The h Bar

naturallyInconsistent

12:39 AM

@Obliv This is very far from correct.

Obliv

12:51 AM

@naturallyInconsistent How? I do the basic potential $U = \frac{kQ_1Q_2}{r}$

where $Q_1$ is helium so $+2$e and $Q_2$ is gold so $+79$e

naturallyInconsistent

@Obliv $$\frac{158e^2}{4\pi\varepsilon_0r}$$

Obliv

where'd that come from?

OH MY GOD

how to multiply two numbers

Should I be converting everything into SI units

Silly Goose

1:43 AM

Under "Berry connection" why does the wiki say that the Berry phase is gauge-dependent en.wikipedia.org/wiki/Berry_connection_and_curvature? I thought that the Berry phase around a closed path is gauge-independent (as claimed and shown in e.g. Sakurai)

It seems that only $e^{i\gamma_n}$ is gauge-invariant (where $\gamma_n$ is the Berry phase for a particular eigenstate labeled by $n$)

so I am confused what Sakurai and other resources mean

naturallyInconsistent

3:41 AM

@Obliv you don't have to, but that is always a good last resort.

@SillyGoose This is nothing new; just like how positions are gauge-dependent upon where you choose the origin while position differences are gauge-independent, Berry phase at any one point is gauge-dependent but its integral over any closed path is gauge-independent.

Ryder Rude

6:42 AM

@Jakobian idk how to interpret this question :P

Jakobian

7:26 AM

@RyderRude If for a platonist everything in mathematics exists as a physical object then nothingness should also exist. So they should know what nothing is

Slereah

Platonists don't believe they are physical objects

That's what forms are for

Ryder Rude

7:41 AM

@Jakobian but 1. Nothingness isn't part of mathematics 2. Like Slereah says, Platonists think those things exist in another realm

Jakobian

according to wikipedia the theory of forms is more narrow understanding of platonism

@RyderRude the empty set fills the role of nothingess

Ryder Rude

I'm not sure in what sense a platonist imagines sets to exist

the ZFC universe exists

and empty set is in that universe

Jakobian

I'm not sure if platonist is sure in what sense they imagine sets to exists either

Ryder Rude

it is all non sensical anyway. I dont think Platonists know what they mean

@Jakobian exactly

but i get the Platonist viewpoint. Would u rather be an ultrafinitist (the biggest natural number is what the universe can store) or a platonist (natural numbers exist even tho large numbers may not exist in the universe)?

i prefer formalism, but formalism can never define natural numbers

Jakobian

@RyderRude its not a dichotomy

Ryder Rude

7:47 AM

so the only other choices are Platonism and ultrafinitism

Jakobian

again, its not a dichotomy

Ryder Rude

what other choice do u have

i think it is reasonable to have a platonist view of "standard natural numbers". They simply exist and we are trying to model them using axioms

like we model phenomena using physics

Jakobian

Formalism doesn't need either ultrafinitism or platonism to work

Ryder Rude

But Godel theorem says any definition of natural numbers using formalism will have non standard models. So it is not actually a definition of natural numbers

it is just an (partial) attempt to model natural numbers

Jakobian

and?

Slereah

7:53 AM

Sets did not really exist in the modern understanding until the 19th century

Ryder Rude

then what actually are natural numbers? @Jakobian

Jakobian

you don't need formalism to talk about natural numbers

it doesn't matter what natural numbers even are, you just need few small natural numbers which exist because you know they do in your head

you don't need to formally define them or whatever

this is without taking any position either - not ultrafinitism and not platonism

Ryder Rude

ok if u don't formally define them , to be able to talk about a thing called natural numbers, u r assuming that they are. In what sense they are, if not in the Platonist sense?

Jakobian

Uh? No

what are you talking about

Ryder Rude

this question : is the collection of natural numbers something?

is this a meaningful collection to talk about

Jakobian

7:57 AM

I am not assuming natural numbers exist, lol. I can count and I can name this process of having one, two, three or four elements. This doesn't need any type of formalism

its like arguing that definitions can't be perfectly defined

yes, they are suggestions for concepts that we know what those concepts are

how do you know a table exists? Do you assume it is?

