University Lowbrow Astronomers

Gravity, Part 1: What Einstein Did For Astronomy.

by Dave Snyder
Printed in Reflections: January, 2006.

The College of Literature Science and the Arts (LS&A for short) recently instituted “theme semesters.” For Fall 2005, the theme was “100 Years Beyond Einstein” (2005 is the hundredth anniversary of Einstein’s miraculous year, which I’ll explain below). There were classes, lectures and other events connected with Einstein. One of the lectures, “What Astronomy Has Done For Einstein,” was given by Dr. Joceyln Bell-Burnell.

Joceyln Bell-Burnell was born Susan Jocelyn Bell. Her PhD work involved a then recently discovered class of objects known as quasars. In the late 60’s she and her advisor Antony Hewish used radio telescopes to study quasars. She noticed some signals that repeated with a regular pattern, but no one knew how they were generated.

As a joke, the signals were given the label “Little Green Man 1” (since no one knew what they were, perhaps they were from extra-terrestrials). Soon it was realized it could be explained by a natural process: a new type of object, called a pulsar, was responsible.

Shortly after this discovery she married Martin Burnell, and now uses the name Joceyln Bell-Burnell.

In 1974, Hewish along with Sir Martin Ryle, were awarded the Nobel Prize in Physics in part because of the role Hewish played in the discovery of pulsars. Many people (myself included) believe that Bell-Burnell should have been included in the 1974 award. Nevertheless, Bell-Burnell has received many other awards including the the Michelson Medal of the Franklin Institute.

Dr. Bell-Burnell began her talk with Einstein. Einstein was born in Germany in 1879, but renounced his German citizenship in 1896. He graduated from a Swiss university in the year 1900. He was a man without a country until 1901 when he was granted Swiss citizenship. He had trouble getting a job, but found a position at the Patent Office in Bern, Switzerland. He worked there for several years including the miraculous year 1905. That year Einstein wrote five papers. In chronological order:

(Ok, I just lied, there actually was a sixth paper, but it really was just an elaboration of earlier work).

Before I continue, I must make an important distinction. “The Theory of Relativity” is really two different theories: Special Relativity and General Relativity. Special Relativity was developed during 1905; it is covered in part in “On the Electrodynamics...” and in part in “Does the Inertia of a Body....” The later paper, in three short pages, has all of the thinking necessary to derive E=mc2, however the equation itself did not appear in print until later. Ten years later Einstein developed a different theory called General Relativity. I’ll get to General Relativity in a moment.

“A New Determination...” and “On the Motion...” deal with atoms and molecules. Before these papers there was some doubt about the existence of atoms, after these papers were published and accepted there was no doubt. “A New Determination...” was submitted to the University of Zurich and Einstein was granted a PhD based on that paper.

Some years earlier experimenters noticed that light shining on metal often created an electric current, this became known as the photoelectric effect; but a theory that completely explained it did not exist until “On a Heuristic Point of View...” appeared. Before that paper, physicists believed that light propagated as waves. This paper shows that light propagates as particles. (Einstein initially referred to these particles by the term “quanta of light,” but we now call these particles “photons.” A hundred years later, our understanding of light is more complicated, light is neither a particle nor a wave, but it sometimes behaves like a particle and sometimes it behaves like a wave).

The rest of the talk has nothing to do with these papers.

Special Relativity only describes objects moving in a straight line with constant velocity. Einstein knew that Special Relativity was incomplete.

Einstein returned to Germany in 1914, but did not reapply for German citizenship. He accepted a research position at the University of Berlin. At the time, the best theory of gravity was based on Newton’s laws. But Einstein had problems with it. Over the next couple years, he developed General Relativity, his theory of gravity. General Relativity makes predictions that are similar to Newton’s equations, but there are slight differences. It also involves mathematics that is more complicated than either Newton’s equations or any of Einstein’s 1905 work. Many of the equations of Special Relativity involve simple algebra, this is not true of General Relativity.

This work was finally published in 1916. While the 1905 work was a major accomplishment, other scientists probably could have replicated it if Einstein hadn’t done the work first. It is hard to imagine who would have invented General Relativity if Einstein hadn’t.

1916 was the middle of World War I; Britain was on one side and Germany was on the other. Most British hated the Germans and everything associated with Germany. Dr. Bell-Burnell gave several examples of how this hatred expressed itself, such as the vandalism of stores with German names.

One English astronomer, Arthur Eddington, didn’t participate in this hatred. Eddington was the Secretary of the Royal Astronomical Society and part of his responsibilities was evaluating incoming papers to be published. Einstein’s work on General Relativity was one of these papers. The paper was clearly identified with the University of Berlin, other scientists would have seen such a paper and discarded it along with anything else German. Eddington did not discard the paper, he read it and after he grasped the theory, he explained it to other astronomers and to the general public. Eddington was well respected and good at communicating. Without Eddington’s help, it would have been much longer before Einstein’s ideas gained recognition.

Eddington also helped verify the conclusions of the theory. Newton’s laws predicted that path of light from a star would be bent by the gravity of the sun by about 1.75 seconds of arc (the angle will vary depending on the exact situation). General Relativity also predicts bending, but the amount is exactly twice as large (by about 3.50 seconds of arc). Eddington thought that a solar eclipse would be the easiest way to measure the bending and verify the theory (normally glare from the sun makes this measurement impossible, during a solar eclipse the sun’s light is blocked and light from nearby stars can be seen and measured).

