Here is a message to the citizens of the United States from the “Canada Party”.
What can I say. If Trump becomes president, being way ahead may not be a bad idea.
Feb 212016
Feb 202016
OK, my Linux friends… try not to make the mistake that I made earlier tonight.
I was trying to stop a process in the gentlest way possible, buy sending it a hangup signal to its numerical process ID, e.g., 12345. The syntax was supposed to be this:
kill -1 12345
Unfortunately this is not what I typed. Because it was an afterthought that I’d use a hangup signal (instead of the default kill signal) I entered the option after the process ID, like this:
kill 12345 -1
A second or two later, I lost my xterm session. In fact, I lost all my xterm sessions. My mail client disconnected. I could not even telnet into the server anymore. For all practical intents and purposes, it seemed dead as a doorknob.
OK, not completely dead. I was able to log back in through its physical keyboard, only to find out that apart from core processes, nothing was running. No SQL server. No Web server. No SSH demon. No name server. And so on.
What the !#@@#@!& have I done?
I looked at the command long and saw the last command that I typed. I quickly checked the man page of kill and indeed… what I typed instructed kill to terminate process 12345 (using the default kill signal) and then, using the same default kill signal, terminate all processes with a pid greater than 1.
Bravo. What a clever boy. I promise I’ll try not to do that again anytime soon.
Still, I was able to bring everything back to life without rebooting the server. I hate reboots.
Feb 162016
The other day, I ran across a question on Quora: Can you focus moonlight to start a fire?
The question actually had an answer on xkcd, and it’s a rare case of an incorrect xkcd answer. Or rather, it’s an answer that reaches the correct conclusion but follows invalid reasoning. As a matter of fact, they almost get it right, but miss an essential point.
The xkcd answer tells you that “You can’t use lenses and mirrors to make something hotter than the surface of the light source itself”, which is true, but it neglects the fact that in this case, the light source is not the Moon but the Sun. (OK, they do talk about it but then they ignore it anyway.) The Moon merely acts as a reflector. A rather imperfect reflector to be sure (and this will become important in a moment), but a reflector nonetheless.
But first things first. For our purposes, let’s just take the case when the Moon is full and let’s just model the Moon as a disk for simplicity. A disk with a diameter of \(3,474~{\rm km}\), located \(384,400~{\rm km}\) from the Earth, and bathed in sunlight, some of which it absorbs, some of which it reflects.
The Sun has a radius of \(R_\odot=696,000~{\rm km}\) and a surface temperature of \(T_\odot=5,778~{\rm K}\), and it is a near perfect blackbody. The Stephan-Boltzmann law tells us that its emissive power \(j^\star_\odot=\sigma T_\odot^4\sim 6.32\times 10^7~{\rm W}/{\rm m}^2\) (\(\sigma=5.670373\times 10^{-8}~{\rm W}/{\rm m}^2/{\rm K}^4\) is the Stefan-Boltzmann constant).
The Sun is located \(1~{\rm AU}\) (astronomical unit, \(1.496\times 10^{11}~{\rm m}\)) from the Earth. Multiplying the emissive power by \(R_\odot^2/(1~{\rm AU})^2\) gives the “solar constant”, aka. the irradiance (the terminology really is confusing): approx. \(I_\odot=1368~{\rm W}/{\rm m}^2\), which is the amount of solar power per unit area received here in the vicinity of the Earth.
The Moon has an albedo. The albedo determines the amount of sunshine reflected by a body. For the Moon, it is \(\alpha_\circ=0.12\), which means that 88% of incident sunshine is absorbed, and then re-emitted in the form of heat (thermal infrared radiation). Assuming that the Moon is a perfect infrared emitter, we can easily calculate its surface temperature \(T_\circ\), since the radiation it emits (according to the Stefan-Boltzmann law) must be equal to what it receives:
\[\sigma T_\circ^4=(1-\alpha_\circ)I_\odot,\]
from which we calculate \(T_\circ\sim 382~{\rm K}\) or about 109 degrees Centigrade.
