What is dark matter?
An invisible substance thought to make up a quarter of all the “stuff” in the universe, dark matter leaves its gravitational fingerprints all over the cosmos. But despite decades of trying, scientists have failed to capture a single speck of dark matter, in part because they don't have a clear idea of what it actually is.
But what if the solution to the mystery of dark matter is that dark matter doesn't actually exist? What if this ghostly stuff is just a phantom of astronomers’ imaginations? Could there be another answer to the puzzles dark matter was invoked to solve?
Since the 1930s, astronomers have suspected that galaxies contain more mass that we can account for. That’s because, when astronomers clock the speed of stars circling around the center of the Milky Way and of galaxies moving in distant clusters, they all seem to be going too fast. They are going so fast that they should overtake the force of gravity tugging them inward and fly out into the void beyond. Yet something holds them back.
That “something,” most astronomers believe, is dark matter: matter we can’t see yet which has enough mass to keep those speeding stars in stable galactic orbits. But what is dark matter? Scientists have largely ruled out all known materials. The consensus is that dark matter must be a new species of particle, one that interacts only very weakly with all the known forces of the universe except gravity, with which it interacts as strongly as ordinary matter does. Dark matter is invisible and intangible, its presence detectable only via the gravitational pull it exerts.
But not every astronomer is satisfied with this interpretation. Some, like Stacy McGaugh at the University of Maryland, College Park, believe that the definition of dark matter is so slippery that it is impossible to prove or disprove. Researchers might be able rule out the existence of any specific conjectured form of dark matter particles, but "we cannot falsify the concept, so if one fails, we are free to make up another," says McGaugh. "This cycle can be endless — as long as we're convinced as a community that it has to be dark matter, we won't take alternatives seriously, but we can never be disabused of the concept of dark matter."
Instead of relying on mystery particles, a small community of researchers suggests an intriguing alternative: What if the answer lies in changing what we know about the laws of gravity? The leading alternative to dark matter is known as Modified Newtonian Dynamics (MOND). The assumption is that at large scales, the laws of gravity are different from Einstein's theory of general relativity. "MOND merely tweaks the way a known force, gravity, works—we don't have to accept that the universe is filled with invisible mass," McGaugh said.
In general, by tweaking Newton's laws of gravity when it comes to orbits at large scales, MOND predicts the velocities of stars within galaxies even better than dark matter does. "It works so well it seems there must be something to it," McGaugh said. MOND works especially well on a class of galaxies known as low surface brightness galaxies, very faint galaxies without bright centers, explains theoretical cosmologist Priyamvada Natarajan at Yale University. "It's better than dark matter at explaining the rotation curves of these galaxies, the speeds at which stars in a galaxy orbit the center."
However, critics point out that dark matter beats out MOND on other astronomical puzzles. "The biggest problem is perhaps clusters of galaxies—though MOND works well in individual galaxies, it doesn't fit clusters terribly well," McGaugh said.
In fact, even with MOND, there is still a need for dark matter. "The need for dark matter in such a theory is horrible," McGaugh said. "On the other hand, it is a fairly limited problem in scope—we believe there is more than enough ordinary matter in the universe that is yet undetected that would easily suffice to make up the difference."
Skeptics of MOND, however, point at the Bullet Cluster, two colliding clusters of galaxies. There is a clear separation of luminous and unseen matter seen there exactly matches what one would expect with the dark matter model—dark matter, being largely intangible even to itself, would "feel" the forces of the collision very differently than ordinary matter. MOND advocates say that although unseen matter could be involved, it might again be unseen forms of ordinary matter.
Maps of the cosmic microwave background—radiation left over from the Big Bang—also provide strong support for dark matter. Temperature aberrations seen in the cosmic microwave background seem to reflect the presence of both ordinary matter, which interacts with both matter and radiation, and dark matter, which influences matter but is essentially invisible to radiation.
So MOND advocates have a difficult task: Their theory must explain all the puzzles that dark matter has already solved, and it must present a new way of accounting for everything Einstein's theory of general relativity currently explains. For instance, general relativity proposes that matter and energy curve spacetime, creating the effect we know of as gravity. Massive bodies curve spacetime enough to visibly bend light, an effect known as gravitational lensing that astronomers have witnessed for decades. "We cannot explain the phenomenon of gravitational lensing without general relativity, and this is where MOND spectacularly fails," Natarajan said.
"It has proven hard to construct a relativistic version of MOND,” acknowledges McGaugh. “If one is going to introduce a new theory, it has to encompass existing, successful theories."
Meanwhile, physicists continue the quest to directly detect dark matter particles. "There are no significant results yet, but I am optimistic," says Natarajan. "In any case, I'm quite comfortable as it is with the evidence for the existence of dark matter."
But until physicists actually “see” a dark matter particle, researchers will continue to investigate alternatives to the dark matter model. "It could be wrong," McGaugh says. "We do not understand all there is to understand yet—there do remain fundamental mysteries to explore."
This is the first part of a two-part series on critics of dark matter and dark energy. Return next week for a look at alternatives to dark energy.
Editor's picks for further reading
FQXi: Out of the Darkness
Physicist Glenn Starkman is evaluating alternatives to general relativity.
NOVA scienceNOW: The Dark Matter Mystery
In this video, explore the evidence for dark matter.
Scientific American: What if There is no Dark Matter?
Could modifications to the theory of gravity eliminate the need for dark matter?