Slereah

@RyderRude Depends on who you ask!

Ryder Rude

yes. We do have examples of natural numbers in the real world. But is there such a thing as the collection of all natural numbers? @Jakobian

Slereah

People had the notion of a collection certainly but that wasn't really formal

Jakobian

@RyderRude yes, because using concepts outside of formalism now I can write what natural numbers are inside of formalism

Ryder Rude

@Slereah yes. this is y i used the word "collection". It is meant to be informal, because natural numbers can't be formally sefined

Slereah

8:00 AM

People tended to talk more about universals in olden times for what we might associate with sets as we do today

The essence of a given characteristic that every object of the same kind shares

Jakobian

natural numbers can be formally defined, you are wrong

Ryder Rude

@Jakobian but formalism can't define them..

Jakobian

so what? Formalism can define them once you have them

and you only need few of them to define what they mean in formalism

Ryder Rude

@Slereah oh

these ideas of "essence" are all vague. But again, it is supposed to be informal

@Jakobian what do u mean

Jakobian

I mean what I mean. I don't know what you're asking

Ryder Rude

8:03 AM

The way i look at it is : we see some natural numbers irl, and we try to capture their properties in formalism, but we are never able to fully capture it @Jakobian

Jakobian

I don't know, thats a claim

Amit

@RyderRude Have you taken a leaf from Wildberger's book? ;)

Jakobian

are we never able to fully capture them? I think that requires you to take some position like platonism or ultrafinitism

Ryder Rude

@Amit no :P

@Amit it is probably a waste of time

math is good as it is, no need to modify

Amit

I didn't mean it in a negative way

Jakobian

8:06 AM

@Amit yuck

Ryder Rude

@Amit i know. :)

Amit

If it interests you , why not. Maybe intuitionists (if that's the right category) have something to contribute too y'know

@Jakobian lol

Ryder Rude

@Jakobian i meant that there are always non standard models. this is a fact that requires no philosophical position

Amit

No using proof by induction if you don't believe in infinite sets ;( OTOH fighting with one hand tied behind your back sometimes makes you develop muscles others didn't

Ryder Rude

@Amit i think one can reject Platonism and simultaneously not try to modify math to not include infinite sets

i also sort of don't reject ultrafinitism, but I'm not sure. Either way, infinite sets in math are completely fine

Amit

8:09 AM

Sure. In fact Platonism in my mind is at least in the same line of thought that made us invent the concept of infinite sets. Insofar as Platonism is closely related to putting no limits on the level of abstraction

Jakobian

Wildberger just repeats arguments he heard as something novel

I don't know where to look for these muscles in that

@RyderRude maybe you misunderstood what I was saying

Ryder Rude

@Amit yes. I think Platonism is closely related to the acceptance of infinite sets. As in was just saying, what do we call standard natural numbers if not some platonic object

Amit

Honestly I don't know his work closely enough. I think he may have developed a new formalism for Trigonometry as part of the refusal to "accept" that the symbol $\sin$,$\cos$, etc. just "do what we expect". But I didn't dig deeply into that.

Jakobian

by capturing natural numbers, I understand that you want them to coincide with the ones outside of formalism

Ryder Rude

@Amit idk either. I am repulsive to "grand alternative ideas"

lol

@Jakobian yes

Jakobian

8:12 AM

@RyderRude you don't need to refute infinite sets if you're not a platonist. Infinite sets always exists no matter your position, because they are written as mathematics

Even if you are an ultrafinist you will accept infinite sets as written, just perhaps not that they represent something in the real world

Ryder Rude

@Amit maybe Wildberger thinks infinite sets derive contradiction, which is y he wants to modify math

Jakobian

An ultrafinists would have no problem to understand ZFC. But it would probably be useless for them

