As Larry Kellogg said in his lunar-update newsletter, people who didn’t believe before that the Moon landing happened are unlikely to be convinced by this, but it’s still darn nice to be able to see nearly 40-year old footsteps on the Moon from orbit:
Apollo 14 footsteps
Forty years ago this morning, Apollo 11 was launched: Neil Armstrong and Buzz Aldrin were on their way to land at Mare Tranquilitatis, in the most significant journey in human history to this date.
The scary part is that this year also marks the 37th anniversary of the last trip to the Moon, indeed the last voyage by a human being beyond low Earth orbit.
I was only 6 when Armstrong and Aldrin landed on the Moon, and I had no doubt in my mind that by the time I turn 46, there would be people on the Moon, on Mars, possibly on select satellites of Jupiter and Saturn, perhaps even on their way to the stars.
Now that I am 46, I am doubtful that I will live long enough to see another human fly beyond low Earth orbit. This is not a pleasant thought. Perhaps I’ll be lucky enough to live another 40 years in good physical and mental health, and get a chance to be proven wrong.
Until then, I keep dwelling on the irony of the fact that nowadays, most of the documentaries you can find on manned deep space missions and exploration of the Moon are aired on the History Channel.
The premier Internet physics and astronomy preprint archive, ArXiv, seems to be having some serious problems tonight. I used the catchup interface to check for new papers, only to find messages like this:
Apparently all new papers are unavailable, and many older papers, too… I checked briefly and found papers dating back to last October that appear to have vanished. Including some half a dozen or so papers of my own.
I sure hope they keep backups!
I recently read a review of Weinberg’s wonderful new book, Cosmology, a 2009 sequel of sorts to his 1972 classic, Gravitation and Cosmology. The reviewer mentioned two other books, that of Mukhanov and that of Dodelson, as books worth having. Mukhanov’s Physical Foundations of Cosmology was already on my bookshelf (and, like the reviewer, I also consider it worth having) but not Dodelson’s book… so I decided to buy it.
I was not disappointed: it is an excellent cosmology book. In particular, it offers a very thorough introduction to the quantitative aspects of physical cosmology.
However… although the book was published only six years ago, it feels surprisingly dated. Through no fault of the author, to be clear: it’s just that cosmology has made tremendous progress in a few short years. I can think of two things in particular: results from the Wilkinson Microwave Anisotropy Probe (WMAP), first released in 2005, providing precision maps of the cosmic microwave background, allowing accurate detection of the so-called acoustic peaks; and ever improving large scale galaxy surveys, notably the Sloan Digital Sky Survey (SDSS), providing spectra for many hundreds of thousands of galaxies, yielding 3D density maps of the deep cosmos that can be used to test models of structure formation.
The results speak for themselves. For instance, Dodelson’s book gives 12.6 ± 1.1 billion years as the age of the Universe… in contrast, the latest WMAP result is 13.73 ± 0.12 billion years, a tenfold improvement in the accuracy of the estimate. I guess it’s not an enviable task to write a book for a field that is changing as rapidly as Modern Cosmology… which also happens to be the title of Dodelson’s book.
I found this gem of a sentence on the Web site of the Embassy of the Islamic Republic of Iran here in Ottawa:
“The Islamic Republic of Iran will register acts of all these states whose records are filled with support for terrorism, pro-colonialist policies for colonizing the oppressed nations, support for the despotic regimes, arming some with weapons of mass destruction and support for anarchy in all parts of the world as disdainful behavior and stipulates that they can not cast doubt on the excellent democratic election held recently in the Islamic Republic of Iran by no means advising them to change their miscalculated approach vis-à-vis the developments having taken place in Iran because designers of the chess game are closely monitoring their behavior and calculating them in the future relations.”
This sentence reminds me of Soviet-era propaganda leaflets. I wonder if the Islamic Republic of Iran has hired propagandists from the former Soviet Union who were left unemployed after 1991.
Anyhow, what exactly are they saying here? Something is wrong with this sentence. They say that,
The Islamic Republic of Iran
- will register, as disdainful behavior,
- acts of all these states whose records are filled with
- support for terrorism,
- pro-colonialist policies for colonizing the oppressed nations,
- support for the despotic regimes, arming some with weapons of mass destruction and
- support for anarchy in all parts of the world
and
- stipulates that they can not cast doubt on the excellent democratic election held recently in the Islamic Republic of Iran
by no means advising them to change their miscalculated approach vis-à-vis the developments having taken place in Iran
because
designers of the chess game are closely monitoring their behavior and calculating them in the future relations.
