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PhysicsOverflow

A new Question and Answer site for Physics at a graduate-level and above has started last week on Friday (not yesterday, the week before). The site is called PhysicsOverflow and can be found at http://physicsoverflow.org. The name is in analogy to MathOverflow, or MathsOverflow, a “research-level” (relating to cutting-edge research) Mathematics Q&A site found at http://mathoverflow.net. The site seeks to be a high-level Q&A site combined with a “Reviews” section for refreeing research papers, etc.

A wide variety of subfields, including Theoretical Physics, Experimental Physics, PhenomenologyAstronomyComputational Physics, Applied Physics, Mathematics which need a physicist’s point of view, and generally Physics, are on-topic on PhysicsOverflow (PO/PhO).

It is worth to see the welcome post containing somethings useful for a new user to the public beta, and the to-eventually be comprehensive FAQ.

Wait, public beta? Does this mean that the site will go down if it doesn’t receive enough activity?

No. The term “public beta” is used because there are a few important things remaining to be done during this phase:

  • Install any needed plugins, etc. and focus on site design and a physics-ish look to the site.
  • To watch how fast users gain reputation, and set reputation-based permissions based on this.
  • Import the graduate-level questions remaining to be imported from Physics Stack Exchange.
  • Write a lot of tag wikis.
  • Work on creating a “Reviews” section for reviewing research papers etc.

What is the “Reviews” section about? See my post here.

Regarding the software, the following is copied from my post here:


 

We use Question2Answer v1.6.2 with the following standard Q2A-provided plug-ins:

  • Basic AdSense (not enabled yet)
  • FaceBook Login (will never be enabled)
  • Event Logger
  • reCaptcha
  • Tag Cloud Widget
  • XML Sitemap

The following external plug-ins:

And the following plug-ins by polarkernel:

  • Physics Overflow Attributions 
  • Physics Overflow MaThJaX 
  • Merge User Accounts 
  • Regain TP account page (disabled)
  • Reset account 
  • Search for User 
  • Import SE thread  
  • Physics Overflow Buttons Plugin  
  • Correct User   
  • Rename User 
  • Adjust Imported Votes
  • Reverse Serial Voting  

The theme that we use the PhysicsOversnow (officially PO-theme) by polarkernel which is based on the Snow theme by Q2A market.

AnchorBelow are some differences from the SE software:

Stack Exchange Physics Overflow (Q2A)
Comment Voting Only positive Positive and Negative
Vote Counts   Net score displayed[1] Vote counts displayed
Downvote rep change A fifth or two of upvotes Same as upvotes
Accepting answers Yes[2] Disabled
Approve suggested edit 2 users needed 1 user enough
Bookmarking “Favouriting”[3] Bookmarking[4]
Autodeletion Inactive questions auto-deleted Questions never auto-deleted
Comment length $\leq$ 600 characters Almost unlimited

[1]: Users with at least 1k rep, or who have installed a userscript, may click on net score to see vote counts

[2]: The idea of accepting answers was completely unnecessary as the decision gives the false impression that the accepted answer is really the best.

[3]: And prominently displayed near the “upvote”/”downvote” buttons, making it a misleading cue for  question rating.

[4]: Can be used for any purpose wanted, but should not be mixed up and made a cue for question rating

2013 in review

The WordPress.com stats helper monkeys prepared a 2013 annual report for this blog.

Here’s an excerpt:

A New York City subway train holds 1,200 people. This blog was viewed about 6,400 times in 2013. If it were a NYC subway train, it would take about 5 trips to carry that many people.

Click here to see the complete report.

The Friedmann Equation, the FLRW Metric, the Cosmological Constant, and Dark Energy

A short overview.

Experimental tests of String Theory

Edit: By the way, have a look at this: http://arxiv.org/find/all/1/all:+AND+kane+AND+kumar+acharya/0/1/0/all/0/1 a list of papers relevant to this topic.  