ONE night in June 2007, I got to watch astronomer Sandra Faber put the 10-meter Keck II telescope through its paces. She was observing galaxies in a region of the sky called the Extended Groth Strip, in the direction of the constellation Ursa Major. We sat in the cozy confines of the telescope control room, far below the telescope’s perch near the 13,796-foot-high summit of the Mauna Kea volcano in Hawaii.
Around midnight, Faber wrapped up her observations and we stepped out for a few minutes under the night sky. “I take comfort in the fact that it is a beautiful universe, and we belong here and that we fit,” Faber mused. “This is our home.”
Faber, a professor at the University of California, Santa Cruz, was referring to the idea that there is something uncannily perfect about our universe. The laws of physics and the values of physical constants seem, as Goldilocks said, “just right.” If even one of a host of physical properties of the universe had been different, stars, planets, and galaxies would never have formed. Life would have been all but impossible.
Take, for instance, the neutron. It is 1.00137841870 times heavier than the proton, which is what allows it to decay into a proton, electron and neutrino—a process that determined the relative abundances of hydrogen and helium after the big bang and gave us a universe dominated by hydrogen. If the neutron-to-proton mass ratio were even slightly different, we would be living in a very different universe: one, perhaps, with far too much helium, in which stars would have burned out too quickly for life to evolve, or one in which protons decayed into neutrons rather than the other way around, leaving the universe without atoms. So, in fact, we wouldn’t be living here at all—we wouldn’t exist.
Examples of such “fine-tuning” abound. Tweak the charge on an electron, for instance, or change the strength of the gravitational force or the strong nuclear force just a smidgen, and the universe would look very different, and likely be lifeless. The challenge for physicists is explaining why such physical parameters are what they are.
This challenge became even tougher in the late 1990s when astronomers discovered dark energy, the little-understood energy thought to be driving the accelerating expansion of our universe. All attempts to use known laws of physics to calculate the expected value of this energy lead to answers that are 10120 times too high, causing some to label it the worst prediction in physics.
“The great mystery is not why there is dark energy. The great mystery is why there is so little of it,” said Leonard Susskind of Stanford University, at a 2007 meeting of the American Association for the Advancement of Science. “The fact that we are just on the knife edge of existence, [that] if dark energy were very much bigger we wouldn’t be here, that’s the mystery.” Even a slightly larger value of dark energy would have caused spacetime to expand so fast that galaxies wouldn’t have formed.
That night in Hawaii, Faber declared that there were only two possible explanations for fine-tuning. “One is that there is a God and that God made it that way,” she said. But for Faber, an atheist, divine intervention is not the answer.
“The only other approach that makes any sense is to argue that there really is an infinite, or a very big, ensemble of universes out there and we are in one,” she said.
This ensemble would be the multiverse. In a multiverse, the laws of physics and the values of physical parameters like dark energy would be different in each universe, each the outcome of some random pull on the cosmic slot machine. We just happened to luck into a universe that is conducive to life. After all, if our corner of the multiverse were hostile to life, Faber and I wouldn’t be around to ponder these questions under stars.
This “anthropic principle” infuriates many physicists, for it implies that we cannot really explain our universe from first principles. “It’s an argument that sometimes I find distasteful, from a personal perspective,” says Lawrence Krauss of Arizona State University in Tempe, Arizona, author of A Universe From Nothing. “I’d like to be able to understand why the universe is the way it is, without resorting to this randomness.”
And he’s not the only one who feels this way. Nobel laureate Steven Weinberg of the University of Texas at Austin once told me, “I would, and most physicists would, prefer not to have to rely on anything like the anthropic principle, but actually to be able to calculate things.”
Nonetheless, there is growing and grudging acceptance of the multiverse, especially because it is predicted by a theory that was developed to solve one of the most frustrating of fine-tuning problems of all—the flatness of our universe.
Spacetime today is flat, not curved—meaning that two rays of light that start out parallel stay parallel, neither converging nor diverging. This has been confirmed to exquisite precision by measurements of the cosmic microwave background, the radiation left over from the big bang. That means that a cosmological parameter called Omega, which dials in the curvature of spacetime, is very close to one. But for today’s universe to have an Omega anywhere near one, its value just one second after the big bang had to be exactly one to precision of about fourteen decimal places. This smacked of fine-tuning.
But in 1979, the physicist Alan Guth, now of MIT, discovered a way to get that value of Omega without fine-tuning. Guth showed that in the instants after the big bang, the universe would have undergone a period of exponential expansion. This sudden expansion, which Guth called “inflation,” would have rendered our observable universe flat regardless of the value of Omega before inflation began.
Imagine starting with a small balloon whose surface is curved and blowing it up some forty orders of magnitude. Any small piece of the balloon’s surface will now look flat. In the inflationary view, that’s what happened to our universe—our local patch of spacetime looks flat regardless of the curvature of spacetime before inflation began.
Some physicists believe that inflation continues today in distant pockets of spacetime, generating one new universe after another, each with different physical properties. Inflation, therefore, walks both sides of the fine-tuning line: It lends credence to the anthropic principle by predicting a multiverse, but it also reminds us that parameters we once thought were fine-tuned, like Omega, can be explained by a more fundamental theory. “The history of physics has had that a lot,” says Krauss. “Certain quantities have seemed inexplicable and fine-tuned, and once we understand them, they don’t seem to so fine-tuned. We have to have some historical perspective.”
We’ll gain such perspective only after we have a fundamental theory of everything—or perhaps when we detect signs of other universes. The urge to understand our universe from first principles and not ascribe it to some divine force compels us to seek scientific explanations for what seems to be an incredible stroke of luck.
