Friday, March 14, 2008

3.14

DR. WHO David Tennant as Sir Arthur Eddington in the upcoming production EINSTEIN AND EDDINGTON.

For today's mathematicians, it is easy to remember that 3.14 is Einstein's birthday. Today we are used to overnight fame, and from this perspective it seems that Einstein's ideas were accepted quickly. It was years before Einstein and his papers became public knowledge. A century later we can review how long that took.

In the 5th year of the century Einstein's four major papers are published. He is still working in the patent office and has not received his PhD. Fortunately Max Planck is an editor and sees the value in Einstein's photoelectric effect. If not for Planck, Einstein's papers might not have been published for years.

After Einstein's publication, the response is a deafening silence. Not until the 9th year of the century does Einstein get an academic job. Not until the 11th year does SCIENTIFIC AMERICAN magazine make any mention of Einstein's work. In the 15th year Einstein finally completes his General Theory, but few people notice. The 14th to 18th years are occupied by a long and costly war.

In the 19th year of the century Arthur Eddington makes his famous eclipse expedition. Though a respected British scientist and Director of the Cambridge Observatory, Eddington at 36 is younger than Einstein. He would have been college age upon first reading Einstein's papers. Some jokingly claim that Eddington is one of only three people including Einstein who understood Relativity. As one of the younger generation, Eddington is open to testing new ideas.

On November 6 of the 19th year Eddington's results are announced at the Royal Society. Today Wendy Freedman and others suspect that Eddington "cooked the books" to support Einstein. The next morning the Times of London announces: "Revolution in Science--New Theory of the Universe--Newton's Ideas Overthrown." Three days later the New York Times picks up the story and Einstein's fame spreads like wildfire. (This is about the time a JDEM would begin returning data.)

Copernicus published his "Revolutionibus Oblure Coelestium" in 1543, but not until the late 17th century was the Sun-centred model taught in universities. Along the way Giordano Bruno was burned at the stake and Galileo sentenced to house arrest. As late as the 1660's Isaac Newton heard lectures on the Ptolemaic system in Cambridge. Before Einstein came a communications revolution more profound than today's internet, telephones and telegraphs transmitting at the speed of light. Even with this quantum leap in technology, Einstein's ideas took more than a decade to spread around the world.

The number 3.14159 may have still more significance. As the wondrous Kea has noted, the difference between $\pi$ and 3 is 4.507034 percent, exactly the proportion of baryonic matter in the Universe. This is a check on the shape of Space/Time. If the Universe were a shape other than a sphere, that proportion would be different. This may be part of something our century will discover.

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Quantum said...

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6:00 AM
nige said...

Thanks for this very nice history. I think that Eddington definitely did "cook the books" to support Einstein.

I've got Eddington's book "Space Time and Gravitation" (Cambridge University Press, 1st ed., 1920).

The frontispiece of that book is a photograph of one of the telescopes used to determine that Einstein was correct.

It's a telescope with a clockwork powered mechanical device that keeps the telescope aligned on the elipsed sun for the duration of the eclipse.

The problem is that all materials such as the metal telescope casing tend to expand/contract as a function of temperature, and temperature varies during the eclipse (it gets cooler).

This causes some distortion.

Since the star displacements are tiny compared to the effect of temperature caused contraction of the instruments, there is an immense amount of "noise" in the data.

Eddington measured all the star displacements, then chose to ignore those that were way off what was expected. By choosing suitable pieces of data to include in the averaging, he got an average displacement that was closer to Einstein's prediction than an average of all the raw data indicated.

His book, by the way, is quite nice. Eddington explains in a simple way that Einstein's general theory of relativity predicts double the deflection of starlight that Newton's theory predicts (if light is treated as particle-like bullets being deflected by gravity), because the deflection of any object by gravity depends on the velocity of the object. As the object's velocity increases to c, it's gravitational fall doubles.

The physical explanation is that if you fire bullets (travelling a velocity v << c) past the sun, they speed up as they approach the sun then slow down after they have reached the closest distance to the sun and begin going away from the sun.

In that case, the gravitational potential energy gained by the bullet is partly used to change the speed of the bullet.

In the case of light, this can't happen, because gravity doesn't affect the speed of light, only the velocity (i.e. the direction).

As light approaches the sun, a full 100% of the gained gravitational potential energy of the light is devoted to changing the direction that the light is travelling (i.e. causing deflection), and no energy is wasted in changing the speed of light.

Because gravitational potential energy in the case of light is used with 100% efficiency for deflecting the trajectory of the light, it gets deflected more that the Newtonian law (which assumes that objects speeds are varied) predicts. It turns out that for a bullet at low speed approaching the sun, 50% the gravitational potential energy gained ends up changing the speed of the bullet, and the other 50% ends up deflecting the trajectory of the bullet.

Since 100% of the gravitational potential energy is used to deflct the trajectory of a light ray, Einstein's general relativity predicts 100%/50% = twice the deflection of light that Newton's theory (assuming light to be non-relativistic bullets) predicts.

Yet another way to look at the physics of light ray deflection by gravity is to look at the directions of the electromagnetic field lines in a photon and compare their direction to the radial gravitational field lines from the sun. Exactly 100% electromagnetic field lines in a photon are in the plane transverse to the direction of propagation, so on the average (say at the distance of closest approach of the photon to the sun), half of the electromagnetic field lines will effectively point in the direction of the gravitational field lines. But for a slow-moving bullet, the electromagnetic field lines act in all directions (it is only if such a bullet moves at a velocity approaching c that Lorentz contraction squashes the field from spherical geometry into a planar disc), so only half as many of them effectively interact with the radial gravitational field lines from the sun.