Hmmm… they seem to be telling us that despite all the bad things they say about our disdainful behavior, they are NOT advising us to change our miscalculated approach. The reason for this surprising advice has to do with the designers of the game of chess. Okay, I know that chess may have arrived in Europe from India by way of Persia, but what do the long dead inventors of one of the world’s most popular games have to do with the reelection of Ahmedinejad?
Maybe they are trying to confuse us intentionally, in order to deflect our attention away from a study that suggests that the election was seriously rigged. They really shouldn’t bother. This study says that the election was likely rigged because the final two digits of provincial results show unlikely statistics. But unlikely is not the same as impossible, and unless they can quantify how much more likely this outcome is in a rigged election, the study means nothing; after all, 1-2-3-4-5-6 is as likely to win in a random 6/49 lottery draw as any other number combination, and if they pick these numbers next week, it does not prove fraud by the lottery corporation. For that claim, one would also have to quantify the increased likelihood that a fraudulent draw is more likely to produce the 1-2-3-4-5-6 result when compared to a truly random draw.
I was channel-surfing for news this morning, and I caught a segment on CTV’s morning show about “dirty electricity”.
I shall refrain from calling the gentleman being interviewed using a variety of unflattering names, because it would not be polite, and in any case, it’s not the person but the message that I take issue with.
Basically, he put a bunch of electronic devices like cordless phones, baby monitors, Wi-Fi routers or even fluorescent light bulbs on a test bench, plugged them in, and then held a contraption with an antenna and a speaker close to them. The contraption was making loud noises, from which this gentleman concluded that these devices “emit radiation”, and “send dirty electricity back through the wires”.
So then… what? The whole Universe is emitting similar radiation at radio frequencies. Any warm object, including the walls of your house, emits radiation at such frequencies and higher. And why should I care?
Of course, it helps dropping a few scary phrases like, “skyrocketing rates of autism”. Oh, he wasn’t saying that they are related. Why should he? Merely mentioning autism while he’s talking about “dirty electricity” is enough to suggest a connection.
Just to be clear about it, almost all electronic devices emit radio frequency radiation that can then be picked up by a suitable receiver and converted into loud and scary noise. When I was 10 or so and got my first pocket calculator, I had endless fun holding it close to an AM receiver and listening to its “song”. Later, when I had my first programmable calculator, I could tell by listening to the sounds on a nearby radio if it was still executing a program, or even if it displayed the expected result or just showed an error condition. Modern calculators use so little power that their transmissions cannot be picked up so easily, but does this mean that the old calculators were a health threat? Of course not.
At such low frequencies, electromagnetic radiation does not interact with our bodies in harmful ways. To cause genetic damage, for instance, much shorter wavelengths would be needed, you need to go at least to the ultraviolet range to produce ionization and, possibly, damage to DNA. At lower frequencies, most emissions are not even absorbed by the body very effectively. The little energy that is being absorbed may turn into tiny currents, but those are far too tiny to have any appreciable biological impact. Note that we are not talking about holding a cell phone with a, say, 0.3W transmitter just an inch from your brain (though even that, I think, is probably quite harmless, never mind sensationalist claims to the contrary); we are talking about a few milliwatts of stray radio frequency emissions not mere inches, but feet or more from a person.
As to “dirty electricity”, any device that produces a capacitive or inductive load on the house wiring will invariably feed some high frequency noise back through the wiring. Motors are the worst offenders, like vacuum cleaners or washing machines. Is this a problem? I doubt it. House wiring already acts as a powerful transmission antenna, continuously emitting electromagnetic waves at 60 Hz (in North America); so what if this emission is modulated further by some higher frequency noise?
But even if I am wrong about all of this, and low-frequency, low-energy electromagnetic radiation has a biological effect after all… study it by all means, yes, but it is no excuse for CTV to bring a scaremongerer with his noisy gadget (designed clearly with the intent to impress, not measure) on live television.
The reason why I am concerning myself with more Maxima examples for relativity is that I am learning some subtle things about Brans-Dicke theory and the Parameterized Post-Newtonian (PPN) formalism.
Brans-Dicke theory is perhaps the simplest modification of general relativity. Instead of the gravitational constant, G, the theory has a scalar field φ, and the theory’s Lagrangian now reads
L = [φR − ω∂μφ∂μφ/φ] / 16π.
Here, R is the curvature scalar and ω is an unspecified constant of the theory.
The resulting field equations are just like Einstein’s, except for two things. First, the field equations for the metric now have additional terms containing derivatives of φ; second, there is a new field equation for the scalar field φ that basically says that the d’Alembertian of φ is proportional to the trace of the stress-energy tensor.