Editor's picks for further reading
FQXi: The Patchwork Multiverse
Raphael Buosso examines links between string theory, dark energy, and the multiverse.
FQXi: Testing the Multiverse
Hiranya Peiris looks for evidence of other universes in the cosmic microwave background radiation.
Skeptical Inquirer: Anthropic Design: Does the Cosmos Show Evidence of Purpose?
Victor Stenger provides a critical analysis of the "so-called anthropic coincidences."
TED: Why Is Our Universe Fine-Tuned for Life?
In this video, Brian Greene asks why our universe appears so exquisitely tuned for life.
There is a thin line between a bang and a whimper.
For stars, this line is called the Chandrasekhar Limit, and it is the difference between dying in a blaze of glory and going out in a slow fade to black. For our universe, this line means much more: Only by exceeding it can stars sow the seeds of life throughout the cosmos.
The Chandrasekhar Limit is named for Subrahmanyan Chandrasekhar, one of the great child prodigies. Chandrasekhar graduated with a degree in physics before reaching his twentieth birthday. He was awarded a Government of India scholarship to study at Cambridge, and in the fall of 1930 boarded a ship to travel to England. While aboard the ship—still before reaching his twentieth birthday—he did the bulk of the work for which he would later be awarded a Nobel Prize.
By the 1920s—a decade before Chandrasekhar began his journey to England—astronomers had realized that Sirius B, the white dwarf companion to the bright star Sirius, had an astoundingly high density—more than a million times the density of the sun. An object of this density could only exist if the atoms comprising the star were so tightly compressed that they were no longer individual atoms. Gravitational pressure would compress atoms so much that the star would consist of positively-charged ions surrounded by a sea of electrons.
Prior to the discovery of quantum mechanics, physicists knew of no force capable of supporting any star against such gravitational pressure. Quantum mechanics, though, suggested a new way for a star to hold itself up against the force of gravity. According to the rules of quantum mechanics, no two electrons can be in the exact same state. Inside an extremely dense star like Sirius B, this means that some electrons are forced out of low energy states into higher ones, generating a pressure called electron degeneracy pressure that resists the gravitational force. This makes it possible for a star like Sirius B to achieve such extreme density without collapsing in on itself.
This discovery was made by Ralph Fowler, who would later become Chandrasekhar’s graduate supervisor. But Chandrasekhar realized what Fowler had missed: The high-energy electrons inside the white dwarf would have to be traveling at velocities near the speed of light, invoking a set of bizarre relativistic effects. When Chandrasekhar took these relativistic effects into account, something spectacular happened. He found a firm upper limit for the mass of any body which could be supported by electron degeneracy pressure. Once this limit—the Chandraskehar limit—was exceeded, the object could no longer resist the force of gravity, and it would begin to collapse.
When Chandrasekhar published these results in 1931, he set off a battle with one of the greatest astrophysicists of the era, Sir Arthur Eddington, who believed that the white dwarf state was the eventual fate of every star. At a conference in 1935, Eddington told his audience that Chandrasehkar’s work “was almost a reduction ad absurdum of the relativistic degeneracy formula. Various accidents may intervene to save a star, but I want more protection than that. I think there should be a law of Nature to prevent a star from behaving in this absurd way!”
Chandrasekhar was deeply hurt by Eddington’s reaction, but colleagues can disagree profoundly and still remain friends. Chandrasekhar and Eddington remained friends, went to the Wimbledon tennis tournament together and went for bicycle rides in the English countryside. When Eddington passed away in 1944, Chandrasekhar spoke at his funeral, saying “I believe that anyone who has known Eddington will agree that he was a man of the highest integrity and character. I do not believe, for example, that he ever thought harshly of anyone. That was why it was so easy to disagree with him on scientific matters. You can always be certain he would never misjudge you or think ill of you on that account.”
Vindication would eventually come to Chandrasekhar when he was awarded the Nobel Prize in 1983 for his work. The Chandrasekhar Limit is now accepted to be approximately 1.4 times the mass of the sun; any white dwarf with less than this mass will stay a white dwarf forever, while a star that exceeds this mass is destined to end its life in that most violent of explosions: a supernova. In so doing, the star itself dies but furthers the growth process of the universe—it both generates and distributes the elements on which life depends.
The life of a star is characterized by thermonuclear fusion; hydrogen fuses to helium, helium to carbon, and so on, creating heavier and heavier elements. However, thermonuclear fusion cannot create elements heavier than iron. Only a supernova explosion can create copper, silver, gold, and the “trace elements” that are important for the processes of life.
Lighter elements like carbon, oxygen, and nitrogen are also essential to life, but without supernova explosions, they would remain forever locked up in stars. Being heavier than the hydrogen and helium that comprise most of the initial mass of the stars, they sink to form the central core of the star—just as most of the iron on Earth is locked up in its core. If stars are, as Eddington believed, destined to become white dwarfs, those elements would remain confined to the stellar interior, or at best be delivered in relatively minute quantities to the universe as a whole via stellar winds. Life as we know it requires rocky planets to form, and there simply is no way to get enough rocky material out into the universe unless stars can deliver that material in wholesale quantities. And supernovae do just that.
The Chandrasekhar Limit is therefore not just as upper limit to the maximum mass of an ideal white dwarf, but also a threshold. A star surpassing this threshold no longer hoards its precious cargo of heavy elements. Instead, it delivers them to the universe at large in a supernova that marks its own death but makes it possible for living beings to exist.