It is indeed impossible to use any arrangement of infrared optics to focus this thermal radiation on an object and make it hotter than 109 degrees Centigrade. That is because the best we can do with optics is to make sure that the object on which the light is focused “sees” the Moon’s surface in all sky directions. At that point, it would end up in thermal equilibrium with the lunar surface. Any other arrangement would leave some of the deep sky exposed, and now our object’s temperature will be determined by the lunar thermal radiation it receives, vs. any thermal radiation it loses to deep space.
But the question was not about lunar thermal infrared radiation. It was about moonlight, which is reflected sunlight. Why can we not focus moonlight? It is, after all, reflected sunlight. And even if it is diminished by 88%… shouldn’t the remaining 12% be enough?
Well, if we can focus sunlight on an object through a filter that reduces the intensity by 88%, the object’s temperature is given by
\[\sigma T^4=\alpha_\circ\sigma T_\odot^4,\]
which is easily solved to give \(T=3401~{\rm K}\), more than hot enough to start a fire.
Suppose the lunar disk was a mirror. Then, we could set up a suitable arrangement of lenses and mirrors to ensure that our object sees the Sun, reflected by the Moon, in all sky directions. So we get the same figure, \(3401~{\rm K}\).
But, and this is where we finally get to the real business of moonlight, the lunar disk is not a mirror. It is not a specular reflector. It is a diffuse reflector. What does this mean?
Well, it means that even if we were to set up our optics such that we see the Moon in all sky directions, most of what we would see (or rather, wouldn’t see) is not reflected sunlight but reflections of deep space. Or, if you wish, our “seeing rays” would go from our eyes to the Moon and then to some random direction in space, with very few of them actually hitting the Sun.
What this means is that even when it comes to reflected sunlight, the Moon acts as a diffuse emitter. Its spectrum will no longer be a pure blackbody spectrum (as it is now a combination of its own blackbody spectrum and that of the Sun) but that’s not really relevant. If we focused moonlight (including diffusely reflected light and absorbed light re-emitted as heat), it’s the same as focusing heat from something that emits heat or light at \(j^\star_\circ=I_\odot\). That something would have an equivalent temperature of \(394~{\rm K}\), and that’s the maximum temperature to which we can heat an object using optics that ensures that it “sees” the Moon in all sky directions.
So then let me ask another question… how specular would the Moon have to be for us to be able to light a fire with moonlight? Many surfaces can be characterized as though they were a combination of a diffuse and a specular reflector. What percentage of sunlight would the Moon have to reflect like a mirror, which we could then collect and focus to produce enough heat, say, to combust paper at the famous \(451~{\rm F}=506~{\rm K}\)? Very little, as it turns out.
If the Moon had a specularity coefficient of only \(\sigma_\circ=0.00031\), with a suitable arrangement of optics (which may require some mighty big mirrors in space, but never mind that, we’re talking about a thought experiment here), we could concentrate reflected sunlight and lunar heat to reach an intensity of
\[I=\alpha_\circ\sigma_\circ j^\star_\odot+(1-\alpha_\circ\sigma_\circ)j^\star_\circ=3719~{\rm W}/{\rm m}^2,\]
which, according to Ray Bradbury, is enough heat to make a piece of paper catch a flame.
So if it turns out that the Moon is not a perfectly diffuse emitter but has a little bit of specularity, it just might be possible to use its light to start a fire.
Feb 132016
This is what greeted me earlier this morning when I looked at my outdoor thermometer:
Brrrr. And tomorrow it’s supposed to get even colder. Where is that global warming that we were promised?
Feb 122016
I saw a question on Quora about humans and gravitational waves. How would a human experience an event like GW150914 up close?
Forget for a moment that those black holes likely carried nasty accretion disks and whatnot, and that the violent collision of matter outside the black holes’ respective event horizons probably produced deadly heat and radiation. Pretend that these are completely quiescent black holes, and thus the merger event produced only gravitational radiation.
A gravitational wave is like a passing tidal force. It squeezes you in one direction and stretches you in a perpendicular direction. If you are close enough to the source, you might feel this as a force. But the effect of gravitational waves is very weak. For your body to be stretched by one part in a thousand, you’d have to be about 15,000 kilometers from the coalescing black hole. At that distance, the gravitational acceleration would be more than 3.6 million g-s, which is rather unpleasant, to say the least. And even if you were in a freefalling orbit, there would be strong tidal forces, too, not enough to rip your body apart but certainly enough to make you feel very uncomfortable (about 0.25 g-forces over one meter.) So sensing a gravitational wave would be the least of your concerns.
