The tale of Albert Eiunstein’s “greatest blunder.”

By: Neil deGrasse Tyson.

Sung to the tune of “The Times They Are A-Changin’”:

                    Conic gather ‘round, math phobes,

                    Wherever you roam

                    And admit that the cosmos

                    Around you has grown

                    And accept it that soon

                    Yon won’t know what’s worth knowin

                    Until Einstein to you

                    Becomes clearer.

                    So you’d better start listenin’

                    Or you’ll drift cold and lone

                    For the cosmos is weird, gcttin’ weirder.

                                                   —The Editors (with apologies to Bob Dylan)

C osmology has always been weird.

Worlds resting on the backs of turtles, matter and energy coming into existence out of much less than thin air. And now, just when you’d gotten familiar, if not really comfortable, with the idea of a big bang, along comes something new to worry about . A mysterious and universal pressure pervades all of space and acts against the cosmic gravity that has tried to drag the universe back together ever since the big bang. On top of that, “negative gravity” has forced the expansion of the universe to accelerate exponentially, and cosmic gravity is losing the tug-of-war.

For these and similarly mind-warping ideas in twentieth—century physics, just blame Albert Einstein. Einstein hardly ever set foot in the laboratory; he didn’t test phenomena or use elaborate equipment. He was a theorist who perfected the “thought experiment,” in which you engage nature through your imagination inventing a situation or a model and then working out the consequences of some physical principle.

If—as was the case for Einstein—a physicist’s model is intended to represent the entire universe, then manipulating the model should be tantamount to manipulating the universe itself. Observers and experimentalists can then go out and look for the phenomena predicted by that model. If the model is flawed, or if the theorists make a mistake in their calculations, the observers will detect a mismatch between the model’s predictions and the way things happen in the real universe. That’s the first cue to try again, either by adjusting the old model or by creating a new one.

One of the most powerful and far-reaching theoretical models ever devised is Einstein’s theory of general relativity, published in 1916 as “The Foundation of the General Theory of Relativity” and refined in 1917 in Cosmological Considerations in the General Theory of Relativity.” Together, the papers outline the relevant mathematical details of how everything in the universe moves under the influence of gravity. Every few years, laboratory scientists devise ever more precise experiments to test the theory, only to extend the envelope of its accuracy.

Most scientific models are only half baked, and have some wiggle room for the adjustment of parameters to fit the known universe. In the heliocentric universe conceived by the sixteenth-century astronomer Nicolaus Copernicus, for example, planets orbited the Sun in perfect circles. The orbit-the-Sun part was correct, but the perfect-circle part turned out to be a bit off. Making the orbits elliptical made the Copernican system more accurate.

Yet, in the case of Einstein’s relativity, the founding principles of the entire theory require that everything take place exactly as predicted. Einstein had, in effect, built a house of cards, with only two or three simple postulates holding up the entire structure . (Indeed, on learning of a 1931 book titled 100 Authors Against Einstein, he responded, “Why one hundred? If I am incorrect, one would have been enough.”)

That unassailable structure—the fact that the theory is fully baked—is the source of one of the most fascinating blunders in the history of science. Einstein’s 1917 refinement of his equations of gravity included a new term—denoted by the Greek letter lambda—in which his model universe neither expands nor contracts. Because lambda served to oppose gravity within Einstein’s model, it could keep the universe in balance, resisting gravity’s natural tendency to pull the whole cosmos into one giant mass. Einstein’s universe was indeed balanced, but, as the Russian physicist Alexsandr Friedmann showed mathematically in 1922, it was in a precar--ious state—like a ball at the top of a hill, ready to roll down in one direction or an-other at the slightest provocation. Moreover, giving something a name does not make it real, and Einstein knew of no counterpart in the physical universe to the lambda in his equations.

E instein’s general theory of relativity called CR by verbally lazy cognoscenti- radically departed from all previous thinking about the attraction of gravity. Instead of settling for Sir Isaac Newton’s view of gravity as “action at a distance” (a conclusion that discomfited Newton himself), CR regards gravity as the response of a mass to the local curvature of space and time caused by some other mass. In other words, concentrations of mass cause distortions—dimples, really—in the fabric of space and time. Those distortions guide the moving masses along straight-line geodesics, which look like the curved trajectories that physicists call orbits. John Archibald Wheeler, a physicist at Princeton University, put it best when he summed up Einstein’s concept this way: “Matter tells space how to curve; space tells matter how to move.

In effect, CR accounts for two opposite phenomena: good ol’ gravity, such as the attraction between the Earth and a ball thrown into the air or between the Sun and the Earth; and a mysterious, repulsive pressure associated with the vacuum of space—time itself. Acting against gravity, lambda preserved what Einstein and every other physicist of his day had blown the chance to predict the expanding universe himself, Einstein discarded lambda, calling its introduction his life’s “greatest blunder.”

T hat wasn’t the end of the story, though.

