Dec 302015

It is nice to have a paper accepted on the penultimate day of the year by Physical Review D.

Our paper in question, General relativistic observables for the ACES experiment, is about the Atomic Clock Ensemble in Space (ACES) experiment that will be installed on board the International Space Station (ISS) next year. This experiment places highly accurate atomic clocks in the microgravity environment of the ISS.

How accurate these clocks can be depends, in part, on knowledge of the general relativistic environment in which these clocks will live. This will be determined by the trajectory of the ISS as it travels through the complex gravitational field of the Earth, while being also subject to non-gravitational forces, most notably atmospheric drag and solar radiation pressure.

What complicates the analysis is that the ACES clocks will not be located at the ISS center-of-mass; therefore, as the ISS is quite a large object subject to tidal accelerations, the trajectory of the ACES clocks is non-inertial.

To analyze the problem, we looked at coordinate transformation rules between the various coordinate systems involved: geocentric and terrestrial coordinates, coordinates centered on the ISS center-of-mass, and coordinates centered on ACES.

One of our main conclusions is that in order for the clock to be fully utilized, the orbit of the ISS must be known at an accuracy of 2 meters or less. This requirement arises if we assume that the orbits are known a priori, and that the clock data are used for science investigations only. If instead, the clock data are used to refine the station orbit, the accuracy requirement is less stringent, but the value of the clock data for scientific analysis is also potentially compromised.

It was an enjoyable paper to work on, and it is nice to end the year on a high note. As we received the acceptance notice earlier today, we were able to put the accepted version on arXiv just in time for it to appear on the very last day of the year, bearing the date December 31, 2015.

Happy New Year!

 Posted by at 8:57 pm
Dec 242015

It has become a habit of mine. On Christmas Eve Day, I like to offer my best wishes to all my friends, members of my extended family, and indeed to all good people on this Earth with the words of the first three human beings in history who left our planet and entered orbit around another celestial body: The astronauts of Apollo 8, who accomplished their historic mission at the end of one of the most tumultuous years since World War 2, 1968.

And as they emerged from the dark side of the Moon and reestablished radio contact with the Earth, they greeted their fellow humans by quoting from the Book of Genesis. They then finished their broadcast with these unforgettable words: “And from the crew of Apollo 8, we close with good night, good luck, a Merry Christmas and God bless all of you – all of you on the good Earth.

 Posted by at 5:00 pm
Dec 242015

Here is the Weather Network’s forecast for today that was made a couple of days ago:

No, they weren’t lying. Here is what my thermometer showed just a few minutes ago:


And it’s already less than what it was; the temperature dropped from 16.4 to 16.2 degrees Centigrade in the past half hour.

May not be impressive for a place like Dubai or Mumbai but lest we forget, I live in Ottawa, supposedly the second coldest capital city on Earth.

Needless to say, we are not going to have a white Christmas this year.

 Posted by at 11:42 am
Dec 162015

The reason for my trip to China was to participate in the 3rd workshop on the TianQin mission.

TianQin is a proposed space-borne gravitational wave detector. It is described in our paper, which was recently accepted for publication in Classical and Quantum Gravity. The name, as typical for China, is poetic: it means a zither or harp in space or perhaps (sounds much nicer in English) a celestial harp. A harp that resonates in response to continuous gravitational waves that come from binary pulsars.

Gravitational waves are notoriously hard to detect because they are extremely weak. To date, we only have indirect confirmation of gravitational waves: closely orbiting binary pulsars are known to exhibit orbital decay that is consistent with the predictions of Einstein’s gravity.

Gravitational radiation is quadrupole radiation. It means basically that it simultaneously squeezes spacetime in one direction and stretches it in a perpendicular direction. This leads to the preferred method of detection: two perpendicular laser beams set to interfere with each other. As a gravitational wave passes through, a phase shift occurs as one beam travels a slightly longer, the other a slightly shorter distance. This phase shift manifests itself as an interference pattern, which can be detected.

But detection is much harder in practice than it sounds. Gravitational waves are not only very weak, they are also typically very low in frequency. Strong gravitational waves (relatively speaking) are produced by binaries such as HM Cancri (aka. RX J0806.3+1527) but even such an extreme binary system has an orbital period of several minutes. The corresponding gravitational wave frequency is measured in millihertz, and the wavelength, in tens or hundreds of millions of kilometers.

There is one exception: inspiraling neutron star or black hole binary systems at the very end of their lives. These could produce detectable gravitational waves with frequencies up to even a kilohertz or so, but these are random, transient events. Nonetheless, there are terrestrial detectors such as LIGO (Laser Interferometer Gravitational-wave Observatory) that are designed to detect such events, and the rumor I heard is that it may have already happened. Or not… let’s wait for the announcement.

But the continuous waves from close binaries require a detector comparable in size to the wavelength of their gravitational radiation. In short, an interferometer in which the laser beams can travel at least a few hundred thousand kilometers, preferably more. Which means that the interferometer must be in space.

This is the idea behind LISA, the Laser Interferometer Space Antenna project. Its current incarnation is eLISA (the “e” stands for “evolved”), a proposed European Space Agency mission, a precursor of which, LISA Pathfinder, was launched just a few days ago. Nonetheless, eLISA’s future remains uncertain.

