## Thursday, October 24, 2013

### Spacetime kills the second law of thermodynamics, real or paradox?

This summer, among many other things, have read the famous book of Susskind and Lindesay about black hole information paradox. Casually just after finishing ir's reading I have to teach in private tuition (hope I am saying it right ) statistical mechanics (a conventional introduction with the main average topics). In doing that I have revised the foundations of it from the viewpoint of what I had read in the Susskind, and also some other aspects that one must face when triying to apply  statistical mechanic reasoning to non physical problems (for example ecology (I collaborated with a guy working in mathematical ecology for a while).

There are a few things that I am thinking about, but for the present entry I will concentrate in an easy mental experiment that, at least apparently, violates the second law of thermodynamics. The key of the violation is the lack of a proper definition of energy in general relativity, but for the present case I don't even need to go into mathematical details about it. My idea was clear, take a situation where that problem in the energy definition rises a paradox that violates the second law. I tried a few strategies that possible also work, but in the end I found a really easy one that I think is simple and representative.

I have found that the easier way of attack is to use the Clausius enunciate: No physical process can transfer heat from a cold body to a warm one. The way to circunvate the law is as follows: Take two  "black bodies", for example the canonical ones consisting of a cavity with photons in equilibrium with the walls that are at different temperatures. Now in the warmer one open the also canonical small hole that allow a photon, or a few ones, to scape. This is made in an expanding universe, the photons that have exit form the body travel in that space time loosing energy. Them they arrive at the coldest body. The photons of the warmer body initially had more energy that the ones in the coldest body, but now, after travelling in the expanding space time, arrive to the second with less energy that the photons in the cold body. That means that the cold body becomes coldest after it gets in equilibrium with that photons. Now we make the reverse procedure, we send some photons from the cold (now coldest) body to the warmest one. But, as this is an imaginary experiment, choose to do so when the universe is contracting (for example we make the experiment in the edge of the time when a FRW goes for the expanding to the contracting phase). In the travel on this contracting universe the photons gain energy and when they arrive to the warmest body they can be, if we wait enough, be more energetic than the ones in equilibrium with the warm body and so they actually  drive it hotter. As far as we can make the experiment as far as we want from anything else we are in a closed system and in that closed system we have effectively transferred heat from a cold body to a hot one, breaking the second law.

Of course we have not counted the entropy of spacetime, but how could we do so? In the Hawking laws of black holes we learned that classical gravity worked as entropy, the area of a black hole playing the role of entropy. And  it is well known how the Hawking radiation, a semiclassical effect (so taking quantum mechanics into play) gave a further argument. String theory (and ulterior works using  only geometry and CFT, the kerr/CFT correspondence) gave microscopic support to that correspondence among gravity and thermodinamics. And also are were known the, probably wrong, ideas about gravity as entropy, that have gained a rebirth with the paper of Verlinde about "gravity as en entropic force". But in this mind experiment I don't use nothing special in GR, something like an horizon, or quantum effects. Neither is any claim about saying that gravity is entropy. The whole point is that, if there is no mistake, if you don't know how to count the entropy of the spacetime, in this nonstationary case, you can violate the second law of thermodynamics, and that looks very unfunny, isn't it? ;)

The most similar situation that I know is the famous case of Hawkings telling once (and later felling shame about the idea) that in a contracting universe entropy would go in the opposite direction, and the worries of Sean Carrol and others about the thermodynamic arrow. But as far as I know none made such an explicit case as the one I am presenting here.

Just to avoid some trivial criticisms I clarify that in GR the energy of a body (or a system of bodies) is the time component of a cuadrivector, so it is not an invariant. As E=Q-W (first law) and $\Delta S= \Delta Q /T$ entropy also should be some time component of some cuadrivector and that makes it's precise definition somewhat tricky, but as far as I see this experiment could be suited in a single reference system so we don't need to care about that things.

Well, this is the idea, and probably I am making some very trivial mistake, or this simply has already been considered and discarded, but as I don't know for sure than that is the case I present the idea here so anyone can blame me if necessary ;).

## Friday, September 27, 2013

### Conference about the inmeditate future of particle physics afther the Higgs discovering

As you can have read in the Peter Woit blog this week there was a meeting in Madrid, in the institute of theorethical physics, auspiced by the CSIC (consejo superior de investigaciones científicas, close to the UAM , autonomous university of Madrid) with the title " Why mH= 126 GeV? .

