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As if you didn’t have enough to worry about, the universe in recent decades was discovered to wield a mysterious pressure that issues forth from the vacuum of space and that acts opposite cosmic gravity. Not only that, this “negative gravity” will ultimately win the tug-of-war, as it forces the cosmic expansion to accelerate exponentially into the future.
For the most mind-warping ideas of twentieth-century physics, just blame Einstein.
Albert 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, by inventing a situation or model and then working out the consequences of some physical principle. In Germany before World War II, laboratory-based physics far outranked theoretical physics in the minds of most Aryan scientists. Jewish physicists were all relegated to the lowly theorists’ sandbox and left to fend for themselves. And what a sandbox that would become.
As was the case for Einstein, if a physicist’s model intends 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 uncover a mismatch between the model’s predictions and the way things happen in the real universe. That’s the first cue for a theorist to return to the proverbial drawing board, by either adjusting the old model or creating a new one.
One of the most powerful and far-reaching theoretical models ever devised, already introduced in these pages, is Einstein’s general theory of relativity—but you can call it GR after you get to know it better. Published in 1916, GR outlines the relevant mathematical details of how everything in the universe moves under the influence of gravity. Every few years, lab scientists devise ever more precise experiments to test the theory, only to further extend the envelope of the theory’s accuracy. A modern example of this stunning knowledge of nature that Einstein has gifted us, comes from 2016, when gravitational waves were discovered by a specially designed observatory tuned for just this purpose.† These waves, predicted by Einstein, are ripples moving at the speed of light across the fabric of space-time, and are generated by severe gravitational disturbances, such as the collision of two black holes.
And that’s exactly what was observed. The gravitational waves of the first detection were generated by a collision of black holes in a galaxy 1.3 billion light-years away, and at a time when Earth was teeming with simple, single-celled organisms. While the ripple moved through space in all directions, Earth would, after another 800 million years, evolve complex life, including flowers and dinosaurs and flying creatures, as well as a branch of vertebrates called mammals. Among the mammals, a sub-branch would evolve frontal lobes and complex thought to accompany them. We call them primates. A single branch of these primates would develop a genetic mutation that allowed speech, and that branch—Homo sapiens—would invent agriculture and civilization and philosophy and art and science. All in the last ten thousand years. Ultimately, one of its twentieth-century scientists would invent relativity out of his head, and predict the existence of gravitational waves. A century later, technology capable of seeing these waves would finally catch up with the prediction, just days before that gravity wave, which had been traveling for 1.3 billion years, washed over Earth and was detected.
Yes, Einstein was a badass.
When first proposed, most scientific models are only half-baked, leaving wiggle room to adjust parameters for a better fit to the known universe. In the Sun-based “heliocentric” universe, conceived by the sixteenth-century mathematician Nicolaus Copernicus, planets orbited in perfect circles. The orbit-the-Sun part was correct, and a major advance on the Earth-based “geocentric” universe, but the perfect-circle part turned out to be a bit off—all planets orbit the Sun in flattened circles called ellipses, and even that shape is just an approximation of a more complex trajectory. Copernicus’s basic idea was correct, and that’s what mattered most. It simply required some tweaking to make it more accurate.
Yet, in the case of Einstein’s relativity, the founding principles of the entire theory require that everything must happen exactly as predicted. Einstein had, in effect, built what looks on the outside like a house of cards, with only two or three simple postulates holding up the entire structure. Indeed, upon learning of a 1931 book entitled One Hundred Authors Against Einstein,†† he responded that if he were wrong, then only one would have been enough.
Therein were sown the seeds of one of the most fascinating blunders in the history of science. Einstein’s new equations of gravity included a term he called the “cosmological constant,” which he represented by the capital Greek letter lambda: ?. A mathematically permitted but optional term, the cosmological constant allowed him to represent a static universe.
Back then, the idea that our universe would be doing anything at all, other than simply existing, was beyond anyone’s imagination. So lambda’s sole job was to oppose gravity within Einstein’s model, keeping the universe in balance, resisting the natural tendency for gravity to pull the whole universe into one giant mass. In this way, Einstein invented a universe that neither expands nor contracts, consistent with everybody’s expectations at the time.
The Russian physicist Alexander Friedmann would subsequently show mathematically that Einstein’s universe, though balanced, was in an unstable state. Like a ball resting on the top of a hill, awaiting the slightest provocation to roll down in one direction or another, or like a pencil balanced on its sharpened point, Einstein’s universe was precariously perched between a state of expansion and total collapse. Moreover, Einstein’s theory was new, and just because you give something a name does not make it real—Einstein knew that lambda, as a negative gravity force of nature, had no known counterpart in the physical universe.
