April 2010 – Spinor Info

Scalar-tensor gravity and conformal transformations

Apr 302010

When I started this here blog site, my intent was to write a lot about physics. I ended up writing a lot less about physics than I wanted to, in part because a lot of the physics I’m thinking about is “work-in-progress” which would not be appropriate to write about until, well, until it is appropriate to write about it!

But, there are a few exceptions. Lately, I’ve been thinking a lot about scalar-tensor gravity. Indeed, as I am waiting for the completion of a virus scan (could my recent computer troubles have been caused by a virus? I now took out my computer’s hard drive, put it in an external enclosure, and I am scanning it using a “known good” computer) I am thinking about it now.

Einstein’s gravity theory (tensor gravity) can be written up using the Lagrangian formalism. This is the infamous Einstein-Hilbert Lagrangian, which takes the form L = [(−1/16πG)(R + 2Λ) + L_M]√−g, where G is the gravitational constant, R is the so-called curvature scalar, Λ is the cosmological constant, g is the determinant of the metric, and L_M is the Lagrangian representing matter.

In one of the simplest modifications of Einstein’s gravity, Jordan-Brans-Dicke theory, the gravitational constant G is promoted from constant to field: it becomes variable, and a “kinetic term” is added to the Lagrangian representing the kinetic energy carried by this scalar field.

In this theory, gravity is still determined by the geometry of space-time. However, in addition to matter, there is this scalar field (which carries mass-energy and is thus a further source of gravity in addition to matter.) Then, this scalar field also determines the strength of coupling between matter and space-time (i.e., the extent to which a unit mass of matter bends space-time.)

Now it so happens that it is possible to transform away this variable gravitational constant and make it truly constant by a mathematical transformation called a conformal transformation. Basically, it amounts to reparameterizing space-time in such a way that the value of the gravitational constant becomes the same everywhere. (This transformation is described as switching from the Jordan frame to the Einstein frame.) However, this transformation is not without cost. As we transform away the coupling between the geometry of space-time and the scalar field, we end up introducing a variable coupling between the matter Lagrangian L_M and the scalar field. The physics is now different! The geometry of space-time is now determined by a fixed coupling constant as in Einstein’s theory, but the trajectory of matter is no longer determined by geometry alone: there is an extra force, a so-called scalar force, acting on matter.

At first sight, this might seem weird. A simple mathematical transformation should not change the physics, or should it? Well… it does yet it doesn’t. If you fire a cannonball in Jordan-Brans-Dicke theory and calculate its trajectory, it will trace the same trajectory regardless which frame, the Jordan or the Einstein frame, you use to calculate it. It’s the interpretation of this trajectory that differs between the two frames. In the Jordan frame, the cannonball is said to follow a geodesic trajectory, but that geodesic, i.e., the curvature of spacetime, is affected by a varying gravitational constant. In the Einstein frame, the cannonball’s trajectory is not a geodesic anymore; the geodesic trajectory is determined by a fixed gravitational constant, but on top of that, an extra force deflects the cannonball.

One particular kind of scalar-tensor theory can be written in a form in which there is no variable gravitational constant and no coupling between the scalar field and matter either. This is the so-called “minimally coupled” scalar-tensor theory, in which the scalar field influences matter only indirectly: the scalar field has mass-energy, which gravitates, and this contributes to the overall gravitational field. Things can get tricky here: a scalar-tensor theory may be written in a form that does not look like a minimally coupled theory at all, yet it may be possible to transform it into one by an appropriate conformal transformation. However, this is not always the case: for instance, Jordan-Brans-Dicke theory cannot be transformed into a minimally coupled scalar-tensor theory this way, the two classes of theories are manifestly different.

When things get really interesting is when additional fields are present in a more complex theory, such as scalar-tensor-vector gravity. In that case, a conformal transformation can have surprising consequences on the coupling between these additional fields and the scalar field.

Computer woes and a FORTRAN joke

Computers 2 Responses »

Apr 292010

I’ve been having computer trouble. My main (but soon-to-be backup) computer has been acting up lately. Since I fixed the broken heatsink, it crashed several times. Is it aging hardware? Is it a virus? An instability due to a recent update? Or perhaps, possibly, the result of the fact that most recently, I plugged the network into the gigabit Ethernet interface, as opposed to the 100Base-T one? (This motherboard has two network connectors.) I know for a fact that the gigabit Ethernet interface used to cause problems, but I thought that was fixed by driver updates ages ago. Perhaps not.

Anyhow, since I swapped the network cable, the system has been stable for days. Today, its video driver crashed, but that’s not new: the complicated driver set of my ATI All-In-Wonder card (combination high-end graphics and TV tuner card; well, whatever passed for high-end in 2005, that is) was never 100% stable, but it is stable enough for reasonably reliable use. Today’s crash, too, was recoverable: I was able to Remote Desktop into the machine from another computer. So… I still don’t know what has been causing the real crashes in recent weeks.