The conferences have been recorded in video and are available online (including the slides). This morning is having place the last set of talks. IT begins at 10 00 so if you live somewhere in the UE maybe you still can get a plane and arrive to the dinner after the last talk, or, if you live in Madrid you can get the next train or bus to Cantoblanco and probably you could arrive to most of the talks.

I find the topics pretty interesting from a phenomenology viewpoint because some clues on where to be reasonable to watch for new physics. I'll try to post some review of the most interesting ideas exposed if I find time for it.

## Monday, May 06, 2013

### Proposal for an Ig Milner prize (or trantor prize)

Ok. Now that we have the Milner  prize I think that it is time to go a little bit further. The nobel prize has it's counterpart, the Ig nobel, so it would be fun to have an  Ig Milner. or Trantor prize. remember Trantor is the planet that is the centre of the galactic empire in the Asivmovs book's about the foundation.  In that literary universe physics has discovered almost everything and the physicists mainly get prestige by doing formal or ideological revisions of the already established physics which have not consequence in making new discoverings (they even don't care about it).

Well, the idea would be to give a symbolic prize to works that are superficially correct but are totally useless, or even make no sense at all when one looks at it's closely. I think that they would also be works which are specially ambitious and prepotent. To avoid injuring people who is beginning and could get too injured in their professional life by the bad press I guess that it would be better that the candidates to the prize would be people with a well established position.

Also it could be given a prize -maybe in an slightly separate category- to papers that are correct but specially fun, or exotic.

For the first edition I would make a few suggestions.

One candidate would be the AMPS paper about firewalls. Better than trying to explain the details myself  I suggest reading some posts of Lubos on the subject, this being the last one at the date of writing this:

### An apologia for firewalls

An even better candidate, in my humble opinion, would be Lee Smollin for his last book. I would link the Lubos review but I think that would be to unfair because it is well known that "crackpot" is the more polite word that could characterise Lubo's opinion about Smollin.   That's why I give a link to Sabines blog, who also have a closer knowledge of Lee because she was a former collaborative of him: Book review: “Time Reborn” by Lee Smolin.

Well, my last candidate would be for the exotic side. It is an article where the author - Benjamin K. Tippett - designs a metric that could fit a literary writing by Francis Wayland Thurston. The whole felling of the paper is something like a scientific description of the worlds of chuthlhu. I give here the link and the abstract:

# Possible Bubbles of Spacetime Curvature in the South Pacific

In 1928, the late Francis Wayland Thurston published a scandalous manuscript in purport of warning the world of a global conspiracy of occultists. Among the documents he gathered to support his thesis was the personal account of a sailor by the name of Gustaf Johansen, describing an encounter with an extraordinary island. Johansens descriptions of his adventures upon the island are fantastic, and are often considered the most enigmatic (and therefore the highlight) of Thurstons collection of documents.
We contend that all of the credible phenomena which Johansen described may be explained as being the observable consequences of a localized bubble of spacetime curvature. Many of his most incomprehensible statements (involving the geometry of the architecture, and variability of the location of the horizon) can therefore be said to have a unified underlying cause.
We propose a simplified example of such a geometry, and show using numerical computation that Johansens descriptions were, for the most part, not simply the ravings of a lunatic. Rather, they are the nontechnical observations of an intelligent man who did not understand how to describe what he was seeing. Conversely, it seems to us improbable that Johansen should have unwittingly given such a precise description of the consequences of spacetime curvature, if the details of this story were merely the dregs of some half remembered fever dream.
We calculate the type of matter which would be required to generate such exotic spacetime curvature. Unfortunately, we determine that the required matter is quite unphysical, and possess a nature which is entirely alien to all of the experiences of human science. Indeed, any civilization with mastery over such matter would be able to construct warp drives, cloaking devices, and other exotic geometries required to conveniently travel through the cosmos.

Of course everyone is free to make his own suggestions, and, if they don't like the idea, to explain their reasons.

## Thursday, March 21, 2013

### And the third milnor prizes goes to Polyakov (maybe)

I didn't write a single line about the second milner prize so I'll write a brief post about the third.

As can be read in "not even wrong" and in the blog of matt strassler it seems (but is not confirmed at the time of writing this entry) that the winner of the this third prize is Alexander Polyakov.