Ryder Rude

@Jakobian yes. this is why i wrote "closely related", but not exactly. Maybe historically, platonist stuff played a role in us thinking about infinite sets

but yeah, u can accept infinite sets while not think that they exist

@Jakobian yes

Amit

@RyderRude I listened to a few of his lectures. I don't find that interesting enough personally, and I think that the motivation for doing that kind of work may be misguided, but the work itself can lead to interesting results. As I said, if you tie a hand behind your back while fighting for the pure fun and discovery, I'm all for it. Not out of some grand ideology -- that part I find redundant and sometimes obnoxious ;)

Ryder Rude

where i find Platonism and infinite sets to be "exactly related" is things like belief in "standard natural numbers" @Jakobian

becuz idk what else standard means if not Platonism

Amit

8:17 AM

e.g. when someone like that digresses into exactly why philosophically there can't be infinite sets. I rather just move on and take that as a working assumption to see what happens, no need to make excuses :P

Ryder Rude

@Amit yeah...ultrafinitist systems are worth exploring to see what results they produce. I read somewhere that everything in standard math can technically be done in finitist math, but I'm not sure

but even then, finitist systems have potential infinity. Ultrafinitist systems don't have potential infinity, i think

@Amit i would prefer to discuss philosophy first because i like these discussions :P but yeah, people can be annoying if they speak from ideology

@Amit what i read is that finitist math can reproduce standard results but it's just cumbersome

Jakobian

what is finitist math

Amit

how do we flag AI generated answers?

Ryder Rude

@Jakobian i made this post about it long ago

7

A: What is the mathematical definition of "standard arithmetic/standard natural numbers"?

Your use of the word "intuitive" means that we're entering philosophical waters. In ZFC, as you know, one can prove the formal version of the assertion "there is, up to isomorphism, only one model of the second-order Peano axioms". But as you are also aware, there are non-standard models of ZFC (...

Michael says :

> Roughly, my dream is to show that “the” standard model is a much more nebulous notion than many seem to believe

@Jakobian it has arbitrarily large sets, but no infinite sets

sorry it's John Baez who said the quote. Michael is paraphrasing

This means John Baez doesn't believe the standard natural numbers is an unambiguous entity. And this is how he avoids Platonism

Jakobian

Finitist math is nonsensical concept for me then

even an ultrafinist can work with infinite sets via formalism

Ryder Rude

8:29 AM

yes, but finitist math isn't nonsensical. A finitist can work with infinite sets, yes. But as u say, a finitist may not find it the right model to work with

and finitist math is just an axiomatic system without the axiom of infinity. So it's not non sensical

but other people may find it useless

Jakobian

As a model it might have some value

but not particularly because that someone is a finitist

Ryder Rude

lemme see if i can find the post which said it can reproduce standard math

Amit

@RyderRude Yes, it's the mixing of the two subjects I don't like

1k actions -- do I get a Sombrero hat?? ^_^

Ryder Rude

@Jakobian oh

do u think large set theories have contradiction at some point like Russel's paradox?

if contradiction happens, then at some point, we have to reject some large infinity

but i don't see why it would happen. Russell's paradox only happens when u can define "the set of all sets"

Jakobian

@RyderRude the ones with large cardinals?

Ryder Rude

8:40 AM

yes

Jakobian

probably unlikely

Ryder Rude

probably

i can summarise two positions : 1. Standard natural numbers is a nebulous notion 2. Standard natural numbers is a thing that axioms try to model, just like physics would model the universe

not sure how ultrafinitistism fits into these positions

Maybe ultrafinitism is just the position that numbers upto $~10^{500}$ (whatever the universe can handle physically) are not nebulous, anything else is nebulous

Amit

lol, I seem to have come across a serial AI generating user in the review queue. The first time he did it naively, the second time he seems to have asked the AI to write in a more casual style 😂

nickbros123

8:55 AM

@RyderRude thats what computers do. in binary, if the mantissa of a 64 bit number is all 111..., its considered infinity

Ryder Rude

@nickbros123 oh

@nickbros123 but it's just a notation. Just like $\infty$ means infinity in math

It's not actual infinity. We can never encounter actual infinity irl

Amit

OTOH biologically every cell comes from a previous cell, the first one came from somewhere too , etc. It's not clear whether or not our past is infinite

Ryder Rude

@Amit what do people gain from this :P

Amit

@RyderRude Reputation? Satisfaction in deceiving the system? No idea...

