@0celo7

thanks a bunch

Hi guys

Anybody there?

I need some information about huygen's principle

Can anyone helps please?

@Slereah @Jim @JohnRennie

@Majid You can ask and see if someone could help

In other word, the envelope coincides with the wavefront for any n or just even n?

@Blue I have a good doubtful Indian book now

@Majid oh, I had kind of the same question

never got a satisfactory answer

if you come up with something reasonable, you may want to add an answer here

wait, why do people say it only works for even dimensions?

see the link above

@AccidentalFourierTransform you know evans?

I thought you weren't about the PDE life

yes, he's my buddy

we have coffee every other week

and he tells me about his kids

wow, that's quite a long way to travel for coffee

we recently divorced his wife

she was cheating on him

she was into algebra or something IIRC

where in evans

what in where?

hold on

why are you looking this up in evans

evans is a physicist whisperer

he speaks a language we understand

ITS HERE [redacted]

wow that flag was fast

lol, looks like there is not much drama ;)

@AccidentalFourierTransform this is pretty confusing

the Wiki page says that it's wrong when n=2, but all of the pictures are n=2

life is pretty confusing

so are the pictures wrong?

is Wikipedia wrong? is Ted Cruz the Zodiac killer? I guess we'll never know

but yeah you have a point

Or are the pictures just projections of the n=3 situation?

where is @ACuriousMind when you need him

How Can Pictures Be Real If Our Eyes Aren't Real

you're on fire today

youre gonna miss my shenanigans when I die

when will that be?

yesterday

RIP in peace

no ghosts allowed

we are firmly anti-ghost here

yeah, let us keep this chat unitary please

$\hbar \hbar^\dagger=1$ pls

@0celo7 I've always actually been kinda confused about that too - if the mathematicians are right and Huygens' principle doesn't work for the wave equations two dimensions, does it not work for surface waves on water?

That is, can we show it doesn't hold with a rather simple experiment with water?

oh but I made a simulation of the double slit experiment in 2D when I was wee

and it did work

So I learned Huygen's principle from Arnold, who makes no mention of the dimension mattering

And the Wiki article is pretty vague about what they really mean

and Evans -- not sure wtf he's talking about there.

watch yo mouth there

evans is my pal

what are you gonna do, flag me?

@ACuriousMind I smell a very straightforward main site question

@AccidentalFourierTransform's question was unnecessarily complicated

I've just looked at the Stanford lecture notes and they say that Huygen's principle is defined as "disturbances all travel at exactly speed c", which is very different to Huygens principle being about the shape of wavelets...

Yeah, I think these are different principles.

@0celo7 do as you please, but imma close your question as duplicate of mine

@AccidentalFourierTransform I will find you and fight you.

(an that's the Huygens principle that works in odd dimensions for $n\geq 3$)

yeah, you have H's principle for the Schrodinger equation

which is independent of $d$

and the H's principle for the wave equation

which depends on $d$

thus my question

which never got an answer

I'm not really sure what Evans means by a "sharp wavefront"

it seems that if we were in a world with one more dimension, the double slit experiment would look different when done with electrons and with light

Wait wait

What is n for string theory

for M theory

$n\in\mathbb C$

it is 9

damn, I was about to disprove M theory

or 10 or 11, who knows

it's 9+1

@AccidentalFourierTransform Erm... I don't see how a double slit experiment makes any sense in a 1D world...

no I meant 4+1 instead of 3+1

Ah, just noticed the 'more' in there - my bad!

What does evans mean by "continues to have effects even after the leading edge of the wavefront passes?"

effects on what?

he probably means something about the mollified version of the fundamental character

can you please stop trolling for once

that or the dual thingy

ok :-(

right, I think what evans is saying is that the disturbance propagates inside of the light cone, i.e. subluminally

very interesting

alright alright alright

sleepy time

ciao people

cheers

I am not sure if I have asked this before, so I will ask again.

Is it possible to read the Landau Lifshitz Course of Theoretical Physics immediately after reading the Feynman Lectures on Physics, or do I need intermediate books?

I know all the math I need, and I am just asking about the physics part.

@ACuriousMind this algebra is too abstract

what the heck is a group algebra

I heard it once in a spectral theory talk and didn't get it there either

@0celo7 It's...just the algebra generated by taking formal sums of group elements. It is intended to be a rather abstract object

@ACuriousMind I have no idea what that is supposed to mean.