Clever people tell you that Brans-Dicke theory is practically excluded by solar system data, as it would only work for insanely high values of ω. They demonstrate this by building approximate solutions for the theory using the PPN formalism, and find that one of the PPN parameters, γ, will have the value of γ = (1 + ω) / (2 + ω); on the other hand, observations by the Cassini spacecraft restrict γ to |γ − 1| < 2.3 × 10−5, so |ω| must be at least 40,000.
Now here’s the puzzling bit: if you solve Brans-Dicke theory in a vacuum, you find that the celebrated Schwarzschild solution of general relativity still applies: keeping φ constant, you just get back this common solution which is known to fit solar system data well, and which has, most importantly, γ = 1 and the value of ω doesn’t matter.
So which is it? Is it γ = 1 or is it γ = (1 + ω) / (2 + ω)? Something is amiss here.
This dilemma can be resolved once you realize that whereas general relativity has a unique spherically symmetric, static vacuum solution, this is not the case for Brans-Dicke theory. This theory has an infinite family of spherically symmetric, static vacuum solutions. Indeed, I think you could actually use the value of γ to parameterize this solution space. However, once you allow some matter into that vacuum, no matter how little, you are locked in to a specific solution, for which γ = (1 + ω) / (2 + ω). In other words, the only vacuum solution that is consistent with the notion of taking the limit of a matter solution by gradually removing matter is NOT the Schwarzschild solution of general relativity, but another, incompatible solution.
This has extremely important implications for our work on MOG. So far, we have obtained a vacuum solution that appears consistent with observations on scales from the solar system to cosmology. However, a recent paper by Deng et al. challenges this work by suggesting that the MOG PPN parameter γ is not 1 and hence, the theory runs into the same trouble as Brans-Dicke theory in the solar system. Is this true? Did we pick a vacuum solution that happens to be inconsistent with matter solutions? This is what I am trying to investigate.
Some moderately interesting Maxima examples.
First, this is how we can prove that the covariant derivative of the metric vanishes (but only if the metric is symmetric!)
load(itensor); imetric(g); ishow(covdiff(g([],[i,j]),k))$ %,ichr2$ ishow(contract(canform(contract(canform(rename(expand(%)))))))$ ishow(covdiff(g([i,j],[]),k))$ %,ichr2$ ishow(canform(contract(rename(expand(%)))))$ decsym(g,2,0,[sym(all)],[]); decsym(g,0,2,[],[sym(all)]); ishow(covdiff(g([],[i,j]),k))$ %,ichr2$ ishow(contract(canform(contract(canform(rename(expand(%)))))))$ ishow(covdiff(g([i,j],[]),k))$ %,ichr2$ ishow(canform(contract(rename(expand(%)))))$
Next, the equation of motion for a perfect fluid:
load(itensor);
imetric(g);
decsym(g,2,0,[sym(all)],[]);
decsym(g,0,2,[],[sym(all)]);
defcon(v,v,u);
components(u([],[]),1);
components(T([],[i,j]),(rho([],[])+p([],[]))*v([],[i])*v([],[j])
-p([],[])*g([],[i,j]));
ishow(covdiff(T([],[i,j]),i))$
ishow(canform(%))$
ishow(canform(rename(contract(expand(%)))))$
%,ichr2$
canform(%)$
ishow(canform(rename(contract(expand(%)))))$
Finally, the equation of motion in the spherically symmetric, static case:
load(ctensor); load(itensor); K:J([i],[])=covdiff(T([i],[j]),j); E:ic_convert(K); ct_coords:[t,r,u,v]; lg:ident(4); lg[1,1]:B; lg[2,2]:-A; lg[3,3]:-r^2; lg[4,4]:-r^2*sin(u)^2; depends([A,B,T,rho,p],[r]); derivabbrev:true; cmetric(); christof(mcs); J:[0,0,0,0]; ev(E); T:ident(4); T[1,1]:rho; T[2,2]:T[3,3]:T[4,4]:p; J,ev;
These examples are probably not profound enough to include with Maxima, but are useful to remember.
I’ve been learning a lot about Web development these days: Dojo and Ajax, in particular. It’s incredible what you can do in Javascript nowadays, sophisticated desktop applications running inside a Web browser. I am spending a lot of time building a complex prototype application that has many features associated with desktop programs, including graphics, pop-up dialogs, menus, and more.