But then… you’d not really be sensing it anyway. You would be hearing it.
Most of the gravitational wave power emitted by GW150914 was in the audio frequency range. A short chip rising in both pitch and amplitude. And the funny thing is… you would hear it, as the gravitational wave passed through your body, stretching every bit a little, including your eardrums.
The power output of GW150914 was stupendous. Its peak power was close to \(10^{56}\) watts, which exceeds the total power output of the entire visible universe by several orders of magnitude. So for a split second, GW150914 was by far the largest loudspeaker in the known universe.
And this is actually a better analogy than I initially thought. Because, arguably, those gravitational waves were a form of sound.
Now wait a cotton-picking minute you ask. Everybody knows that sounds don’t travel in space! Well… true to some extent. In empty space, there is indeed no medium that would carry the kind of mechanical disturbance that we call sound. But for gravitational waves, space is the medium. And in a very real sense, they are a form of mechanical disturbance, just like sound: they compress and stretch space (and time) as they pass by, just as a sound wave compresses and stretches the medium in which it travels.
But wait… isn’t it true that gravitational waves travel at the speed of light? Well, they do. But… so what? For cosmologists, this just means that spacetime might be represented as a “perfect fluid with a stiff equation of state”, i.e., its energy density and pressure would be equal.
Is this a legitimate thing to say? Maybe not, but I don’t know a reason off the top of my head why. It would be unusual, to be sure, but hey, we do ascribe effective equations of state to the cosmological constant and spatial curvature, so why not this? And I find it absolutely fascinating to think of the signal from GW150914 as a cosmic sound wave. Emitted by a speaker so loud that LIGO, our sensitive microphone, could detect it a whopping 1.3 billion light years away.
Feb 112016
If this discovery withstands the test of time, the plots will be iconic:
The plots depict an event that took place five months ago, on September 14, 2015, when the two observatories of the LIGO experiment simultaneously detected a signal typical of a black hole merger.
The event is attributed to a merger of two black holes, 36 and 29 solar masses in size, respectively, approximately 410 Mpc from the Earth. As the black holes approach each other, their relative velocity approaches the speed of light; after the merger, the resulting object settles down to a rotating Kerr black hole.
When I first heard rumors about this discovery, I was a bit skeptical; black holes of this size (~30 solar masses) have never been observed before. However, I did not realize just how enormous the distance is between us and this event. In such a gigantic volume, it is far less outlandish for such an oddball pair of two very, very massive (but not supermassive!) black holes to exist.
I also didn’t realize just how rapid this event was. I spoke with people previously who were studying the possibility of observing a signal, rising in amplitude and frequency, hours, days, perhaps even weeks before the event. But here, the entire event lasted no more than a quarter of a second. Bang! And something like three solar masses worth of mass-energy are emitted in the form of ripples in spacetime.
The paper is now accepted for publication and every indication is that the group’s work was meticulous. Still, there were some high profile failures recently (OPERA’s faster-than-light neutrinos, BICEP2’s CMB polarization due to gravitational waves) so, as they say, extraordinary claims require extraordinary evidence; let’s see if this detection is followed by more, let’s see what others have to say who reanalyze the data.
But if true, this means that the last great prediction of Einstein is now confirmed through direct observation (indirect observations have been around for about four decades, in the form of the change in the orbital period of close binary pulsars) and also, the last great observational confirmation of the standard model of fundamental physics (the standard model of particle physics plus gravity) is now “in the bag”, so to speak.
All in all, a memorable day.
Feb 062016
I just came across this gem of an example of bad coding in the C language.
Most C implementations allow arrays as function arguments. What is less evident (unless you actually bothered to read the standard, or at least, your copy of Kernighan and Ritchie from cover to cover) is that array arguments are silently converted to pointers. This can lead to subtle, difficult-to-spot, but deadly programming errors.
