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.
– Frank Borman from Apollo 8, December 24, 1968
Dec 242012
Dec 202012
I have received a surprising number of comments to my recent post on the gravitational potential, including a criticism: namely that what I am saying is nonsense, that in fact it is well known (there is actually a resolution by the International Astronomical Union to this effect) that in the vicinity of the Earth, the gravitational potential is well approximated using the Earth’s multipole plus tidal contributions, and that the potential, therefore, is determined primarily by the Earth itself, the Sun only playing a minor role, contrary to what I was blabbering about.
But this is precisely the view of gravity that I was arguing against. As they say, a picture is worth a thousand words, so let me try to demonstrate it with pictures, starting with this one:
It is a crude one-dimensional depiction of the Earth’s gravity well (between the two vertical black lines) embedded in the much deeper gravity well (centered) of the Sun. In other words, what I depicted is the sum of two gravitational potentials:
$$U=-\frac{GM}{R}-\frac{Gm}{r}.$$
Let me now zoom into the area marked by the vertical lines for a better view:
It looks like a perfectly ordinary gravitational potential well, except that it is slightly lopsided.
So what if I ignored the Sun’s potential altogether? In other words, what if I considered the potential given by
$$U=-\frac{Gm}{r}+C$$
instead, where \(C\) is just some normalization constant to ensure that I am comparing apples to apples here? This is what I get:
The green curve approximates the red curve fairly well deep inside the potential well but fails further out.
But wait a cotton-picking minute. When I say “approximate”, what does that tell you? Why, we approximate curves with Taylor series, don’t we, at least when we can. The Sun’s gravitational potential, \(-GM/R\), near the vicinity of the Earth located at \(R=R_0\), would be given by the approximation
$$-\frac{GM}{R}=-\frac{GM}{R_0}+\frac{GM}{R_0^2}(R-R_0)-\frac{GM}{R_0^3}(R-R_0)^2+{\cal O}\left(\frac{GM}{R_0^4}[R-R_0]^3\right).$$
And in this oversimplified one-dimensional case, \(r=R-R_0\) so I might as well write
$$-\frac{GM}{R}=-\frac{GM}{R_0}+\frac{GM}{R_0^2}r-\frac{GM}{R_0^3}r^2+{\cal O}\left(\frac{GM}{R_0^4}r^3\right).$$
(In the three-dimensional case, the math gets messier but the principle remains the same.)
So when I used a constant previously, its value would have been \(C=-GM/R_0\) and this would be just the zeroeth order term in the Taylor series expansion of the Sun’s potential. What if I include more terms and write:
$$U\simeq-\frac{Gm}{r}-\frac{GM}{R_0}+\frac{GM}{R_0^2}r-\frac{GM}{R_0^3}r^2?$$
When I plot this, here is what I get:
The blue curve now does a much better job approximating the red one. (Incidentally, note that if I differentiate by \(r\) to obtain the acceleration, I get: \(a=-dU/dr=-Gm/r^2-GM/R_0^2+2GMr/R_0^3\), which is the sum of the terrestrial acceleration, the solar acceleration that determines the Earth’s orbit around the Sun, and the usual tidal term. So this is another way to derive the tidal term. But, I digress.)
The improvement can also be seen if I plot the relative error of the green vs. blue curves:
So far so good. But the blue curve still fails miserably further outside. Let me zoom back out to the scale of the original plot:
Oops.
So while it is true that in the vicinity of the Earth, the tidal potential is a useful approximation, it is not the “real thing”. And when we perform a physical experiment that involves, e.g., a distant spacecraft or astronomical objects, the tidal potential must not be used. Such experiments, for instance tests measuring gravitational time dilation or the gravitational frequency shift of an electromagnetic signal are readily realizable nowadays with precision equipment.
But it just occurred to me that even at the pure Newtonian level, the value of the potential \(U\) plays an observable role: it determines the escape velocity. A projectile escapes to infinity if its overall energy (kinetic plus potential) is greater than zero: \(mv^2/2 + mU>0\). In other words, the escape velocity \(v\) is determined by the formula
$$v>\sqrt{-2U}.$$
The escape velocity works both ways; it also tells you the velocity to which an object accelerates as it falls from infinity. So suppose you let lose a rock somewhere in deep space far from the Sun and it falls towards the Earth. Its velocity at impact will be 43.6 km/s… without the Sun’s influence, its impact velocity would have been only 11.2 km/s.
