Einstein adds a constant

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Stars are giant places that produce microscopic change. Through stars, the atoms of the universe have bccome more elaborate over time: stars knit protons and neutrons into more complex nuclei. Calcium, iron, oxygen, and carbon have increased 1000-fold in the last 12 billion years, judging their abundance in the past from spectra of the oldest stars in our galaxy. A mix of type I and type II supernovae erupting over several billion years, plus the contributions of less spectacular stars, produces the chemical abundances of the solar system. Most of the enrichment of our galaxy took place early in its history, before the sun formed 5 billion years ago from a typical scoop of this nutritious cosmic soup. The gas in the Milky Way today is only a little richer in heavy elements than the sun is tecause stars were forming (and exploding) more vigorously in the first 5 billion years of the Milky Way's history than in the last 5 billion years.

Spectra tell us about chemistry, but they also can reveal motion. An analogy with sound may help. We've all heard the characteristic pattern of sound as a car zooms by on a highway. Imagine a lonely hitchhiker as cars pass by on the interstate. The hitchhiker hears "ZOOOOOM," not just a shift in the loudness as the car gets closer, but a definite change in pitch from high to low just as the car zooms by. A shift in pitch from high to low tells you, even with your eyes shut, just when the car switches from approaching you

(with the hope, no matter how slim, that it might stop) to receding from you. The driver doesn't noticc any changc as he blasts by you, just the steady hum of the engine and wheels, and perhaps a little peripheral blur of your outstretched thumb.

The shift in the apparent pitch of sound produced by a moving source is called the Doppler effect. This was proposed by Christian Doppler in 1842, in a paper at the Royal Bohemian Society for Sciences in Prague. The technology of the steam engine made it feasible to test the Doppler effect. In 1845, a skeptical Dutchman named Christoph Ballot set out to refute Doppler's theory. He placed trumpeters on a railroad car, and assembled musically trained listeners next to the track. Contrary to his expectation, Ballot's listeners heard a change in pitch, about as big as the step from one key on a piano to the next, as the trumpeters swept by.

To us, the Doppler effect is common sense, but that's only because we're used to machines that move at a noticeable fraction of the speed of sound. An 18-wheel Freightliner on Interstate 80 in Nevada is hauling along at 12 percent of the speed of sound, and its pitch drops down the equivalent of four keys on the piano as it blasts by. You no longer need to be a musician to detect the Doppler effect. The Doppler effect probably was not common sense for Cro-Magnon Man. Cro-Magnons didn't have highways, trucks, or trumpets.

However, we're just like our ancestors when it comes to the Doppler effect for light—that is not common sense for us. The wavelength of an atom's emission is a steadier source than any trumpeter can aspire to be. The wavelength, which we perceive as color, for an atom's emission or absorption lines is shifted a little to the blue if an atom is approaching and shifted a little to the red if the atom is moving away. But the speed of light is one million times the speed of sound, so for the same speed, the shift is a million times smaller for light than for sound and lies well below the threshold to detect a color change—even for Martha Stewart. That's why this effect is part of legend for lonesome railroad whistles, but not for their headlights. Everyday objects do not zoom by at an appreciable fraction of the speed of light, so the Doppler effect for light isn't a common sense phenomenon.

Astronomers measure the velocity of a star from the shift produced in the wavelengths of its absorption or emission lines. Here's the recipe: Gather light with a telescope, spread it out into a spectrum with a prism or grating, then carefully measure the wavelengths of the lines. Compare the measured wavelengths with the wavelengths from identical atoms, say of calcium or any other element, measured when the atoms are sitting quietly in a flame in your laboratory. The shift in wavelength tells the speed. Stars in the Milky Way galaxy have speeds measured this way of a few kilometers per second Lip to a few hundred kilometers per sccond as they mill around randomly like sailboats txtforc the starting gun, or as they systematically orbit the ccnter of our galaxy.

In the opening years of the 1900s, the Milky Way galaxy was the known universe. So if you were Albert Einstein in 1917, and you consulted your favorite astronomer about motions in the universe, the astronomer (in Einstein's case, Willcm dc Sitter, professor of astronomy at the University of Leiden in the Netherlands) could confidently tell you that spcctra show the stars have relatively small speeds and not much pattern to their motion. This is true, but because the Milky Way is not the whole universe, it led Einstein down a legendary path of error and regret.