Take this simple function, for instance:
void fun(int arr[100])
{
printf("REPORTED SIZE: %d\n", sizeof(arr));
}
Can you guess what its output will be? Why, arr is declared as an array argument of 100 ints, so the output should be, on most systems, 400 (ints being 4 bytes in length), right?
Not exactly. Let me show you:
int main(int argc, char *argv[])
{
int theArr[100];
printf("THE REAL SIZE: %d\n", sizeof(theArr));
fun(theArr);
return 0;
}
On a 64-bit Linux box, this program compiles cleanly, and produces the following output:
THE REAL SIZE: 400 REPORTED SIZE: 8
Similarly, on Windows, using a 32-bit version of Microsoft’s C compiler, I once again get a clean compile and the program outputs this:
THE REAL SIZE: 400 REPORTED SIZE: 4
The morale of this story: Array arguments are pure, unadulterated evil. Avoid them when possible. They offer no advantage over pointer arguments, but they can badly mislead even the most experienced programmer. Compilers still allow array arguments, mainly for historical/compatibility reasons I guess, but it is unconscionable that they don’t even provide a warning when this abuse of syntax happens.
Jan 292016
Eons ago, back when dinosaurs still roamed the Earth, George W. Bush was still a first-term president, there were only five Star Wars films and Java applets were still cool, I created an applet that showed what Mars would look like if its surface was covered by oceans.
I liked what I did so I added the capability to use other data sets, including data sets for the Earth.
The applet is worthless now, or almost so. Java applets are no longer supported in Google’s Chrome browser. They were never really supported on mobile platforms. Even in browsers that do still support Java, the user has to go through hoops and add my domain as a security exception (not recommended) to allow my unsigned applet to run; all this a result of vain attempts to address the security risks inherent in Java and its implementations.
Anyhow, the applet still works if you can run it. And this is what the Earth looks like today:
Someone recently asked what our planet would look like if it was devoid of oceans. If sea levels were 5000 meters below the present value, the planet would still have a shallow ocean in place of the Pacific. Otherwise, though, it would be mostly dry land with only some inland seas where the Atlantic and the Indian oceans used to be. It would be possible to walk from pole to pole without wetting your feet; however, you might get a tad thirsty along the way, and there’d not be much rain either.
Decrease ocean levels by another 1000 meters to 6000 below present sea levels, and the last remaining ocean is gone:
Finally, at 7000 meters, the only open water that remains would be in places of the deepest ocean trenches. (Mind you, even then, some of these seas would still be up to four kilometers deep.)
I was also asked what things would look like if the seas rose. There is a surprising amount of change to coast lines by an increase of a mere 50 meters:
Florida is gone; Western Europe looks noticeably different. Increase the sea level rise to 200 meters, and now the change is rather more dramatic:
India is now an island or almost so (there may be some land bridges connecting it to the Asian continent that are too narrow to be visible at this map’s resolution). Much of Europe, Russia, Australia, South America, and the eastern parts of North America, gone.
Finally, at 1000 meters, only mountain ranges remain:
With this little dry land left, there is not much in the way of storms; like Jupiter with its Great Red Spot, the Earth might also develop long-lived storms that circumnavigate the planet many times before dissipating.
Jan 282016
If you are not following particle physics news or blog sites, you might have missed the big excitement last month when it was announced that the Large Hadron Collider may have observed a new particle with a mass of 750 GeV (roughly 800 times as heavy as a hydrogen atom).
Within hours of the announcement, a flurry of papers began to appear on the manuscript archive, arxiv.org. To date, probably at least 200 papers are there, offering a variety of explanations of this new observation (and incidentally, demonstrating just hungry the theoretical community has become for new data.)
Most of these papers are almost certainly wrong. Indeed, there is a chance that all of them are wrong, on account of the possibility that there is no 750 GeV resonance in the first place.
I am looking at two recent papers. One, by Buckley, discusses what we can (or cannot) learn from the data that have been collected so far. Buckley cautions researchers not to divine more from the data than what it actually reveals. He also remarks on the fact that the observational results of the two main detectors of the LHC, ATLAS and CMS, are somewhat in tension with one another.