So using somewhat more poetic language, the relationship of us, surface dwellers, to distant parts of the universe, is determined primarily not by the gravity of the planet on which we stand, but by the gravitational field of our Sun… or maybe our galaxy… or maybe the supercluster of which our galaxy is a member.
As I said in my preceding post… gravity is weird.
The following gnuplot code, which I am recording here for posterity, was used to produce the plots in this post:
set terminal gif size 320,240 unset border unset xtics unset ytics set xrange [-5:5] set yrange [-5:0] set output 'pot0.gif' set arrow from 0.5,-5 to 0.5,0 nohead lc rgb 'black' lw 0.1 set arrow from 1.5,-5 to 1.5,0 nohead lc rgb 'black' lw 0.1 plot -1/abs(x)-0.1/abs(x-1) lw 3 notitle unset arrow set xrange [0.5:1.5] set output 'pot1.gif' plot -1/abs(x)-0.1/abs(x-1) lw 3 notitle set output 'pot2.gif' plot -1/abs(x)-0.1/abs(x-1) lw 3 notitle,-0.1/abs(x-1)-1 lw 3 notitle set output 'pot3.gif' plot -1/abs(x)-0.1/abs(x-1) lw 3 notitle,-0.1/abs(x-1)-1 lw 3 notitle,-0.1/abs(x-1)-1+(x-1)-(x-1)**2 lw 3 notitle set xrange [-5:5] set output 'pot4.gif' set arrow from 0.5,-5 to 0.5,0 nohead lc rgb 'black' lw 0.1 set arrow from 1.5,-5 to 1.5,0 nohead lc rgb 'black' lw 0.1 replot unset arrow set output 'potdiff.gif' set xrange [0.5:1.5] set yrange [*:*] plot 0 notitle,\ ((-1/abs(x)-0.1/abs(x-1))-(-0.1/abs(x-1)-1))/(-1/abs(x)-0.1/abs(x-1)) lw 3 notitle,\ ((-1/abs(x)-0.1/abs(x-1))-(-0.1/abs(x-1)-1+(x-1)-(x-1)**2))/(-1/abs(x)-0.1/abs(x-1)) lw 3 notitle
Dec 182012
There is something curious about gravity in general relativity. Specifically, the gravitational potential.
In high school, we were taught about this mysterious thing called “potential energy” or “gravitational potential”, but we were always assured that it’s really just the difference between potentials that matters. For instance, when you drop a stone from a tall tower, its final velocity (ignoring air resistance) is determined by the difference in gravitational potential energy at the top and at the bottom of the tower. If you study more sophisticated physics, you eventually learn that it’s not the gravitational potential, only its gradient that has physically observable meaning.
Things are different in general relativity. The geometry of spacetime, in particular the metric and its components are determined by the gravitational potential itself, not its gradient. In particular, we have
$$
g_{00} = 1 – \frac{2GM}{c^2r}
$$
in the infamous Schwarzschild metric, where \(g\) is the metric tensor, \(G\) is the universal gravitational constant, \(c\) is the speed of light, \(M\) is the mass of the gravitating object, and \(r\) is the distance from it. Since the Newtonian gravitational field is given by \(U=-GM/r\), this means
$$
g_{00} = 1 – \frac{2}{c^2}U.
$$
This quantity has physical significance. For instance, the angle by which light is deflected when it passes near a star is given by \(4c^{-2}U\).
So then, what is the value of \(U\) here on the surface of the Earth? Why, it’s easy. The mass of the Earth is \(M_E=6\times 10^{24}\) kg, its radius is roughly \(R_E=6.37\times 10^6\) m, so
$$
\frac{1}{c^2}U_E=\frac{GM_E}{c^2R_E} \simeq 7\times 10^{-10}.
$$
You could be forgiven for thinking that this is the right answer, but it really isn’t. For let’s just calculate the gravitational potential of the Sun as felt here on the Earth. Yes, I know, the Sun is quite a distance away and all, but play along, will you.
The mass of the Sun is \(M_\odot=2\times 10^{30}\) kg, its distance from the Earth is \(R_\odot=1.5\times 10^{11}\) m. So for the Sun,
$$
\frac{1}{c^2}U_\odot=\frac{GM_\odot}{c^2R_\odot} \simeq 10^{-8}.
$$
Whoops! This is more than an order of magnitude bigger than the Earth’s own gravitational potential! So right here, on the surface of the Earth, \(U\) is dominated by the Sun!