Ryder Rude

@Amit the time since big bang be finite tho

Amit

9:00 AM

Or do you mean, from review tasks? lol

Ryder Rude

@Amit no.. lol

@Amit that's a good explanation

Amit

@RyderRude are we sure? the jury is still out on that I believe

I mean on how much of a genesis is this event

and would we ever know, too

Ryder Rude

also, i think time is undefined near big bang due to quantum time

Amit

I am only suggesting, just because personal memory is finite, doesn't necessarily imply biology is not the end result of a potentially infinite process

undefined sounds promising

nickbros123

@RyderRude it would be slightly different because we actually have infinite numbers on $R$ before we meet $-\infty$ and $+\infty$, i.e, finite operations on $R$ itself can never reach $\infty$, but in computers they can. just do s=s+1/n loop on C++ and see where u get infinity :)

Ryder Rude

9:07 AM

@Amit i just mean that it's not classical .maybe other some description

nickbros123

but again R doesnt exist in computers

Ryder Rude

@Amit maybe

@nickbros123 yes. I also think R may not exist irl either

R^4 is just a model to approximate spacetime

nickbros123

$sqrt(2)$ doesnt exist? but I can draw it with compass and straightedge :)

Ryder Rude

or rather, even if it does exist, u can never know that

e.g. space could be boundless... but ur experience is always finite

@nickbros123 it is an idealisation

nickbros123

does the hypotenuouse of a 1 cm isosceles right triangle not exist?

Ryder Rude

9:11 AM

it exists as math idea, which, as far as we know, models some real objects well

but can never know if the correspondence is exact, i.e. if real numbers are in the ontology of the universe

to verify an exact correspondence, u would have to actually deal with an infinite set in ur experience, using infinite precision measurements and the verification of it. But ur experience is finite, so that is impossible

Slereah

@nickbros123 Wrong : r-project.org

Ryder Rude

but if u were an infinite being like an onmipresent god, u may verify things like the existence of an unbounded space. so such a god can accept infinite sets without having to believe in it

assuming those sets exist

nickbros123

@Slereah touche

Ryder Rude

also, if the god were omnipotent, they would be able to realise the Banach Tarski experiment :P

nickbros123

oh man, this is way too much philosophy for my mind to take

Ill go and solve an integral now to cleanse my palatte

PM 2Ring

9:33 AM

@Amit Use a custom flag, and clearly explain why the answer is problematic. Note that gen AI content is permitted. From physics.stackexchange.com/help/gen-ai-policy

> Generative artificial intelligence (a.k.a. GPT, LLM, generative AI, genAI) tools can be used to generate content for Physics Stack Exchange, but this content must be properly referenced as per our guidance.

But also see

82

Q: Please don't use computer-generated text for questions or answers on Physics

For the impatient reader, the guidance is in the title: please don't use computer-generated text for questions or answers on Physics. Computer-generated text violates our expectation that users are posting substantially original content. Computer-generated text which is not identified as such i...

And

208

Q: Physics.SE remains a site by humans, for humans

We, the moderators of physics.SE, are deeply concerned about the recently announced "network policy" regarding computer-generated content on the SE network, which effectively attempts to forbid moderators from issuing suspensions or deleting posts for the undisclosed usage of computer-generated c...

discussion questions answers policy

Ryder Rude

@nickbros123 u will love philosophy eventually :)

@Amit in the three positions i summarised, which one do you prefer

Amit

10:02 AM

@PM2Ring Thank you, so that post may need a change of title

I ended up flagging as VLQ, will next time use a custom flag

Ryder Rude

> One ultrafinitist mathematician I know defines the largest integer to be the largest integer that will ever be referenced by humans.