From Fig. 2: Best fit regions (1 and 2σ) of a spin-0 mediator decaying to diphotons, as a function of mediator mass and 13 TeV cross section, assuming mediator couplings to gluons and narrow mediator width. Red regions are the 1 and 2σ best-fit regions for the Atlas13 data, blue is the fit to Cms13 data. The combined best fit for both Atlas13 and Cms13 (Combo13) are the regions outlined in black dashed lines. The best-fit signal combination of all four data sets (Combo) is the black solid regions.
The other paper, by Davis et al., is more worrisome. It questions the dependence of the presumed discovery on a crucial part of the analysis: the computation or simulation of background events. The types of reactions that the LHC detects happen all the time when protons collide; a new particle is discerned when it produce some excess events over that background. Therefore, in order to tell if there is indeed a new particle, precise knowledge of the background is of paramount importance. Yet Davis and his coauthors point out that the background used in the LHC data analysis is by no means an unambiguous, unique choice and that when they choose another, seemingly even more reasonable background, the statistical significance of the 750 GeV bump is greatly diminished.
I guess we will know more in a few months when the LHC is restarted and more data are collected. It also remains to be seen if the LHC can reproduce the Higgs discovery at its current, 13 TeV operating energy; if it does not, if the Higgs discovery turns out to be a statistical fluke, we may witness one of the biggest embarrassments in the modern history of particle physics.
Jan 282016
There is an interesting paper out there by Guerreiro and Monteiro, published a few months ago in Physics Letters A. It is about evaporating black holes. The author’s main assertion is that because of Hawking radiation, not even an infalling ray of light can ever cross the event horizon: rather, the event horizon evaporates faster than the light ray could reach it, neatly solving a bunch of issues and paradoxes associated with black holes and quantum physics, such as the problems with unitarity and information loss.
I find this idea intriguing and very appealing to my intuition about black holes. I just read the paper and I cannot spot any obvious errors. I am left wondering if the authors appreciated that the Vaydia metric is not a vacuum metric (indeed, it is easy to prove that a spherically symmetric time-dependent solution of Einstein’s field equations cannot be a vacuum solution; there will always be a radial momentum field, carrying matter out of or into the black hole) but it has no bearing on their conclusions I believe.
Now it’s a good question why I am only seeing a paper that is of great interest to me more than six months after its publication. The reason is that although the paper appeared in a pre-eminent journal, it was rejected by the manuscript archive, arxiv.org. This is deeply troubling. The paper is certainly not obviously wrong. It is not plagiarized. Its topic is entirely appropriate to the arXiv subject field to which it was submitted. It is not a duplicate, nor did the authors previously abuse arXiv’s submission system. Yet this paper was rejected. And the most troubling bit is that we do not know why; the rejection policy of arXiv is not only arbitrary, it seems, but also lacks transparency.
This manuscript archive is immensely valuable to researchers. It is one of the greatest inventions of the Internet era. I feel nothing but gratitude towards the people who established and maintain this repository. Nonetheless, I do not believe that such an opaque and seemingly arbitrary rejection policy is justifiable. I hope that this will be remedied and that arXiv’s administrators will take the necessary steps to ensure that in the future, rejections are based on sound criteria and the decisions are transparently explained.
Jan 282016
This is NASA’s week of tragedy.
Today is the 30th anniversary of the loss of the space shuttle Challenger with seven souls on board. One of my notable memories of this event is that it was the first time that I recall that the national broadcaster in then still communist Hungary didn’t dub a speech of Ronald Reagan. I think the speech was actually carried live (it took place at 5 PM EST, which would have been 11 o’clock at night in Hungary; late, but not too late) and it may have been subtitled, or perhaps not translated at all, I cannot remember. For me, it was also the first disaster that I was able to record on my VCR; for days afterwards, my friends and I replayed and replayed the broadcasts, trying to make sense of what we saw. (Sadly, those tapes are long lost. My VCR was a Grundig 2000 unit using a long-forgotten standard. After I left Hungary, I believe my parents used it for a while, but what ultimately happened to it and my cassettes, I do not know.)