There would be an eclipse of the sun in 1919; at the time of the eclipse, the sun would be in the Hyades. If you take a photograph of the Hyades before the eclipse, and another during the eclipse, there should be a shift in the positions of the stars due to the Sun’s gravity. They planned an expedition to observe the eclipse, but World War I was still going on which made preparations difficult. Fortunately the war ended in late 1918, even so it was a difficult experiment. The eclipse path started in Brazil, passed over the South Atlantic and ended in West Africa. Making these measurements from a ship is almost impossible (and was not attempted), both Brazil and West Africa are frequently cloudy and there were problems with the telescopes.

In spite of the problems, the experiment was conducted and the results confirmed Einstein’s equations. It attracted a lot of public attention, perhaps because the public was tired of war, and eagerly wanted something else to talk about. There were headlines in the New York Times and other publications. Einstein soon become well known: There was a joke that only three people understood General Relativity (this was never true, but that doesn’t stop ideas like this from spreading). Someone asked Eddington about this. After the initial question, the exchange went something like this

Eddington: Oh Dear Me!

Questioner: Don’t be modest Eddington!

Eddington: I’m not being modest, I’m trying to think who the third person is.

Einstein was awarded the Nobel Prize in Physics in 1921. The Nobel committee specifically stated that the award was not for his work on relativity since it was “an unproven idea,” rather the award was given for his work on the photoelectric effect. Einstein was born in Germany but was a swiss citizen; he did part of his work in Switzerland and part in Germany. This created a diplomatic problem as both countries wanted to claim Einstein as a Nobel Laureate. Dr. Bell-Burnell did not know how this problem was resolved.

There have a number of applications of General Relativity. In 1979 radio astronomers discovered a pair of quasars with identical properties but 6 arc seconds apart. Before General Relativity, this was difficult to explain. However suppose there is just one quasar, and there is a galaxy located between the earth and the quasar.

In at the diagram above, the galaxy is marked G, the earth is marked E and the quasar is marked Q.

Light from the quasar is bent by the galaxy: it travels from Q to G’ to E and it travels Q to G” to E. An earth-bound observer would see what appears to be two identical quasars, one at Q’ and the other at Q”.

This bending can also create structures called Einstein Rings and called Einstein Crosses. This behavior is similar to what happens when a lens bends light, so the object in the middle is called the lensing object. The lensing object might be a star, a galaxy or even a cluster of galaxies. Typically light is bent by an angle of 1 second for a single galaxy, and 30 seconds for clusters of galaxies. By observing double quasars, rings or crosses, and assuming General Relativity is correct, it is possible to figure out how much mass the lensing object has.

We can estimate the total mass of a lensing object from the angle. If you estimate the mass of a galaxy and compare this to the observed velocities of stars within the galaxy, the velocities are too fast and the galaxy should fly apart. They do not; we now believe material called “dark matter” prevents this. By studying the lensing effect from galaxies and clusters of galaxies, we are able to determine the mass of these objects and in turn how much dark matter is present.

When a small object is directly between us and a galaxy, it can cause lensing. We call this microlensing.

In the diagram above, light from a galaxy (G) travels to the Earth (E). Nearby a dim star is moving from (S) to (S’). (The diagram is not to scale, the star is much closer to the Earth than the galaxy is). When the star is between the Earth and the galaxy, the light is bent slightly and the amount of bending changes as the star moves. By carefully measuring the light from many objects, we can detect the presence of stars or other objects too dim to observe in other ways. We’ve seen a lot of these events. In a few cases we see not just a hidden star, but something smaller as well. No one is certain, but the smaller objects just might be planets.

Another example is the orbit of Mercury. Mercury travels in an ellipse around the sun. However it isn’t a perfect ellipse, the other planets, particularly Jupiter, perturb the orbit and it precesses. In the late 1800’s astronomers worked out how much precession should be present, there was 43 arc seconds a year more precession than could be accounted for. Even though the effect was tiny, it bothered astronomers. The favored explanation was a hidden planet, which became known as Vulcan, resulted in extra precession. There isn’t room to explain the details here, but after General Relativity was described, it was realized that General Relativity predicts more precession than Newton’s equations do, exactly the amount to account for Mercury’s orbit. Vulcan was no longer necessary.

This precession effect is larger for binary pulsars, Dr. Bell-Burnell gave two examples, one with a precession of 4.2 degrees a year and the other with a precession of 17 degrees a year. In both cases the entire precession was due to General Relativity. While textbooks typically use Mercury’s orbit as an example, she suggested that pulsars might be a better example to use when teaching physics students.

Another example is gravitational waves. Einstein predicted that an object under acceleration will emit waves, which we now call gravitational waves. Unfortunately we’ve never observed these waves directly (there are some projects that may eventually detect these waves, but they are a few years off).

That doesn’t mean there is no evidence for gravitational waves. Suppose we have two stars in orbit. Accelerating objects, such as orbiting stars, emit gravitational waves. When a star emits a gravitational wave, it losses energy and thus losses mass. Kepler’s laws suggest that as stars lose mass, they must move toward each other and speed up. Then they emit more gravitational waves and speed up.

This has been observed. Some astronomers had monitored a binary pulsar for thirty years. The orbit was getting smaller and the velocities increasing in exactly way that General Relativity predicts it should.

That’s enough for now; I plan in a future article to discuss other aspects of gravity.

While most of the material for this article came Dr. Bell-Burnell’s talk, I also used the following book:

______. 1998. Einstein’s Miraculous Year: Five Papers That Changed the Face of Physics. John Stachel editor. Princeton University of Press: Princeton, New Jersey.

It contains new translations of all five papers I mentioned earlier.

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This page originally appeared in Reflections of the University Lowbrow Astronomers (the club newsletter).
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