I’ve also been learning a lot about the intricacies Brans-Dicke gravity and about the parameterized post-Newtonian (PPN) formalism. Brans-Dicke theory is perhaps the simplest modified gravity theory that there is, and I have to explain to someone why the gravity theory that I spend time working on doesn’t quite behave like Brans-Dicke theory. In the process, I find out things about Brans-Dicke theory that I never knew.
And, I’ve also been doing a fair bit of SCPI programming this month. SCPI is a standardized way for computers to talk to measurement instrumentation, and an old program I wrote used to use a non-standard way… not anymore.
Meanwhile, in all the spare time that I’ve left, I’ve been learning Brook+, a supercomputer programming language based on C… that is because my new test machine is a supercomputer, sort of, with its graphics card that doubles as a numeric vector processor capable in theory of up to a trillion single precision floating point instructions per second… and nearly as many in practice, in the test programs that I threw at it.
I’m also learning a little more about the infamous cosmological constant problem (why is the cosmological constant at least over 50 orders magnitude too small but not exactly zero?) and about quantum gravity.
As I said in the subject… busy days. Much more fun though than following the news. Still, I did catch in the news that Susan Boyle lost in Britains Got Talent… only because an amazing dance group won:
I heard on CBC Newsnet that according the US hurricane center, there is a 50% likelihood that this year will be an average year, hurricane-wise.
I am still pondering whether or not this statement had any information content.
Given the less than perfect record of the Ariane 5 launch vehicle, there was reason for concern given that two new great observatories, Herschell and Planck, were launched on the same rocket this morning. Fortunately, the launch was successful, and both spacecraft are now on their merry way. Herschell is an infrared/submillimeter wavelength telescope, while Planck is “WMAP on steroids”, expected to provide much higher resolution views of the cosmic microwave background than its predecessor.
The space shuttle Atlantis is on its way to the Hubble Space Telescope. If the planned repairs are successful, Hubble may get another five years or more before it has to be decommissioned. Originally, the plan was to return it to the Earth, but in the wake of Columbia, that has been deemed to risky… now, it will be deorbited, to ensure that its large mirror (which is not expected to burn up in the atmosphere) doesn’t fall on an inhabited area. But hopefully, that is still many years away.
I saw the package that is now in the belly of Atlantis when I was at Goddard last summer. Well, maybe not quite the same package as, after the repair mission was postponed, I believe they added a few bits to it, but still, it’s largely the same.
Sadly, this mission may also be the very last really useful mission of the shuttle fleet. That is not to say that they won’t fly several more missions… but they are all to the International Space Station, and while I am an enthusiastic supporter of manned space exploration, flying meaningless circles in low Earth orbit just isn’t it… it’s a waste of money, and a pointless risk to the astronauts’ lives.
It’s April 27, in Ottawa, supposedly the second (third? sixth?) coldest capital city in the world. The temperature outside is presently 30.5°C outside (30°C according to the Weather Network) and still rising. Weren’t we wondering this time last year (okay, maybe a little earlier, but just a little) whether or not we were going to break the all-time snowfall record?
I’ve run the first realistic tests of the kind of computation that I am planning to perform on my new machine with the GPU “supercomputer” card. Here is a “before” picture:
Self-gravitating star cluster on the CPU
And now, the exact same program running on the GPU:
Self-gravitating star cluster on the GPU
I’d say that’s quite an improvement. To say the least.
The calculation in this case computed the self-gravitational forces in a cluster of 10,000 stars… it seems that the GPU can perform this computation at least 20 times a second. That’s quite remarkable.
Watching the outrage over the DHS memos that purportedly target all Americans on the political right as potential enemies of the state, I have come to the realization that a great many political conspiracy theories are based on a trivial error in formal logic: namely, that the implication operator is not commutative.
The implication operator, A → B (A implies B) is true if A is false (B can be anything) or if both A and B are true. In other words, it is only false if A is true but B is false. However, A → B does not imply B → A; the former is true when A is false but B is true, but the latter isn’t.
Yet this is what is at the heart of many conspiracy theories. For instance, a DHS report might say, that those on the fringe of the political right are motivated by the Obama government’s more permissive stance on stem cell research. Some draw the conclusion that this report implies that all who are troubled by Obama’s stance on this issue must be right-wing extremists. I could write this symbolically as follows: we have
member(e, s) → prop(e, p)
where member(e, s) means that e is a member of set s, and prop(e, p) means that e has property p. This symbolic equation cannot be reversed: it does not follow that prop(e, p) → member(e, s).
