In a recent post in Cosmic Variance, Sean Carroll recalls his personal experiences when talking about the metric system in the US, one of only 3 countries that have not officially adopted the SI system. What really amazes me is that even in physics we have some remarkably poor decisions about units, the usual decision to measure E (the electric field) and B (the magnetic field) in different units seems to me ridiculous and is a common point of confusion among begginers (so E and B compose the electromagnetic field but each one has different units?), probably the reason for this is that the mks are much more popular in engineering but I still insist that cgs units avoid obscuring the structure of the theory. I also dislike some modern physics textbooks that in the chapter devoted special relativity never get to writing time as ct, for a nice discussion of this (and other topics in SR) look at the classic book Spacetime Physics by Taylor and Wheeler.

On practical issues it just seems that not adopting an almost worldwide systems of units is more of a hassle than just adopting it, specially because many units are similar (the meter is just a bit larger than a yard and a pound is almost half kilogram). There have been some remarkable incidents in this regard that are noteworthy: In 1983 a Boeing 767 jet ran out of fuel at 12 000 m (40,000 feet) with 61 passengers aboard, this was caused by a units issue, this is the origin of the Gimli Glider expression in western Canada which means making a spectacular foul-up, also the US$ 125 million Mars Climate Orbiter was destroyed by a metric mixup.

Finally, there is article about this metrification issue in Wikipedia where you can read the different approaches to this problem in many countries, probably US can follow the example of Ireland in this regard. Look at the map showing the countries that use the metric system, only the black ones don't use it.

## Saturday, May 27, 2006

## Thursday, May 25, 2006

### Happy Towel Day !!!

Today is Towel Day! If you have read Douglas Adams' book The Hitchhiker's Guide to the Galaxy you can remember that a towel is the most useful object around:

"The Hitchhiker's Guide to the Galaxy has a few things to say on the subject of towels. A towel, it says, is about the most massively useful thing an interstellar hitchhiker can have. Partly it has great practical value—you can wrap it around you for warmth as you bound across the cold moons of Jaglan Beta; you can lie on it on the brilliant marble-sanded beaches of Santraginus V, inhaling the heady sea vapours; you can sleep under it beneath the stars which shine so redly on the desert world of Kakrafoon; use it to sail a mini raft down the slow heavy river Moth; wet it for use in hand-to-hand combat; wrap it round your head to ward off noxious fumes or to avoid the gaze of the Ravenous Bugblatter Beast of Traal (a mindboggingly stupid animal, it assumes that if you can't see it, it can't see you—daft as a brush, but very, very ravenous); you can wave your towel in emergencies as a distress signal, and of course dry yourself off with it if it still seems to be clean enough. More importantly, a towel has immense psychological value. For some reason, if a strag [non-hitch hiker] discovers that a hitchhiker has his towel with him, he will automatically assume that he is also in possession of a toothbrush, face flannel, soap, tin of biscuits, flask, compass, map, ball of string, gnat spray, wet weather gear, space suit etc., etc. Furthermore, the strag will then happily lend the hitchhiker any of these or a dozen other items that the hitchhiker might accidentally have 'lost'. What the strag will think is that any man who can hitch the length and breadth of the galaxy, rough it, slum it, struggle against terrible odds, win through, and still knows where his towel is, is clearly a man to be reckoned with." (The Hitchhiker's Guide to the Galaxy, Chapter Three).

I actually forgot the towel in the morning just to be reminded of the importance of the day by classmates... ohh well, I hope you enjoy this day.

## Saturday, May 20, 2006

### Urban legends

We have all heard this urban legend: A student arrives late to a class (or test) and tries to solve a particullary difficult problem posed in the blackboard which later turns to be an unsolved problem. Well this story is true and has happened (as far as I know) at least two times.

The first story regards George Bernard Dantzig, famous for the simplex algorithm and also one of the founders of linear programming. Here are Dantzig's own words:

During my first year at Berkeley I arrived late one day to one of Neyman's classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework - the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever.

About six weeks later, one Sunday morning about eight o'clock, Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them.

