Too many talks to remember…

Difficulty level:   

It has been a hectic but successful day, with 12 hours of cycling around Brisbane and attending talks! I started with a part-drive, part-cycle to Southbank, navigating the rain, to watch two documentaries screened for the World Science Festival. “Mapping the Future: The Power of Algorithms” was an interesting discussion of what “predictive analytics” based on “big data” can foretell of human behaviour. “The Joy of Logic” was too introductory for me, but I was interested in the quirky anecdotes about the Vienna Circle of philosophers.

Next I cycled to the University of Queensland to hear Scott Stephens, editor of the (Australian) ABC’s Religion and Ethics website, on “To See or Not to See: Recovering Moral Vision in a Media Saturated Age”. He was critical of the pettiness of media in a democratic society, citing causes including commercialisation of news, the Watergate scandal, and the media’s change from reporting on politics to deliberately influencing it. Also the rise of social media means news organisations pander to popular taste and attempting to “go viral”. I was reminded of Alain de Botton’s commentary and alternative news experiment.

Immediately afterwards I rushed off to a presentation by George Musser, an editor at Scientific American. Researchers feel popular science reporting at this level and below can be too “dumbed-down” and/or sensationalist. Musser tried to unify the roles of “scientist” and “journalist”: science is his original background, but he also defended a journalist perspective to his audience. He said hot topics include cosmology, anything with “quantum” in the title, mind/consciousness, and others (I can certainly see these emphases in the science festival). But trends change — dinosaurs used to be popular, as was water on Mars but people are sick of hearing about that.

The next talk would be a personal highlight. But first I’ll mention for completeness that last night I attended “The first scientists: Aboriginal science in Queensland” panel discussion. The room was completely packed, the most full for the science festival so far, apparently. There were interesting tidbits such as some man in remote northern Queensland who lost part of a finger to a crocodile, then wrapped it in a local bark, a natural anaesthetic; I would have preferred more concrete examples like this.

Lunch with some visitors

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This is an epic week for science in Brisbane! Lots of experts are in town for the World Science Festival. The astrophysics group from my uni, the University of Queensland, had lunch today with Josh Frieman (from Chicago) and Douglass Scott (from Vancouver). I had a great time.

From left to right: Merryn, Douglas Scott, Colin (author of Colin’s Cosmos), Sam, Tamara Davis, Josh Frieman, and Ed. A mixture of students, professors, and a postdoc; others had already left by this point.

Frieman is the director of the Dark Energy Survey (DES), a large international collaboration which is mapping the skies to measure the expansion of the universe by dark energy. Probably every local at lunch except me was a member of either the Australian version “AusDES”, and/or the Australian astrophysics organisation “CAASTRO” which also shouted lunch incidentally. (My research in relativity is a little different from these groups, being more theoretical, but they are the closest I have to a research community here, and so I was very happy to be invited! A big thank-you to Tamara who is conscientious about that.)

I had a good chat with Douglas, whom I was sitting next to. He shared with the table about one of his students who is studying modified gravity theories (that is, other than Einstein’s general relativity), and how every 3 months he knocks on Douglas’ door with another discovery about why general relativity is superior. He generously asked me about my research, and I explained my analysis of distances in relativity, though it might sound trivial. I also mentioned black hole volumes and new coordinate system(s) I had discovered, and that just recently I had been learning about rotating black holes to potentially extend these results to that situation, which I believe no-one has done before apart from a few specific cases.

I missed some fun photo opportunities with other students ;-). Sam grabbed a sneaky sip of Josh C.’s iced chocolate when it arrived. Then he made up for it by spoon-feeding Josh ice-cream in a faux-romantic moment. Sam seemed unphased by our eminent guests, but kept up his usual cheeky humour!

While Josh (Frieman) is in town for the science festival, Douglas is in Australia to visit a couple of universities. It also turned out he’s going to a music festival tonight, and I joked that his real ulterior motive had come out! He admitted he once gave a talk at Caltech partly because his favourite band was playing in Los Angeles. Tamara left for the science festival. I had a haircut this morning, thinking I should clean up in case I met some of the celebrity physicists in town but, as you can see from the top photo, a shave was beyond me at this point.

Gravitational waves detected!

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Physicists are very excited, because the first ever direct detection of gravitational waves has just been announced! The signal matches the prediction for two black holes colliding.  This will likely mean a Nobel Prize for someone. This is a tremendous scientific achievement, representing a vast global collaboration between scientists, advanced technology, government funding, and simple good luck.

The signal lasted for just 1/5 of a second, but scientists have extracted an impressive amount of information from it. This video plays the “chirp” which was detected, converting the gravitational wave signal to sound so you can hear it. The video repeats the chirp 8 times, half of those scaled to a higher frequency where human hearing is more sensitive.

