The h Bar

Heisenberg group

In mathematics, the Heisenberg group, named after Werner Heisenberg, is the group of 3×3 upper triangular matrices of the form ( 1 a c 0 1 b ...

important in quantum mechnics

11:26 AM

Elementary group

In algebra, more specifically group theory, a p-elementary group is a direct product of a finite cyclic group of order relatively prime to p and a p-group. A finite group is an elementary group if it is p-elementary for some prime number p. An elementary group is nilpotent. Brauer's theorem on induced characters states that a character on a finite group is a linear combination with integer coefficients of characters induced from elementary subgroups. More generally, a finite group G is called a p-hyperelementary if it has the extension 1 ⟶ C ⟶ ...

They seemed to like primes so much. In here, in most p group examples and also the sylow theorems. Must sit down later and ready carefully on how composites causes trouble

Why would someone bother to write $+$ve and $-$ve with LaTeX instead of writing positive?! I don't know why this irritates me so much, but it does

user116211

I think it has been discussed earlier; but have to check the transcripts when...

@ACuriousMind Less characters to type.

@BalarkaSen But why not +ve and -ve

Why enclose the plus/minus sings in dollars?

@ACuriousMind nicer font?

11:37 AM

@Sanya I have trouble believing that someone who don't care that "+ve" is not a word would care about the font the + is in, but, well, maybe you're right.

Or maybe just instincts to write every symbol in latex.

@ACuriousMind I can only speak for myself, but I tend to put numbers in equation environment to make them look nicer

user116211

Related but not same post by ACM:

user116211

Jun 4 at 13:08, by ACuriousMind

Why do people write "+ve charge" or "+ve direction"? They seem to mean "positive", but "+" does not mean "positi", so why do they append the "-ve" to "+" instead of just writing "+ direction", which would be a shorter abbreviation that carries the same meaning?

e.g. $C_4 \times C_9$ looks elementary? (C_9 is a cyclic p-group with order $9^1=9$, and gcd(4,9)=1)

11:42 AM

Wait

If I pick the sum of hyperreals $(1,0,0,0,...) + (0,1,0,0,0,...) + (0,0,1,0,0,...) + ...$

All terms are equivalent to 0

But shouldn't the sum be 1

Or even worse if I pick $(1,0,0,0,...) + (0,2,0,0,...) + (0,0,3,...)$

Then the sum would be infinite

@Slereah Well, did you show that taking the quotient to get the hyperreals commutes with infinite sums (or limits in general)?

I'm still on chapter 3

Currently hyperreals aren't even defined as sequences

Just as some metamathematical extension of $\Bbb R$

Then I'd hold off on that question

@yuggib halp

I'm guessing it doesn't work since that sum would be equivalent to the infinite sum of $(0,0,0,0,...)$

But I'm not sure how

Q: In charging by induction a charged body mirrors its Energy to another body without transferring it, is that not a violation of Energy conservation?

0

This is more less like the ice pail experiment where I will recover the energy I used in charging the sphere when I contact the sphere to the container and extra electric energy when I Earth the container. This mirror effect can be amplified when you place a charged sphere in many other spheres o...

electrostatics experimental-physics energy-conservation

am I the only one who has no clue what this is about?

11:49 AM

Nope, you're not alone :P

user116211

@Sanya What is mirrors?

@MAFIA36790 I guess to duplicate onto something?

user116211

So reflection transformation?

I guess ... not too sure about all of it

Hey can somebody explain me what Nobel Prize for Physics 2016 is about in in laymen terms(terms I can understand)

user116211

11:56 AM

Anyways, concentrating on my studies.

"opological phase transitions and topological phases of matter""

Sylow theorems

In mathematics, specifically in the field of finite group theory, the Sylow theorems are a collection of theorems named after the Norwegian mathematician Ludwig Sylow (1872) that give detailed information about the number of subgroups of fixed order that a given finite group contains. The Sylow theorems form a fundamental part of finite group theory and have very important applications in the classification of finite simple groups. For a prime number p, a Sylow p-subgroup (sometimes p-Sylow subgroup) of a group G is a maximal p-subgroup of G, i.e. a subgroup of G that is a p-group (so that the...

One day, I am going to plug everywhere that says p a composite number, and see how this whole thing will crumble in order to udnerstand why they can only use primes

dead?

anyway will checkout chat later...

@Secret Take $A_4$, which is of order $12$. $6$ divides it, but it has no subgroup of such order.

wait does Robinson ever actually define hyperreals as sequences

I'm not sure

12:09 PM

hey I have a problem

user116211

Everyone has problems.