lol

it is from here math.stackexchange.com/a/1989842

Amit

@RyderRude This has an element related to the various simulation theories. A number can't exist in the simulation until explicitly referenced

Ryder Rude

oh

it is pretty absurd. But how does one know induction proofs works beyond numbers one bothers to check

it is kind of a mathematical solipsism

not taking anything on faith

but it is nonsense in the end. u may as well say that the only numbers that exists is the one u r thinking of at the moment

Slereah

Lakatos' own Wario

Amit

@Slereah Does this stuff help with GR? :P

Slereah

10:12 AM

@Amit I mean to do science, you need to know what science is

Amit

@Slereah I'm in favor of it generally.. but these people seem to have taken it quite a few steps further than that.

Lakatos I think was more into Philosophy of math didn't he?

Slereah

He did quite a lot on science too

Also GR was essentially just a philosophical exercize originally :p

just a lot of Machian wanking

Amit

I see. I tried to read his "Proofs and Refutations", and it was just too much after several pages... but I really liked what he was trying to do there

Slereah

It is a fun book

His fun science book is strangebeautiful.com/other-texts/…

nickbros123

@RyderRude I dont really see myself doing that, ngl. Foundations is something I will probably not care too much about. In fact, I hardly brought myself to care about set theory all that much. I just read the axiom of choice section in the book and moved on

Amit

10:20 AM

@Slereah lol, wanking is a bit misleading isn't it, I gather the beginning with the equivalence principle came to settle something that bothered Einstein, I can't recall how he came to it exactly

@Slereah Cool

Slereah

that was just one of the philosophy of science problem of the era

Trying to figure out how to do mechanics without specific frames

Ryder Rude

@nickbros123 but philosophy is broader. Maybe u will be interested in philosophy of science (epistemology stuff) and philosophy of consciousness

nickbros123

maybe; maybe when life frees up I might look into that stuff

Amit

@Slereah Is it part of his cosmopolitical approach to humanity? ;) I say that because I have recently read a bit of a Bohm biography. The author annoyed me slightly by trying to relate his Marxist/Communist leaning to the way he approached problems in Plasma (the collective is important, that kind of idea). I mean interesting idea but really.. are we going to interpret the work of every scientist by his ideology now?

Slereah

I'm not sure it's entirely without merit

Amit

10:24 AM

That makes it more annoying :D

Slereah

Marxism had very strong ties to philosophy of science

Amit

Right, Engels was quite into it if I recall

Slereah

Hell my thesis advisor was a Soviet man and during his class on phase transition he brought up dialectics

Amit

If political ideologies are tied up in some way to novel physical concepts, perhaps we should try to invent a few crazy ideologies just for the sake of the progress of science :P

@Slereah But that's really interesting

naturallyInconsistent

@Amit I watched enough of the front few lectures of his fully, until I realised that he was just working with $\sin^2$ as one of his quantities of interest, and yes, if you have that, you can do all the usual trigonometric stuff, and that a lot more "angles" would have rational values to play with, not just the special trio of 30, 45, 60 degrees. But then you also realise that there is no uniform circular measure, no symmetry between $\cos$ and $\sin$, and the missing stuff are still

requiring real numbers to patch up. This means that the scheme, which was advertised as doing stuff using rational numbers, is misleadingly oversold.

And then I just bailed. No point investing time and effort into something that is vastly inferior to the standard treatment.

Arjun

10:57 AM

@nickbros123 tf what you're doing here discussing philosophy pal?We got real analysis and QM exams tomorrow!