Anyhow, after restarting the system, I logged back onto my Linux server from it, and I was presented with the usual UNIX login fortune cookies. Including one I never saw before, and one that only those can truly appreciate who used to program in FORTRAN and are familiar with implicitly declared variables and the default implicit declaration rules:

“God is real, unless declared integer.”

Ontario politics

Canada, Education, Health, Politics 1 Response »

Apr 252010

So a few days ago, I wrote a blog entry about Ontario’s new grade school curriculum. The one that has since been withdrawn due to objections by conservative groups. I have to concede: they may have a point. I used no words in my blog post that were not used in the curriculum itself, yet the result was apparently too strong for Facebook; their automated software did not pick up and paste the entry onto my Facebook page.

Still, I stand by what I said: after I looked at the actual curriculum (as opposed to the sensationalized headlines about it) there really was nothing in it that a sane person could possibly object to. It’s not about sanity, of course, it’s about politics, which is why Ontario Liberals decided to abandon the updated curriculum after all. They can only fight one battle at a time, they say, according to the Toronto Star. I just wish that the battle they chose to keep fighting was this one, as opposed to the astonishingly braindead idea of messing up pharmacies by blocking payments to them by generic drug companies. Or the HST… which would have been a good idea back when the GST was introduced, but now, it’s just a badly disguised tax grab.

208 pages about teaching masturbation and anal intercourse

Canada, Education 1 Response »

Apr 222010

If you listened to Canadian news recently, like I did, you could be forgiven if you got the impression that Ontario’s liberal government released a 208 page curriculum that will teach first graders about masturbation and anal intercourse.

I actually took the trouble this morning and looked at the document in question. I was curious, has Ontario really become Liberal Hell?

Yes, the document does mention masturbation. Once. (Grade 6).

And yes, it does mention anal intercourse, not once, but three times (Grade 7). The context? Delaying sexual activity and avoiding sexually transmitted diseases.

While sexual education is an important subject in these 208 pages (Human Development and Sexual Health being one of the topic titles) the curriculum is not about sex. It is titled Health and Physical Education, and that’s precisely what it is about, with sexuality being a prominent, but certainly not dominant, part.

For those who are upset that children might learn about the genitalia of the opposite sex at school, from (presumably) responsible and respectful teachers, all I ask is this: would it be better if they learned the same from Playboy? Hmmm, silly me, who cares about Playboy anymore. How about learning about said body parts from your friendly neighborhood Internet predator. Be realistic and consider what children have access to (and who has access to children!) every time they sit down in front of a computer with an Internet connection, or just browse the Web on a smartphone. Perhaps hearing about “sexting” first from a teacher is not such a bad idea after all.

I would be horrified if grade school teachers were required to give graphic demonstrations to first graders about anal sex. But the idea that a 12-year old might learn about the function of his or her own body parts, might even learn, o horror of horrors, that said body parts can be a source of pleasure, that people might choose to live together in part because they have sex together, that there are, heaven forbid, people who prefer the company of people of the same sex, and that knowing some of the “dirty details” might enable even a 13-year old to make better decisions and avoid making life-altering mistakes way too early in their lives… no, that does not frighten me.

Loud Web pages

Internet No Responses »

Apr 162010

I’m wondering: how many times does it happen every night that someone quietly browsing the Web (perhaps when others in the house are already asleep) is startled by sudden blaring music coming from his computer, curses loudly, and closes the Web browser in a mad panic?

It happens to me from time to time.

I don’t know what the marketing theory is behind these let-us-startle-the-person-who-clicked-on-our-link-with-blaring-audio pages, but if there are any marketing types out there reading this, well, let me assure you: the only possible reaction you get from me is closing the Web page in question in the above-mentioned mad panic, accompanied with rather crude utterances in both English and Hungarian, and an oath never to buy whatever product or service you were advertising, indeed, preferably never to visit your site again.

Airspace closed

Aviation, Weather and Climate No Responses »

Apr 152010

Just like after 9/11, the airspace of an entire region is closed today, grounding thousands of flights in the UK and Northern Europe.

Unlike on 9/11, this time around the closure is not the result of the panicked, knee-jerk reaction of clueless politicians and officials. It is the result of a volcanic eruption in Iceland:

The plume, clearly visible in this Eumetsat image, is a grave threat to aviation. 28 years ago, volcanic ash almost brought down a British Airways 747 full of passengers, and since then, numerous airliners have been damaged as they flew through similar plumes. Grounding all flights in the affected areas seems like a dramatic, but justified response to a very real threat.

Now the question is this: how long? According to news reports, the eruption shows no signs of abating. Will they keep flights grounded for days, even weeks if necessary?

Houston, we have a problem

Space No Responses »

Apr 112010

Apollo 13, NASA’s “most successful failure”, was launched forty years ago today. One thing I didn’t know about the timing of the accident is the fact that the tank rupture occurred on the fifth stirring of the oxygen tank, which normally would have taken place 120 hours into the mission, when the lunar module was already on the Moon’s surface. Without the lunar module to serve as a lifeboat, the fate of the spacecraft would have been sealed. However, an unrelated sensor problem caused them to stir the tank more frequently, causing the accident to occur earlier.