To be honest I don't really know which theorems are the ones mentioned in this story, but I found a paper of that time (1940) that should be the one mentioned in the story:

The second story regards a very nice theorem in differential geometry that I know well: the Fary-Milnor Theorem. The legend says that John Milnor (a classmate of the famous John Nash), was sleeping in class while the proffesor explained three unsolved problems in knot theory and when he woke up he copied from the blackboard the three problems (which he assumed were assigned as homework). A week later he turned in solutions for every problem!!! Among these problems was the Fary-Milnor theorem. This gives me an opportunity to discuss this nice theorem.

The curvature K (which should be the greek letter kappa) is a function with real values over some set C (which denotes a parametrization by arc length). This theorem says that if we calculate the total curvature (by doing the integration in the trajectory) then:

if the parametrized curve C don't have any knots, this means that C can be deformed in to a circumference without been teared. Of course if C has knots then

Actually the total curvature is always bigger or equal than 2*pi and only equals 2*pi if C represents a circumference, just as we should expect. The formal statement of this result is the Fary-Milnor theorem.

John Milnor would later receive the Fields Medal for his proof that a 7-dimensional sphere can have several differential structures (28 to be exact), this result opened the field of differential topology

The first story regards George Bernard Dantzig, famous for the simplex algorithm and also one of the founders of linear programming. Here are Dantzig's own words:

During my first year at Berkeley I arrived late one day to one of Neyman's classes. On the blackboard were two problems which I assumed had been assigned for homework. I copied them down. A few days later I apologized to Neyman for taking so long to do the homework - the problems seemed to be a little harder to do than usual. I asked him if he still wanted the work. He told me to throw it on his desk. I did so reluctantly because his desk was covered with such a heap of papers that I feared my homework would be lost there forever.

About six weeks later, one Sunday morning about eight o'clock, Anne and I were awakened by someone banging on our front door. It was Neyman. He rushed in with papers in hand, all excited: "I've just written an introduction to one of your papers. Read it so I can send it out right away for publication." For a minute I had no idea what he was talking about. To make a long story short, the problems on the blackboard which I had solved thinking they were homework were in fact two famous unsolved problems in statistics. That was the first inkling I had that there was anything special about them.

To be honest I don't really know which theorems are the ones mentioned in this story, but I found a paper of that time (1940) that should be the one mentioned in the story:

- G. B. Dantzig 1940. On the non-existence of tests of "Student's" hypothesis having power functions independent of σ, Annals of Mathematical Statistics, Volume 11, number 2, pp186-192

The second story regards a very nice theorem in differential geometry that I know well: the Fary-Milnor Theorem. The legend says that John Milnor (a classmate of the famous John Nash), was sleeping in class while the proffesor explained three unsolved problems in knot theory and when he woke up he copied from the blackboard the three problems (which he assumed were assigned as homework). A week later he turned in solutions for every problem!!! Among these problems was the Fary-Milnor theorem. This gives me an opportunity to discuss this nice theorem.

The curvature K (which should be the greek letter kappa) is a function with real values over some set C (which denotes a parametrization by arc length). This theorem says that if we calculate the total curvature (by doing the integration in the trajectory) then:

if the parametrized curve C don't have any knots, this means that C can be deformed in to a circumference without been teared. Of course if C has knots then

Actually the total curvature is always bigger or equal than 2*pi and only equals 2*pi if C represents a circumference, just as we should expect. The formal statement of this result is the Fary-Milnor theorem.

John Milnor would later receive the Fields Medal for his proof that a 7-dimensional sphere can have several differential structures (28 to be exact), this result opened the field of differential topology

## Saturday, May 13, 2006

### Science In Mexico

I have been trying to write an entry about science awareness in the country but for some reason I have not been able to finish it. One of the points I try to emphasize is that despite most people knows the quacks like Jaime Maussan or Carlos Trejo (the first one is known worldwide for a series of ufo related scams, and the former claims to have detected ghosts making him a clear candidate to join the faculty of a new degree offered by Coventry University), few of them can name a mexican scientist and the general idea of the people here is that Mexico hasn't made any contribution to science.

