# Shores of the Dirac Sea

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## Unstable Universes

Posted in gravity, high energy physics, Physics, thermodynamics on February 19, 2013 | 7 Comments »

It’s a fine day for the Universe to die, and to be new again! Well, maybe not, but the Internet is abuzz with a reincarnation of the unstable universe story. (You can also see it here, or here, the whole thing is trending in Google). In other works, this is known as tunneling between vacua. And if you have followed the news about the Landscape of vacua in string theory, this should be old news (that we may live in a unstable Universe, which we don’t know). For some reason, this wheel gets reinvented again and again with different names. All you need is one paper, or conference, or talk to make it sound exciting, and then it’s “Coming attraction: the end of the Universe …. a couple of billion years in the future“.

The basic idea is very similar to superheated water, and the formation of water bubbles in the hot water. What you have to imagine is that you are in a situation where you have  a first order phase transition between two phases. Call them phase A and B for lack of a better word (superheated water and water vapor), and you have to assume that the energy density in phase A is larger than the energy density in phase B, and that you happened to get a big chunk of material in the phase A. This can be done in some microwave ovens and you can have  water explosions if you don’t watch out.

Now let us assume that someone happened to nucleate a small (spherical) bubble of phase B inside phase A, and that you want to estimate the energy of the new configuration. You can make the approximation that the wall separating the two phases is thin for simplicity, and that there is an associated wall (surface) tension $\sigma$ to account for any energy that you need to use to transition between the phases. The energy difference (or difference between free energies) of the configuration with the bubble and the one without the bubble is

$\Delta E_{tot} = (\rho_B-\rho_A) V +\sigma \Sigma$

Where $\rho_{A,B}$ are the energy densities of phase A, phase B, $V$ is the volume of region B, and $\Sigma$ is the surface area between the two phases.

If $\Delta E_{tot}>0$, then the surface term has more energy stored in it than the volume term. In the limit where we shrink the bubble to zero size, we get no energy difference. For big volumes, the volume term wins over the area, and we get a net lowering of the energy, so the system would not have enough energy in it to restore the region filled with phase B with phase A. In between there is a Goldilocks bubble that has the exact same energy of the initial configuration.

So if we look carefully, there is an energy barrier between being able to nucleate a large enough Goldilocks bubble so that there is no net change in energy from a situation with no bubble. If the bubbles are too small, they tend to shrink, and if the bubbles are big they start to grow even bigger.

There are two standard ways to get past such an energy barrier. In the first way, we use thermal fluctuations. In the second one (the more fun one, since it can happen even at zero temperature), we use quantum tunneling to get from no bubble, to bubble. Once we have the bubble it expands.

Now, you might ask, what does this have to do with the Universe dying?

Well, imagine the whole Universe is filled with phase A, but there is a phase B lurking around with less energy density. If a bubble of phase B happens to nucleate, then such a bubble will expand (usually it will accelerate very quickly to reach the maximum speed in the universe: the speed if light) and get bigger as time goes by eating everything in its way (including us). The Universe filled with phase A gets eaten up by a universe with phase B. We call that the end of the Universe A.

You need to add a little bit more information to make this story somewhat consistent with (classical) gravity, but not too much. This was done by Coleman and De Luccia, way back in 1987. You can find some information about this history here. Incidentally, this has been used to describe how inflating universes might be nucleated from nothing, and people who study the Landscape of string vacua have been trying to understand how this tunneling between vacua might seed the Universe we see in some form or another from a process where these tunneling events explore all possibilities.

You can reincarnate that into Today’s version of “The end is near, but not too near”. We know the end is not too near, because if it was, it would have already happened. I’m going to skip this statistical estimate: all  you have to understand is that the expected time that it would take to statistically nucleate that bubble somewhere has to be at least the age of the currently known universe (give or take). I think the only reason this got any traction was because the Higgs potential in just the Standard model, with no dark matter,  with no nothing more in all its possible incarnations is involved in it somehow.

Next week: see baby Universe being born! Isn’t it cute? That’s the last thing you’ll ever see: Now you die!

Fine print: Ab initio calculations of the “vacuum energies”  and “tunneling rates” between various phases are not model independent. It could be that the age of the current Universe is in the trillions or quadrillions of years if a few details are changed. And all of these details depend on the physics at energy scales much larger than the standard model, the precise details of which we don’t know much at all. The main reason these numbers can change so much is because a tunneling rate is calculated by taking the exponential of a negative number. Order one changes in the quantity we exponentiate lead to huge changes in estimates for lifetimes.

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## Bad science reporting versus good science reporting

Posted in thermodynamics, tagged science reporting, thermodynamics on January 4, 2013 | 3 Comments »

Today I was greeted with the following line

Quantum Gas Temperature Drops Below Absolute Zero

This is the way the news about a quantum system that is effectively at negative temperature was reported in Wired. The thing is, negative temperatures are hotter than any finite positive temperature.