This post is intended to dismiss some of the claims that “String Theory isn’t testable“;.  So, let’s first list out some of the claims we hear about the experimental testability of  String Theory, in random discussions,  on comments by trolls on tRF , and by the well-known crackpots, (dubbed “Smoit”, but I suggest “Woilin”):

  • String Theory disagrees with well-known Physics!  
  • Ya, whatever, fine, but it agrees with everything, so that basically means that String Theory isn’t testable! It’s like, pseudo-science!  
  • Ok, ok, but it isn’t testable at today’s energy scales, alright? Ha!   
  • Well, fine, whatever, but it has been experimentally disproven!   
  • Ok, fine, WHATEVER, but it hasn’t been experimentally proven, at least, ok? Ha! How will you counter that?!    

Ok, so let’s counter each of them.

————————————————————————————————————————————————————————————————————-  String Theory does agree with well-known Physics.  

It is a trivial excercise to show that String Theory agrees with General Relativity.

One starts with the beta functionals, which describe the breaking of conformal symmetry due to the presence of the Dilaton. To keep Conformal Symmetry, these functionals must be set to be 0.

The coupling of the string to the Dilaton Field is described by the following action integral:

To derive the beta functionals, one may do this in Riemann Normal Coordinates (see at Wikipedia or at the n(Cat)Lab).

The breakdown of conformal invariance would then be: \\\

With the beta functionals given by:

To impose conformal invariance, these beta functionals must vanish, as follows:

These are the field equations for the graviton, dilaton, and photon fields respectively. Notice that they have a rather fundamental basis, conformal invariance. We need to focus on this one:

This is obviously the field equation for gravity. Notice that I have removed one term on the way. This term is . This is because I have assumed that the Riemann Curvature Tensor is negligibly small.

I don;’t need to.

However, in the limit of little gravity, and no dilaton, this becomes the ordinary vacuum Einstein Field Equation.

String Theory also agrees with the Minimal Supersymmetric Standard Model (MSSM) as shown by [1] (pdf  here).    Upon Supersymmetry breaking, this means that it also agrees with the Standard Model j.

————————————————————————————————————————————————————————————————————-  String Theory is testable.     

What does String Theory predict?

It predicts scattering amplitudes, caisimir energy, superpartners, gravitons, an infinitude of particles in a mass spectrum, gravitons, extra dimensions, AdS/CFT, and what not?  Talking about AdS/CFT, see this recent paper  by Raju and Papadogmias [2] (pdf here)   and this one by Papawdogmias and Raju [3] (pdf here).         This means the prediction of certain operators in the conformal boundary.

————————————————————————————————————————————————————————————————————-

String Theory is testable at today’s energy scales.        

Firstly, that isn’t a valid deleteion argument, as it  is still testable.

Secondly, the Supersymmetry-related predictions of String Theory just depend on a certain number of parameters, called the Supersymmetry breaking parameters. For an  supersymmetric string theory (like a manifold compactification of M-Theory), it is in fact possible to test the effects of supersymmetry, because the supersymmetry breaking  energy parameter is low enough!.

————————————————————————————————————————————————————————————————————-

String Theory has withstood experimental tests.       

Huh, no. The only experimental result in contrary to the predictions of String Theory is probably [4] (PDF here). Other than this,  String Theory has in fact been supported by experimental predictions. Also, the experiment does not rule out compactification lengths smallernthan half a milimetre.

————————————————————————————————————————————————————————————————————-

String Theory has had experimental verification repeatedly.   

See this article at the Mathematics and Physics Wikia (Introduction to String Theory)  for the entire list.

Note that the 125 GeV Higgs actually serves as an experimental support for String Theory.

————————————————————————————————————————————————————————————————————-

So basically, these criticisms of String Theory are just some ingeniously crafted Markov Chains, cooked up by a computer repairman at the Mathematics Department of the University of Columbia, aka the “Troll King“, and popularised by the popular media, such as “Scientific American”, a magasine devoted to making people unscientific and dog-ma-believing.

Kerr-Newmann Metric, Kerr-Newmann Black Holes

Kerr metric, Kerr Black holes, Kerr time dilation, Kerr everything!

Test – LaTeX 2: Wiki Pedia – style LaTeX (image) formatting.