My humble contribution to remedy this consists in offering you the following facts about science done by mexican scientists:

My humble contribution to remedy this consists in offering you the following facts about science done by mexican scientists:

- Vanadium was discovered in Mexico by Andrés Manuel del Río.
- The first oral contraceptive (norethindrone) was invented in Mexico by Luis E. Miramontes, Carl Djerassi and George Rosenkranz of the mexicam company Syntex. In 2004, the invention of Luis E. Miramontes was chosen as the twentieth most important one of all the times. The election was organized by SCENTA, an initiative of The Engineering and Technology Board of the United Kingdom.
- Mario Molina (Nobel Prize in Chemistry, 1995) discovered the role of CFCs in the depletion of the ozone layer.
- Guillermo Haro discovered the Herbig-Haro objects, he and his coworkers discovered flare stars, paving the way for the theory of star formation. The three color technique for Schmidt plates developed in Tonantzintla turned to be crucial in the detection of quasars. The work of Guillermo Haro and colleagues paved the way for making astronomy the strongest science in Mexico.
- Microquasars were discovered by Luis Félipe Rodríguez in collaboration with the argentinian astronomer Félix Mirabel.
- The famous Alcubierre warp drive a theoretical (don't expect any faster than light ship to be constructed) mechanism of superluminal speed is the work of Miguel Alcubierre.
- Marcos Moshinsky's work (the transformation parenthesis for functions of harmonic oscillation) was fundamental to the study of nuclear structures.
- The theory (and observations) of star formation has received crucial contributions by mexican astronomers like Jorge Cantó, Susana Lizano and Arcadio Poveda.
- Carlos Frenk (the second most cited scientist in Europe) is mexican and has made crucial contributions to cosmology, particullary in the issue of structure formation
- Guillermo Gonzalez Camerena patented the mechanism for the first color TV (consider the number of hours you have enjoyed this invention).
- Manuel Sandoval Vallarta pioneered the efforts to understand cosmic rays, showing clearly that the rays were composed by charged particles (and not gamma rays as tought at that time) attracted by the Earth's magnetic field (this is known as the Lemaître-Vallarta theory). An experimental group in Mexico city lead by Luis W. Alvarez carried a series of experiments proposed by Vallarta, showing that cosmic rays are mostly composed by protons and showed the east-west effect.
- Antonio Lazcano, the author of the best-seller The Origin of Life is a world leader on the study of the emergence of life and one of the pioneers of astrobiology.
- Do you know that Jacob Bekenstein (the first to suggest the entropy of black holes) is mexican?

## Thursday, May 11, 2006

### Trends

I have been playing with the latest gadget from google labs: Google Trends. It seems it appeared last year but it wasn't avalaible to general public until now.

Some of the results are amazing, in science the trends by region are clearly dominated by Asia showing clearly the importance of science in that region. Now let's look at the cities, for the term astrophysics, the searches are concentrated in: Pasadena (home of Caltech), Oxford (UK), Cambridge (UK), Bangalore, Cambridge (USA, home of Harvard and MIT), New Delhi, Mumbai, Chennai and Delhi, all of them in India.

In particle physics Oxford (UK) and Geneva (home of CERN, the biggest particle physics laboratory in the world) clearly dominate the scene with Cambridge(USA) in a distant third place. I couldn't resist to compare the trends in astrophysics and particle physics, and the results show that astrophysics is a bit more popular, but there is a peak in particle physics around mid 2004 when it surpassed astrophysics, I don't know the reason for sure, I speculate it is related to the results of the RHIC.

PD: If you live in Mexico you should find this trends quite interesting. The reason that the red line (the one corresponding to the PRI) don't appears is that the term do not have enough search volume to show graphs! You can even follow the trends of the leading candidates to presidency, the results are fascinating, you can see how the popularity of Andres Manuel Lopez Obrador was unbelievably high during the impeachment process but currently he is way below Felipe Calderon, you can even see how Felipe Calderon was completely unknown before 2005 then matched the popularity of Roberto Madrazo and is now in the lead (at least in terms of web presence).

Some of the results are amazing, in science the trends by region are clearly dominated by Asia showing clearly the importance of science in that region. Now let's look at the cities, for the term astrophysics, the searches are concentrated in: Pasadena (home of Caltech), Oxford (UK), Cambridge (UK), Bangalore, Cambridge (USA, home of Harvard and MIT), New Delhi, Mumbai, Chennai and Delhi, all of them in India.