Editor's picks for further reading
BBC: Test Tubes and Tantrums: Arthur Stanley Eddington and Subrahmanyan Chandrasekhar
In this radio program, discover the history of one of the nastiest disagreements in astrophysics.
FQXi: Exploding the Supernova Paradigm
In this blog post, Zeeya Merali investigates gaps in our understanding of supernova explosions.
Nobelprize.org: Subramanyan Chandrasekhar – Autobiobraphy
This essay is part of the series Beautiful Losers.
Plato believed that he could describe the Universe using five simple shapes. These shapes, called the Platonic solids, did not originate with Plato. In fact, they go back thousands of years before Plato; you can find stone models (perhaps dice?) of each of the Platonic solids in the Ashmolean Museum at Oxford dating to around 2000 BC, as pictured below. But Plato made these solids central to a vision of the physical world that links ideal to real, and microcosm to macrocosm in an original, and truly remarkable, style.
AN1927.2727-31 Neolithic Carved Sandstone Balls, Copyright Ashmolean Museum, University of Oxford.
Let me explain, first, what the Platonic solids are. To begin, consider something simpler: regular polygons. Regular polygons, by definition, are two-dimensional shapes bounded by sides of equal length, each making the same angles with its neighbors. Equilateral triangles, squares, regular pentagons, and so on are all regular polygons. Platonic solids are the three-dimensional analog of regular polygons, and prove to be far more interesting. Platonic solids are bounded by regular polygons, all of the same size and shape. One can prove mathematically that there are exactly five Platonic solids. Here they are:
The Platonic solids and their proposed identification with fundamental world-elements
The tetrahedron has four triangular faces, the cube six square faces, the octahedron eight triangular faces, the dodecahedron twelve pentagonal faces, and the icosahedron twenty triangular faces. Plato proposed that four of these solids built the Four Elements: sharp-pointed tetrahedra give the sting of Fire, smooth-sliding octahedra give easily-parted Air, droplety icosahedra give Water, and lumpish, packable cubes give Earth. The dodecahedron, at last, is the shape of the Universe as a whole. Later Aristotle emended Plato's system, suggesting that dodecahedra provide a fifth essence—the space-filling Ether.
Plato's ideas lent dignity and grandeur to the study of geometry, and greatly stimulated its development. The thirteen and final book of Euclid's Elements, the grand synthesis of Greek geometry that is the founding text of axiomatic mathematics, culminates with the construction of the five Platonic solids, and a proof that they exhaust the possibilities. Scholars speculate that Euclid planned the Elements with that climax in mind from the start.
From a modern scientific perspective, of course, Plato's mapping from mathematical ideals to physical reality looks hopelessly wrong. The four (or five) ancient “elements” are not simple substances, nor are they usable building blocks for constructing the material world. Today's rich and successful analysis of matter involves entirely different concepts. And yet...
In its general approach, and its ambition, Plato's utterly mistaken theory anticipated the spirit of modern theoretical physics. His program of describing the material world by analyzing (“reducing”) it to a few atomic substances, each with simple properties, existing in great numbers of identical copies, coincides with modern understanding.
Deeper still penetrates his insight that symmetry defines structure. Plato sensed enormous potential in the fact that asking for perfect symmetry leads one to discover a small number of possible structures. Based on that foundation, and a few clues from experience, the outlandish synthesis that his philosophy suggested should be possible, to realize the World as Ideas, might be achievable. And clues were there to be found: Near-coincidence between the number of perfect solids (five) and the number of suspected elements (four); suggestions of how observed qualities might reflect underlying shapes (e.g., the sting of fire from the sharp points of tetrahedra). One must also admire the boldness of genius in seeing an apparent defect in the theory—five solids for four elements—as an opportunity for crowning creation, either with the Universe as a whole (Plato) or with space itself (Aristotle).
Modern physicists, when seeking equations to describe the unfamiliar laws of the microcosm, must make guesses based on fragmentary information. Optimistically—and lacking constructive alternatives—they have turned, as Plato did, to symmetry as their guide. Symmetry of equations is perhaps a less familiar idea than symmetry of shapes, but there is nothing obscure or mystical about it. We say an equation, like a shape, displays symmetry when it allows changes that make no change. So for instance the equation
X = Y
has a nice symmetry to it, because exchanging X for Y changes it into this:
Y = X
and this transformed equation expresses exactly the same content as the original. On the other hand X = Y + 2, say, turns into Y = X + 2, which expresses something else entirely. As this baby example demonstrates, symmetric equations can be rare and special, even when the symmetry involves quite simple transformations.
The equations of interest for physics are considerably richer, of course, and the "changes that make no change" we hope they allow are much more extensive and elaborate. But the central idea inspiration remains, as it was for Plato, the hope that symmetry defines a few interesting structures, and that Nature chooses one (or all!) of those most beautiful possibilities.
Plato's Beautiful Loser was, in hindsight, a product of premature, and immature, ambition. He tried to leap directly from beautiful mathematics, some imaginative numerology, and primitive, cherry-picked observations to a Theory of Everything. In this his ambition was premature. Also, Plato failed to draw out specific consequences from his ideas, or to test them critically. He sketched an inspiring world-model, but was content to "declare victory" without engaging any serious battles. The mature and challenging form of scientific ambition, which aspires to understand specific features of the world in detail and with precision, emerged only centuries later.
How far can you compress something before you reach nature’s ultimate breaking point—that is, before you create a black hole?
Inspired by Einstein’s theory of general relativity and its novel vision of gravity, the German physicist Karl Schwarzschild took on this question in 1916. His work revealed the limit at which gravity triumphs over the other physical forces, creating a black hole. Today, we call this number the Schwarzschild radius. The Schwarzschild radius is the ultimate boundary: We can receive no information from the black hole that lies within it. It is as if a portion of our universe has been cut off.