Does your book not tell you the definition of the group algebra?

It says exactly what you say

I missed the first lecture because of scheduling issues

I'm trying to catch up

Hey @0celo7 it seems you don't go to the math room anymore, or maybe I mistook you for someone else with a similar name.

so we've got a ring R and a group G, and we just make this set $RG$ with a bunch of elements "called" $\sum r_ig_i$, and then define addition and multiplication in a sensible way?

@WillHunting I haven't had a reason to go there

@0celo7 Yes. The sensible ways are that addition is just addition of coefficients $\sum_i r_i g_i + \sum_i r'_i g_i = \sum_i (r_i + r'_i)g_i$ and the multiplication works as in the group. (sorry, that multiplication was wrong)

Writing down the multiplication is a bit difficult, but you can also view it as the polynomial ring in $\lvert G\rvert$ variables $g_1,\dots, g_n$, where you replace every monomial of degree more than one by the group element it is actually equal to - i.e. if $g_2 g_4 = g_8$ in the group, then you replace every occurence of $g_2 g_4$ by $g_8$.

@ACuriousMind Right.

So it's like $R[g_1,\dotsc,g_n]$

@0celo7 Yes, but with all the relations from the group among the $g_i$ instead of the standard polynomial ring where the $g_i$ are independent.

@ACuriousMind do you have to cancel?

presumably not

you just "can"

Well, I think the standard way to write an element of the group algebra would be fully cancelled. Which might be rather laborious to arrive at if the group is not very small, but fortunately one rarely need to do explicit computations in the group algebra

@ACuriousMind ok, so it's a reasonable thing

"polynomial ring with cancellations" is much clearer than whatever you said before

of course polynomials are formal linear combinations too :)

@ACuriousMind Do you get:

i clicked over to this tab and saw that image

i'm not even going to ask

@ACuriousMind ???

@heather you're too young

okay, yeah, now I definitely don't want to know

@0celo7 Not really, I don't know whose body that is.

@ACuriousMind Sigh, I've given up all hope

GODS I WAS STRONG

@ACuriousMind what is a unital homomorphism?

is it not true that $1\mapsto 1$ for any homo?

ACM doesn't know any memes.

@BalarkaSen do you know that one?

@0celo7 Only if you work in the category of unital rings.

@BalarkaSen always

No, I don't watch Game of Thrones.

I don't know any algebra

what the heck is the center of a ring

oh, same thing as for a group

@ACuriousMind Uhh, what the heck does an $R$-algebra have to do with algebras

algebra seems to be more terminology than anything

@0celo7 I'm confused - what is the definition of "algebra" you're using there?

Jesus Christ

@0celo7 Some feel the need to call these "unital", since if you have non-unital rings a generic morphism doesn't need to that

@ACuriousMind He states at the beginning that all rings have unit

then he restates it every time there's a ring

he seems quite insistent

Maybe he's a unitarian :P

@ACuriousMind vector space with multiplication

@ACuriousMind boo

actually in the definition of group algebra, is it an algebra?

what's the field?

@0celo7 The complex numbers, usually

what the actual f

where are there complex numbers now

Oh, I mean that you usually choose $R=\mathbb{C}$

no, he leaves it general

he says it's a free $R$-module

so it's not a vector space?

@0celo7 Ah, then you should see that a "vector space (over a field $\mathbb{F}$) with multiplication" is an $\mathbb{F}$-algebra, but that the notion of $R$-algebra makes sense for general rings

@0celo7 It's not a vector space if $R$ is not a field, no. "Free module" is essentially what one calls a "vector space over a ring".

I know what a free module is

@ACuriousMind So an $R$-algebra is an $R$-module with multiplication?

@0celo7 Yes, that's one way to say it.

...what's another?

It's equivalent to saying that an $R$-algebra is a ring $S$ together with a ring morphism $R\to S$.

jesus christ, what?

@0celo7 The morphism defines the $R$-module structure, and $S$ being a ring is responsible for the "with multiplication"

@ACuriousMind Well he also sayus that the image of the homo should be in the center of $S$

@0celo7 Oh, yes, if you allow the multiplication to be non-commutative, then yes