/sci/ - Science & Math

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>>4549097
i'm not anywhere near cern, but that's what everyone in my department is claiming. i don't share the same opinion. i'm sorry for sounding so hostile.

>>4549057
yeah, i know. all i've been hearing so far though is that it was 'a bad idea', lol.

>>4549070
in addition to what i’ve mentioned, there are many other formulations (such as those found in string theory) which use gauge-gravity duality to take a large-n limit onto qft, or to formulate gravity in some manner with open strings on branes.

this is one of the clearest non-mathematical explanations i’ve found:
http://arxiv.org/abs/gr-qc/0602037

If you know a bit of math, i’d be happy to elaborate further.

the ‘holographic universe’ is derived and related to the concepts of ads/cft, ads/qcd, gauge-gravity duality, etc. it’s a very interesting formulation of cft and may have some physical reality; and even if not it has countless applications in other fields of physics (fluid dynamics and solid state stuff, mainly). personally, i do a lot of work with lattice/monte-carlo simulations, so i'm actively using ads/qcd in my code all the time.

holography cannot be explained easily without some sort of background in mathematics - laden in topology, manifolds, and geometry. the most common type of holography is matter/information/energy/whatever projected onto a conformal boundary. you can imagine particles in space (three dimensional of course) ‘projected’ onto a piece of paper that you curved a little bit so it appears as if it were a sphere. this is the lower dimensional limit, as the paper (for our example, here) is two dimensional. the particles floating around in this higher 3d space, after some conformal transformations, very specific physical conditions (mainly involving gravity/coupling strength), and mathematical manipulation, appear as ripples or ‘fluctuations’ on this piece of paper. everything described on the paper can be translated into the higher three dimensional space, and vice versa. that's pretty much it. anything more in depth than this is /very/ difficult to explain in nontechnical terms, and i (and i’m sure any other physicist on here) couldn’t do it here without taking up pages.

the standard case is to think of a mixed loop representation with some loops assocated to one theory, and the rest to another. this is valid for all yang-mills fields coupled to gravity, with each gauge field individually treated quantizable. the problem then arises on coupling to a high energy unified theory, which is where loops break down, and the non-fantasy land divisions of physics kick in.

i cannot believe this shit is allowed to be published.

tegmark should honestly give us a public demonstration to confirm his crackpot logic.

this looks like a fun thread. pic related is a pretty hot topic right now, especially with the pushes to cut cern funding.

>- what do I need to know?
you need to like and appreciate the field - do not go into it otherwise, as you'll waste a spot for someone else who enjoys it and has the potential to contribute. you will be in debt. you will not get a good pay. you must do research in undergrad to get into a decent graduate study program.

>- how long will it take?
3 years for undergrad + roughly 4 for grad. i'm wrapping up my program much quicker (again it varies on what you are doing/how efficient you are), i'll be in postdoc next year with my dissertation done in a couple of months from now.

>how much is it going to cost?
this is totally variable. undergrad will be pricey without scholarships if your in the united states. a doctoral program is practically free if you have a professorship and are doing research elsewhere, otherwise you're just going to get a pretty small stipend and qualify for food stamps.

this statement is too ambiguous to draw any conclusion from.

>>4544683
>>4544667
>>4544526
>>4544502
>>4544294
i'll have to agree with this.

>>>/x/

>>4543889
and who are you? some first-year knucklehead? wait till you get to postdoc, kid, or actually do some research. formalism is crucial for clarity, especially if it can completely change what the term means if you slay away from the standard notation. if you've noticed, i worked out the entire solution for him. this problem is obviously part of a proof showing that a massive vector field has so-and-so many degrees of freedom (else what is the point of including some of those terms in the action), and confusing four vectors with cosmological constants is asking for trouble. i've been doing physics for a very long time, and enjoy it greatly. i like to prepare students to go out in the field and communicate effectively with others without having to spend time circle jerking notation. you cannot communicate an idea effectively using broken english.

>>4544036
it is still sloppy, and it correlates to poor understanding of what the action in the problem is representing. the op originally didn't even know what all of the terms were if you've read correctly.