A closely related mistake is the confusion of the universal and existential operators. The existential operator (usually denoted with an inverted E, but I don’t have an inverted E on my keyboard, so I’ll just use a regular E), E(s, p) says that the set s has at least one member to which property p applies. The universal operator (denoted with an inverted A; I’ll just use a plain A), A(s, p) says that all members of set s have property p. Clearly, the two do not mean the same. Yet all too often, people (on both sides of the political aisle, indeed a lot of the politically correct outrage happens because of this) make this error and assume that once it has been asserted that E(s, p), it is implied that A(s, p). (E.g., a logically flawless statement such as “some blacks are criminals” is assumed to imply the racist generalization that all blacks are criminals.)
One might wonder why formal logic is not taught to would be politicians. I fear that in actuality, the situation is far worse: that they do know formal logic, and use it to their best advantage assuming that you don’t.
I am watchin Deep Impact tonight, a ten-year old film about a comet impacting the Earth. Why the Canadian History Channel is showing this film is a good question. Future history? Imagined history?
But putting that question aside, the movie made me go to Wikipedia again, and I ended up (re-)reading several articles there relating to the issue of global warming and controversies surrounding it.
One thing that struck me (and not for the first time) is this: criticism of global warming theories are often dismissed by the assertion that these go “against the mainstream” or are “not supported by scientific consensus.”
And global warming is by no means the only area of science where such arguments are frequently invoked. Take two topics that I have become involved with. There is scientific consensus that the inadequacy of Einstein’s theory of gravitation to explain the rotation of galaxies and large scale features of the universe is due to “dark matter” and “dark energy”. Even though no one knows what dark matter (or dark energy) is made of, and no one actually detected any dark matter or dark energy ever, the idea is treated as fact. True, dark matter theory can explain a few things and even made a few minor (but nonetheless impressive) predictions, but that doesn’t necessarily make it true, and it certainly doesn’t make the theory the only kid on the block worth considering. Still, try proposing an alternative gravity theory: no matter how firmly rooted in real physics it is, you will be fighting an uphill battle.
Or take the Higgs boson. This hypothetical particle (often along with the graviton) is often portrayed as if it has already been detected. It hasn’t. Indeed, the only thing experiments have accomplished to date is that they excluded the possibility that the Higgs boson exist at nearly the two-σ level. There are also significant unresolved issues with the Higgs boson that put the theoretical validity of the idea into question. Yet the “scientific consensus” is that the Higgs boson exists, and if you try to propose a quantum field theory without the Higgs, well, good luck!
Just to be clear about it, I am not saying that the climate skeptics got it right, and for all I know, maybe there is dark matter out there in abundant quantities, along with Higgs bosons behind every corner. But not because this is what the “scientific consensus” says but because the theory is supported by facts and by successful predictions. Otherwise, the theory remains “just a theory”, as the creationist crowd likes to say… neglecting the inconvenient fact that, of course, the theory of evolution is supported by an abundance of facts and successful predictions.
North Korea’s news agency informs us that the satellite their country launched overnight is orbiting normally, transmitting immortal revolutionary songs.
Too bad that according to NORAD, the launch vehicle’s second and third stages, along with the payload, are at the bottom of the Pacific ocean.
The gravitational theory that I’ve been working on for some time with John Moffat is called STVG, or Scalar-Tensor-Vector Gravity. It grew out of Moffat’s investigation of Nonsymmetric Gravity.
There is also a phenomenological formula called MOND (MOdified Newtonian Dynamics) that effectively flattens out the acceleration curve at high radii from a point source. MOND is nothing more than a formula designed by its creator, Mordechai Milgrom, to solve a specific problem, namely the rotation curves of galaxies. It is not rooted in any theory, and in fact, it is known to contradict some; for instance, it violates the law of conservation of energy and momentum. This is why Jacob Bekenstein endeavored to create a relativistic theory called TeVeS, which fixes MONDs problems, while still gives the approximate MOND acceleration formula in the case of weak fields.
Both STVG and TeVeS are gravity theories, and both happen to incorporate tensor, vector, and scalar fields. Beyond that, however, there’s nothing in common between the two theories.
Unfortunately, many Wikipedians don’t know this, and try from time to time to merge the STVG and TeVeS articles. Hopefully not any longer… I just posted a long, fairly complete description of STVG on Wikipedia.
Some interesting papers on ArXiv today: the variation of a fundamental constant, a new class of galaxies discovered in the Sloan Digital Sky Survey, and finally, an notable essay on quantum physics.
Folks working on quantum computers are busy trying to make sure that entangled states remain entangled, because decoherence is death for a quantum computation. But now, Gross et al. showed that too much entanglement may not be a good thing: it can result in quantum computers that offer no improvements in efficiency over conventional computers.