Off and on over the decades, theoreticians would exhume lambda—more commonly known as the “cosmological constant”—from the graveyard of dis-credited theories. Then, sixty-nine years later, in 1998, science exhumed lambda one last time, because now there was evidence to justify it. Early that year two teams of astrophysicists—one led by Saul Perlmutter of Lawrence Berkeley National Laboratory in Berkeley, California; the other by Brian Schmidt of Mount Stromlo and Siding Springs Observatories in Canberra, Australia—rnade the same remarkable announcement. Dozens of the most distant supernovas ever observed they said, appeared noticeably dimmer than expected—a disturbing finding, given the well-documented behavior of this species of exploding star. Recon-ciliation required that either those distant supernovas acted quite differently from their nearer brethren, or else they were as much as 15 percent farther away than the prevailing cosmological models had placed them.

Not only was the cosmos expanding, but a repulsive pressure within the vacuum of space was also causing the expansion to accelerate. Something had to be driving the universe outward at an ever-increasing pace. The only thing that “naturally” accounted for the acceleration was lambda, the cosmological constant. When the physicists dusted it off and put it back in Einstein’s original equations for general relativity, the state of the universe matched the state of Einstein’s equations.

T o an astrophysicist, the super-novas used in Perlmutter’s and Schmidt’s studies are worth their weight in fusionable nuclei. Each star explodes the same way, igniting a similar amount of fuel, releasing a similarly titanic amount of energy in a similar period of time, and therefore achieving a similar peak luminosity. Hence these exploding stars serve as a kind of yardstick, or “standard candle,” for calculating cosmic distances to the galaxies in which they explode, out to the farthest reaches of the universe.

Standard candles simplify calculations immensely: since the supernovas all have the same wattage, the dim ones are far away and the bright ones are nearby. By measuring their brightness (a simple task), you can tell exactly how far away they are from you . If the luminosities of the supernovas were not all the same, brightness alone would not be enough to tell you which of them are far from Earth and which of them are near. A dim one could be a high-wattage bulb far away or a low-wattage bulb close up.

Fine. But there’s a second way to measure the distance to galaxies: their speed of recession from our Milky Way, a recession that’s part and parcel of the overall cos-mic expansion. As Hubble was the first to show, the expansion of the universe makes distant objects race away from us faster than the nearby ones do. By thus measuring a galaxy’s speed of recession (another straight forward task), you can deduce its distance from Earth.

If those two well-tested methods give different distances for the same object, some -thing must be wrong. Either the supernovas are bad standard candles, or our model for the rate of cosmic expansion as measured by galaxy speeds is wrong.

Well, something was wrong in 1998. It turned out that the supernovas are splendid standard candles, surviving the careful scrutiny of many skeptical investigators . Astrophysicists were left with a universe that is expanding faster than they had ever thought it was. Distant galaxies turned out to be even far ther away than their recession speed had seemed to indicate. And there was no easy way to explain the extra expansion without invoking lambda, the

cosmological constant.

Here, then, was the first direct evidence that a repulsive pressure permeated the universe, opposing gravity. That’s what resurrected the cosmological constant overnight. And now cosmologists could estimate its numerical value, because they could calculate the effect it was having: the difference between what they had ex-pected the cxpansion to be and what it actually was.

That value for lambda suddenly signified a physical reality, which now needed a name . “Dark energy” carried the day, suitably capturing our ignorance of its cause . The most accurate measurements done to date have shown dark energy to be the most prominent thing in town

T he shape of our four-dimensional universe comes from the relation between the amount of matter and energy that inhabits the cosmos and the rate at which the cosmos is expanding. A convenient mathematical measure of that shape is usually written as the uppercase Greek letter omega (Q). If you take the matter—energy density of the universe, and divide it by the matter energy density required to just barely halt the expansion (known as the “critical” density), you get omega.

 Because both mass and energy cause space-tune to warp, or curve, omega effectively gives the shape of the cosmos . If omega is less than one, the actual mass—energy falls below the critical value, and the universe expands forever in every direction for all of time. In that case, the shape of the universe is analogous to the shape of a saddle, in which initially parallel lines diverge. If omega is equal to one, the universe expands forever, but only barely so; in that case the shape is flat, preserving all the geometric rules we all learned in high school about parallel lines . If omega exceeds one, parallel lines converge, and the universe curves back on itself, ultimately recollapsing into the fireball whence it came.

At no time since Hubble discovered the expanding universe has any team of observers ever reliably measured omega to be anywhere close to one. Adding up all the mass and energy they could measure, dark matter included, the biggest values from the best observations topped out at about 0.3. Since that’s less than one, as far as observers were concerned, the universe was “open” for the business of expansion, riding a one-way saddle into the future.

