@ACuriousMind @Obliv In particular, I am very very VERY bad at physical thinking, which is why I often end up doing a lot of unnecessary algebra crunching while a problem can actually be solved via a clever trick
: 28517217 I also have a weird attitude to mathematics and physics, in that I often found myself solving physics problems like a mathematician, and mathematics problems like a physicist
For example one reason why I can remember the Exchange Lemma of linear algebra is because the way it is proved reminds me of phagocytosis
Quantum fields are weird. You cannot even think of them as something similar to orbitals because even orbitals have some definite shape.
They are not like chaos either because they don't generally have a fractal like structure nor resemble a strange attractor
As the answer said, all you can really said is that in some region, the field take nonzero values, and these nonzero values don't generally distribute like a lump because fields cannot be localised in general
QUOTE: And what I have said above is only an approximation because in general you can't localise a field so that it only has a non-zero value in some bounded region. The best you can do is change the field so that you will have a higher probability of seeing a photon in some region.
The above discussion alone would mean that a photon doesn't have a trajectory, but in general the situation is even less trajectory friendly than that. Different photons with the same energy aren't distinguishable: all you can say is "there are so many lumps in the field in this region".
What I’ve gotten so far looks like this (I’m going to present everything as neatly as possible):
for part a) :
$d_{m’m}^{j}{(\theta)} = <jm’|e^{-i{\theta}J_{2}}|jm>$
now, I saw that Euler’s Equation is $e^{-ix} = cos(x) - isin(x)$. I went through, and did as follows:
$e^{{-i{\theta}}/2}|jm>...
To start with, it seems everywhere is so quiet, no club activities, chatroom is empty, not much major news, not much change in a day's routine
It's as if time has stood still, and the world is not really changing The only place where time seemed to be still flowing, is that there is slow progress in the research project
Im a Computer Science Student with String physisch background, nur vety wrack formal Math Education In physisch the most advanced Theorie coursr I Tool was Quantum statistics, nur I have absolutely no knowledge about Quantum Field theorys. What Books Wolf you recomend for me?
In a paper appearing today on arXiv, Wie et al. have used the close coincidence of the time of arrival of gamma rays from GRBs and the detection of single 3-30 TeV neutrinos at the IceCube observatory, to say that the velocity difference between neutrinos and photons is no bigger than
$$ | v-c | <...
Is there a similar notion to a transition state in particle physics, given how people working at accelerators often talked about how there are various channels that a particle can decay into, and we often talked about branching ratios and whether the energy momentum is sufficient to produce some particles with a certain rest mass?
And here I thought 12262 was alone this weird insistence to try and formulate SR and GR in terms of axioms that mostly only use set-theory. Turns out they can cite books on that.
Like...why would anyone waste their time formulating and working with strange axioms for Minkowski space if all you end up with at the end is just something that's equivalent to $\mathbb{R}^{1,3}$, anyway?
Microsoft deletes 'teen girl' AI after it became a Hitler-loving sex robot = Female bot goes loco at once; the girlie is evil extremist firebrand tart.
I'm having some trouble understanding the counting procedure for the number of independent components of Riemann curvature tensor $R_{iklm}$ in 4D spacetime. (The answer is supposed to be 20, but I'm trying to understand how so!)
Let's do it sequentially:
Since we are looking at a rank 4 tenso...
@Secret FYI (AIKWTYBWECAU!): My aim is to project the covector as a contour map in $\mathbb{R}^n$ onto the face of the n-parallelpiped that is opposite to the ith column vector so that the row vector information can be encoded into the pictorial representation. However, as this proof shows, there exists nontrivial cases where this is impossible, meaning that the pictorial representation has to be modified to address that
@Danu Thanks for that input, but let's break down Caroll's argument wherein he uses both symmetry and antisymmetry at once. I mean, I am thinking more on the lines of Weber, Arfken, Harris, wherein we want to see how antisymmetry reduces 256 to 36 first up, and only later, you place the requirement of symmetry which reduces the no. to 21.
@TheDarkSide I find your post very hard to read, and I don't get what it is that confuses you about the 36. You have to choose the first and the second and the third and the fourth index as pairs of distinct indices, since the tensor vanishes if the first/third is the same as the second/fourth. From $\{1,2,3,4\}$, you can sample 6 such pairs: 12,13,14,23,24, and thus 36 possibilities to choose two such pairs.
Thanks @Danu and @ACuriousMind - because I seem to have understood that argument, and because I feel silly for not having got it directly, I now feel tempted to think harder to make sense of those 112 vanishing components and 84 double counted ones, before I ask in this chat.
@Danu I mean I really don't know what you mean when you say life outside academics. Most of the time I just read something - it may not always be math I am reading. Would you consider that academic activity?
I suppose, if you're an undergraduate or beginning grad student, anything you do because you think it will help you in a class (one you're currently taking, or one you expect to take in the future) counts as academics. Anything else counts as non-academic life.
What I’ve gotten so far looks like this (I’m going to present everything as neatly as possible):
for part a) :
$d_{m’m}^{j}{(\theta)} = <jm’|e^{-i{\theta}J_{2}}|jm>$
now, I saw that Euler’s Equation is $e^{-ix} = cos(x) - isin(x)$. I went through, and did as follows:
$e^{{-i{\theta}}/2}|jm>...
Im a Computer Science Student with String physisch background, nur vety wrack formal Math Education In physisch the most advanced Theorie coursr I Tool was Quantum statistics, nur I have absolutely no knowledge about Quantum Field theorys. What Books Wolf you recomend for me?
I'm having some trouble understanding the counting procedure for the number of independent components of Riemann curvature tensor $R_{iklm}$ in 4D spacetime. (The answer is supposed to be 20, but I'm trying to understand how so!)
Let's do it sequentially:
Since we are looking at a rank 4 tenso...