However, there is a lot more to the black hole story, which actually starts in the late 1700s with a little-known scientist named John Michell. Michell devised the torsion balance, a piece of equipment which enables the strength of forces to be computed quite accurately. He gave his torsion balance to Henry Cavendish, who used it to obtain the first accurate measurement of the weight of the Earth. Charles Augustin de Coulomb later used a torsion balance to establish the strength of electrical attraction and repulsion, and high-tech torsion balances are still an important measurement tool today.
Michell was the first person to conceive of the possibility of a gravitational mass so large that light could not escape from it, and was then able to come up with an estimate of how large such a body must be. Though Michell’s calculation did not produce the right answer—after all, he was working with Newton’s laws, not Einstein’s, and the speed of light was not known to high accuracy at the time—he deserves great credit for being the first to imagine the cosmic beasts we now know as black holes.
More than a century later, Karl Schwarzschild would be the first to correctly analyze the relation between the size of a black hole and its mass. It was 1916, and he was a soldier stationed on the Russian front. But he was not your typical soldier. A distinguished professor specializing in astrophysics, he enlisted in the German army when he was more than forty years old. His reading matter at the front was also different from the reading matter preferred by the ordinary soldier. Albert Einstein had just published his General Theory of Relativity, and Schwarzschild not only managed to obtain a copy (probably no mean feat in itself, considering the circumstances), but was able to do significant research in the thick of a war zone. Although Schwarzschild survived the hazards of battle, he sadly fell victim to pemphigus, a disease which ravaged his immune system, and died within a year—but not before he discovered the number that now bears his name.
Schwarzschild showed that any mass could become a black hole if that mass were compressed into a sufficiently small sphere—a sphere with a radius R, which we now call the Schwarzschild radius. To calculate the Schwarzschild radius of any object—a planet, a galaxy, even an apple—all you need to know is the mass to be compressed. The Schwarzschild radius for the Earth is approximately one inch, meaning that you could squish the entire mass of the Earth into a sphere the size of a basketball and still not have a black hole: light emitted from that mass can still escape the intense gravitational pull. However, if you squeeze the mass of the Earth into a sphere the size of a ping-pong ball, it becomes a black hole.
To Schwarzschild, black holes were merely a theoretical possibility, not a physical reality. It wasn’t until later in the twentieth century that it was shown that any star with a mass larger than twenty times that of the Sun would eventually collapse and become a black hole—a number much smaller than Michell’s original calculation.
Does the Schwarzschild radius define the “size” of a black hole? The answer is both yes and no. On one hand, theorists believe that all the “stuff” inside a black hole collapses into a singularity, an infinitely small and infinitely dense point well inside the boundary defined by the Schwarzschild radius. If you could visit a black hole, you wouldn’t perceive a physical boundary along the surface defined by the Schwarzschild radius. However, you would in fact be at a very special location: You would be traversing the “event horizon” of the black hole, the point-of-no-return from which nothing, not even light, can escape.
The Schwarzschild radius also suggests a second way to think about the density of the black hole. Though the density of the singularity is infinite, the density of a black hole can also be defined as the black hole’s mass divided by the volume of a sphere with the Schwarzschild radius. By this accounting, Earth-mass black hole is dense beyond belief. After all, a ping-pong ball has a volume of a few cubic inches and the mass of the Earth is six sextillion tons (give or take a few quintillion), so the density of an Earth-mass black hole is on the order of sextillion tons per cubic inch.
One surprising quirk of this mathematics, however, is that the larger the mass, the lower the density of the black hole. That’s because the Schwarzschild radius increases in proportion to the amount of mass—an object with twice as much mass as the Earth will have a Schwarzschild radius that is twice as large as the Earth’s. But density is mass divided by volume, and the volume of a sphere increases as the cube of its radius. If you double the size of the Schwarzschild radius, thus accommodating twice as much mass in the black hole, you increase the volume by a factor of 2 x 2 x 2 = 8. The density of the larger black hole will only be one-quarter of the density of the smaller one. So every time you double the mass in a Schwarzschild radius black hole, thus doubling the radius, the density decreases by a factor of 4.
This has a simple but rather surprising consequence. The Schwarzschild radius of a black hole whose mass is equal to that of a galaxy is so large that the density of that black hole is less than one one-thousandth the density of air on the surface of the Earth!
That probably isn’t what you picture when you think of a black hole. In fact, thanks to modern computer graphics, we all share a vision of a black hole as an ominous, totally black sphere surrounded by swirling stars and planets, with those nearby spiraling into eventual annihilation. And yet our very first picture of these bizarre objects came neither from an artist’s pen or a telescope’s lens: It came from mathematics, and from one number that traced the perimeter of physics itself.
Is our universe just one of many? The “multiverse” has occupied the pages of theorists’ notebooks for decades. Now, astronomers are on the brink of testing this hypothesis as they begin the search for evidence of universes beyond our own.
Though the first test, using data from a satellite called WMAP, came up empty-handed, cosmologists are now turning their attention to fresh results from the European Space Agency’s Planck satellite, which is mapping the cosmic microwave background radiation and creating an all-sky temperature map with three times greater resolution than its predecessor. If other universes exist, it is possible that they have collided with our own universe. Physicists believe that such a collision would leave an imprint on the background radiation in the form of a disc-shaped region of very-slightly different temperature than the surrounding background. Planck’s improved resolution will sharpen the edges of any collision-induced disc in the background radiation.
