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9:13 PM
@0celo7
thanks a bunch
 
Hi guys
Anybody there?
I need some information about huygen's principle
Can anyone helps please?
 
@Majid You can ask and see if someone could help
 
9:30 PM
Good idea.Thanks!
I am not from Physic and need some information about huygen's principle.
I read that it worked for just even dimension
But its equation is written for any n,
It seems that some part of it is valid for all dimension?
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
 
9:50 PM
@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
 
9:51 PM
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 ;)
 
10:01 PM
@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
 
10:04 PM
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
 
10:11 PM
@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?
 
10:16 PM
@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 $n\geq 3$)
 
10:17 PM
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
 
10:19 PM
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?
 
10:23 PM
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
 
10:30 PM
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
 
10:39 PM
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 $g_8$.
 
11:05 PM
@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
 
11:26 PM
@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
 
11:42 PM
@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
 
11:46 PM
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
"Having defined the group algebra, we may now define a representation of G over
R to be a unital RG-module."
 
@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
 
11:54 PM
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?
 
11:56 PM
@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?
 
11:58 PM
Hi guys. I have a question and if anybody can help me, I would be thankful. There is any law that says that the envelope coincides with the wave front for any n? If I am not wrong huygen's principle is valid just for even dimensions.

There is some part of huygen's principle which is valid for all dimension?
 
@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
 

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