\oint_C\left(\mbox{Random}^{\mathrm{rubbish}}\right)\cdot\mbox{d}\vec r = 0 …

Intuition behind AdS/CFT

I have used MathJax in this post, only to find that MathJax isn’t supported here. For the correct version, view my post at Psi Epsilon (MathJax).

Many of us may have heard of the AdS/CFT correspondence.

A $D$ – dimensional string theory in Anti-de-Sitter (AdS) space is exactly equivalent to $D-1$ dimensional Conformal field theory (CFT), such as Quantum Yang-Mills theory, etc.

That just sounds a bit crazy right? How can a string theory be equivalent to a mere CFT, of all things?

But in reality, the confusion only arises from the way it is phrased. It should be phrased in terms of the Holographic principle. Then you ask, “What is this Holographic principle?”.

The information stored inside a reigon is completely described by the information on its boundary.

Ugh…… The information inside a water bottle (which is the information in the water) is equivalent to the information on the bottle’s surface itself, which is the information in plastic? Is this alchemy, or something?

But holography is a law of nature and there’s nothing wrong about it. Let us start with some obvious examples.

1. Stokes’s theorem

Ok, consider a field originating from a certain point. To make things simple, let us say its a vector field, and it is actually the field of forces (field of the electromagnetic force, as opposed to an electromagnetic field, but the latter would work too). Now, let us say there is some 2-dimensional surface $S$ , with a boundary curve $C$. The work done by the force field along this curve, is given by:

$$\oint \vec f\cdot\mbox{d}\vec r$$

This really just follows from $\mbox{d} W=\vec F\cdot\vec r$. You may already start to see where this is going! What is the flux of the curl of the force field through the surface? We know that it is, equal to:

$$\iint_S\left(\nabla\times\vec f\right)\cdot\hat n \mbox{ d}S $$

(Admittedly, it is foolish to say the integral of the “curl of the force field”, because it has a very limited physical meaning, unless you use stokes’ theorem).

Now what does Stokes’ theorem, more specifically, the Kevin-Stokes’ theorem, say?

$$\oint \vec f\cdot\mbox{d}\vec r = \iint_S\left(\nabla\times\vec f\right)\cdot\hat n \mbox{ d}S $$

In other words, the flux of the curl through the surface, is exactly equivalent to the work done on the boundary, which is, the curve! .

2. Gauss’s theorem

Consider the sum of the divergences within a volume $V$. Then, Gauss’s theorem tells us that that is equivalent to :

$$\iint_S\vec f \cdot \hat n \mbox{ d}S = \iiint_V \nabla\cdot\vec f\mbox{ d}V$$

I.e. a property of the reigon is equivalent to a property of the surface.

3. Black holes

Consider two observers, observer A, and observer B, . Observer B is falling into a black hole, whereas observer A is outside. Then, for simplicity, say, the black hole, is Schwarzschild, so that the time dilation is then:

$$\frac{\mbox{d}t}{\mbox{d\tau} = \frac1{\sqrt{1-\frac{r_s}r}}$$

Which is an obvious result from the Schwarzschild metric.

Then, this means that Observer A is going to observe that Observer B’s time scales get shrunk, so that Observer B will appear to move towards the black hole slower, and slower, and finally stop at the event horizon. However, for Observer B himself, everything will appear normal, from his reference frame. I.e. what is going on inside the black hole (as observer B observes it) seems to go on on the surface of the black hole (the event horizon, of the black hole, now you know why it’s called an “event horizon”.) for Observer A. This is also a resolution to the Hawking information Paradox. The information is encoded on the event horizon, which is why it doesn’t disappear.

So, this just means that the information inside a reigon is completely encoded on to its boundary. So, this means, that,… ?

It is the Holographic principle.

Now, what about AdS/CFT?

$D$ – dimensional Anti-de-Sitter space has a $D-1$-dimensional boundary, which is governed by a Conformal field theory, and the Anti-de-Sitter space itself, is governed by a string theory.

So, in other words,

String theory in Anti-de-Sitter space is exactly equivalent to a Conformal Field Theory on its boundary.

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