go over your day, especially over emotionally intense moments if there were any, before going to bed... you may dream less

But my worst nightmares come when I stay up late obsessing over something I don't understand and I dream Math breaking all night

What I noticed was that I apparently improved my dream-memory abilities and I could remember 1 or even 2 dreams per night

With lucid dreaming, I found that what works best for me is waking up early and going back to bed. It seems they come more easily if I'm already rested

Maybe it has something to do with the conscious "day time" mind trying to intrude upon the dream

But I lost interest in lucid dreams after a while, lol it's kind of funny, because I'm sure in many cases I can take control of a dream, in other words it feels lucid "enough", but I recall myself in the dream, just thinking that I can't be bothered... let the dream compute itself, why should I control it.. lol

@Amit I tried everything. I even filled my house with post-its saying "Am I dreaming?" to start doing reality checks

Even then, I would rarely do that in my dreams and if I did I wasn't really getting conscious. Instead, I was dreaming of getting conscious for how much I had obsessed about it :P

@Mr.Feynman The problem may have been that you made it too much of a conscious activity... you need something that would make its way to the unconscious... in other words, more of a conditioning / brainwashing almost than a conscious attempt...

@Amit I'd like to give it a try at least. I want to see if I can do computations in my dreams

@Amit Yes, I realized that some during the process. I was hopeless though

That would be interesting, it's kind of opposite to the type of stuff the mind wants to do there it seems

Sometimes I would also perform reality checks in my dreams, but I couldn't realize that the weird phenomena were unreal

Maybe that's also because I'm a very distracted person in real life too

A guy I know lucid dreams every night apparently (he claims so at least)

That's why they suggest very simple stuff, like looking into yourself in the mirror and seeing if you can make the image disappear by thought

If you just form a habit of going to the mirror every hour and trying to make yourself disappear, it may be enough

Through the looking glass as they say lol

The point is that even if I disappeared, I wouldn't realize that it's a dream

I'm completely brainwashed

lol, the habit should include asking yourself the question of whether it's a dream

Yes sure, I would do that in dreams too without realizing the truth

Interesting... I can suggest also trying to sleep in different places. Maybe a worse or better mattress can do the trick

That's also because in my average dreams I'm not myself. I'm not even a person, more like an... entity?

And the world is acausal

Ahhh, if you're an entity it's not a dream ^_^

Sure but it's not that easy :P

This stuff is beyond me actually, I think sleep is precious enough to say... if it works, don't screw with it, lol

At least, the habit to write down/tell my dreams helped me remember in greater detail

@Amit lol

I never wrote stuff down but it could be fun... trying to see whether there's any connection and pattern in them

@SillyGoose C. S. Lewis wrote the Narnia books. He wasn't a mathematician. Lewis Carroll, aka Rev C. Dodgson, wrote the Alice books. He was a mathematician. en.wikipedia.org/wiki/Lewis_Carroll

@Amit also, while you write you remember a lot more

Writing is magic... they really used to believe that back in the day... that if you write without a good reason for example you are creating "demons" :)

Sure, when I fail some problem I create demons that will haunt me all night

lol

That's a modern twist I suppose

Related: automatic writing. en.wikipedia.org/wiki/Automatic_writing

Yes... also, even the words imply magic without us noticing... we "spell" words, cast spells via words...

@PM2Ring I didn't mean to take the discussion there...

I started it ^_^

Are you a witch

lol, once a friend saw me cooking something and said that I looked like a wizard making a magical soup

It's really hard to read in your dreams. I think it might actually be impossible, and when it seems like you're reading stuff your brain is faking it. Similarly, when using a calculator or computer in your dreams, your brain just makes stuff up, ChatGPT style. ;)

lol, that may be interesting if we can somehow prove that ChatGPT can only communicate as well as a person who is dreaming

but it would explain a lot

hah, that one needs context :)

Oh gosh I’ve mixed up my C’s and my Lewis’s XD

Quack

quack!

i did not realize nLab was made like for category theory...

they don't make it a big secret

XD

a book about an acausal world would be interesting

probably exists :P

pynchon is perhaps close at least as a first time reading experience XD

I've tried reading Wallace's Infinite Jest several times and it definitely is an acausal experience :P