Planck is also studying a property of the background radiation called polarization, which describes the angle at which the electromagnetic waves vibrate in relation to the direction they are traveling. (You encounter polarization every time you slip on polarized sunglasses; because sunlight reflected off the horizontal surface of a road or a body of water becomes polarized, these special lenses can selectively block it out, reducing glare.) Polarization is a sensitive probe of the conditions that prevailed when the photons were released. Though WMAP was not sensitive enough to see any patterns in the polarization of the photons, Planck, with three times more sensitivity, is expected to see such patterns, which just might contain the fingerprint of so-called "bubble collisions."
What would such a signal look like? Matthew Kleban of New York University and his colleagues have shown that bubble collisions should leave two highly-polarized rings surrounding the temperature disc.
“According to our predictions for the probability of these bubble collisions, we are more likely to see larger discs than smaller discs,” says Kleban. “And it turns out that for larger discs, polarization is actually a very sensitive test. The signal is more distinctive, and it gets stronger as the disc gets bigger.”
So, if we did see such signatures in the Planck data, what would it prove?
“It would be conclusive of the fact that before our observable universe was formed, there was this precursor phase, and you could say with great certainty that that precursor phase still exists, somewhere, and that we are one small little pocket in a much, bigger multiverse,” says Matthew Johnson of the Perimeter Institute for Theoretical Physics. “It would be fairly direct evidence for the existence of a multiverse.”
That would be revolutionary. It would also focus attention on an unorthodox view of quantum mechanics which is already growing in popularity: the many-worlds hypothesis.
Proposed in the 1950s by physicist Hugh Everett, the many-worlds hypothesis takes a radical view of what happens to the wave function—the equation that spells out the probability of finding a quantum system in a particular state—when a measurement is made. In Niels Bohr’s Copenhagen Interpretation, any time we make a measurement, the wave function “collapses,” giving us one outcome from an infinity of possibilities. Everett argued that the wave function never collapses. Rather, every possibility exists in a parallel universe. This suggests a staggeringly large number of other worlds.
But are they the same “other worlds” predicted by eternal inflation? Recent work by Leonard Susskind of Stanford University and Raphael Bousso of the University of California, Berkeley, hints that the many worlds of quantum theory and the multiverse of eternal inflation might be two sides of the same coin. By linking eternal inflation with Everett’s many worlds, Susskind and Bousso hope to establish the physical meaning of the probabilistic predictions that have confounded quantum physicists for decades.
Yet even if bubble universes exist, the odds might be against spotting a collision. “Everyone thinks that we would have to be lucky,” says Susskind. “I would not try to estimate just how lucky, but at least somewhat lucky.” After all, our universe is much, much bigger than what we can see—so the collision may lie beyond our cosmic horizon.
Henry David Thoreau once wrote, “The universe is wider than our views of it.” That is true, of course. But the quest to find evidence of universes beyond our own shows that our “view” of the universe is a window that widens just as far as technology, theory, and the laws of physics can stretch it.
The vast space that we call our universe might be just a small speck in a fabric dotted with other universes, maybe an infinite number of them. We could be living in what physicists call a multiverse. It is a tantalizing prospect, but verifying it has remained in the realm of fantasy--until now. For the first time, the theorists have a testable prediction: Collisions with nearby universes could have left a mark in the cosmic microwave background, the fossil radiation of the big bang. Now, the hunt is on to detect the echoes of these collisions, which would provide the first experimental evidence for the existence of other universes.
Let’s back up a bit and see why physicists think there may be universes beyond our own in the first place. Fractions of a second after the big bang, our universe is thought to have expanded exponentially in a phase called inflation. Soon after inflation was proposed by the physicist Alan Guth, now of MIT, other physicists, including Andrei Linde of Stanford University and Alex Vilenkin of Tufts University, realized that once inflation got going, it should never end. According to this idea, now called “eternal inflation,” what we think of as the vacuum of space isn’t actually empty; it contains energy that makes it unstable and prone to form new bubble-like vacuums, much like bubbles of air emerging in boiling water. Each bubble inflates in turn, and new bubbles can form within it. In this view, our universe is just one of a huge and ever-increasing number of bubbles, each capable of giving rise to a new universe.
But how does one turn such esoteric theory into experimentally verifiable fact? Our best shot, according to Matthew Johnson of the Perimeter Institute for Theoretical Physics in Waterloo, Canada, and his colleagues, is to seek out evidence that one of these bubble universes collided with our own. Such a collision would create perturbations in the fabric of spacetime which would leave an imprint on the cosmic microwave background radiation.
The background radiation is the universe’s first light, made up of photons that were released throughout the universe a mere 370,000 years after the big bang. The photons contain information about the state of the universe at that instant, and that state would have been influenced by events close to the big bang—such as inflation itself or even a collision with other bubbles.
Johnson and his colleagues calculated that a collision would leave a distinct disc-shaped imprint on the background radiation. The temperature inside the imprint would be ever-so-slightly different from the temperature outside the disc. Properties such as the size of the disc, which could range from a few fractions of a degree to half the sky, and the intensity of the temperature difference between the inside and the outside of the disc, would depend on the exact nature of the collision.
The team then set about predicting how many collisions one should expect to find in the data collected by NASA’s WMAP satellite, a telescope designed specifically to probe the minute variations in the CMB, and what the traces of those collisions would look like to WMAP. Their result may be a bit of a downer for fans of the multiverse—they discovered that the data are most consistent with zero collisions--but that is not the end of the story. It is possible that the instrument simply isn’t sensitive enough to detect the traces of collisions with other universes. In fact, there are a few spots in the data that match the kind of signal expected from bubble collisions, but the result is not statistically significant. Random fluctuations in the background radiation could also create such patterns.
