Least-squares and timing noise

Figure 4 from the paper: residuals and spectrum

Working with long-term pulsar timing data sets is a nuisance because of so-called "timing noise". Not only is this noise above and beyond the usual observational uncertainties, perhaps because it is torque noise, it tends to be strongest at low frequencies (it is very "red"). Often so much so that leakage from the very lowest frequencies dominates at all analysis frequencies. Various people, myself included, have tried various approaches for dealing with this noise, but a recent arxiv paper shows real promise:

Pulsar timing analysis in the presence of correlated noise

W. Coles, G. Hobbs, D. J. Champion, R. N. Manchester, J. P. W. Verbiest

Pulsar timing observations are usually analysed with least-square-fitting procedures under the assumption that the timing residuals are uncorrelated (statistically "white"). Pulsar observers are well aware that this assumption often breaks down and causes severe errors in estimating the parameters of the timing model and their uncertainties. Ad hoc methods for minimizing these errors have been developed, but we show that they are far from optimal. Compensation for temporal correlation can be done optimally if the covariance matrix of the residuals is known using a linear transformation that whitens both the residuals and the timing model. We adopt a transformation based on the Cholesky decomposition of the covariance matrix, but the transformation is not unique. We show how to estimate the covariance matrix with sufficient accuracy to optimize the pulsar timing analysis. We also show how to apply this procedure to estimate the spectrum of any time series with a steep red power-law spectrum, including those with irregular sampling and variable error bars, which are otherwise very difficult to analyse.

I'd like to look at it in more detail and try some of the techniques on test data.

Radio vortices

Quantum mechanics, no one will be surprised to hear, is weird. In particular, photons can carry angular momentum - circularly polarized light can set objects spinning. But it turns out that light can carry orbital angular momentum as well. It's really not very clear to me quite what this means in terms of photons. In terms of classical waves, it's weird but I think I get it: if you look at the spatial distribution of the light in a beam, you may find that the phase is constant across the whole beam. But you might also find that the phase varies. Now, it has to be continuous, but you can imagine that as you make a circle around the beam center, you find the phase increases by an integer multiple of two pi. This gives you a continuous phase in a way that is topologically different from the constant-phase situation. As I understand it, this is what is called wrapping number.

Now this would just be another weirdness from the world of (classical!) waves except that there seem to be applications for it. In particular there's a paper on the arxiv about using this for communications purposes.

Science fiction has no imagination, part 1

Every so often I come across something that makes me think that the supposedly imaginative field of science fiction can't hold a candle to reality for weirdness. Today's installment is an arxiv paper in which the authors are seriously discussing quantum teleportation as a way to combine signals from telescopes to form an interferometer:

Longer-Baseline Telescopes Using Quantum Repeaters

Daniel Gottesman, Thomas Jennewein, Sarah Croke

We present an approach to building interferometric telescopes using ideas of quantum information. Current optical interferometers have limited baseline lengths, and thus limited resolution, because of noise and loss of signal due to the transmission of photons between the telescopes. The technology of quantum repeaters has the potential to eliminate this limit, allowing in principle interferometers with arbitrarily long baselines.