Had the crew of Apollo 13 died in space, it has long been assumed that their spacecraft would have served as a frozen tomb for their bodies, orbiting the Sun. But now, some argue that the orbit of Apollo 13 was such that it would have returned to the Earth and burned up in the atmosphere just a few weeks later. I am not sure how you can really tell, with uncontrolled gas leaks, a tumbling spacecraft, and no precision radio-metric navigation data.

Love, Hate and Propaganda

History, Television No Responses »

Apr 112010

I’m watching a six-part CBC documentary miniseries titled Love, Hate and Propaganda, which looks, from a perspective of 70 years, at the role of propaganda during WW2. While the series is enjoyable (though shallow, like most historical documentaries are), I am coming to the conclusion that after 70 years, propaganda is still alive and well.

Take these sentences, for instance, explaining the beginning of The Blitz:

In the beginning, Germans attack military and industrial installations, but as time goes by, bombs get closer and closer to the big cities.

September 7th. They hit London. The Blitz begins.

So how does it compare to a more neutral, factual description of the same from Wikipedia? Let’s see:

In late August 1940 […] the Luftwaffe attacked industrial targets in Birmingham and Liverpool. This was part of an increase in night bombing brought about by the high casualty rates inflicted on German bombers in daylight.

During a raid on Thames Haven, on 24 August, some German aircraft […] strayed over London and dropped bombs in the east and northeast parts of the city, Bethnal Green, Hackney, Islington, Tottenham and Finchley. This prompted the British to mount a retaliatory raid on Berlin the next night with bombs falling in Kreuzberg and Wedding, causing 10 deaths. Hitler was said to be furious, and on 5 September, at the urging of the Luftwaffe high command, he issued a directive “for disruptive attacks on the population and air defences of major British cities, including London, by day and night”. The Luftwaffe began day and night attacks on British cities, concentrating on London. This relieved the pressure on the RAF’s airfields.

In the CBC’s version of events, there is no doubt that the indiscriminate bombing of civilian targets was the invention of the evil Nazi state. Wikipedia’s facts are more nuanced: it appears that the first intentional bombing of civilian targets may have actually been conducted by the RAF! This remains true regardless of the evil nature of the Nazi empire or the fact that it was them, not Britain, who started the most devastating war in history.

So, it seems, Love, Hate and Propaganda is guilty of the very thing that it purports to expose: by skewing the facts, it becomes a work of propaganda.

End of an Era

History No Responses »

Apr 092010

The CBC titled its broadcast “End of an Era”; its live coverage of the special ceremony remembering Vimy Ridge, on account of the fact that Canada’s last WWI veteran died just a short while ago.

My thought? If only all countries remembered war the way Canada does: not the glory, but the loss and the sacrifice. Perhaps the world would be a better place.

One lousy plastic bit

Computers 1 Response »

Apr 032010

One lousy plastic bit. That’s all that was needed to take out my main workstation while I was in Hungary.

Fortunately, it did not interfere with my ability to access my data, as I was set up with a backup workstation that I could access using Remote Desktop while traveling. But still, it was most annoying when my wife called and asked if it was me that was messing with that computer, as it was at first making some strange noises, and then went dark.

The plastic bit in question was one of the bits to which the CPU heat sink is latched. It broke. The heat sink didn’t quite fall off, but as it was no longer pushed securely against the CPU, the CPU overheated and shut down. (A good thing, too. Some older generation CPUs failed to shut down under such circumstances and instead, burned a nice black hole in the middle of the motherboard.)

Grumble, I am old enough to remember when TVs had tubes and the repairman was a regular visitor. Back then, solid state electronics held a promise: it was supposed to last forever. But that’s because nobody at the time foresaw all the innovative ways modern computers have come up with to die at the most inopportune moments. What worries me is that the same thing, a computer disabled because of one lousy plastic bit, can happen anytime anywhere… even if said computer, say, is the one running the fly-by-wire system of a modern jetliner or controls the X-ray dose you receive in a medical device.

Of course those systems are redundant. But so was mine… I did have that backup workstation, after all. Nonetheless… I wish these things were a tad more reliable.

It’s good to be home

Personal, Weather and Climate No Responses »

Apr 032010

I’m back from a week-long trip to Hungary, visiting my Mom, relatives, and friends. Apart from the fact that the second half of my trip was made unnecessarily unpleasant by some cold bug I picked up on the flight from here to there, it was fun. But, it’s good to be home, even though, it seems, I came home in the middle of a heat wave. Yesterday, the heat almost killed me when I was looking for my car at Montreal airport (cars have the nasty habit of moving about when you leave them in large, public lots) while hauling my 60-pound suitcase. Today, it’s going to be even warmer. (No, we’re told, it’s not global warming… it’s the same El Niño weather that brought an unusually cold spring to parts of Europe.) I better check to see if our A/C still works after its winter hibernation.