Einstein’s general theory of relativity radically departed from all previous thinking about gravitational attraction. Instead of settling for Sir Isaac Newton’s view of gravity as spooky action-at-a-distance (a conclusion that made Newton himself uncomfortable), GR regards gravity as the response of a mass to the local curvature of space and time caused by some other mass or field of energy. In other words, concentrations of mass cause distortions—dimples, really—in the fabric of space and time. These distortions guide the moving masses along straight-line geodesics,††† though they look to us like the curved trajectories we call orbits. The twentieth-century American theoretical physicist John Archibald Wheeler said it best, summing up Einstein’s concept as, “Matter tells space how to curve; space tells matter how to move.”††††
At the end of the day, general relativity described two kinds of gravity. One is the familiar kind, like the attraction between Earth and a ball thrown into the air, or between the Sun and the planets. It also predicted another variety—a mysterious, anti-gravity pressure associated with the vacuum of space-time itself. Lambda preserved what Einstein and every other physicist of his day had strongly presumed to be true: the status quo of a static universe—an unstable static universe. To invoke an unstable condition as the natural state of a physical system violates scientific credo. You cannot assert that the entire universe is a special case that happens to be balanced forever and ever. Nothing ever seen, measured, or imagined has behaved this way in the history of science, which makes for powerful precedent.
Thirteen years later, in 1929, the American astrophysicist Edwin P. Hubble discovered that the universe is not static. He had found and assembled convincing evidence that the more distant a galaxy, the faster the galaxy recedes from the Milky Way. In other words, the universe is expanding. Now, embarrassed by the cosmological constant, which corresponded to no known force of nature, and by the lost opportunity to have predicted the expanding universe himself, Einstein discarded lambda entirely, calling it his life’s “greatest blunder.” By yanking lambda from the equation he presumed its value to be zero, such as in this example: Assume A = B + C. If you learn later that A = 10 and B = 10, then A still equals B plus C, except in that case C equals 0 and is rendered unnecessary in the equation.
But that wasn’t the end of the story. Off and on over the decades, theorists would extract lambda from the crypt, imagining what their ideas would look like in a universe that had a cosmological constant. Sixty-nine years later, in 1998, science exhumed lambda one last time. Early that year, remarkable announcements were made by two competing teams of astrophysicists: one led by Saul Perlmutter of Lawrence Berkeley National Laboratory in Berkeley, California, and the other co-led by Brian Schmidt of Mount Stromlo and Siding Spring observatories in Canberra, Australia, and Adam Riess of the Johns Hopkins University in Baltimore, Maryland. Dozens of the most distant supernovas ever observed appeared noticeably dimmer than expected, given the well-documented behavior of this species of exploding star. Reconciliation required that either those distant supernovas behaved unlike their nearer brethren, or they were as much as fifteen percent farther away than where the prevailing cosmological models had placed them. The only known thing that “naturally” accounts for this acceleration is Einstein’s lambda, the cosmological constant. When astrophysicists dusted it off and put it back into Einstein’s original equations for general relativity, the known state of the universe matched the state of Einstein’s equations.
The supernovas used in Perlmutter’s and Schmidt’s studies are worth their weight in fusionable nuclei. Within certain limits, each of those stars explodes the same way, igniting the same amount of fuel, releasing the same titanic amount of energy in the same amount of time, thereby reaching the same peak luminosity. Thus they 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 close by. After measuring their brightness (a simple task), you can tell exactly how far they are from you and from one another. If the luminosities of the supernovas were all different, you could not use brightness alone to tell how far away one was in comparison with another. A dim one could be either a high-wattage bulb far away or a low-wattage bulb close up.
All fine. But there’s a second way to measure the distance to galaxies: their speed of recession from our Milky Way—recession that’s part and parcel of the overall cosmic expansion. As Hubble was the first to show, the expanding universe makes distant objects race away from us faster than nearby ones. So, by measuring a galaxy’s speed of recession (another simple task), one can deduce a galaxy’s distance.
If those two well-tested methods give different distances for the same object, something 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. It turned out that the supernovas were splendid standard candles, surviving the careful scrutiny of many skeptical investigators, and so astrophysicists were left with a universe that had expanded faster than we thought, placing galaxies farther away than their recession speed would have otherwise indicated. And there was no easy way to explain the extra expansion without invoking lambda, Einstein’s cosmological constant.
Here was the first direct evidence that a repulsive force permeated the universe, opposing gravity, which is how and why the cosmological constant rose from the dead. Lambda suddenly acquired a physical reality that needed a name, and so “dark energy” took center stage in the cosmic drama, suitably capturing both the mystery and our associated ignorance of its cause. Perlmutter, Schmidt, and Reiss justifiably shared the 2011 Nobel Prize in physics for this discovery.
The most accurate measurements to date reveal dark energy as the most prominent thing in town, currently responsible for 68 percent of all the mass-energy in the universe; dark matter comprises 27 percent, with regular matter comprising a mere 5 percent.