Or is it? Let’s just quickly check what the gravitational potential of the Milky Way is here on the Earth. The Sun is zipping around the center in what we believe is a roughly circular orbit, at a speed of 250 km/s. We know that for a circular orbit, the velocity is \(v_\star=\sqrt{GM_\star/R_\star}=\sqrt{U_\star}\), so
$$
\frac{1}{c^2}U_\star = \frac{v_\star^2}{c^2} \simeq 7\times 10^{-7}.
$$
This is almost two orders of magnitude bigger than the gravitational potential due to the Sun! So here, on the surface of the Earth, the gravitational potential is dominated by the large concentration of mass near the center of the Milky Way, some 8 kiloparsecs (25 thousand light years) from here. Wow!
But wait a minute, is this the end? There is the Local Supercluster of galaxies of which the Milky Way is part. Its mass \(M_V\) is believed to be about \(10^{15}\) times the mass of the Sun, and it is believed to be centered near the Virgo cluster, about 65 million light years or about \(R_V=6.5\times 10^{23}\) meters away. So (this is necessarily a crude estimate, but it will serve as an order-of-magnitude value):
$$
\frac{1}{c^2}U_V=\frac{GM_V}{c^2R_V} \simeq 2.3\times 10^{-6}.
$$
This value for the gravitational potential right here on the Earth’s surface, astonishingly, is more than 3,000 times the gravitational potential due to the Earth’s own mass. Is this the end? Or would more distant objects exert an even greater influence on the gravitational field here on the Earth? The answer is the latter. That is because as we look further into the distant universe, the amount of mass we see goes up by the square of the distance, but their gravitational influence goes down by only the first power of the distance. So if you look at 10 times the distance, you will see 100 times as much matter; the gravitational influence of each unit of matter will decrease by a factor of 10 but overall, with a hundred times as much mass, the total gravitational influence will still go up tenfold.
So the local gravitational field is dominated by the most distant matter in the universe.
And by local gravitational field, I of course mean the local metric, which in turn determines how light is deflected, how clocks slow down, how the wavelength of photons shifts.
Insanely, we may not even know how fast a “true” clock in our universe runs, one that is free of gravitational influences, because we don’t know the actual magnitude of the sum total of all gravitational influences here on the Earth.
Gravity is weird.
Dec 182012
I came across this a while back; one of the most astonishing places on Earth, near the village of Derweze (also spelled as Darvaza) in Turkmenistan.
Situated in an already lunar looking landscape in the Karakum desert, there is a crater that is unlike anything on the real Moon: it’s a crater full of fire. The ground collapsed here in 1971 after Soviet geologists were drilling for oil and found natural gas instead. The gas was ignited in the hope that it would safely burn off in days… it has been burning ever since.
Dec 142012
In just a few minutes, it will be exactly 40 years that the crew of Apollo 17 took off from the Moon, ending humanity’s last excursion to date on our satellite.
Incredibly, no human ventured beyond low Earth orbit since.
Dec 132012
From the latest issue of New Scientist:
Dec 132012
Imagine a world with weather. Hydrocarbon rains falling from an orange sky onto a deadly cold surface with chunks of ice as hard and as dry as rock; or onto vast hydrocarbon seas driven by freezing winds.
Meanwhile, through the orange haze overhead, you may glimpse a giant orb, filling half the sky, and surrounded by an even more magnificent flat ring.
This world exists. It’s Saturn’s moon Titan, the only body in the solar system other than the Earth with a stable liquid on its surface and genuine weather with precipitation and a “hydrological” cycle.
And now we know for sure that Titan has real rivers. Dubbed “Mini Nile” on NASA’s Web site, this 400 km long hydrocarbon river is the largest seen to date, and it appears to be filled with liquid along its entire length.
I truly envy those humans who, hopefully on a not too distant day in the future, will stand on the banks of this river, perhaps not even wearing a pressure suit just heated clothing and a breathing mask, and stare at this river in awe.
What will they find in the liquid? Is it harboring some primitive form of life?
Dec 082012
One of my favorite photographs ever, in fact one that I even use on my Facebook timeline page as a background image, was taken by a certain Bill Anders when he was flying almost 400,000 km from the Earth. Anders was one of the first three members of our species who flew to another celestial body (albeit without landing on its surface; that came a bit later.)