Slereah

@Amit That was pretty much the gimmick of marxism

Scientific politics

nickbros123

11:13 AM

@Arjun Needed a break from all the open balls

Amit

@Slereah Maybe, but more often than not just a gimmick to come across as modern and intellectual. I suspect very few cared deeply about scientific progress

Slereah

Depends on the ones

Plenty of people Believed

Amit

I take it that Bohm was an exception, but I don't have statistical evidence ;)

Slereah

You should try reading a Lawvere paper

First math paper I've seen to cite Mao

Ryder Rude

@Arjun just write about philosophy of real numbers in the exam

nickbros123

11:24 AM

Q12) Construct real numbers from rationals using cauchy completion

my answer: Rationals dont exist

Ryder Rude

lol

Slereah

11:41 AM

There's no lack of philosophy on the $\mathfrak{kontinuum}$

Amit

why is it with $\mathfrak{k}$?

Arjun

@RyderRude Lol,I wish it worked like that

Slereah

@Amit You're gonna have to ask Hieronymus Andreae, the creator of Fraktur

Amit

@Slereah Why are you so cultured... 🤣

Slereah

wikipedia

Amit

11:51 AM

😂😂

I'm very uncultured. For example, when I see an author using $\xi$ I get so disheartened... I know I would have to replace that with another symbol when writing anything down because I'm incapable of reproducing it on paper.... 😏

Slereah

part of learning physics is learning to draw $\xi$ and $\zeta$

Amit

I can't come to grips with $\xi$, it looks too much like an $\varepsilon$ that haven't paid a visit to the barber for too long

@Slereah but let's go back to the basics, do you write $x$ by drawing two intersecting lines, or two tangent curves? :P

Slereah

I do a little cross

PM 2Ring

The one that annoys me the most is $\Gamma$. Sure, it's easy to write. But it's almost impossible to avoid accidentally turning it into F ;)

Amit

@Slereah a bit surprising but economical

@PM2Ring $\Gamma$'s I love, for some reason. Maybe it's those good GR vibes... 😉

@PM2Ring But I actually can't see how that problem arises -- not if you draw them without lifting the pen from the paper like I'm used to

PM 2Ring

12:05 PM

I mostly write $x$ as two osculating curves. But I did try a cross style for a while, years ago, when I used a fountain pen. (First do a fancy line from upper left to lower right, with serifs, then cross it with a plain line).

Amit

@PM2Ring Why did you try to change? The osculating version is clearly the one with more pedigree isn't it? ;)

PM 2Ring

@Amit Once I lift the pen, some part of my brain thinks I'm writing an F and wants to add the lower horizontal.

Amit

@PM2Ring Ohh yeah I get it now. This stuff happens to me too, muscle memory playing tricks

PM 2Ring

@Amit I like fonts. I wasn't trying to change my default style, but I wanted to get comfortable writing a few different fonts. One of my brothers-in-law worked as a signwriter. He can write / paint a lot of fonts.

Amit

@PM2Ring I think that's perhaps why I adopted the habit of making the last small segment, coming from the top right corner, more pronounced. It's a way to tell myself "this is the last line" ;)

PM 2Ring

12:10 PM

Yep

Amit

@PM2Ring Ah, nice

PM 2Ring

On a related note, a habit I picked up from one of my highschool teachers is to add a little downward serif at the end of a $\sqrt{\cdot}$ radical sign. It makes it look like the radical sign is properly enclosing its contents.

Here's a geometry probability thing I learned recently that makes heavy use of the gamma function: math.stackexchange.com/a/4965944/207316

Ryder Rude

im not used to writing things. The pen somewhat goes out of control when i try

but i can still do it, but with some effort

PM 2Ring

I do a lot of stuff digitally. But I prefer paper when doing algebra, calculus, geometry. Although I do enjoy writing code to create geometrical diagrams.

Ryder Rude

i mostly just read. But im finding that i need to write to be able to understand things

PM 2Ring

12:26 PM

You can't read a decent mathematics book without writing. If it's hardcore, by the time you finish, the number of pages you've written should be similar to the number of pages that you've read. ;)

Amit

@PM2Ring So you may find this useful: tex.stackexchange.com/questions/29834/closed-square-root-symbol :)

PM 2Ring

@Amit Lovely!