The LIGO detectors have two 4km long pipes housing laser light for detecting gravitational waves. This is the Hanford, Washington instrument
The signal was picked up by the two “LIGO” detectors in the United States. These have two 4km long pipes at right angles, housing laser light which measures the miniscule expansion and contraction of space caused by a passing gravitational wave. This is the Hanford, Washington instrument; the other is in Livingston, Louisiana.

But understand that calling it “sound” is metaphorical, for instance when someone gave a demonstration by playing a cello on Australian Broadcasting Corporation (ABC) TV. A gravitational wave is a ripple through the “fabric” of space itself and travels at the speed of light, whereas a sound wave transmits via air molecules bumping together and travels a million times more slowly. It should also be clarified that the gravitational waves would have been emitted for a far longer period than 0.2 seconds, it’s just they were too weak to be detected by us.

Gravitational waves are a consequence of general relativity, and were first predicted by Einstein in 1916. Though not an area of my research so far, I have looked in-depth at the measurement of distances in relativity, which is somewhat related. I look forward to learning and sharing more.

A new 9th planet?

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There’s news today that some scientists predict the existence of a ninth planet. No one has actually found anything, but this is inferred from the orbits of certain icy objects in the outer Solar System. It may have 10 times the mass of the Earth, and take 10,000 or 20,000 years to orbit the Sun, due to its distance far beyond the known planets.Planet NineScientists from the California Institute of Technology (Caltech) claim “Planet Nine” would have an orbit like the above (yellow) to account for the depicted handful of bodies (purple orbits) lying in one direction. They hope to detect it in the next 5 years. It’s not my area, and I have no opinion on this personally, but am happy to wait and see what consensus forms. Still, it’s an opportunity to share some history of planetary discovery.

Artist's conception of the hypothetical Planet Nine
Artist’s conception of the hypothetical Planet Nine

This has happened before. Neptune was discovered because of irregularities in the orbit of Uranus. Pluto was discovered by the same motivation. (Further irregularities in Neptune and Uranus’ orbits had led to a search. However it turned out Neptune’s mass had been overestimated, and besides Pluto was too small to affect these planets much.) Similarly the unexplained rotation of Mercury’s orbit led to speculation of a new innermost planet “Vulcan”, but just like the Star Trek planet it remains fictional. In fact Einstein successfully explained Mercury’s behaviour using an early version of general relativity.

World Science Festival in Brisbane

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World Science Festival BrisbaneThe World Science Festival is coming to Brisbane on 9–13 March, 2016. This might be the first time it’s been held outside of New York City.

There’s a lot of astrophysics and relativity, including some big names, but it’s expensive. Sean Carroll, author of a good relativity textbook , will discuss the accelerating universe with Nobel prizewinner and Aussie Brian Schmidt (who will also be on “Breakfast with the Brians”), and others. Tamara Davis, my Master’s thesis supervisor, will discuss relativity with string theorist and author Brian Greene and others. The drama “Light Falls” written by Brian Greene about Einstein’s discovery of general relativity looks great, but I don’t want to pay $69/$89. Another drama about Einstein’s personal side was written by Alan Alda, who was the main character of M*A*S*H.

Light Falls dramaMadness Redefined” also looks interesting. But I think I’ll just drop in briefly on the Sunday, for the free documentary Science and Islam and maybe the free “Street Science” demonstration. I’ve also booked tickets for a maths documentary on “predictive analytics” about modelling our lives, maybe from internet data.

Tetrad for Schwarzschild metric, in terms of e

Difficulty level:   ★ ★ ★

The following is a natural choice of orthonormal tetrad for an observer moving radially in Schwarzschild spacetime with “energy per unit rest mass” e:

    \begin{align*} e_{\hat 0}^\mu &= \left(e\Schw^{-1},\pm\eroot,0,0\right) \\ e_{\hat 1}^\mu &= \left(\pm\Schw^{-1}\eroot,e,0,0\right) \\ e_{\hat 2}^\mu &= \left(0,0,\frac{1}{r},0\right) \\ e_{\hat 3}^\mu &= \left(0,0,0,\frac{1}{r\sin\theta}\right) \end{align*}

The components are given in Schwarzschild coordinates. (The ± signs are not independent — they must be either both +1 or both -1. Note that e does not distinguish between inward and outward motion. There is additional freedom to define any of these vectors as their negative.)

We normally think of e as invariant, where there is a presumption of freely falling / geodesic motion, but even if not we can regard it as an instantaneous value.