@BalarkaSen Agreed with the counterexample

(However, it might be not very satisfying for me because I don't understand the underlying reason for all these counterexamples and how it arises (only knowing that there is a counterexample and how it is a counterexample). I will try to check myself on that later)

whenever I learn something new in school, like magnetism, I want to know everything about it, and end up asking questions like why the magnetic fields even exist and stuff

and why they have the shape that they have

but all answers that I get is either of collage level physics or inclue calculus

user228700

@MAFIA36790 LOL XD

user116211

@MartianCactus Magnetic field lines have no real existence.

12:11 PM

so when I reach these levels will they teach me these things in advance and will it clear all my querries?

@MartianCactus:the only solution is say bye to procrastination and work damn hard to get there

and at the end of the day

@MAFIA36790 well then why do the iron nails align themselves in a specific pattern?

become satified with answer that

physics never answer 'why'

@Xasel yes but being a 10th grader..i don't think I can understand all that QM math

@Xasel ha nice joke

user228700

@MartianCactus I understand where you're coming from :-) I have the same "problem" but don't consider this to be a burden, because being curious is one of the best qualities for a human to possess.

12:13 PM

didnt newton ask why the apple fell? Not how

@MartianCactus Yes and no. Once you understand calculus (and a lot of other math) you will understand a lot more about physics, and how physical theories actually work. But your question of "Why does the magnetic field have the shape it has?" will simply be replaced by "Why do magnetic fields obey the equations they do?". And if you managed to find a theory that explains that, you'll ask "why" that theory is true...

user116211

@Xasel Why?

Physics is ultimately not meant to "answer why questions", but to provide models to predict what happens in reality.

4

@Kaumudi but being curious and not able to find the solution after soo many questions is even harder

@MAFIA36790:why is the question of eternity better left unanswered :P

user116211

12:14 PM

@Xasel ;D

@ACuriousMind so its an endless chain afterall

@MartianCactus For all I know, yes

so noone knows why magnetic field lines exist?

No, because that's not a well-defined question.

What does that even mean?

12:15 PM

@MartianCactus:I can only refer you to books...the guys here can show you the way..but you have to walk it yourself...

Heh, @BalarkaSen, two posts, same thought :)

why magnetic lines exist IS well defined

great minds think alike

??

i mean the magnetic field lines just can't pop into existance

there has to be a reason

well in phsyics nothing exist we just create mathemtical models to study the nature quantatively to some extent

12:17 PM

That sounds equivalent to "why am I in the world? I must have a purpose"

user228700

@MartianCactus Yes, perhaps, but as you learn more, trust that many of the misconceptions that are the root of these ill-defined questions will become clearer and you will realize the meaning of what ACM has said, about the point of physics being to provide models to predict realty.

@MartianCactus Field lines are just fictions. You can't see a field line in reality. What you see is e.g. a compass pointing towards a wire. We invented the concept of "fields" and "field lines" to explain this and predict similar situations.

@Slereah well, the sum $(0,1,0,\dotsc)+(0,1,0,\dotsc)$ is not a sum of hyperreals

The "field lines" taught in many classes and used by physicists to visualize field strengths are purely to guide the eye; they don't have physical meaning.

oh

12:18 PM

Why not

Magnetic field lines do not exist. You see some effect in reality which you attribute to the field and its lines, but the field does not exist.

@ACuriousMind He's probably asking why the field lines look like they way they do, whatever that means.

because to sum hyperreals you have to sum equivalence classes

But then which representation do you pick

Check this oyt:van.physics.illinois.edu/qa/listing.php?id=27163

12:19 PM

@Slereah the one you wish, but you have to be coherent

Q: Do electric and magnetic lines of force physically exist?

5

As per my imagination any thing can't impose force on the other by not giving even a touch(i,e action at a distance). So I thought there must be some physical existence of lines of force. Although virtual particles hypothesis has been proposed. Up to my knowledge virtual particles are just said t...

quantum-mechanics electromagnetism forces electricity electrostatics

also I don't really get the concpt of volt..

colt?

Same rep for same number?

edited

12:19 PM

The concept of colt would be easy: Point at someone you want dead, pull trigger ;)

@Slereah the sum of two equivalence classes $[a]$ and $[b]$ is the equivalence class $[a+b]$

Also Robinson indeed has an extension of Hilbert spaces to hyperreals

XDXD

Which is nice

hmm.... do you understand the concept of energy and mathematical constuct to study it's evolutionn with time like potentiaal energy

12:20 PM

Much better than the ultrametric ones

Guns and bombs are the easiest things in the world.