In particle physics Oxford (UK) and Geneva (home of CERN, the biggest particle physics laboratory in the world) clearly dominate the scene with Cambridge(USA) in a distant third place. I couldn't resist to compare the trends in astrophysics and particle physics, and the results show that astrophysics is a bit more popular, but there is a peak in particle physics around mid 2004 when it surpassed astrophysics, I don't know the reason for sure, I speculate it is related to the results of the RHIC.

PD: If you live in Mexico you should find this trends quite interesting. The reason that the red line (the one corresponding to the PRI) don't appears is that the term do not have enough search volume to show graphs! You can even follow the trends of the leading candidates to presidency, the results are fascinating, you can see how the popularity of Andres Manuel Lopez Obrador was unbelievably high during the impeachment process but currently he is way below Felipe Calderon, you can even see how Felipe Calderon was completely unknown before 2005 then matched the popularity of Roberto Madrazo and is now in the lead (at least in terms of web presence).

## Tuesday, May 09, 2006

## Monday, May 08, 2006

### Can we test M Theory in the LHC?

A few years ago if you told someone that higher dimensions could be detected with current technology they would certainly look you as a crackpot. The idea of additional dimensions is older than you might think, it actually goes back to the work of Kaluza and Klein (in the 1920's,) who discovered that if we introduce and additional spacial dimension curled in a really small radius to general relativity the resulting set of equations not only included the Einstein field equations, but also Maxwell equations!!! Despite it eventually failed as a unified theory of gravity and electromagnetism the idea was explored again when theories of supergravity suggested that in 11 dimensions the unification of all known forces could be possible. In the early eighties it was clear that supergravity wasn't the answer to unification (it was not renormalizable), but a few years later the famous result by Schwarz and Green that superstring theories in 10 dimensions were free of anomalies, anyway by the beginning of the 1990's the field was starting to stagnate, until the work of Polchinsky and Witten showed that the different string theories were only different descriptions of a single theory and also that 11 dimension supergravity was a low energy approximation!!! During this time the additional dimensions still were considered as small and curled, avoiding any realistic attempt of detection.

The announcement that 10-D string theories and 11-D supergravity were related was considered the second string revolution, in this revolution not only strings but also new objects called branes came into spotlight. The branes lead to to the Randall-Sundrum models, in this models our Universe is a five-dimensional space and the elementary particles except for the graviton are localized on a (3 + 1)-dimensional brane or branes. Since this models were proposed the detection of higher dimensions seems possible.

The approach is to create a high energy graviton which could leak in to the extra dimensions and disappear. Of course we do not detect directly the graviton, but we can see that energy and momentum were carried by some invisible particle. So this is the simplest kind of experiment you can do, and if you can eliminate other kinds of possibilities for things that carry off energy invisibly, you would then be able to claim that you've seen evidence for extra dimensions of space. Let's be honest, rather than a test of M-Theory this is really a test of large additional dimensions and not of M-Theory itself (we don't even know it's dynamics), anyway the Randall-Sundrum models are clearly the products of some ideas introduced in the second string revolution and any experimental evidence of them will clearly show we are in the right track.

You can see a technical account here by Joe Lykken. Anyway you should note that the real chance of detecting this additional dimensions in the LHC is very small, even in the proposed ILC that should allow us to do better measurements in this issue the chances are scarce, but the nice thing is that we have at least a chance to do an experimental confirmation of the this models.

By the way, if you are on the Loop Quantum Gravity camp, there are also some experimental predictions (concerning light propagation) which I will comment in a future post that are actually accessible and can definitely verify or falsify the theory .

The announcement that 10-D string theories and 11-D supergravity were related was considered the second string revolution, in this revolution not only strings but also new objects called branes came into spotlight. The branes lead to to the Randall-Sundrum models, in this models our Universe is a five-dimensional space and the elementary particles except for the graviton are localized on a (3 + 1)-dimensional brane or branes. Since this models were proposed the detection of higher dimensions seems possible.