The present-day image of our galaxy as one among billions of similar galaxies was not the common-sense view or even the prevailing view among experts when Einstein was young. By counting stars in the Milky Way, astronomers hoped to gauge the extent and shape of the system in which the sun is cmtxxldcd. But dust between the stars made this a treacherous undertaking. In some directions, the counts of faint stars thinned out because there really were fewer stars, so astronomers correctly inferred we lived in a flattened, disklike system. But in other directions, the star counts fell off with distance because the light of these stars was absorbed by intervening interstellar dust, distorting our true location in that disk. Dust is always a bugaboo in astronomy.

The result was a 1900s view of the Milky Way in which the sun might as well l)e at the center as any other place, and in which the Milky Way might possibly be the whole universe. If you're in a lx>at in a fog, it always looks like you're at the ccntcr of things The

Figure 4. t. The Milky Way This image shows dust clouds silhouetted against the bright bu|ge at the center of our galaxy Notice that the dust makes the bulge look dimmer and redder, a* interstellar dust removes more blu>e light than red light Courtesy of Axel Mel linger (Also see color insert)

cosmic fog was absorption by dust that gave the illusion of the sun sitting centrally in an extended, flattened system shaped something like the grindstone in an old mill. The small velocities of the stars seemed to show that this whole system was neither expanding nor contracting, but just sitting there, inert and unchanging. Yet by 1930, every element of this picture was completely reversed—our location far from the center of our galaxy was clearly established, the Milky Way was seen to be just one of a huge numljer of equivalent galaxies, and the whole cosmic fabric was oteerved to be stretching out.

Just as the journey inward led to an understanding of atomic nuclci and the source of stellar energy by the 1930s, the journey outward clcarcd away the fog of misunderstanding about our location and the state of the universe. In 1916, Albert Einstein was trying to understand how gravity works in the universe. After his great success in 1905, creating the theory of relativity, inventing the photon, and demonstrating the reality of atoms, he was no longer a technical expert third class (with provisional appointment) working at the Swiss Patent Office, revolutionizing physics in the moments snatched between inspecting dynamo designs and rejecting perpetual motion machines. By 1915, Einstein had been transformed into Herr Professor Doctor in Berlin at the Kaiser Wilhelm Institute, where he was struggling to construct the mathematical structure of his theory of general relativity: the theory of gravity expressed as geometry. Einstein was building a new way to look at gravity as the effect of curved space, employing the mathematics explored in the 1800s by the imaginations of Gauss and Riemann. It was a demanding struggle—by the time Einstein finished his work, he described himself as "zufriedert aber ziemlich kaputf ("content but rather worn out").1

Einstein is famous for taking the esthetic approach to physical theory. His innate sense of mathematical beauty helped guide his ideas about how the world works. But no matter how much he joked about instructing the Creator on the proper design of the universe, Einstein knew that the ultimate test of a theory is not how much you like the idea, but how well it describes the real world. In Einstein's curved space, mass (or the mass equivalent of energy) warps the fabric of space-time. Light or physical objects move through that curved space along paths that are determined by the curvature. This was a radical and new approach to gravitation. Einstein knew it was beautiful, but needed experimental tests to see if it was correct.

Allien Einstein diligently computed the orbit of the innermost planet, Mercury, in his new theory. Since Mercury orbits closest to the sun, it feels the strongest gravitational effects, and its orbit was the best place to look for a difference between the new theory and Newton's durable creation of the 1600s. Mercury's orbit is very nearly an ellipse, tracing out the same path around the sun every 88 days. But not quite. The orbit is not exactly closed, so like a giant spirograph, the long axis of Mercury's orbit slowly swings around, advancing 565 arcseconds2 per century, so that the direction the long axis of the orbit points will make a complete circuit in 225,000 years. In Newtonian gravity, this "precession," the slow reorientation of the orbit in space, is caused by the gravitational effects of the other planets, most importantly, the most massive—Jupiter. In 1859, Leverrier computed the expected amount of precession, later revised by Simon Newcomb as about 43 arcseconds per century smaller than the observed amount. No one understood where this additional precession came from.

One way to get the orbit to rotate slowly with no change to Newton's gravitation would be to have an unseen planet, with the proposed name of Vulcan, close to the sun, hidden from our view, supplying just what was needed to distort the orbit of Mercury. This seems a little far-fetched, because there was no other evidence for Vulcan, though we have grown accustomed to inferring the presence of invisible masses from their observed effects. In fact, there was a strong precedent, since the discovery of the planet Neptune in 1846 followed an analysis of otherwise unexplained motions of the planet Uranus But in Einstein's theory of gravity the curvature of space near the sun produces just a tiny bit more bending in the path of a planet than you'd calculate from the inverse square law of Newtonian gravity. The net result is just a liny bit more gravitation, a more sharply curved orbit near the sun, and extra precession, without inventing any planets. When Einstein did the arithmetic, he reported feeling "palpitations of the heart.'H The extra shift in the orbit he computed due to general relativity came out to be 43 arcseconds per century, just what was missing. Quantitative agreement with the facts has the ring of truth. And it is very exciting.