Everybody who has ever read a book on string theory know the name because of the Polyakov's action and the Polyakov path integral that are the very basics of the worldsheet aspect of string theory. Besides string theory Polyakov has made very valuable contributions to QFT such as instantons and magnetics mopopoles.

All in one it is clear that the prize is absolutely well deserved. In fact my only concern is why he hasn't also a nobel prize. It is absolutely clear that there are people awarded with a nobel who have by far less merits than Polyakov for the prize. Well, at this point I think that among theorists the milner prize should be more valued than the nobel not only for the money but for the prestige of the previous winners.

By the way, if someone wonders why I write so few posts in the last times there is an easy answer: The LHC is doing a hard work to hide any possible evidence of physics beyond the standard model. The Higgs is of the most boring type possible and no SUSY, no extra dimensions no nothing. Well, this is not the end of the world for theorethical physcis and it is sure that some surprises could be around the corner (but maybe not where people usually expects them xD) but it would have been fun to have some BTSM physics in colliders at this point.

## Friday, November 23, 2012

### Mathajax, note 10.1 and more

I have become really tired of the problems to have a proper way to display math in blogspot. I had previously used a latex renderer but I have had problems with it. On one hand the server has changed in a few occasions, and in another the blogspot people have deleted the modifications of the template that allows the to be used.

Because of that I had become somewhat frustrated. After all some entries with maths in this blog doesn't work any more and I don't like the idea of change the template every time that the server of latex changes in the future.  I have been observing that from a months to now the Lubos blog uses mathajax and it looks like it is an stable solution so I have decided to give it a chance.

This a text equation using the mathajax plugin:

$ds ^2=H^{-2} dt^2 + H^2 dx^2$

Ok, to have an easy way to display formulas is fun, but it is only part of the game. You need to write them. That seams a trivial task, write the latex code. Yeah, it is truth, I know the latex code for math and I know how to write a full Latex document also, of course. But, you know, that is "last year technology. I mean, this year has arrived the note 10.1, the tablet version of the note family of tablets. It was presented in February  at the MWC in Barcelona (Spain) and it arrived the stores (and my home the very first day it was on sell) this September. Among the many goodies of that tablet is the math handwriting recognition that you can see working in this video:

That feature works really ok. it recoginzed well ther formula  (the plain text handwriting recognition works also fine, of course) and send the equation to wolphram alpha (if you want so) but it has an annoying aspect, it doesn't allows you to get the latex code that correspond to the formula. This feature has also been added to the phablets and I have used it in the note 5.3 (the original) form around march, long before getting the note 10.1. That means that writing an equation using latex has become a "too primitive" way to do things.

Well, I have been learning to do android programs. But as far as I have had a bad experience in the recent past with writing for the symbian platform (I ended an app, send it to the nokia store, passed the quality standards, but never seen it published in the store so I have not made any money of the app) I have been somewhat reluctant to get too involved in that business. Still I have learned enough to know the theory of how to do a virtual keyboard that could allow write latex in a really easy way. I mean, for writing an alpha letter you need to type \alpha, and similar for other greek letters. It would be easiest to have an $\alpha$ symbol in the keyboard and that when you type it it would appear in the suggestion bar (candidate view) the option to write the latex code (that would be the default one), the mathajax code or the actual character. And similarly for many other math symbols. Maybe in the future I could make this keyboard, but if somewhat reading this blog entry decides to do it before I wouldn't ask him any money for the idea ;).

Well, a latex keyboard would be fun. But it would be better still that the math recognition of the note would allow the option to show the latex code. I know that there is a SDK for the S-pen of the note, but I don't know if it allows access to the code of the math recognition program (I seriously doubt it, but I still have not watched too much the SDK). If so it would be fine that somewhat would try to write a variant of the S-note program that would include that latex presentation option. Of course if someone of Samsung reads this entry they are invited to include that functionality in an update. I really like the note tablet and I absolutly think that is the best tablet of the moment, specially for people who need to use equations often. If that LaTeX extra functionality is added it would convert a wonderful product into an even better one :)-

## Sunday, August 12, 2012

### The arrival of the Milner prices of fundamental physic

This month came by surprise a new international prize for physicists. It is oriented for works of relevance in theoretic development, even if the theories worked hasn't be tested and they can't probably be for a large amount of time. It is created by a Russian physic doctorate Yuri Milner and it is named Fundamental Physics Prize.