Still, Johnson is pleased. “Before this analysis these ideas seemed untestable,” he says. “It seemed like science fiction, but it’s not. It’s very exciting that you can rigorously do science in this theory. You might be unlucky and not see anything, but that’s kind of beside the point. It’s testable.”
Next week, discover what’s next in the search for signs of the multiverse.
To celebrate Thanksgiving, we've asked some of our contributors and friends to tell us what physics they are most thankful for. We hope you'll join the conversation by sharing your own thoughts in the comments section. On Thanksgiving day, we'll have more thoughts from physicists, plus some of our favorite reader comments, on our Twitter feed, @novaphysics. Just look for the #thanksphysics hashtag. Wishing a safe, happy, and inspiring holiday to all!
Frank Wilczek: I'm thankful that the world gives us puzzles we can solve, but not too easily.
James Stein: I’m thankful that physics both intrigues the intellect and is a major driver of technological improvement. While this is true of science in general, energy is the ultimate coin of the universe, and physics is the means by which we discover how it is produced, how it is transformed, and how we can use it to better our lives.
Delia Schwartz-Perlov: I'm grateful to be living at this moment in history, when dark energy hasn’t been dominating our universe for too long, and we are therefore still able to see our magnificent universe. Creatures living billions of years in the future will not be able to see all of this.
Jim Gates: Physics is the only piece of magic I've ever seen. I'm grateful for real magic.
Sean Carroll: I'm thankful for the arrow of time, pointing from the past to the future. Without that, every moment would look the same.
Clifford Johnson: I'm thankful for the "Hoyle resonance" of carbon 12. It is an excited state of carbon that allows it to be produced in stars from helium collisions. Hoyle realized that this is the only way that the carbon we are all made of could be produced, and so reasoned the fact that he (a human, made of 18% carbon) was around to puzzle over the problem was a prediction of the existence of this state. The resonance was later discovered by nuclear physicists, with exactly the properties he said it should have.
James Stein: I’m thankful for Michael Faraday’s discovery of the principle of electromagnetic induction. It made it possible to use electricity to advance the human condition, and I think it is the single most productive discovery in the history of physics.
Delia Schwartz-Perlov: I’m eight months pregnant, so I am grateful for the physics that enables ultrasound. It is pretty amazing and exciting to see what’s going on in there.
Edward Farhi: As the physicist Ron Johnson once said, I'm grateful to quantum mechanics for an interesting life.
Once upon a time—roughly 13.7 billion years ago, to be more precise—our universe was created in the Big Bang. From a virulent exploding fireball bursting with elementary particles, the universe evolved into the pitch-black expanse we currently observe, majestically sprinkled with star-studded galaxies. But is this really the full story? Today, cosmologists are learning that the incredible tale of our universe might be just one slim chapter in a much bigger volume: a book of universes that is infinitely large—and that is still being written.
In this video, I’ll explain why scientists think that our universe may be just one of many. I invite you to watch the pencast, then read on!
Our entire observable universe is very large, having a diameter of roughly 40 billion light years, and encompassing hundreds of billions of galaxies, each of which may contain billions of stars. Yet in the version of cosmology that I study, called eternal inflation, this is just a small fraction of an infinitely large universe which itself is only one out of an infinite number of other universes! Each of these “other” universes is the product of its own “local” big bang. Instead of being the ultimate creation event, our Big Bang merely marks the emergence of our local universe into the far grander “multiverse,” like a lone bubble materializing in an infinite flute of fizzing champagne. Each bubble represents an infinite universe, and our cosmic champagne flute is home to an infinite number of bubbles!
Bubbles within bubbles: The multiverse of eternal inflation.
So where do all the bubbles come from? Why couldn’t we just have one universe? Cosmologists believe that our universe experienced a period of very rapid expansion, called inflation, in the moments after the Big Bang, and they have confirmed this with a great deal of observational and theoretical evidence. It turns out that if the universe ever underwent an inflationary stage, then, even if inflation ends in one place, elsewhere inflation will continue. Once inflation starts, it never ends! The result is a mind-boggling proliferation of universes.
But there is more than one way to make a multiverse. The multiverse also emerges from string theory, which suggests that we actually live in 10 or 11 dimensions, not the mundane four (three spatial dimensions plus time) that we're used to! That’s seems like a stretch, but since string theory is our best candidate for getting gravity and quantum mechanics to agree with each other, we need to take the idea of extra dimensions seriously. Since we only experience four dimensions, we must ask: where did all the extra dimensions go? This is where an idea called “compactification” comes in. Physicists have been able to show that if we start with a higher dimensional world, some of the extra dimensions can be "compactified" so that we don't "experience" them directly. However, different compactifications describe lower dimensional universes with different physical properties, so we can experience them indirectly!
It turns out that there is a huge number of different ways to compactify these extra dimensions—googols of ways, in fact! All these different options offer a huge menu of different types of possible universes.
Take eternal inflation and add it to string theory, and you have not just an enormous number of possible universes, but a mechanism for creating them. Eternal inflation sees to it that the multiverse actually gets populated by each option on the menu via an ongoing process of nested bubble nucleations.