A second test for general relativity was to measure the landing of light as it passed through the warped space near the mass of the sun. This was a more important test than solving the problem with the orbit of Mercury. The discrepancy in Mercury's orbit had Ix^en an astronomical riddle for 50 years. The new test was more significant because the same theory, without any adjustments, also predicted a completely new effect that had never been observed. Accounting for the old is good, but making new predictions is an excellent feature for a scientific theory. It gives the observers a way to see if you arc wrong. Predictions are a theory's way of living dangerously.

After a false start, Einstein's completed theory predicted a deflection of starlight at the limb of the sun of 1.75 arcseconds, a small but measurable amount. World War I was raging, so even benign communications between Berlin and London were not gtx>d. Einstein sent a copy of his paper to Willem de Sitter in I^iden, in the Netherlands, and de Sitter passed on his copy to Arthur Stanley

Eddington in England. In 1916, Eddington was 34 years old, already Plumian Professor of Astronomy at Cambridge and a brilliant theoretical worker who quickly mastered the mathematics of differential geometry that Einstein had employed to describe curved space. Eddington was also in chargc of the Royal Astronomical Society's journal, Monthly Notices, and he arranged for de Sitter to write three long articles in English that introduced Einstein's new theory to the scientific world outside Germany. Eddington became a powerful champion of Einstein's ideas, promoting them among scientists and explaining them to a wider public.

There is no higher compliment a scientist can give to a theory than personal action to test it. Eddington put his own effort into testing Einstein's prediction. When World War T was concludcd by the Armistice in November 1918, Eddington was ready to travel to the island of Principe in the Gulf of Guinea off the coast of Africa for the cclipse of 29 May 1919 while a second expedition traveled to Sobral, in Brazil. By the greatest good fortune, the black sun at the moment of total eclipse would be right in the middle of the Hyadcs, a group of bright stars that make up the head of Taurus, the Bull. Their undeflected positions could be precisely measured in advance and their positions on the sky should be measurably altered by the warping of spacc near the sun's edge.

In the aftermath of the First World War, with Berlin still under blockade, this expedition was a touching example of the way science, and especially astronomy, is sometimes able to transcend nationalism. The Earth does look small when viewed from a cosmic perspective, and it is hard to imagine how the energctit: fratricide of mustard gas, artillery bombardment, tanks, and trench warfare would look to puzzled observers from Sirius. In any case, Eddington (who was a Quaker and a pacifist) got on a boar to travel for six months to test the predictions of Einstein (who was a pacifist, bur definitely nor a Quaker). Eddington later called the eclipse measurement "the greatest moment in my life.'"4

The result of this observation, "a deflection of light takes place in the neighborhood of the sun and ... it is of the amount demanded by Einstein's generalized theory of relativity," was reported to a joint meeting of the Royal Society and the Royal Astronomical

Society, on 6 November 1919 by the Astronomer Royal, Sir Frank Dyson, who had proposed the eclipse expedition. The next morning, the Times of London asserted, "it is confidently believed by the greatest experts that enough has been done to overthrow the certainty of ages, and to require a new philosophy of the universe." On hearing of the result, Einstein is reported to have said that if the prediction had not been verified, "Then I would be sorry for the dear Lord—the theory is correct.

Observation of new effects that were not predicted in Newton's theory of gravity gave Einstein's radical view of gravity as geometry the weight of truth. Dyson, who reported the measurement, wrote to George Ellery 1 lale, the creator of the Mount Wilson Observatory in Pasadena, California saying, "I was myself a skeptic, and expected a different result." Hale wrote back disarmingly, "I congratulate you on the splendid results you have obtained though I confcss the complications of the theory of relativity arc altogether tcx) much for my comprehension. . . . However, this dcx?s not decrease my interest in the problem, to which we will try to contribute to the test of our ability." Hale's unfamiliarity with general relativity's rarefied mathematical heights was shared by most astronomers, but his observatory did indeed contribute to the understanding of Einstein's theory, especially as it applies to the universe as a whole. It was at Hale's Mount Wilson Observatory, in the decade after Einstein found himself so suddenly famous, that Edwin 1 lubble discovered the expansion of the universe. You don't always have to understand the details of the mathematics to contribute to the advance of science. You just have to face in the right direction and go forward with the things that you know how to do.