What's so interesting about Eddington's approach is that he made a real effort to grasp the physics behind Einstein's mathematics.

Eddington did massage his 1919 data, but that was commonplace back then. If you look at Millikan's work on the charge of the electron, he chose arbitrarily which bits of data to average by hand, ignoring all data points that looked way off. He didn't disclose this weeding of data in his published data; it was only disclosed when his lab notebooks were studied many years later

This caused a severe row between Millikan and Felix Ehrenhaft who did the same experiment and got extremely fuzzy data (because he didn't weed out the way-out data points like Millikan).

In the same way, people who replicated Eddington's study of the deflection of starlight by the sun's gravity later got results which were far less certain than Eddington's claims. If you are trying to ascertain whether Newton's prediction (1 unit) or Einstein's prediction (2 units) is right, and you get a result of say 1.5 give or take a factor of 2, then the experimental data doesn't help you discriminate at all.

Eddington was fortunate to have a good prediction to fiddle his data to match by ignoring false values.

Millikan wasn't as lucky as Eddington. He got the Nobel Prize in 1923 for determining(falsely) the electric charge of the electron, just by ignoring data points that didn't cluster around one particular value. because Millikan didn't have a theoretical prediction to fiddle his data to fit, the cluster of data points he decided to publish was not centred around the real value. Ehrenhaft who didn't arbitrarily purge his data of far-out data points, missed out on a Nobel Prize in consequence: the penalty for not fiddling your data to claim a degree of precision which was unwarranted by the data, was the failure to secure Nobel's accolade:

http://www.aps.org/publications/apsnews/200608/history.cfm

In 1910 Millikan published the first results from these experiments, which clearly showed that charges on the drops were all integer multiples of a fundamental unit of charge. But after the publication of those results, Viennese physicist Felix Ehrenhaft claimed to have conducted a similar experiment, measuring a much smaller value for the elementary charge. Ehrenhaft claimed this supported the idea of the existence of “subelectrons.”

Ehrenhaft’s challenge prompted Millikan to improve on his experiment and collect more data to prove he was right. He published the new, more accurate results in August 1913 in the Physical Review. He stated that the new results had only a 0.2% uncertainty, a great improvement of over his previous results. Millikan’s reported value for the elementary charge, 1.592 x 10^-19 coulombs, is slightly lower than the currently accepted value of 1.602 x 10^-19 C, probably because Millikan used an incorrect value for the viscosity of air.

It appeared that it was a beautiful experiment that had determined quite precisely the fundamental unit of electric charge, and clearly and convincingly established that “subelectrons” did not exist. Millikan won the 1923 Nobel Prize for the work, as well as for his determination of the value of Plank’s constant in 1916.

But later inspection of Millikan’s lab notebooks by historians and scientists has revealed that between February and April 1912, he took data on many more oil drops than he reported in the paper. This is troubling, since the August 1913 paper explicitly states at one point, “It is to be remarked, too, that this is not a selected group of drops, but represents all the drops experimented upon during 60 consecutive days.” However, at another point in the paper he writes that the 58 drops reported are those “upon which a complete series of observations were made.” Furthermore, the margins of his notebook contain notes such as, “beauty publish” or “something wrong.”

Did Millikan deliberately disregard data that didn’t fit the results he wanted? Perhaps because he was under pressure from a rival and eager to make his mark as a scientist, Millikan misrepresented his data. Some have called this a clear case of scientific fraud. However, other scientists and historians have looked closely at his notebooks, and concluded that Millikan was striving for accuracy by reporting only his most reliable data, not trying to deliberately mislead others. For instance, he rejected drops that were too big, and thus fell too quickly to be measured accurately with his equipment, or too small, which meant they would have been overly influenced by Brownian motion. Some drops don’t have complete data sets, indicating they were aborted during the run.

6:04 AM
L. Riofrio said...

Fascintaing explanation Nige; it could be in a book. Today we know that some particles have fractional charge 2/3 or 1/3. Wendy Freedman also wondered how many undergraduates doing the oil-drop experiment have discovered fractional charge, then eliminated the results!

7:11 AM
Pioneer1 said...

Yes, I agree. It is really fascinating revelations about how physics allows cooking data by physicists and then gives them Nobel Prize. I would really like to read about Wendy Freedman's claim that Eddington cooked his books. Can you give a reference? I know that Eddington left the telescope in the field for a year and that was a problem.

2:42 PM
L. Riofrio said...

For pioneer: Wendy Freedman's comments were in a personal conversation we had. Imagine if Eddington has not been a believer in Relativity. He could easily have cooked the books the other way and the world would have taken no notice of Einstein.

The controversy is mentioned in Hawking's "Brief History of Time," and a good article can be found at http://philipball.blogspot.com/2007/09/arthur-eddington-was-innocent-this-is.html

8:10 PM
Pioneer1 said...

Thanks. I remember reading that the physicist S. Chandrasekhar believed that the British government blackmailed Eddington and told him to come back with verification. Eddington did not have a choice.

For me the lesson is that, as far as physics is concerned, the first page of the New York Times has infinitely more scientific authority than the Memoirs of the Royal Astonomical Society.

2:42 PM
robert d said...

Although the speed of light, c, is relatively fast, it is not that fast. What is supposed or predicted to actually be constraining the speed of light to be what it is?

Snapping out,

d

6:45 AM
Catherine said...

Great article. I was wondering if you had anymore comments by Wendy Freedman. I'm doing a paper on her and it's hard to find anything biographical about her.

2:48 PM