In 1878—before Einstein was born, before quantum mechanics, before we knew that our galaxy was one among many—a well-known physicist named Phillip von Jolly told young Max Planck, a student aspiring to a career in physics, “In this field, almost everything is already discovered, and all that remains is to fill a few unimportant holes.”
Little did von Jolly realize how seriously he had underestimated the depth and quantity of those “unimportant holes,” and he certainly had no idea that Planck was to play a vital role in helping to fill them. Fortunately for us, Planck was not turned off by Jolly’s remark, and replied that he was not so much interested in discovering new things as in understanding what was known. This might sound unusual, as most scientists are motivated by a combination of two things: a desire to understand, coupled with the urge to discover. Discovery and understanding go hand-in-hand; together they move science forward, and as science moves forward, the quality of our lives improves. Planck’s career was ultimately characterized by the discovery of something truly new, something which would lead to a deeper understanding of perhaps one of the great questions in all science: how the universe enables life to exist.
Chemistry tells us that the smallest amount of water is a water molecule, and any container of water consists of a staggering number of identical water molecules. In order to resolve an underlying problem in the theory of energy distribution, Planck wondered, What if energy worked the same way? What if there were a smallest unit of energy, just as there is a smallest unit of water? The idea that energy could be expressed in discrete units, or “quantized,” was fundamental to the development of quantum theory. Indeed, you might say that Planck put the “quanta” in quantum mechanics.
So what is this smallest unit of energy? Planck hypothesized the existence of a constant, now known as Planck’s constant, or h, which links a wave or particle’s frequency with its total energy. Today, we know that
h = 6.6262 x 10-34 Joule⋅second
Planck’s constant has had profound ramifications in three important areas: our technology, our understanding of reality, and our understanding of life itself. Of the universal constants—the cosmic numbers which define our Universe—the speed of light gets all the publicity (partially because of its starring role in Einstein’s iconic equation E = mc2), but Planck’s constant is every bit as important. Planck’s constant has also enabled the construction of the transistors, integrated circuits, and chips that have revolutionized our lives.
More fundamentally, the discovery of Planck’s constant advanced the realization that, when we probe the deepest levels of the structure of matter, we are no longer looking at “things” in the conventional meaning of the word. A “thing"—like a moving car—has a definite location and velocity; a car may be 30 miles south of Los Angeles heading east at 40 miles per hour. The concepts of location, velocity, and even existence itself blur at the atomic and subatomic level. Electrons do not exist in the sense that cars do, they are, bizarrely, everywhere at once, but much more likely to be in some places than in others. Reconciling the probabilistic subatomic world with the macroscopic everyday world is one of the great unsolved problems in physics—a not-so-unimportant hole that even von Jolly would have recognized as such.
Finally, Planck’s constant tells us how the universe is numerically fine-tuned to permit life to exist. Carl Sagan, one of the great popularizers of science, was fond of saying that “We are all star stuff”—the chemicals which form our bodies are produced in the explosions of supernovas. The fundamental nuclear reaction eventually leading to the explosion of a supernova is the fusion of four hydrogen atoms to produce a single atom of helium. In the process, approximately 0.7% of the mass is converted to energy via E=mc2. That’s not much, but there is so much hydrogen in the Sun that it has been radiating enough energy to warm our planet for more than four billion years—even from a distance of 93,000,000 miles—and will continue to do so for another five billion years.
This 0.7% is known as the efficiency of hydrogen fusion, and our understanding of it is one of the consequences of Planck’s investigations. It requires a great deal of heat to enable hydrogen to fuse to helium, and the hydrogen atoms in the sun are moving at different speeds, much like cars on a freeway move at different speeds. The slower-moving hydrogen atoms just bounce off each other; they are insufficiently hot to fuse. Higher speeds, though, mean higher temperatures, and there is a small fraction of hydrogen atoms moving at sufficiently high speeds to fuse to helium.
The 0.7% efficiency of hydrogen fusion is what is sometimes referred to as a “Goldilocks number.” Like the porridge that Goldilocks eventually ate, which was neither too hot nor too cold, but just right, the 0.7% efficiency of hydrogen fusion is “just right” to permit the emergence of life as we know it. The process of hydrogen fusion is an intricate high-speed, high-temperature ballet. The first step of this reaction produces deuterium, an isotope of hydrogen whose nucleus consists of one proton and one neutron. In this process, two protons slam into one another, causing one of the protons to shed its electrical charge and metamorphose into a neutron. If the efficiency of hydrogen fusion were as low as 0.6%, the neutron and proton would not bond to each other to form a deuterium atom. In this case, we’d still have stars—huge glowing balls of hydrogen—but no star stuff would ever form because the porridge would be too cold to create helium, the first step on the road to creating the elements necessary for life.
On the other hand, if hydrogen fusion had an efficiency of 0.8%, it would be much too easy for helium to form. The hydrogen in the stars would become helium so quickly that there wouldn’t be much hydrogen left to form the molecule most essential for life—water. Star stuff would be produced, but without water life as we know it would not exist. Maybe something else would take the place of water, and maybe life could evolve—but not ours.
Planck’s quantization of energy was an essential step on the road to the theory of quantum mechanics, which is critical to our understanding of stellar evolution. Science hasn’t filled in all the pieces of the puzzle of how life actually evolved, but quantum mechanics did begin to answer the question of how the pieces got there in the first place, and probably even Philipp von Jolly would recognize that as an important hole in our knowledge of the universe that desperately needed to be filled. But perhaps the greater lesson is this: The very moment when it feels like “almost everything is already discovered” may be the moment that the universe is about to yield up its biggest surprises—if you’re not afraid to dig in to a few holes.