Amit

:) too bad it ain't built in

Ryder Rude

@PM2Ring yes

@PM2Ring i tried it but i realised it need to do the exercises

Bml

@Obliv I am asking why the entropy change of a closed system for an irreversible isochoric transformation is the same as that of a closed system for a reversible isochoric transformation (and so also for an isobaric one),

since in general the entropy change of a closed system for an irreversible transformation is not the same as that of a closed system for a reversible transformation (just think of an adiabatic transformation: the entropy change for a reversible adiabatic in a closed system is zero because there is no heat exchange, while for an irreversible adiabatic in a closed system it is nonzero despite the fact that, by definition, a transformation is adiabatic when heat exchange is zero).

Amit

12:35 PM

When I solve a textbook problem, I find that unless it is quite easy and I already know how ~90% of the solution would look like, I am incapable of working on it directly via a TeX editor and the likes. It is too limiting when you want to scribble ideas away...

Lucky Chouhan

@Amit textbook problems are based on some previous pages

with obvious facts.

Amit

@LuckyChouhan I'm not sure what you mean to say

Lucky Chouhan

@Amit I mean when you study any standard math book. Then try to solve exercise at the end of the chapter or sections you'll realize that oh, all of these problems/exercises are obvious and those which are not obvious are almost obvious which is very rare.

@RyderRude and @RyderisnotRude. do you guys know about Sounds of Isha?

Amit

@LuckyChouhan Oh, first of all I was thinking about physics textbooks... secondly, even with regards to Math Idk if that's quite correct. For one thing, I found that some math exercises requiring you to prove statements can be quite tricky. Also, there are cases where in the chapter itself some theorem is an "exercise left for the reader" to prove, and then you need that theorem in the context of a more general exercise...

Lucky Chouhan

@Amit yeah!

Ryder Rude

12:50 PM

@LuckyChouhan no..

Ryder Rude

1:00 PM

@Amit i use paper

Sine of the Time

I paint on the walls

Ryder Rude

@SineoftheTime lol

Relativisticcucumber

1:20 PM

@SillyGoose the new cm hw got less hands

thank god

imbAF

1:33 PM

I was reading an article about the energy momentum derivation, and the following was said:
"Since kinetic energy is the energy of motion, it is only logical to assume that the change in kinetic energy during motion will manifest as a change in total mass as well, giving the idea of relativistic mass a bit more credibility."
Isn't it more logical to assume that a change in kinetic energy during motion is the result of velocity change and not mass ?

naturallyInconsistent

Just ignore it.

imbAF

One additional thing

Would it be correct to say that for an object that is moving E=mc^2 where m is the relativistic mass (\gamma m_0) is equal to E=\sqrt{p^2c^2 m_0^2c^4} ?

Ryder Rude

2:02 PM

@imbAF yes

Also, $p$ is relativistic momentum here

imbAF

and the relativistic momentum how it's expressed

In the sense p=mv ?

Ryder Rude

2:18 PM

@imbAF $p=\gamma mv$

PM 2Ring

@imbAF In SR, momentum is just $p = mv\gamma$, where $m$ is rest mass. That's more useful than relativistic mass because momentum is a vector.

imbAF

So then one can write: $E^2=m^2c^2(c^2+\gamma^2v^2)$ ?

Ryder Rude

2:33 PM

@imbAF yes, for massive particles. $E^2=p^2c^2+m^2c^4$ works for massless particles too, it gives $E=|pc|$

Mr. Feynman

@PM2Ring I have sometimes written down two or three pages just to explain a line in a proof :P

Jakobian

@RyderRude platonists beg to differ

Ryder Rude

@Jakobian but for Platonists, infinities exist in other realms

also, human experience is finite even for Platonists. So u can't encounter infinity irl

Jakobian

The meaning of "infinite set" depends on your foundations. Its not as meaningful unless you are in ZFC to be honest

@RyderRude you are claiming that space is finite too?