Yesterday, I read a very interesting article about Anders, both his trip on board Apollo 8 and his life afterwards. The article also touched upon the topic of religion.
The message radioed back by the crew of Apollo 8 is probably the most memorable Christmas message ever uttered by humans. (Or maybe I am biased.) And yes, it starts with the words from Genesis, but I always viewed it the way it was presumably intended: as an expression of awe, not as religious propaganda.
The curious thing, as mentioned in the article, is that it was this trip around the Moon that changed the traditional Christian viewpoint of Anders about Earthlings created by a God in his own image.
“When I looked back and saw that tiny Earth, it snapped my world view,” Anders is quoted as saying. “Are we really that special? I don’t think so.”
Well, this pretty much sums up why I am an atheist. I’d like to believe that it’s not hubris; it’s humility.
Dec 032012
Update (September 6, 2013): The analysis in this blog entry is invalid. See my September 6, 2013 blog entry on this topic for an explanation and update.
It has been a while since I last wrote about a pure physics topic in this blog.
A big open question these days is whether or not the particle purportedly discovered by the Large Hadron Collider is indeed the Higgs boson.
One thing about the Higgs boson is that it is a spin-0 scalar particle: this means, essentially, that the Higgs is identical to its mirror image. This distinguishes the Higgs from pseudoscalar particles that “flip” when viewed in a mirror.
So then, one way to distinguish the Higgs from other possibilities, including so-called pseudoscalar resonances, is by establishing that the observed particle indeed behaves either like a scalar or like a pseudoscalar.
Easier said than done. The differences in behavior are subtle. But it can be done, by measuring the angular distribution of decay products. And this analysis was indeed performed using the presently available data collected by the LHC.
Without further ado, here is one view of the data, taken from a November 14, 2012 presentation by Alexey Drozdetskiy:
The solid red line corresponds to a scalar particle (denoted by 0+); the dotted red line to a pseudoscalar (0−). The data points represent the number of events. The horizontal axis represents a “Matrix Element Likelihood Analysis” value, which is constructed using a formula similar to this one (see arXiv:1208.4018 by Bolognesi et al.):
$${\cal D}_{\rm bkg}=\left[1+\frac{{\cal P}_{\rm bkg}(m_{4\ell};m_1,m_2,\Omega)}{{\cal P}_{\rm sig}(m_{4\ell};m_1,m_2,\Omega)}\right]^{-1},$$
where the \({\cal P}\)-s represent probabilities associated with the background and the signal.
So far so good. The data are obviously noisy. And there are not that many data points: only 10, representing 16 events (give or take, as the vertical error bars are quite significant).
There is another way to visualize these values: namely by plotting them against the relative likelihood that the observed particle is 0+ or 0−:
In this fine plot, the two Gaussian curves correspond to Monte-Carlo simulations of the scalar and pseudoscalar scenarios. The position of the green arrow is somehow representative of the 10 data points shown in the preceding plot. The horizontal axis in this case is the logarithm of a likelihood ratio.
On the surface of it, this seems to indicate that the observed particle is indeed a scalar, just like the Higgs. So far so good, but what bothers me is that this second plot does not indicate uncertainties in the data. Yet, judging by the sizable vertical error bars in the first plot, the uncertainties are significant.
However, to relate the uncertainties in the first plot, one has to be able to relate the likelihood ratio on this plot to the MELA value on the preceding plot. Such a relationship indeed exists, given by the formula
$${\cal L}_k=\exp(-n_{\rm sig}-n_{\rm bkg})\prod_i\left(n_{\rm sig}\times{\cal P}^k_{\rm sig}(x_i;\alpha;\beta)+n_{\rm bkg}\times{\cal P}_{\rm bkg}(x_i;\beta)\right).$$
The problem with this formula, from my naive perspective, is that in order to replicate it, I would need to know not only the number of candidate signal events but also the number of background events, and also the associated probability distributions and values for \(\alpha\) and \(\beta\). I just don’t have all the information necessary to reconstruct this relationship numerically.
But perhaps I don’t have to. There is a rather naive thing one can do: and that would be simply calculating the weighted average of the data points in the first plot. When I do this, I get a value of 0.57. Lo and behold, it has roughly the same relationship to the solid red Gaussian in that plot as the green arrow to the 0+ Gaussian in the second.