The approach is to create a high energy graviton which could leak in to the extra dimensions and disappear. Of course we do not detect directly the graviton, but we can see that energy and momentum were carried by some invisible particle. So this is the simplest kind of experiment you can do, and if you can eliminate other kinds of possibilities for things that carry off energy invisibly, you would then be able to claim that you've seen evidence for extra dimensions of space. Let's be honest, rather than a test of M-Theory this is really a test of large additional dimensions and not of M-Theory itself (we don't even know it's dynamics), anyway the Randall-Sundrum models are clearly the products of some ideas introduced in the second string revolution and any experimental evidence of them will clearly show we are in the right track.

You can see a technical account here by Joe Lykken. Anyway you should note that the real chance of detecting this additional dimensions in the LHC is very small, even in the proposed ILC that should allow us to do better measurements in this issue the chances are scarce, but the nice thing is that we have at least a chance to do an experimental confirmation of the this models.

By the way, if you are on the Loop Quantum Gravity camp, there are also some experimental predictions (concerning light propagation) which I will comment in a future post that are actually accessible and can definitely verify or falsify the theory .

## Saturday, May 06, 2006

### Increase your wisdom

The brightest contemporary thinker, George W. Bush has contributed so many intellectual jewels that Jacob Weisberg has decided to compile them online, so all the world can enjoy them.

I can't resist to put some of them here for your intellectual delight:

"Those who enter the country illegally violate the law."

—Tucson, Ariz., Nov. 28, 2005

"I think we are welcomed. But it was not a peaceful welcome."

—Philadelphia, Dec. 12, 2005, on the reception of American forces in Iraq

"It's a time of sorrow and sadness when we lose a loss of life."—Washington, D.C., Dec. 21, 2004

"This notion that the United States is getting ready to attack Iran is simply ridiculous. And having said that, all options are on the table."—Brussels, Belgium, Feb. 22, 2005

"I believe that, as quickly as possible, young cows ought to be allowed to go across our border."

—Ottawa, Nov. 30, 2004

“Mr. Vice President, in all due respect, I’m not sure 80 percent of the people get the death tax. I know this: 100 percent will get it if I’m the president.”

— George W. Bush, St. Louis, Mo., October 18, 2000

And finally some insight on how he arrives to his impressive results:

"I'm also not very analytical. You know I don't spend a lot of time thinking about myself, about why I do things."—Aboard Air Force One, June 4, 2003

The full collection of wisdom is available at:

http://www.slate.com/id/76886/.

I can't resist to put some of them here for your intellectual delight:

"Those who enter the country illegally violate the law."

—Tucson, Ariz., Nov. 28, 2005

"I think we are welcomed. But it was not a peaceful welcome."

—Philadelphia, Dec. 12, 2005, on the reception of American forces in Iraq

"It's a time of sorrow and sadness when we lose a loss of life."—Washington, D.C., Dec. 21, 2004

"This notion that the United States is getting ready to attack Iran is simply ridiculous. And having said that, all options are on the table."—Brussels, Belgium, Feb. 22, 2005

"I believe that, as quickly as possible, young cows ought to be allowed to go across our border."

—Ottawa, Nov. 30, 2004

“Mr. Vice President, in all due respect, I’m not sure 80 percent of the people get the death tax. I know this: 100 percent will get it if I’m the president.”

— George W. Bush, St. Louis, Mo., October 18, 2000

And finally some insight on how he arrives to his impressive results:

"I'm also not very analytical. You know I don't spend a lot of time thinking about myself, about why I do things."—Aboard Air Force One, June 4, 2003

The full collection of wisdom is available at:

http://www.slate.com/id/76886/.

### Have axions been observed?

Unlike the electroweak force (as shown in the famous k long and k short decay experiments), the strong force described by QCD (Quantum Chromodynamics) doesn't seems to violate CP parity, despite QCD allows CP-violation.

In 1977 a model was proposed by R. D. Peccei and H. R. Quinn to explain this. It essentially introduces a new broken symmetry. It's associated Goldstone Boson(essentially a new particle associated to a spontaneously broken symmetry) was called an axion, in an obvious reference to a brand of detergent.

