Jan 222010
 

Here’s a nice tennis ball, photographed from both sides:

It’s a big one, mind you, almost a thousand miles across. It’s Saturn’s moon Iapetus, famous because one side of it is significantly brighter than the other. The explanation, however, is more mundane than that offered in the book version of Clarke’s 2001: A Space Odyssey; the most recent hypothesis is that the discoloration is due to the thermal migration of ice.

 Posted by at 7:44 pm
Aug 252009
 

I’m reading the autobiography of Fred Hoyle, and I’ve been perusing Wikipedia for background, in particular, reading about the Jodrell Bank radio telescope and its founder, Sir Bernard Lovell.

This is how I came across a news item from earlier this year, according to which Lovell recently revealed that back in 1963, he has been targeted by Soviet assassins during a visit to the Soviet Union.

This sounds improbable except… even in recent years, Russian intelligence agents/agencies have been using novel methods in assassination attempts (e.g., radioactive polonium in the case of Litvinenko). Further, the rationale Lovell gives is quite plausible: back in 1963, when satellite-based early warning systems were not yet available, something like Jodrell Bank may very well have served either as an over-the-horizon radar or perhaps using the Moon as a reflector.

Lovell promises to reveal more posthumously. What can I say? Our curiosity can wait. I wish him many more happy and healthy years.

 Posted by at 3:23 am
Jul 082009
 

The premier Internet physics and astronomy preprint archive, ArXiv, seems to be having some serious problems tonight. I used the catchup interface to check for new papers, only to find messages like this:

Problem displaying entry for arXiv:0907.1079

Apparently all new papers are unavailable, and many older papers, too… I checked briefly and found papers dating back to last October that appear to have vanished. Including some half a dozen or so papers of my own.

I sure hope they keep backups!

 Posted by at 3:00 am
Jun 092009
 

The reason why I am concerning myself with more Maxima examples for relativity is that I am learning some subtle things about Brans-Dicke theory and the Parameterized Post-Newtonian (PPN) formalism.

Brans-Dicke theory is perhaps the simplest modification of general relativity. Instead of the gravitational constant, G, the theory has a scalar field φ, and the theory’s Lagrangian now reads

L = [φR − ω∂μφ∂μφ/φ] / 16π.

Here, R is the curvature scalar and ω is an unspecified constant of the theory.

The resulting field equations are just like Einstein’s, except for two things. First, the field equations for the metric now have additional terms containing derivatives of φ; second, there is a new field equation for the scalar field φ that basically says that the d’Alembertian of φ is proportional to the trace of the stress-energy tensor.

Clever people tell you that Brans-Dicke theory is practically excluded by solar system data, as it would only work for insanely high values of ω. They demonstrate this by building approximate solutions for the theory using the PPN formalism, and find that one of the PPN parameters, γ, will have the value of γ = (1 + ω) / (2 + ω); on the other hand, observations by the Cassini spacecraft restrict γ to |γ − 1| < 2.3 × 10−5, so |ω| must be at least 40,000.

Now here’s the puzzling bit: if you solve Brans-Dicke theory in a vacuum, you find that the celebrated Schwarzschild solution of general relativity still applies:  keeping φ constant, you just get back this common solution which is known to fit solar system data well, and which has, most importantly, γ = 1 and the value of ω doesn’t matter.

So which is it? Is it γ = 1 or is it γ = (1 + ω) / (2 + ω)? Something is amiss here.

This dilemma can be resolved once you realize that whereas general relativity has a unique spherically symmetric, static vacuum solution, this is not the case for Brans-Dicke theory. This theory has an infinite family of spherically symmetric, static vacuum solutions. Indeed, I think you could actually use the value of γ to parameterize this solution space. However, once you allow some matter into that vacuum, no matter how little, you are locked in to a specific solution, for which γ = (1 + ω) / (2 + ω). In other words, the only vacuum solution that is consistent with the notion of taking the limit of a matter solution by gradually removing matter is NOT the Schwarzschild solution of general relativity, but another, incompatible solution.

This has extremely important implications for our work on MOG. So far, we have obtained a vacuum solution that appears consistent with observations on scales from the solar system to cosmology. However, a recent paper by Deng et al. challenges this work by suggesting that the MOG PPN parameter γ is not 1 and hence, the theory runs into the same trouble as Brans-Dicke theory in the solar system. Is this true? Did we pick a vacuum solution that happens to be inconsistent with matter solutions? This is what I am trying to investigate.

 Posted by at 12:45 pm
Jan 072009
 

Here’s an article worthy of a bookmark:

http://peltiertech.com/Excel/Charts/XYAreaChart2.html

It offers a way to produce a chart in Microsoft Excel much like this one:

Filled XY area chart

Filled XY area chart

This chart is from something I’m working on, an attempt to test gravitational theories against galaxy survey data.

The link above also comes with a warning: the discussed technique doesn’t work with Excel 2007, due to a (presumably unintentional) change in Excel’s handling of certain complex charts. A pity, but it is also a good example why I am trying to maintain my immunity against chronic upgrade-itis. Two decades ago upgrades were important because they fixed severe bugs and offered serious usability improvements. But today? Why on Earth would I want to upgrade to Office 2007 when Office 2003 does everything I need and more, just so that I can re-learn its user interface? Or make Microsoft richer?

 Posted by at 3:51 pm