The shape of our four-dimensional universe comes from the relationship between the amount of matter and energy that lives in the cosmos and the rate at which the cosmos is expanding. A convenient mathematical measure of this is omega: ?, yet another capital Greek letter with a firm grip on the cosmos.
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.
Since both mass and energy cause space-time to warp, or curve, omega tells us 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, taking on the shape of a saddle, in which initially parallel lines diverge. If omega equals one, the universe expands forever, but only barely so. In that case the shape is flat, preserving all the geometric rules we 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 their telescopes could see, and even extrapolating beyond these limits, dark matter included, the biggest values from the best observations topped out at about ? = 0.3. As far as observers were concerned, the universe was “open” for business, riding a one-way saddle into the future.
Meanwhile, beginning in 1979, the American physicist Alan H. Guth of the Massachusetts Institute of Technology, and others, advanced an adjustment to the big bang theory that cleared up some nagging problems with getting a universe to be as smoothly filled with matter and energy as ours is known to be. A fundamental by-product of this update to the big bang was that it drives omega toward one. Not toward a half. Not toward two. Not toward a million. Toward one.
Hardly 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-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 no more than 5 percent of the critical density. How about the mysterious dark matter? They added that, too. Nobody knew what it was, and we still don’t know what it is, but surely it contributed to the totals. From there we get five or six times as much dark matter as visible matter. But that’s still way too little. Observers were at a loss, and the theorists answered, “Keep looking.”
Both camps were sure the other was wrong—until the discovery of dark energy. That single component, when added to the ordinary matter and the ordinary energy and dark matter, raised the mass-energy density of the universe to the critical level. Simultaneously satisfying both the observers and the theorists.
For the first time, the theorists and observers kissed and made up. Both, in their own way, were correct. Omega does equal one, just as the theorists demanded of the universe, even though you can’t get there by adding up all the matter—dark or otherwise—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, nor had anybody imagined it as the great reconciler of differences.
So what is the stuff? Nobody knows. The closest anybody has come is to presume dark energy is a quantum effect—where 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 be measured. Their transient existence is captured in their moniker: virtual particles. The remarkable legacy of quantum physics—the science of the small—demands that we give this idea 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 10120 times bigger than the experimentally determined value of the cosmological constant. This is a stupidly large factor, leading to the biggest mismatch between theory and observation in the history of science.
Yes, we’re clueless. But it’s not abject cluelessness. Dark energy is not adrift, with nary a theory to anchor it. Dark energy inhabits one of the safest harbors we can imagine: Einstein’s equations of general relativity. It’s the cosmological constant. It’s lambda. Whatever dark energy turns out to be, we already know how to measure it and how to calculate its effects on the past, present, and future of the cosmos.
Without a doubt, Einstein’s greatest blunder was having declared that lambda was his greatest blunder.
And the hunt is on. Now that we know dark energy is real, teams of astrophysicists have begun ambitious programs to measure distances and the growth of structure in the universe using ground-based and space-borne telescopes. These observations will test the detailed influence of dark energy on the expansion history of the universe, and will surely keep theorists busy. They desperately need to atone for how embarrassing their calculation of dark energy turned out to be.
Do we need an alternative to GR? Does the marriage of GR and quantum mechanics require an overhaul? Or is there some theory of dark energy that awaits discovery by a clever person yet to be born?
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, the density of matter and (familiar) energy within the universe diminishes, and the greater becomes lambda’s relative influence on the cosmic state of affairs. With greater repulsive pressure comes more vacuum, and with more vacuum comes greater repulsive pressure, forcing an endless and exponential acceleration of the cosmic expansion.
As a consequence, anything not gravitationally bound to the neighborhood of the Milky Way galaxy will recede at ever-increasing speed, as part of the accelerating expansion of the fabric of space-time. Distant galaxies now visible in the night sky will ultimately disappear beyond an unreachable horizon, receding from us faster than the speed of light. A feat allowed, not because they’re moving through space at such speeds, but because the fabric of the universe itself carries them at such speeds. No law of physics prevents this.
In a trillion or so years, anyone alive in our own galaxy may know nothing of other galaxies. Our observable universe will merely comprise a system of nearby, long-lived stars within the Milky Way. And beyond this starry night will lie an endless void—darkness in the face of the deep.
Dark energy, a fundamental property of the cosmos, will, in the end, undermine the ability of future generations to comprehend the universe they’ve been dealt. Unless contemporary astrophysicists across the galaxy keep remarkable records and bury an awesome, trillion-year time capsule, postapocaplyptic scientists will know nothing of galaxies—the principal form of organization for matter in our cosmos—and will thus be denied access to key pages from the cosmic drama that is our universe.
Behold my recurring nightmare: Are we, too, missing some basic pieces of the universe that once were? What part of the cosmic history book has been marked “access denied”? What remains absent from our theories and equations that ought to be there, leaving us groping for answers we may never find?
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