The Week of 24-30 October in Astrophysics

Here are four interesting papers from arXiv astrophysics:

1) Francesca Valsecchi, Evert Glebbeek, et al, "Formation of the black-hole binary M33 X-7 via mass-exchange in a tight massive system",

M-33 X-7 is a mystery that this paper proports to solve, maybe. This binary object seems to be a ~16 solar mass black hole orbiting a ~70 solar mass hydrogen-rich O-type companion star. This binary system has a period of ~3.5 days. Up until now, no model explained all of the weird things about this system. This paper contrives a set of circumstances to explain it all.

2) Shigehiro Nagataki, "Rotating BHs as Central Engines of Long GRBs: Faster is Better,"

This paper relates the rotational rate of a black hole to the strength of any relativistic jet produced by it. This is based on numerical relativity calculations using a magnetohydrodynamic code. Four different models are run.

3) Joan M. Centrella, John G. Baker, "Black-hole binaries, gravitational waves, and numerical relativity,"

This is a very nice review of black hole modeling and numerical relativity. Of course, one of the primary applications is the support of gravitational wave detectors.

4) Rachid Ouyed, Mathew Kostka, et al, "Quark nova imprint in the extreme supernova explosion SN 2006gy: the advent of the Quark Star,"

A fascinating possibility is that at the center of neutron stars a special form of matter is produced, one where there is a region of free quarks surrounded by a screen of gluons. This is called a quark-gluon plasma. Such a state of matter was speculative for many decades, but recent results from RHIC (Relativistic Heavy Ion Collider) have given indications that this has been achieved. The authors of this paper suggest that the supernova SN2006gy was in fact a supernova that included a boost to the explosion through the release of energy by the conversion of neutons at the center of the developing neutron star, converting the center into more stable strange quark matter. If true, this is a significant event!

Update

Well, we just turned in our NSF proposal to develop the MAST Institute for Scientific Computing. We have letters of interest from Jack Horner, a software engineer from Los Alamos, and from the Unversity of Wisconsin, Madison, Department of Physics.

This is a very cool project!

Now that the propsal is in, I can get back to work on the book!

Theoretical Physics Papers #2

Only two really jumped out at me today:

1) Pablo Arrighi, Jonathan Grattage, A Quantum Game of Life,

I think most of us are familiar with the Game of Life, an example of cellular automata (CA) evolving into structures, some of which seem to be coherent. The hope is that such systems will both demonstrate evolving complexity, and reveal some of the rules for such evolution. This paper describes a universal quantum CA (QCA) in three dimensions that can simulate all other three-dimensional QCAs. One application of this is to study the flow of qubits, another is to simulate quantum gates. This is a very important paper to anyone interested in simulating a quantum computer.

2) Jonathan Hackett, Louis H. Kauffman, Octonions,

This paper is a review of the idea of the octonion, a quaternion with the proprty that a lateral rotation brings about a change in the forward orientation of the quaternion and that this is non-associative. Turning spin up to spin down would be an example of the change in orientation. This is sometimes called the Dirac belt trick.

Some Recent Papers on Theoretical Physics and Mathematical Physics

1) Gary Horowitz, Surprising Connections Between General Relativity and Condensed Matter,

My only objection to this paper is that it seems to be tied to anti-deSitter space (AdS). Proving things in AdS may be easier than proving them in general relativity (AdS is essentially general relativity with a negative cosmological constant), but it cannot gaurantee applicability to the real world (since we seem to have a positive cosmological constant). The paper seems to rely on an observation that black holes in AdS behave like thermal systems of one dimensional lower, and that the string theory/holographic principle of black holes allows you to extract features from general relativity that look a lot like superconductivity.

2) Geoffrey Lovelace, Mark. A. Scheel, Bela Szilagyi, Simulating merging binary black holes with nearly extremal spins,

This fascinating paper describes the merger of two rapidly rotating black holes.

Book Review: Quantum Mechanics by Landau and Lifshitz

Time for another book review, this time volume three of the Course in Theoretical Physics by Landau and Lifshitz. This book is available for sale in the bookstore below. This volume is titled, "Quantum Mechanics (Non-relativistic theory)," and covers, in one volume, standard non-relativistic quantum mechanics, atomic and molecular physics, group theory, and nuclear physics.