Ryder Rude

a platonist would say that all consistent formalisations of set theories exist in the realm. So every possible consistent formalisation of an infinite set exists there

Jakobian

2:38 PM

Locally that is

Why can't you say that this patch of space I belong to right now isn't infinite

Ryder Rude

@Jakobian maybe it is...

Jakobian

So you can't conclude human experience is of finite nature

Ryder Rude

@Jakobian I'm just saying that humans can't experience infinities, regardless of whether infinities exist or dont exist in the universe

Jakobian

@RyderRude I disagree. Where's your proof?

Ryder Rude

@Jakobian brain has finite information holding capacity, both in total, and thereby at a particular moment

Jakobian

2:42 PM

I'm not sure how you measured that

PM 2Ring

ZFC's finger-lickin' good. ;)

Ryder Rude

@Jakobian it is kind of an assumption

Jakobian

Yeah. You're assuming things to show your opinion

Ryder Rude

I dont think I've ever experienced an infinity of information, but maybe I'm making a circular argument

Jakobian

Its an argument by incredulity

Ryder Rude

2:44 PM

ok i will make a much weaker argument

this will establish that the physical existence of infinite sets is in doubt

i know for sure that i have experienced sets of finite cardinality, e.g. a finite number of ducks or even the finite number of decimal digits of a physical measurement

Jakobian

I never seen a set walking so I can't comment. This is in the same level to me as existence of "creator" of the universe

Ryder Rude

but i may or may not have experienced sets of infinite cardinality. Therefore, the existence of those sets is doubtful

Jakobian

Anyway. It doesn't matter because infinity we are clearly not applying to sets here

Ryder Rude

i mean sets in real life, collections of objects

I've for sure seen finite collections of things

Jakobian

Finite cardinality - that becomes unclear even in ZF

And you want me to apply the concept in real life?

Ryder Rude

2:48 PM

i don't mean the mathematical notion of sets..

Bml

Having received no answer here on the chat, I posted this question on Physics SE. Would anyone consider providing an answer for a possible discussion? Thank you.

0

Q: Why is the entropy variation for a closed system in irreversible transformations the same as in reversible transformations, and in other cases not?

Generally, the entropy change for a closed system for an irreversible transformation is not the same in a closed system for a reversible transformation. A clear counterexample is that of an adiabatic transformation. 1.1) Change in entropy in adiabatic reversible transformation for a closed system...

thermodynamics entropy reversibility adiabatic

naturallyInconsistent

@imbAF you can easily prove this to yourself

Ryder Rude

i just mean the irl notion of collections of things, and u can count those things

Jakobian

Lets define finite as this which one can count. Then what do you count when trying to asses finiteness of a patch of space? Is this even a meaningful question?

Ryder Rude

Yes, i cant assign a count to every experience. I'm just saying that i can assign a count to some experiences, therefore finite collections exist

infinite collections may or may not. Maybe space is an infinite collection, but idk for sure

Jakobian

2:51 PM

So we concluded that concepts of finite and infinite aren't necessarily applicable to reality

They are in reference to certain set up

Ryder Rude

yes

but finite things I've directly verified in some experiences. infinite collections are always indirectly verified

so they are in doubt. e.g. space is kind of well modelled by $R^3$. This is indirect evidence of an infinite set

But we can't verify that upto infinite precision

Jakobian

I don't know where you found an infinite collection in real life, or how you was able to speak of such

Ryder Rude

e.g. i modelled space by $R^3$ and it gave me correct predictions, so i sort of concluded that space is $R^3$

Jakobian

But sure, we can't claim there is a way to say something is infinite, or even that we can give it a meaningful interpretation so we can begin checking if it is

At least from collections of things standpoint

Ryder Rude

we can begin to check it...but we can never fully verify it

e.g. if speed of light is constant in all direction, u sort of believe that space is continuous

but u can only check this upto finite precision

but i believe these ideas are only a feature of the mathematical model of a physics theory, not a feature of reality

Jakobian

2:59 PM

@RyderRude to speak about if something is an infinite collection you need to provide a set up in which you will a priori verify if its infinite

So its circular

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