Going by the assumption that my naive shortcut actually works reasonably well, I can take the next step. I can calculate a \(1\sigma\) error on the weighted average, which yields \(0.57^{+0.24}_{-0.23}\). When I (admittedly very crudely) try the transcribe this uncertainty to the second plot, I get something like this:
Yes, the error is this significant. So while the position of the green arrow is in tantalizing agreement with what one would expect from a Higgs particle, the error bar says that we cannot draw any definitive conclusions just yet.
But wait, it gets even weirder. Going back to the first plot, notice the two data points on the right. What if these are outliers? If I remove them from the analysis, I get something completely different: namely, the value of \(0.43^{+0.26}_{-0.21}\). Which is this:
So without the outliers, the data actually favor the pseudoscalar scenario!
I have to emphasize: what I did here is rather naive. The weighted average may not accurately represent the position of the green arrow at all. The coincidence in position could be a complete accident. In which case the horizontal error bar yielded by my analysis is completely bogus as well.
I also attempted to check how much more data would be needed to reduce the size of these error bars sufficiently for a true \(1\sigma\) result: about 2-4 times the number of events collected to date. So perhaps what I did is not complete nonsense after all, because this is what knowledgeable people are saying: when the LHC collected at least twice the amount of data it already has, we may know with reasonable certainty if the observed particle is a scalar or a pseudoscalar.
Until then, I hope I did not make a complete fool of myself with this naive analysis. Still, this is what blogs are for; I am allowed to say foolish things here.
Nov 302012
An article we wrote with Slava Turyshev about the Pioneer anomaly and its resolution, at the request of IEEE Spectrum, is now available online.
It was an interesting experience, working with a professional science journalist and her team. I have to admit that I did not previously appreciate the level of professionalism that is behind such a “members only” magazine.
Nov 052012
It appears that there is middle ground after all between pro-nuclear complacency and anti-nuclear alarmism.
Evan Osnos, writing for The New Yorker, points out that “America’s hundred-and-four nuclear reactors handled hurricane Sandy with far less trouble than other parts of the power grid”. But he goes on to note that a higher storm surge could have caused grave trouble, just as the tsunami did in Japan. He quotes a former nuclear engineer who said that complacency “is precisely that kind of closed or narrow mindedness that allowed Fukushima to happen.” The United States has a significant number of vulnerable plants. Whereas in Japan, the history of the island is known going back well over a thousand years (a history, specifically the history of the tsunami of 869, that Fukushima’s designers chose to ignore, with tragic consequences.) In the US, records only go back a little over three centuries, so if anything, more caution should be warranted.
But Osnos is not advocating shutting down the industry. “the key is not to pretend that the nuclear industry is a house of cards,” he writes, “but to prevent a non-disaster from becoming a disaster.”
Unfortunately, our memory for disasters tends to be alarmingly short. Osnos points out that after a flood wreaked havoc with New York’s subways in 2007, some 30 million dollars were spent on flood protection… and that’s it. Then it was all forgotten. One can only hope that Sandy will leave a more lasting impression when it comes to disaster preparedness, especially when nuclear plants are concerned.
Oct 272012
I gave this post a provocative title intentionally. I am a one-time conservative voter. One reason why I feel disenchanted with conservatives (not just in Canada, mind you) these days is that they seem to have politicized science at every opportunity. Sure, others have done the same thing in the past (liberals are certainly no knights in shining armor) but the past is the past, right now I am worried about the present. Reproductive health, stem cell research, environmental science, climate change, you name it… if they don’t like the result, they attack it, and if the result withstands politically motivated attacks, they move on to attack the researcher. Or, as the case might be, they do their darnedest to undermine the integrity of the data.
This is precisely what happened when Canada’s conservative government eliminated the mandatory “long form” census that was sent to 20% of Canadian households. Sure, there were legitimate privacy concerns that could and should have been addressed (I even wrote a letter to the Chief Statistician myself many years ago when we received the long form census and found some questions a tad sensitive, and the safeguards against being able to personally identify responders inadequate.) But eliminate the long-form census completely, making it “optional”? That is a bone-headed stupid move. The most charitable interpretation is that the government simply didn’t know what they were doing because they don’t understand statistics. A more sinister possibility is that they knew exactly what they were doing, and they are undermining the integrity of Statistics Canada’s data sets on purpose. In light of what has been done and said in recent years, despite my general dislike of conspiracy theories, I am leaning towards accepting this interpretation.
