other kinds of sailing

In finishing up the first draft (yay!) of my paper on sailing, I thought about other kinds of sailing (for the discussion). One is solar sails: In principle if a spacecraft has a sufficiently large solar sail, of which it can change the size and shape, the spacecraft can navigate in arbitrary directions and perform arbitrary three-axis attitude adjustments, by working on a combination of radiation pressure and gravity. It's really very flexible. It makes me want to design a spacecraft!

I also thought about ice boats. An ice boat is like a sailboat with an extremely large keel and almost no water drag. That is, it sails like a sailboat in the limit that the keel gets large but the water drag gets small. This should make ice boats extremely fast at upwind sailing. Maybe I'll try to find an opportunity to sail on ice this winter?

radial velocity with a gas cell

I had a great meeting today with Matt Daunt (NYU), Lily Zhao (Flatiron), and Megan Bedell (Flatiron), in which we described what we need to do to fit a data-driven model to extreme-precision radial-velocity spectra that are taken with a gas cell in the light path. The gas cell imprints lines from known atomic transitions and secures the wavelength calibration of the device. How to use this in a data-driven model. We started by talking about line-spread functions and wavelength solutions and ended up asking some deep questions, like: Do you really need to know the wavelength solution in order to measure a change in radial velocity? I am not sure you do!

vectors, bras, and kets

One of my PhD advisors—my official advisor—was Roger Blandford (now at Stanford). Blandford, being old-school, responded to a tweet thread I started by sending me email. I am trying to move over to always describing tensors and rotation operators and Lorentz transformations and the like in terms of unit vectors, and I realized that the most enlightened community along these lines are the quantum mechanics. Probably because they work in infinite-dimensional spaces often! Anyway, there are deep connections between vectors in a space and functions in a Hilbert space. I'm still learning; I think I will never fully get it.

orthogonalization in SR, continued

Soledad Villar (JHU) and I discussed more the problem of orthogonalization of vectors—or finding orthonormal basis vectors that span a subspace—in special (and general) relativity. She proposed a set of hacks that correct the generalization of Gram–Schmidt orthogonalization that I proposed a week or so ago. It's complicated, because although the straightforward generalization of GS works with probability one, there are cases you can construct that bork completely. The problem is that the method involves division by an inner product, and if the vector becomes light-like, that inner product vanishes.

linear subspaces in special relativity

Who knew that my love of special relativity would collide with my love of data analysis? In the ongoing conversation between Soledad Villar (JHU), Ben Blum-Smith (NYU), and myself about writing down universally approximating functions that are equivariant with respect to fundamental physics symmetries, a problem came up related to the orientation of sets of vectors: In what groups are there possible actions on d-dimensional vectors such that you can leave all but one of the d vectors unchanged, and change only the dth? It turns out that this is an important question. For example, in 3-space, the orthogonal group O(3) permits this but the rotation group SO(3) does not! This weekend, I showed that the Lorentz group permits this. I showed it constructively.

If you care, my notes are here. It helped me understand some things about the distinction between covariant and contravariant vectors. This project has been fun, because I have used this data-analysis project to learn some new physics, and my physics knowledge to inform a data analysis framework.

what is a tensor?

It's finals week, so not much research. But I did get in a useful conversation with Soledad Villar (NYU) about the definition of a tensor (as opposed to a matrix, say). She had a different starting point than me! But we converged to similar things. You can think of it in coordinate-free or coordinate-transform ways, you can think of it in operator terms, and you can think of it as being composed of sums of outer products of vectors. I always thought of a tensor as being a ratio of vectors, in some sense, but that's a very hand-wavey idea.

gravitational clustering, gravitational interferometry

Today Michael Joyce (LPNHE) gave a great talk about analytic and conceptual directions towards understanding nonlinear gravitational growth of structure in the Universe. He focused on the stable-clustering approximation, which dates back to Peebles, is very predictive over a range of scales, and can be used to test simulations. At lunch afterwards, we discussed the great importance of studying gravity analytically, a point made often and well by Roman Scoccimarro (NYU).