One can also check this fact in the Wikipedia entry for negative temperature. The simplest system that has an effective negative temperature is a laser: to get a negative temperature one just needs what is called a population inversion.

In that report it was stated that

Previously absolute zero was considered to be the theoretical lower limit of temperature as temperature correlates with the average amount of energy of the substance’s particles.

The crucial mistake is the expression “Previously absolute zero was considered” which suggests that we have overturned theoretical physics knowledge on its head, because a new and revolutionary temperature below zero has been obtained! Moreover, we have measured systems with negative temperatures at least since the invention of the laser, and actually since the invention of the maser ( a laser in the microwave region).

The news is actually  well reported in Ars technica. In that article they actually explain facts correctly about how to think about negative temperatures.

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## Gravity does not exist?

Posted in Academia, Quantum Gravity, science and society, thermodynamics on July 13, 2010 | 31 Comments »

I happened onto an article on the New York Times abut Erik Verlinde’s take on gravity as an Entropic force. The article was written by Dennis Overbye who most of the time does  a good job of covering high energy physics.  Erik’s work dates from earlier this year and can be found here. To tell the truth, I don’t understand what he’s trying to say in that paper and to me it feels like it’s almost certainly wrong.

However, I don’t want to discuss that paper. What I want to discuss is the following  provocative quote

“We’ve known for a long time gravity doesn’t exist,” Dr. Verlinde said, “It’s time to yell it.”

I don’t believe this is taken out of context,  so we should take it at face value. The statement is obviously wrong, so it sounds like ultra-post-modern pap and makes all physicists working on the subject of quantum gravity look like crazy mad men. I’m sure this sells newspapers, but that is not the point.

When asked for a sound byte can’t people at least say something that is correct and not just provocative?

The proper way to write that statement is that “Gravity is not really a fundamental force “, which is more correct and does not deny gravity its proper place as something that has been observed in nature, however it is less catchy. If we apply the same criteria as used in the above construction, all of the following statements are also correct:

• Hydrodynamics does not exist (it only happens for collections of atoms, but not for individual ones)
• Space and time do not exist (often used when talking about quantum gravity being emergent from somewhere else)
• All emergent phenomena do not exist (they are not fundamental after all).
• I do not exist (I’m an emergent phenomenon).

Reminds me of discussions I have read before at Backreaction, here and see also  here in the Discover magazine about time not existing.

You should also read the following from Asymptotia: But is it real? and also a discussion on What is fundamental, Anyway?

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## Black holes as frozen stars

Posted in gravity, high energy physics, quantum fields, Quantum Gravity, relativity, string theory, thermodynamics on February 19, 2009 | 13 Comments »

We now have a few working examples of a microscopic theory of quantum gravity, all come with specific boundary conditions (like any other equation in physics or mathematics), but otherwise full background independence. In particular, all those theories include quantum black holes, and we can ask all kinds of puzzling questions about those fascinating objects. Starting with, what is exactly a black hole?

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## Maldacena’s information paradox

Posted in high energy physics, Quantum Gravity, string theory, thermodynamics on January 15, 2009 | 55 Comments »

Back in 2001, in a truly beautiful paper, Juan Maldacena formulated a version of Hawking’s information paradox, which has the added advantage that it could be discussed and analyzed in the context of a complete background independent theory of quantum gravity, namely that of the AdS/CFT correspondence.

This variant is similar to the original paradox, formulated for black holes surrounded by flat space, in that it displays a sharp conflict between properties of black holes in classical General Relativity, and basic postulates of quantum mechanics. Alas, it is also different in many crucial ways from the original paradox. Despite that, Juan’s proposed resolution to his paradox seems to have led to Hawking’s arguments, who managed to convince himself (though I think it is fair to say not too many others, unless they were already convinced) that information is not lost after all in the process of black hole formation and evaporation.

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## Everyday physics: pressure cookers.

Posted in Physics, recipes, thermodynamics, tagged hummus, Physics, pressure cookers, recipe, thermodynamics on September 17, 2008 | 12 Comments »

Most graduate students out there can at times feel a lot pressure to perform. Heck, that is not just graduate students. Pressure at work seems to be one of those things that most people can relate to and feel all the time. It gives rise to a lot of stress. I don’t have any good recipe for combating stress that is guaranteed, but cooking sometimes helps. Seeing as what I just wrote is not too funny, maybe I should get to the point and talk about Pressure cookers and as a bonus you get a cooking recipe (no peeking). When in doubt, pick a gadget and explain it, yes sireee. Besides, the explanations that I found on the internet about how pressure cookers work teeter on the edge of crackpottery. Not all are bad, but most don’t really say anything other than water boils at higher temperature at higher pressure which is correct, but unsatisfying. It’s like saying it just works that way.

My 3d rendition of a pressure cooker

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