>>4543840
lol. you need to compute the variation of the action, which in the general case looks something like
<div class="math">\delta \mathcal{S} = \int \delta \phi \frac{\partial \mathcal{L}}{\partial \phi}
+ \delta(\partial_\mu \phi) \frac{\partial \mathcal{L}}{\partial (\partial_\mu \phi)}
+ \delta x^\mu \frac{\partial \mathcal{L}}{\partial x^\mu} \,</div>
then integrate by parts and set <span class="math">\delta S = 0[/spoiler]

this thread is too pathetic.

this appears to be pretty trivial - just use wick's theorem for (a), (b) should follow readily for an ordered operator product expansion, it's just plug and play... and to top it all off you're already given it wick ordered. what exactly do you not understand?

have some decent lecture notes from one of my old colleagues, operator product expansion i believe is covered in some detail:
www.physics.ucla.edu/~nayak/qft-temp.ps

if you don't know what wick's theorem is (you should've taken complex analysis to be in qft, lol), consider an integral of the form
<div class="math">\frac{1}{\sqrt{2 \pi}} \int_{\mathbb{R}} t^{2k} e^{-t^{2}/2} \mathrm{d} t = (2k-1)!! = (2k-1)(2k-3) \cdots (3) (1)</div>

chaos theory? on /sci/? awesome!

anyhow, there aren't any finite attractors as
<div class="math">f^{(n)} (x_{0}, \theta_{0}) = (x_{n}, \theta_{n} mod(2 \pi))</div>
plugging this into mathematica, you can see that
<span class="math">x_{n}[/spoiler] tends to <span class="math">\pm \infty[/spoiler], except for the set <span class="math">x=g(\theta)[/spoiler] (which is unstable).

there are a very few number of solutions to the efes that support 'anti-gravity'. regardless, they are incorrect in some way or another. anti-gravity is fictitious.

>>4545449
oh, right. i forgot /sci/ doesn't support matrices. oh well. you can read the tex yourself.

this really isn't graduate level, but okay...

<div class="math">\sum_{i=1}^{n} y_{i} \mathrm{d} x^{i} |_{p} = \sum_{i=1}^{n} y_{i} \sum_{k=1}^{n} \frac{\partial x^{i}}{\partial x'^{k}} \mathrm{d} x'^{k} = \sum_{k=1}^{n} \left ( \sum_{i=1}^{n} y^{i} \frac{\partial x^{i}}{\partial x'^{k}} \right ) \mathrm{d} x'^{k}</div>
so for a transition map you get
<div class="math">(\psi \circ \phi^{-1})(x^{1},\ldots ,x^{n}, y_{1}, \ldots y_{n}) = (x'^{1}, \ldots , x'^{n}, y'_{1}, \ldots y'_{n})</div>
here <span class="math">y'_{k}[/spoiler] is defined as <span class="math">\sum_{i=1}^{n} y^{i} \frac{\partial x^{i}}{\partial x'^{k}}[/spoiler], where <span class="math">k= 1, \ldots , n[/spoiler]

so the block diagonal matrix is
<div class="math">\frac{\partial (x'^{1}, \ldots , x'^{n}, y'_{1}, \ldots y'_{n})}{\partial (x^{1}, \ldots , x^{n}, y_{1}, \ldots y_{n})} = \begin{pmatrix} \frac{\partial (x'^{1}, \ldots , x'^{n})}{\partial (x^{1}, \ldots , x^{n})} & 0 \\ \frac{\partial (y'_{1}, \ldots , y'_{n})}{\partial (x^{1}, \ldots , x^{n})} & \left ( \frac{\partial (x^{1}, \ldots , x^{n})}{\partial (x'^{1}, \ldots , x'^{n})} \right ) \end{pmatrix}</div>
so then you have
<div class="math">\frac{\partial y'_{k}}{\partial x^{j}} = \sum_{i=1}^{n} y^{i} \frac{\partial}{\partial x^{j}} \left ( \frac{\partial x^{i}}{\partial x'^{k}} \right )</div>
the determinant is easy.
<div class="math">\det \left ( \frac{\partial (x'^{1}, \ldots , x'^{n}, y'_{1}, \ldots y'_{n})}{\partial (x^{1}, \ldots , x^{n}, y_{1}, \ldots y_{n})} \right ) = 1</div>

so, for any two charts in this atlas on <span class="math">T^{*} M[/spoiler] you have a positive determinant (1), implying <span class="math">T^{*} M[/spoiler] is orientable.

>convince politicians
this would/can never happen.

<div class="math">\mathbf{F}=\frac{d}{dt}(m\mathbf{v})</div>

pic related.

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