Enter the Chinese, with TianQin. Whereas eLISA’s configuration of three spacecraft is designed to be in deep space orbiting one of the Earth-Sun Lagrange points with inteferometer arm lengths as long as 1.5 million kilometers, TianQin’s more modest proposal calls for a geocentric configuration, with arm lengths of 150,000 km or so. This means reduced sensitivity, of course, and the geocentric orbit introduces unique challenges. Nonetheless, our colleagues believe that it is fundamentally feasible for TianQin to detect gravitational waves from a known source with sufficient certainty. In other words, the primary mission objective of TianQin is to serve as a gravitational wave detector, confirming the existence of continuous waves emitted by a known binary system, as opposed to being an observatory, usable to find previously unknown sources of gravitational radiation. Detection is always easier: in radio technology, for instance, a lock-in amplifier can be used to detect the presence of a carrier wave even when it is far too weak to carry any useful information.

Theoretical sensitivity curve of the proposed TianQin mission.
Theoretical sensitivity curve of the proposed TianQin mission.

The challenges of TianQin are numerous, but here are a few main ones:

  • First, precisely controlling the orbits of shielded, drag-free test masses such that their acceleration due to nongravitational forces is less than \(10^{-15}~{\rm m}/{\rm s}^2\).
  • Second, precisely controlling the optical path such that no unmodeled effects (e.g., thermal expansion due to solar heating) contribute unmodeled changes more than a picometer in length.
  • Third, implementing time-delay interferometry (TDI), which is necessary in order to be able to compare the phases of laser signals that traveled different lengths, and do so with sufficient timing accuracy to minimize the contributions due to fluctuations in laser frequency.

Indeed, some of the accuracy requirements of TianQin exceed those of eLISA. This is a tall order for any space organization, and China is no exception. Still, as they say, where there is a will…

Unequal-arm Michelson interferometer
Unequal-arm Michelson interferometer.

One thing that complicates matters is that there are legal barriers when it comes to cooperation with China. In the United States there are strong legal restrictions preventing NASA and researchers at NASA from cooperating with Chinese citizens and Chinese enterprises. (Thankfully, Canada is a little more open-minded in this regard.) Then there is the export control regime: Technologies that can be utilized to navigate ballistic missiles, to offer satellite-based navigation on the ground, and to perform remote sensing may be categorized as munitions and fall under export control restrictions in North America, with China specifically listed as a proscribed country.

The know-how (and software) that would be used to navigate the TianQin constellation is arguably subject to such restrictions at least on the first two counts, but possibly even the third: a precision interferometer in orbit can be used for gravitiational remote sensing, as it has been amply demonstrated by GRACE (Gravity Recovery And Climate Experiment), which was orbiting the Earth, and GRAIL (Gravity Recovery And Interior Laboratory) in lunar orbit. Then there is the Chinese side of things: precision navigation requires detailed information about the capabilities of tracking stations in China, which may be, for all I know, state secrets.

While these issues make things a little tricky for Western researchers, TianQin nonetheless has a chance of becoming a milestone experiment. I sincerely hope that they succeed. And I certainly feel honored, having been invited to take part in this workshop.

 Posted by at 5:32 pm
Dec 082015

Hello, Guangzhou. And hello world, from Guangzhou. Here is what I see from my hotel window today:

It is a very interesting place. Today, I had a bit of a walk not just along the main urban avenues, full of neon and LED signs and modern high-tech stores, but also in some of the back alleys, complete with street vendors, stray dogs, and 60-70 year old crumbling buildings, some abandoned. In short… a real city with a real history.

For what it’s worth, I am here on account of a conference about a planned space-borne gravitational wave detector called TianQin.

 Posted by at 2:31 am
Dec 032015

It has been in the news recently that the baboon exhibit at the Toronto Zoo had to close temporarily. The reason: Following the death of the matriarch, there was a power struggle.

The reason why I find this fascinating is that these baboons weren’t fighting for food. They were not fighting for sex. They were not fighting for a more cozy sleeping place or anything else tangible.

No… they were fighting for power.

That such an abstract concept not only exists in the animal world but may even prompt a vicious fight might upset those who maintain illusions about the noble animal world. But then, perhaps the animal world is not that different from the world of humans.

We all came from the same place, after all.

The next time a bellicose politician, ruler or warlord makes a threat, brandishing fancy weapons of war, in some vainglorious quest for power, just think of one word: baboon.

 Posted by at 6:28 pm
Dec 012015

Aspiring US presidential candidate Bernie Sanders reportedly said that it is “profoundly wrong” that the top 1% has more wealth in our society than the bottom 95%.

Today, The Globe and Mail offered a perfect example why.

Look at this group photo:

Notice the people in this picture: The presidents of Indonesia, the United States, France and India, and the Prime Minister of Canada… and Bill Gates.

In other words, five elected leaders (together representing at least one quarter of all of humanity) and one very rich guy who is in this picture only because he has tons of money.

Now don’t get me wrong, I like Bill Gates. I liked him even when it was popular to hate him among the cognoscenti. And Bill Gates is a shining example of the conscientious multibillionaire who spends stupendous sums of his own money to make the world a better place. But I still think it is “profoundly wrong” that he is in this picture. Nobody elected him. He is not representing anybody. He is here simply because he commands wealth that is comparable to the GDP of a not so small country.

 Posted by at 5:33 pm