New developments at MAST

MAST (Madison Area Science and Technology) will be seeking funding from the NSF to open a computational science center and, if funded, it will allow us to offer internships for High School Seniors, Citizen Scientists, Undergraduate Students, Graduate Students, and even Post-docs who are interested in computational science, including, but not limited to: astrophysical fluid dynamics, compact objects, accretion disks, relativity, cosmology, mathematical physics, numerical methods, fluid dynamics, atmospheric modeling, shock wave phenomena, chaotic dynamical systems, scattering, quantum information theory, solution methods for ODEs and PDEs, and bioinformatics. We will handle all necessary educational requirements to bring the students up to speed (including training in Mathematica).

We will even be accepting a number of foreign internships.

The proposal will be submitted to the NSF by 27 October of this year.

Book Project Milestone!

The classical mechanics book I am writing with Leonard Susskind has reached a milestone. As of now the page count stands at just over 100 pages! That is four chapters completed, the first two lectures, an introduction to calculus, and an introduction to Newtonian mechanics.

The Inner Horizon of a Black Hole

Everyone has, by now, heard of black holes. Astronomically, they are likely to have been supermassive stars that exploded, whose remnant gravitationally collapses to a size the is smaller than a function of its mass called the Schwarzschild radius,

where M is the mass of the star. Once collapse passes this point the star is gone and it becomes a new thing, a black hole. Within the Schwarschild radius nothing can escape from the black hole, the escape velocity grows to be more than the speed of light. There is a boundary that we call the event horizon at the Schwarzschild radius, this is what separates the normal spacetime from the weirdness that happens near the black hole.

There are circumstances that can form another surface inside the event horizon. A charged black hole (Riessner-Nordstrøm) can form an inner horizon caused by a charge barrier. A spinning black hole (Kerr) can form an inner horizon due to transfer of angular momentum.

All horizons are places where, in effect, time stops with respect to an outside observer. The inner horizon must also be traversed by anything that falls into the black hole on its way to the singularity predicted to be at its center. The inner horizon gives the possibility of avoiding the singularity, but there seems no way to gaurantee a trajectory through the black hole to avoid the inner horizon prior to crossing the event horizon (you could still cross the inner horizon).

Even if you avoided the inner horizon, it is unlikely that anything other than subatomic particles will survive the experience.

Book Project

I have just finished lecture 2 of Classical Mechanics, that completes three chapters total. This chapter develops the ideas of conservation of energy, conservation of momentum, and the principle of least action.

Musings on the Initial Singularity

For those of you who do not know, the so-called initial singularity is an artifact of Big Bang cosmology implied by the expansion of the universe. If all points in spacetime are moving away from each other (not the matter within spacetime, just the spacetime envirnment-sort of like a river flowing, things in the river flow with it, but are not pulled apart), then it seems reasonable that everything had to start at a point. This time reversal leading to something that looks like a black hole was the subject of Stephen Hawking's thesis around 40 years ago. Other people have studied this time reversal process and have speculated about the dynamics of this singularity. The only problem is that they treat it as a spacetime singularity, like that of a static black hole.

The problem is, it could not have been a spacetime singularity! Spacetime did not yet exist before the Big Bang happened, so there could not have been a spacetime singularity.

This is, of course, one of the reasons why we need a truly quantum theory of gravity. This realization destroys any real chance for unification of the forces, since without spacetime curvature there can be no gravitation; and radiation pressure becomes dominant during the inflationary period. At the moment of the Big Bang, the strong, weak, and electromagnetic forces cause a rapid expansion. Spacetime starts to expand, but without a quantum theory of gravity we cannot understand this process since it is entirely in the regime of quantum mechanical distances, even if the energy densities are huge.

A very deep problem, and one that can only be solved by quantum gravity.

Progress Report for the Last Week

Things I am Working On:

1. Classical Mechanics book: Almost done with lecture 2, should finish today. Thinking about writing a small chapter on dimensional analysis to derive force laws. After lecture 2 I will start on a chapter dealing with vector analysis, and with lecture 3.

2. Book reviews: Quantum Mechanics (Landau and Lifshitz), Advanced University Physics (Rogalski and Palmer).

3. Infinity Computing: Not doing much, though will start to write some code this week.

4. Quantum Computing: Beginning work on a Quantum Computer Simulator.

That's all I have been working on from a theoretical point of view.