\evec{0} is the 4-velocity computed previously. The other vectors can be obtained from substituting \gamma=e\Schw^{-1/2} and V=-\frac{1}{e}\sqrt{e^2-1+\frac{2M}{r}} into the tetrad here. \gamma is determined from -\fvec u\cdot\fvec u_{\rm obs}=\gamma and the equation for e above, then V follows from inverting \gamma\equiv(1-V^2)^{-1/2}. This orthonormal frame is useful for determining the object’s perspective, e.g. tidal forces, visual appearances, etc.

Tetrad for Schwarzschild metric

Difficulty level:   ★ ★ ★ ★

Suppose an observer u moves radially with speed (3-velocity) V relative to “stationary” Schwarzschild observers, where we define V<0 as inward motion. Then one natural choice of orthonormal tetrad is:

    \begin{align*} (\evec{0})^\alpha &= \left(\gamma\Schw^{-1/2},V\gamma\Schw^{1/2},0,0\right) \\ (\evec{1})^\alpha &= \left(V\gamma\Schw^{-1/2},\gamma\Schw^{1/2},0,0\right) \\ (\evec{2})^\alpha &= \left(0,0,\frac{1}{r},0\right) \\ (\evec{3})^\alpha &= \left(0,0,0,\frac{1}{r\sin\theta}\right) \end{align*}

where the components are given in Schwarzschild coordinates. This may be derived as follows.

The Schwarzschild observer has 4-velocity

    \[\fvec u_{\rm obs}=\left(\Schw^{-1/2},0,0,0\right)\]

because the spatial coordinates are fixed, and the t-component follows from normalisation \fvec u_{\rm obs}\cdot\fvec u_{\rm obs}=-1 (Hartle §9.2).

Now the Lorentz factor for the relative speed satisfies -\fvec u\cdot\fvec u_{\rm obs}=\gamma, and together with normalisation \fvec u\cdot\fvec u=-1 and the assumption that the θ and φ components are zero, this yields \evec{0}\equiv\fvec u given above.

We obtain \evec{1} by orthonormality: \evec{1}\cdot\evec{0}=0 and \evec{1}\cdot\evec{1}=1, and again making the assumption the θ and φ components are zero. Note the negative of the r-component is probably an equally natural choice. Then \evec{2} and \evec{3} follow from simply normalising the coordinate vectors.

Strictly speaking this setup only applies for r>2M, because stationary timelike observers cannot exist inside a black hole event horizon! Yet remarkably the formulae can work out anyway (MTW …) .  An alternate approach is local Lorentz boost described shortly.

Hartle … Also check no “twisting” etc…

Radial motion in the Schwarzschild metric, relative to stationary observers

Difficulty level:   ★ ★ ★

Last time we derived the 4-velocity u of a small test body moving radially in the Schwarzschild geometry, in terms of e, the “energy per unit rest mass”. Another parametrisation is in terms of the 3-speed V relative to stationary observers. This turns out to be, in Schwarzschild coordinate expression,


To derive this, first consider the 4-velocity of stationary observers:


We know the “moving” body has 4-velocity u of form u^\mu=(u^t,u^r,0,0) since the motion is radial. The Lorentz factor \gamma\equiv(1-V^2)^{-1/2} for the relative speed is

    \[\gamma=-\fvec u\cdot\fvec u_{\rm{Schw}}\]

Evaluating and rearranging yields u^t=\gamma\Schw^{-1/2}. Normalisation \fvec u\cdot\fvec u=-1 leads to u^r=\pm V\gamma\Schw^{1/2}, after some algebra including use of the identity \gamma^2-1=V^2\gamma^2. We allow V<0 also, and define this as inward motion. Carefully considering the sign, this results in the top equation. (An alternate derivation is to perform a local Lorentz boost. Later articles will discuss this… The Special Relativity formulae cannot be applied directly to Schwarzschild coordinates.)

Some special cases are noteworthy. For V=0, γ=1, and u reduces to uSchw. This corresponds to e=-\fvec\xi\cdot\fveclabel{u}{Schw}=\Schw^{1/2}. Also we can relate the parametrisation by V (and γ) to the parametrisation by e via

    \[\gamma=e\Schw^{-1/2}\qquad V=-\frac{1}{e}\sqrt{e^2-1+\frac{2M}{r}}\]

where the leftmost equation follows from the definition e\equiv-\fvec\xi\cdot\fvec u, and subsequently the rightmost equation from γ=γ(V). For raindrops with e=1, the relative speed reduces to V=-\Schwroot.

We would expect the construction to fail for r\le 2M, as stationary timelike observers cannot exist there, and so the relative speed to them would become meaningless. But curiously, it can actually work for a faster-than-light V>1 “Lorentz” boost, as even the authorities MTW (§31.2, explicit acknowledgement) and Taylor & Wheeler (§B.4, implicitly vrel>1 for r<2M) attest. Sometime, I will investigate this further…