Yesterday marked the 49th anniversary of the Apollo 1 fire that claimed the lives of three astronauts who were hoping to be the first to travel to the Moon. Instead, they ended up burned to a crisp in the capsule’s pure oxygen atmosphere, with no chance of escape. Arguably though, their tragedy resulted in much needed changes to the Apollo program that made it possible for Apollo 11 to complete its historic journey successfully.
And finally, in four days it will be exactly 13 years since the tragedy of Columbia, which disintegrated in the upper atmosphere at the conclusion of a successful 16-day mission. I remember that Saturday all too well. I was working, but I also had CNN running on one of my monitors. “Columbia, Houston, comm check” I heard many times and I knew something already that those in the mission center didn’t: CNN was already showing the multiple contrails over Texas, which could only mean one thing: a disintegrating vehicle. And then came the words, “Lock the doors”, and we knew for sure that it was all over.
Of course the US space program was not the only one with losses. The Soviet program had its own share of tragedies, including the loss of Vladimir Komarov (Soyuz 1 crash, April 24, 1967), three astronauts on boar Soyuz 11 (depressurization after undocking while in space, June 30, 1971), and several deaths on ground during training. But unlike the American cases, these Soviet deaths were not all clustered around the same date.
Jan 272016
I was never a fan of conspiracy theories. Most popular conspiracies are highly improbable: maintaining complete secrecy would require thousands of people to cooperate for many years.
But just how improbably are conspiracies, really? Well, now there is a quantitative estimate, thanks a paper by David Robert Grimes. Grimes used several specific, high-profile cases of actual conspiracies to estimate the likelihood that a conspiracy is revealed by a participant. He found that while the probability that any individual participant betrays the conspiracy may be quite small, the likelihood that the conspiracy is revealed over time nonetheless approaches unity over the years, as demonstrated by the following diagram:
The parameter p in these curves represents the probability that any given participant will break his silence in a given year.
So then, this is it… by Grimes’s calculations, if the Moon landing had been a hoax or if similarly, vaccination or climate change were both just vast conspiracies, these would all have been revealed with a very high likelihood in the span of no more than a few years.
None of this will deter conspiracy theorists, I am sure. If all other arguments fail, they’ll just declare Grimes himself to be a member of the conspiracy, too. Well, for all you know, I may also be an agent of the secret cabal, using my blog to lure the unsuspecting into believing that man walked on the Moon, that vaccines save lives or that anthropogenic climate change is actually happening…
Jan 202016
One of the blessings of being self-employed is that I don’t need to read IT job advertisements on a regular basis.
But for those friends of mine who do, I just came across this gem that helps translate the common buzzwords and catch phrases that appear in these ads:
Don’t let any of this deter you from going after that position… just tamper your expectations.
Jan 142016
Recenly, there was a particular piece of music that caught my attention on CBC’s The Signal: Sapokanikan by Joanna Newsom.
The song begins with the lines,
The cause is Ozymandian
The map of Sapokanikan
is sanded and beveled
The land lone and leveled
By some unrecorded and powerful hand.
This made me re-read Shelley’s timeless poem about the ruined statue of Ozymandias in the desert:
‘My name is Ozymandias, king of kings:
Look at my works, ye Mighty, and despair!’
Nothing beside remains. Round the decay
Of that colossal wreck, boundless and bare
The lone and level sands stretch far away.
And then here is a real-life Ozymandian tale from a few days ago, from China: A 37-meter tall golden statue of Mao erected in the middle of nowhere.
The ending, however, is different: After the statue has been ridiculed on Chinese social media (with many quoting from Shelley’s Ozymandias) the statue was hastily demolished. Wisdom has not yet departed the Middle Kingdom, it seems.
Jan 062016
I’ve become a calendar boy.
Or to be more precise, an illustration in a paper that my friend and colleague, Eniko Madarassy and I published together early last year in Physical Review D found its way to the 2016 calendar of the American Physical Society.
Now if only it came with perks, such as getting a discount on my APS membership or something… but no, in fact they didn’t even bother to tell us that this was going to happen, I only found out today when I opened my mailbox and found the calendar inside. Oh well… It was still a nice surprise, so I am not complaining.
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!
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.“
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.
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.
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| 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…
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| 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.
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.