@Slereah told you so

@Xasel me?

yeah

Oh by the way

For all internal statements

Can I just transfer them dumbly

Or is there something to watch out for

12:21 PM

I suspect you haven't built base structure and planning to build burj-khalifa @MartianCactus

@Xasel nah

@Slereah they hold only for internal objects

I suspect you haven't built base structure and planning to build burj-khalifa @MartianCactus

Well yes

But can I

Or do I have to watch out for like

user228700

@MartianCactus: When you learn physics at school, it is truly very difficult to properly understand everything, because the whole picture is not introduced to us. Eg: It was very difficult for me to understand why a perpendicular force does no work on the body but only later in my stidies did I realize why this is.

12:21 PM

The order of the statement

user228700

It can be difficult to say "OK, I'll learn it properly later", but if u don't have the resources to teach yourself the more advanced stuff, it will have to do. That's mostly how I made it through high school...

first learnt he basics bro..no need to hurry

Or something

sooo why did the school teach us that? Before teaching the imp. stuff bout the base

i.e. if you say "all subsets of reals blah blah" this transfers to "all internal subsets of the hyperreals blah blah"

12:22 PM

because most of them teach you learn definition and pass the exams

That much I got, yeah

so after high school..all those questions start to clear away?

quite unfortunate since most interesting subsets are external

By the way are all finite subsets of R internal?

If I just define them by their members

yes

I suspected

user228700

12:23 PM

@MartianCactus Yes. These questions arise because of misconceptions that in turn arise because of the whole picture not being introduced 'cause it's too advanced.

so first they teach u how things work..then they teach you why things work

@ACuriousMind Though, I am curious whether there is a mathematically rigorous context in which you can show why the magnetic field has index 2 at it's only zero (aka where the magnet is).

That might sound a bit naive, but I admit I know nothing of physics.

user228700

@MartianCactus What do u mean by "how things work" vs. "why things work"? Can u provide an example of this that u have encountered in ur studies?

um...taking the magnetic thing...how the magnetic fields work and why they exist are 2 different questions

It's the same idea in mathematics, we need to learn how things work, before we can start to understand (and prove) why
For physics, there is no proof, but there are experiments to test the model

For classical electromagnetism, magnetic fields are the result of special relativity

12:29 PM

@BalarkaSen Well, from what do you want to show that?

so special relativity and electromagnetism are linked/?

@ACuriousMind That's exactly what I am asking, if there is a workable axiomatic framework in which you can show that.

Bro, you seriously need to learn all the things from gorund-up again if you want more understanding...

You are just shooting arrows in the mist

ha ground up? im in 10th class so i have barely started

much better go buy a good pre-calc and calc books

12:30 PM

@MartianCactus Well, I still don't know what exactly you mean by "why". Asking "why" can never have a satisfying answer: Either the reason stated has itself no reason (then why couldn't you stop asking why one step earlier?) or the chain of reasons continues to infinity, which also makes it useless.

2

@BalarkaSen Well, would knowing it is divergenceless suffice?

by why i mean a hard proof of why they exist

idek for now i gtg

and thoroughly do each question(for every wrong question properly explain what do did wrong and 'why it is wrong' and and what is the right solution and why)

@MartianCactus A proof starting from what givens?

@MartianCactus To write down a proof, you need axioms.

but axioms are (accordint to my understanding ) guesses

user228700

12:33 PM

I agree with Xasel. Like everybody has pointed out, you need to start from the basics. @MartianCactus: I promise you that these questions will cease to exist once u start studying all this much more thoroughly.

things that we dont proof

@Kaumudi oh

ok im going to go now

@MartianCactus You seem to have a wrong idea of what a "proof" means.

maybe i need to learn more before understandih this stuff

user228700

@MartianCactus Yes.

k now bye!!

user228700

12:34 PM

Bye :-)

SR and electromag are linked indeed, but you should be proficient on the stuff at your level before start tackling with the uni level stuff

whats is uni level?

oh

@ACuriousMind I am not convinced divergence determines the index. Look at, like, a circular flow around the origin (eg $(y, -x)$ normalized appropriately). That's index $+1$.

unicorn level

@MartianCactus: mirtitles.org/2012/03/06/…

12:37 PM

ah

Hm