The bending of light caused by the gravitational field of the sun that Eddington measured in 1919 is small, the measurements were difficult, and, in hindsight, faith in the outcome could have played a part in drawing strong conclusions from uncertain data. But there is no doubt now that the phenomenon is real and independent of the observer's mental state. Gravitational bending of light has been observed in many other settings where it produces dramatic effects that are easy to see with modern equipment. Einstein also predicted, in 1936, that the gravitational field of a star

Figure 4.2. Gravitational len&inj; by the galaxy cluster Abell 1218. The curved arcs are gravitationally lensed images of background galaxies, whose light is bent by the matter {mostly dark) in this cluster of galaxies. Courtesy of NASA. A Fmchter and the ERQ Team {STScl. ST ECF). (Also see color insert)

Figure 4.2. Gravitational len&inj; by the galaxy cluster Abell 1218. The curved arcs are gravitationally lensed images of background galaxies, whose light is bent by the matter {mostly dark) in this cluster of galaxies. Courtesy of NASA. A Fmchter and the ERQ Team {STScl. ST ECF). (Also see color insert)

could, in rhe right circumstances, act like a lens to magnify a background source of light.

In special cases, the immense mass of a galaxy cluster warps the space and acts as a natural lens to make a cosmic magnifying glass. A dense cluster sometimes shows thin arcs around the cluster center. This is not light from galaxies in the cluster, but a mirage caused by mass in the cluster, which distorts the image of yet more distant galaxies. It is a little like looking through the base of a wine glass—distant lights are warped into rings. Gravitational lenses are particularly vivid illustrations of Einstein's idea that mass curves space. They also hint at matter whose effects are important but that is not seen. The light of galaxies is emitted from the hot surfaces of stars, but not all matter is hot and not all matter is in stars. The mass in clusters of galaxies is, for the most part, not in the galaxies, but in cold dark matter that we do not sec. What is even more peculiar is that most of this dark matter is probably not made of the neutrons, protons, and electrons that constitute our bodies and the world we know. But the lensing effect gives no hint of composition: it depends only on the mass.

Einstein's initial formulation of general relativity, when applied to the universe as a whole, could accommodate either an expanding or contracting universe. Einstein consulted the fog-bound astronomers of 1917. Oe Sitter correctly reported that the velocities of stars in the grindstone "universe" of the Milky Way were small and gave no hint of cosmic expansion or cosmic contraction. Although his equations looked nicer without it, Einstein faced the facts by sticking an extra term into his equations, the cosmological constant A. This created a mathematical solution that Einstein thought made the universe eternal and static (this was later shown not to be quite correct: it could be static, but only for a moment). The cosmological constant is represented in general relativity by (he Greek letter lambda. Einstein used lowercase A, but (to make it seem more important in an age of grade inflation) we now use the uppercase A. Lambda had no effect on the tests of general relativity in the solar system, but it provided an expansive tendency to space that Einstein adjusted to produce a static universe (if the Milky Way was the universe), as observed.

This mathematical device was completely consistent with his earlier formulation of general relativity, but not necessary. The constant was "cosmological" in the sense that it would make no difference to local physical effects that could be tested by observation in [he solar system, such as gravitational bending of light rays by the sun or the advance of the perihelion of Mercury, but would be important only on the largest distance scales. Theoretical physics values simplicity and elegance, and avoids adding mathematical terms that are not compulsory. In fact, this esthetic principle is elevated to a credo—we call it Occam's razor, a pledge to shave ideas down to their essentials. Occam's razor says, "Entities are not to be multiplied without necessity," or more tersely, "simple pictures are best." But Einstein chose to include the cosmological constant. He stuck it in to match the astronomical data.

Einstein apologized for the cosmological term even as he introduced it:

We admittedly had to introduce an extension of the field equations of gravitation which is not justified by our actual knowledge of gravitation IThe cosmological] term is necessary only for the purpose of making possible a quasi-static distribution of matter, as required by the fact of the small velocities of the stars6

Einstein included the cosmological constant to satisfy the observational evidence as he understand it in 1917. But the observational picture was about to change, and the cosmological constant, already repulsive in one way, was about to acquire a much worse smell. Tn 1917 astronomers thought the Milky Way was the universe and the velocities of stars were the test for cosmic expansion. But spectra of the "spiral nebulae" and measurements made at the telescopes of Mount Wilson changed all that and turned the cosmological constant into a source of regret.

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