M eanwhile, beginning in 1979, Alan H. Guth, a physicist at MIT, and others advanced an adjustment to the big bang theory that cleared up some nagging problems. In brief, Guth explained why things look about the same everywhere in the universe. A fundamental by-product of this up-date to the big bang was that it drove omega toward one. Not toward one-half. Not toward two. Certainly not toward a million. Toward one.

Scarcely a theorist in the world had a problem with that requirement, because it helped get the big bang to account for the global properties of the known universe. There was, however, another little problem: the update predicted three times as much mass and energy as observers could find. Undeterred, the theorists said the observers just weren’t looking hard enough.

At the end of the tallies, visible matter alone could account for very little of the critical density. How about the mysterious dark matter? Nobody knows what dark matter is, but observers knew there is five times as much dark matter as visible matter. They added that in as well. Alas, still way too little mass-energy. The observers were at a loss. “Guys,” they protested, “there’s nothing else out there.” And the theorists answered, “Just keep looking.”

Both camps were sure the other camp was wrong—until the discovery of dark energy. That single component raised the mass-energy density of the universe to the critical level. Yes, if you do the math, the universe holds three times as much dark energy as anything else.

A skeptical lot, the community of astrophysicists decided they would feel better about the result if there were some way to corroborate it. The Wilkinson Microwave Anisotropy Probe (WMAP) was just what the doctors ordered and needed. This NASA satellite, launched in 2001, was the latest and best effort to measure and map the cosmic microwave background, the big bang’s blueprint for the amount and distribution of matter and energy in the universe. Astrophysicists can now say with confidence that omega is indeed equal to one: the matter—energy density of the universe we know and love is equal to the critical density. The tabulation? The cosmos holds 73 percent dark energy , 23 percent dark matter, and a measly 4 percent ordinary matter the stuff you and I are made of.

For the first time ever, the theorists and observers kissed and made up. Both, in their own way, were correct. Omega is one, just as the theorists demanded of the universe, even though you can’t get there by adding up all the matter—dark or other-wise—as they had naively presumed. There’s no more matter running around the cosmos today than had ever been estimated by the observers. Nobody had foreseen the dominating presence of cosmic dark energy.

S o what is this stuff?

As with dark matter, nobody knows.

The closest anybody has come to a reasonable guess is to prestime that dark energy is a quantum effect—whereby the vacuum of space, instead of being empty, actually seethes with particles and their antimatter counterparts. They pop in and out of existence in pairs, and don’t last long enough to he measured. Their transient existence is captured in their moniker: virtual particles.

But the remarkable legacy of quantum mechanics—the physics of the small

demands that we give these particles serious attention . Each pair of virtual particles exerts a little bit of outward pressure as it ever so briefly elbows its way into space. Unfortunately, when you estimate the amount of repulsive “vacuum pressure” that arises from the abbreviated lives of virtual particles, the result is more than 10 to 120 times bigger than the value of the cosmological constant derived from the supernova measurements and WMAP. That may be the most embarrassing calculation ever made, the biggest mismatch betweeii theory and observation in the history of science.

I’d say astrophysicists remain clueless—but it’s not abject cluelessness. Dark energy is not adrift, with nary a theory to call home. It inhabits one of the safest homes we can imagine: Einstein’s equations of general relativity. It’s lanibda. Whatever dark energy turns out to be, we already know how to measure it and how to calculate its effects on the cosmos.

Without a doubt, Einstein’s greatest blunder was having declared that lambda was his greatest blunder.

A remarkable feature of lambda and the accelerating universe is that the repulsive force arises from within the vacuum, not from anything material. As the vacuum grows, lambda’s influence on the cosmic state of affairs grows with it. All the while, the density of matter and energy diminishes without limit. With greater repulsive pressure comes more vacuum, driving its exponential growth—the endless acceleration of the cosmic expansion.

As a consequence, anything not gravitationally bound to the neighborhood of the Milky Way will move away from us at ever-increasing speed, embedded within the expanding fabric of space—time. Galaxies now visible will disappear beyond an unreachable horizon. In a trillion or so years, anyone alive in our own galaxy may know nothing of other galaxies. Our--or our alien Milky Way brethren’s—observable universe will merely comprise a system of nearby stars. Beyond the starry night will lie an endless void, without form: “darkness upon the face of the deep?

D ark energy, a fundamental property of the cosmos, will, in the end, undermine the ability of later generations to comprehend their universe. Unless contemporary astrophysicists across the galaxy keep remarkable records, or bury an awe-some time capsule, future astrophysicists will know nothing of external galaxies-----the principal form of organization for matter in our cosmos. Dark energy will deny them access to entire chapters from the book of the universe.

Here, then, is my recurring nightmare: Are we, too, missing some basic pieces of the universe that once was? What part of our cosmic saga has been erased? What remains absent from our theories and equations that ought to be there, leaving us groping for answers we may never find?

                                                                    Astrophysicist Neil deGrasse Tyson

is the Frederick P. Rose Director of the Hayden Planetarium in New York City.



December 2003. (Pgs. 16-22.)

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