One nice thing about this model is that the axions have no electric charge and interact very weakly with matter, making it an obvious candidate for the dark matter, specially because the theory suggest that axions were created abundantly in the Big Bang. While there haven't been any direct observations of axions, the experiments haven't ruled them out, either.

The PVLAS experiment found a tiny light polarization rotation in strong magnetic fields which seem to suggest the existence of axions. You can read an accessible account of the result here. A second experiment CAST might be able to detect axions from the Sun.

Despite the current results from PVLAS are suggestive at most, a direct detection of axions (maybe by CAST) will have a big impact on our understanding of dark matter.

In 1977 a model was proposed by R. D. Peccei and H. R. Quinn to explain this. It essentially introduces a new broken symmetry. It's associated Goldstone Boson(essentially a new particle associated to a spontaneously broken symmetry) was called an axion, in an obvious reference to a brand of detergent.

One nice thing about this model is that the axions have no electric charge and interact very weakly with matter, making it an obvious candidate for the dark matter, specially because the theory suggest that axions were created abundantly in the Big Bang. While there haven't been any direct observations of axions, the experiments haven't ruled them out, either.

The PVLAS experiment found a tiny light polarization rotation in strong magnetic fields which seem to suggest the existence of axions. You can read an accessible account of the result here. A second experiment CAST might be able to detect axions from the Sun.

Despite the current results from PVLAS are suggestive at most, a direct detection of axions (maybe by CAST) will have a big impact on our understanding of dark matter.

## Thursday, May 04, 2006

### Double Jeopardy

In astronomy there is a well known double jeopardy problem. The number of observatories is small compared to the number of projects requiring telescope time, and it is usually the case (in USA, at least) that you have money for the project but no telescope time, but it can also be the case that you have telescope time but no money to travel. Well I am currently in the second situation !!

In Mexico we have a very productive but rather small astronomical community, with around 100 astronomers plus grad students, but of course many of them work in theoretical models that do not require observational time. We have 3 big optical telescopes, two of them are in the OAN (Observatorio Astronomico Nacional) property of UNAM one of 2m and the other a 1.5 telescope (they also have a big refractor in Tonantzintla, , the remaining one is a 2m telescope in the Guillermo Haro Observatory property of INAOE. The point is that having access to telescope time is not as hard as it is in other countries where the ratio between astronomers and telescope time is much smaller (you still have to write a good proposal, of course).

Our team (working in extragalactic astronomy) got a HUUUGE share of telescope time in the two telescopes of the OAN, 3 weeks to be more precise, and I was supposed to observe in the 1.5m telescope some near elliptic galaxies in infrared. Well, that is scheduled for tomorrow and my wallet is as empty as it can be! Other members of our team will go and I think that we have enough people to do the observations (mainly because a colleague from Birmingham is coming).

The ugly part of things is that I actually requested funds but we (me and two other students) only get less than the half of the requested funds, and the funds wont arrive until june, at least!! It seems that I need better sources of financing. =(

In Mexico we have a very productive but rather small astronomical community, with around 100 astronomers plus grad students, but of course many of them work in theoretical models that do not require observational time. We have 3 big optical telescopes, two of them are in the OAN (Observatorio Astronomico Nacional) property of UNAM one of 2m and the other a 1.5 telescope (they also have a big refractor in Tonantzintla, , the remaining one is a 2m telescope in the Guillermo Haro Observatory property of INAOE. The point is that having access to telescope time is not as hard as it is in other countries where the ratio between astronomers and telescope time is much smaller (you still have to write a good proposal, of course).

Our team (working in extragalactic astronomy) got a HUUUGE share of telescope time in the two telescopes of the OAN, 3 weeks to be more precise, and I was supposed to observe in the 1.5m telescope some near elliptic galaxies in infrared. Well, that is scheduled for tomorrow and my wallet is as empty as it can be! Other members of our team will go and I think that we have enough people to do the observations (mainly because a colleague from Birmingham is coming).

The ugly part of things is that I actually requested funds but we (me and two other students) only get less than the half of the requested funds, and the funds wont arrive until june, at least!! It seems that I need better sources of financing. =(

Subscribe to:
Posts (Atom)