Prior to the seminar, Ellie Schwab-Abrams (AMNH) and I discussed self-calibration for pulsar timing arrays, which we think and hope could lead to a new era of gravitational interferometry and enormously increase the sensitivity to long-term gravitational-wave signals. We decided to start by solving the radio-astronomy problem, which has yet to be solved in the literature, because no radio telescope has the problem that the relative velocities of it's elements are unknown!

photon potential-density pairs?

Gabe Perez-Giz (NYU) gave a blackboard talk at lunch about constructing a stable, bound swarm of photons. Yes, photons! It is the relativistic generalization of the search for potential-density pairs for gravitationally bound objects: Can you find a radial mass distribution that is made up of orbits that are themselves orbits in the potential generated by that mass distribution? The audience was skeptical that any stable solutions could exist, but divided on whether any solutions at all exist. I am with Perez-Giz that it is likely that some solutions do exist. Stability, that's another matter.

big planets, small planets, Earth-like planets

In a low-research day, Tom Barclay (Ames) gave a very nice talk about exoplanets. He made many interesting and novel points. The first was that big planets are still very interesting, because their large impact on the system means that many things can be measured precisely. In particular, he showed examples where you can measure the Doppler beaming of the stellar light resulting from the reflex velocity of the star induced by the planet! Another point was that it is possible to find very tiny planets; he showed some of the smallest planets discovered with Kepler; several are much smaller than Earth. He is personally responsible for the smallest ever. Another point was that there are a few planets now that are debatably and reasonably "habitable". The striking thing is that there aren't yet Earth-sized planets that have been found in year-ish orbits. All known planets are either on shorter orbits or else larger. Time to fix that!

rebinning data, ultrarelativistic

It will be with horror that my reader learns that Lang and I spent part of the morning in a pair-code session binning down SDSS data to larger (less informative) pixels. We had to bin down everything: The data, the error model, the point-spread function, the photometric calibration, the astrometric calibration, etc. Why did we do it, you may ask? Because for the Sloan Atlas project, we are encountering galaxies that are so large on the sky (think M101) that we can't—without major code changes asap—fit the data and model and derivatives into (our huge amount of) memory, even in our (fairly clever) sparse implementation of the problem. The amazing thing is that by the end of the day we (meaning Lang) got something that works: We can run The Tractor on the original data or the rebinned data and it seems to give very similar results. Testing tomorrow!

In the afternoon, Andrew MacFadyen (NYU) gave the Physics Colloquium, about ultrarelativistic plasma problems, motivated by gamma-ray bursts. The most interesting things to me in this business are about universality: In the non-relativistic limit there is the Sedov–Taylor scale-free expanding explosion model. In the ultra-relativistic limit there is the Blandford–McKee jet model. However, on the latter, the different parts of a collimated jet can't actually communicate with one another laterally (for relativistic causality reasons), so there is no possibility of homogeneity. In other words, the jet must be a heterogeneous mixture of jets, in some sense. The mixture fuses together into one jet continuously over time. That seems like a very interesting physics problem. MacFadyen and his group have been doing fundamental work, with awesome visuals to boot.

Rafikov

This afternoon Roman Rafikov (Princeton) gave a nice talk about metallicity anomalies in white dwarfs, with a probable connection to accretion from dust or proto-planetary-like disks. It was all good, but the result I will take to the grave was about accretion induced by Poynting–Robertson drag: Because it is a pure special-relativity effect, the mass accretion rate (mass per unit time) is just the intercepted luminosity (energy per unit time) divided by two factors of the speed of light. That is, it is a perfect converter of energy into mass!

MHD

Jonathan Zrake (NYU) gave a very nice oral candidacy exam today in which he described his relativistic MHD plus cosmic ray particle code that he and Andrew MacFadyen built to test acceleration mechanisms. He gets enormous accelerations and shows that they are—in some circumstances—caused by many little shocks in the turbulent post-shock fluid rather than the big shock (think relativistic outflow or blast wave) behind which the turbulence is growing.