And now the results are beginning to arrive, demonstrating the validity of all those concerns. According to the data collected, the percentage of people in Canada whose mother tongue is English remained the same despite the fact that in the meantime, Canada received 1.1 million new immigrants, 80% of whom had a mother tongue other than English of French. Or that the number of people in Canada whose mother tongue is a non-official language supposedly dropped by 420,000, again despite the above-mentioned immigration statistics.
Of course these results make no sense. What they reflect is a faulty data collection methodology. A methodology forced upon Statistics Canada by a political leadership that finds it appropriate to meddle with science.
The damage due to such meddling is profound and lasting. There is the immediate damage of distorted results. This can be fixed easily; for instance, if Canada were to return to the long form census, this one census could be discarded as an outlier and the long-term integrity of the data would remain assured. But by politicizing the science and polarizing researchers, they undermine the process itself, creating a partisan mindset. Defenders of scientific integrity will unavoidably find themselves participating in political debates and feel forced to adopt polarized positions. Climate scientists often sound more like preachers of a religion than impartial researchers. Could this be, at least in part, due to the polarized atmosphere in which their scientific results are scrutinized? Ultimately, it is the integrity of the scientific process that suffers, and that’s bad news for all of us, regardless of our political views.
Oct 152012
This is not some fringe moron but a Republican representative for Georgia’s 10th district. Member of the Tea Party caucus. And a physician to boot:
Groan. I guess I must be a servant of the Devil then (go, Lucifer!) as I, too, spread the “lie from the pit of hell” called the Big Bang theory. Or the lie called “evolution”. Or the lie called “embryology” (that’s a new one for me; would you know what’s wrong with embryology from a Tea Party perspective?) What next, write down the Friedmann equations, be burned at the stake?
Now this is why, even if everything you told me about Obama and his Chicago lot was the gospel truth, I’d still prefer them over Republicans these days. I’d rather take 21st century corruption than go back to the Middle Ages.
Part of me wonders (hopes, even) that this is just a cynical attempt to attract votes and he is not actually this stone dumb stupid. But I don’t know what it says about the Republican party these days if these are the kinds of votes its representatives go after.
Oct 062012
Wow. If these plots are to be believed, Voyager 1 may have reached the heliopause at last:
This is, well, not exactly unexpected but still breathtaking.
The discovery of the heliopause was one of the “holy grail” science objectives of the extended “interstellar” mission of the twin Voyager spacecraft. If confirmed, it means that Voyager 1 is the first man-made object to have entered the interstellar medium, traveling through a region in the outer solar system that is no longer dominated by charged particles from the solar wind. (Gravitationally, this is still very much our Sun’s domain; there are comets out there with elliptical orbits that extend to many thousands of astronomical units.)
Not bad for a spacecraft that was launched over 35 years ago and flew by Saturn just a few months into the presidency of Ronald Reagan. Its twin finished its flyby of Neptune when the Berlin Wall was still standing. And they are both still alive and well. Voyager 1 is more than 120 astronomical units from the Sun these days. It takes about 17 hours for its radio signal to reach the Earth. If all goes well, it has sufficient electrical power to operate its on-board instruments for another decade or so.
Oct 042012
55 years ago today, the Space Age began when the Soviet Union launched “Elementary Satellite 1”, better known as Простейший Спутник-1; or, in Latin transliteration, as (Prosteishii) Sputnik-1.
Inadvertently perhaps, but Sputnik-1 also launched what is nowadays called “radio science”: observations that utilize a spacecraft’s radio signal to determine the spacecraft’s position (and thus, the forces that act on the spacecraft) and the properties of the medium through which the signal travels. In the case of Sputnik-1, this meant deducing the density of the upper atmosphere (from the drag force acting on the satellite) and the electromagnetic properties of the ionosphere.
Sputnik-1 spent a total of about three months in orbit (22 days operational) before it fell back to the Earth. By then, the Space Race was running full steam ahead, culminating in the manned Apollo Moon landings in 1969… an accomplishment that, today, seems to be more in the realm of fiction than back in 1957.
Sep 212012
I am reading about a new boson.
No, not the (presumed) Higgs boson with a mass of about 126 GeV.
I am reading about a lightweight boson, with a mass of only about 38 MeV, supposedly found at the onetime pride of Soviet science, the Dubna accelerator.
Now Dubna may not have the raw power of the LHC, but the good folks at Dubna are no fools. So if they announce what appears to be a 5-sigma result, one can’t just not pay attention.
The PHOTON-2 setup. S1 and S2 are scintillation counters. From arXiv:1208.3829.
But a 38 MeV boson? That’s not light, that’s almost featherweight. It’s only about 75 times the mass of the electron, for crying out loud. Less than 4% of the weight of the proton.
The discovery of such a lightweight boson would be truly momentous. It would certainly turn the Standard Model upside down. Whether it is a new elementary particle or some kind of bound state, it is not something that can be fit easily (if at all) within the confines of the Standard Model.
Which is one reason why many are skeptical. This discover is, after all, not unlike that of the presumed Higgs boson, is really just the discovery of a small bump on top of a powerful background of essentially random noise. The statistical significance (or lack thereof) of the bump depends fundamentally on our understanding and accurate modeling of that background.
And it is on the modeling of the background that this recent Dubna announcement has been most severely criticized.
Indeed, in his blog Tommaso Dorigo makes a very strong point of this; he also suggests that the authors’ decision to include far too many decimal digits in error terms is a disturbing sign. Who in his right mind writes 38.4935 ± 1.02639 as opposed to, say, 38.49 ± 1.03?
To this criticism, I would like to offer my own. I am strongly disturbed by the notion of a statistical analysis described by an expression of the type model = data − background. What we should be modeling is not data minus some theoretical background, but the data, period. So the right thing to do is to create a revised model that also includes the background and fit that to the data: model’ = model + background = data. When we do things this way, it is quite possible that the fits are a lot less tight than anticipated, and the apparent statistical significance of a result just vanishes. This is a point I raised a while back in a completely different context: in a paper with John Moffat about the statistical analysis of host vs. satellite galaxies in a large galactic sample.
Sep 182012
The other day, I purchased a 32 GB USB stick for fifteen dollars. 32 GB? That is four DVDs. Some 50 or so CD-ROMs. Almost 500 times the hard disk space that I had in my first IBM compatible PC. More than 22,000 3.5″ floppy disks. More than 200,000 single density 5.25″ floppy disks that I used to use with my Commodore 64. More than half a million times the RAM of that Commodore 64. More than 30 million times the memory of a Sinclair ZX-80 from 1980. For less than one tenth the price, I might add, even before adjusting for inflation.
Some people, when they contemplate these numbers, conclude that such leaps could not have just happened; surely, there is alien technology involved. The government knows.
Then again… if we had access to alien supertechnology, don’t you think that the capacity of electric storage batteries would have advanced more than the pitiful factor of 5 or so that distinguishes a modern Li-ion battery from its 150-year old lead-acid cousin?
Sep 132012
Busy celebrating our 20th wedding anniversary yesterday, I forgot that there was another important anniversary on September 12: it was fifty years ago yesterday that a certain John F. Kennedy uttered the words, “We choose to go to the Moon. We choose to go to the Moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too.” And with those words, an astonishing sequence of events took place, and before the 1960s came to an end, two Americans indeed landed on the Moon… a technological feat the like of which the world has not seen since 1972, when the last of the Apollo Moon shots took place.
Sep 062012
Nature had a nice editorial a few days ago about the Pioneer Anomaly and our research, titled “…and farewell to the Pioneer anomaly” (so titled because in the print edition, it is right below the obituary, titled “Farewell to a pioneer”, of Bernard Lovell, builder of what was at the time the world’s largest steerable radio telescope at Jodrell Bank).
Farewell, yes, though I still hope that we will have the wherewithal to publish a longer article in which we provide the details that did not fit onto the pages of Physical Review Letters. We ought to update our review paper in Living Reviews in Relativity, too. We need to prepare for the release of the data used in our analysis. And, if possible, I’d like to spend time tackling some of the open questions we discuss near the end of our last paper, such as analyzing the spin behavior of the two spacecraft or making use of DSN signal strength measurements to improve the trajectory solution.
First things first, though; right now, my priorities are to a) earn money (which means doing things that I actually get paid for, not Pioneer) and b) get ready to have our upstairs bathtub replaced (the workmen will be here Monday morning), after which I plan to do the wall tiles myself (with fingers firmly crossed in the hope that I won’t mess it up too badly.)
Yes, sometimes such mundane things must take priority.
Aug 252012
The first human being ever to walk on the surface of the Moon is no longer with us.
Good bye, Neil Armstrong.