A New View of Gravity
Entropy and information may be crucial concepts for explaining roots of familiar force
Explaining gravity to a small child is simple: All you have to say is, what goes up must come down.
Until the kid asks why.
What can you say? It’s just the way things work. All masses attract each other. Maybe to bright middle schoolers you could explain that spacetime is warped by mass. Or, to high schoolers, you could say that without gravity, the laws of physics would differ for people moving at changing velocities. Yet all those increasingly sophisticated answers merely invite another “Why.” As Sir Isaac Newton himself replied in response to similar questions, “hypotheses non fingo.” Which roughly translates as “I don’t have a clue.”
That such a simple question, about so common a phenomenon, has defied a direct answer for centuries might explain why the physics world has been atwitter lately over a novel attempt to resolve the riddle. A flurry of recent papers have examined this new idea, which mixes principles from string theory and black hole physics with basic old-fashioned thermodynamics. If this notion is right, gravity turns out to be a special sort of entropy, a result of the same physics that drives matter to give up its organization and order as it succumbs to the laws of probability. Toss in a dash of quantum mechanics and a pinch of information theory, and the universe emerges, governed on a grand scale by pretty much the same principles underlying the elastic pull of a rubber band.
While similar ideas have been suggested before, nobody has expressed the gravity-as-entropy story as intriguingly as theorist Erik Verlinde of the University of Amsterdam in an online paper (arXiv.org/abs/1001.0785v1) that appeared in January. Titled simply “On the origin of gravity and the laws of Newton,” Verlinde’s paper cooks up a mathematical pièce de résistance connecting gravity to thermodynamics. His ingredients include the law of entropy, the physics of black holes and some speculative conjectures on how space stores information about the matter and energy within it. His recipe replicates Newton’s law of gravitational attraction, and then with some additional mathematical seasoning he arrives at Einstein’s general relativity, the modern and undefeated champion of gravity theories. Verlinde’s analysis indicates that gravity emerges from physical dynamics analogous to basic thermodynamic processes. “Using only … concepts like energy, entropy and temperature,” he writes, “Newton’s laws appear naturally and practically unavoidably.”
Not everyone is buying, or even understanding, Verlinde’s arguments. Only a few among mainstream physicists express much enthusiasm for his paper. But it has inspired a glut of other work, some extending Verlinde’s idea to encompass the history of the universe. Rapid expansion just after the Big Bang and the more recent accelerating expansion of the universe might all fit into the entropic-gravity picture of reality. And beneath it all may lurk a new worldview emphasizing the primacy of information over matter and energy.
Entropy and information
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Ordinarily, the term entropy is translated into common language as “disorder,” with a tendency for higher entropy taken to mean that things like to get messier. Wood rots, metals rust and structures crumble; substances separated into cold and hot turn lukewarm. Eventually any system not resupplied with useful energy reaches equilibrium, and entropy is maximized.
More technically, entropy is a measure of how likely a system is to be in its particular configuration. Low entropy describes systems with a very improbable arrangement of their parts. Entropy typically equates to disorder because there are usually very few ways for a system to be precisely ordered, but multiple ways to be messed up. (A car’s engine will run only if all the parts are precisely positioned in one specific arrangement; you can scatter the parts around a repair shop in all sorts of ways.) So the most probable outcome for any system (unaided by the input of energy to maintain its order) is messiness — maximum entropy.
Curiously, the equations relating entropy to probability are precisely the same as the math used by computer scientists to quantify information. It turns out that information is the flip side of entropy: Stating that a gas with all its molecules crammed into one corner of a box has low entropy is just another way of saying you have information about where the molecules are. As the molecules spread out, information about their location diminishes and entropy rises.
Such loss of information — or increasing entropy — drives many natural processes, such as osmosis, the mysterious migration of water across a membrane. If you dissolve a substance (say, sugar) in a compartment of water, entropy increases. If you have pure water in an adjacent compartment, separated by a membrane that allows water (but not the sugar) to pass through, you’ve created an “entropy gradient” — lower entropy on one side of the barrier than the other. So the pure water will flow through the membrane to the sugar side, increasing the entropy of the system until equilibrium is reached.
If you don’t know about thermodynamics, it just looks like some force is driving the water across the membrane. Verlinde proposes that the “force” of gravity is driven by a similar (though not really identical) sort of entropy gradient.
He illustrates his idea with “polymer stretching” — in other words, playing with rubber bands. When you stretch a rubber band, some sort of force vigorously attempts to snap the band back to its original shape. Such elastic forces result not from any mystical motivation in the polymer, but merely from the play of probability: There are many more possible arrangements of the pieces making up the polymer when the band is shorter and loose than when taut. So the rubber band’s elastic force is entropic — the stretched polymer is in a very improbable configuration, and snapping back to its resting state restores equilibrium and maximum entropy. Gravity, Verlinde asserts, is similar in the sense that masses move in ways that also produce more probable, higher-entropy arrangements.
Verlinde is not the first to relate gravity to thermodynamics. In 1995, Ted Jacobson of the University of Maryland demonstrated that the equations of Einstein’s general theory of relativity could be derived from basic thermodynamic principles. That result drew on work in the 1970s by Jacob Bekenstein and Stephen Hawking, who discovered parallels between ordinary thermodynamics and the physics of black holes, regions of such intense gravity that nothing that enters can ever exit. Bekenstein showed that a black hole has entropy, determined by all the matter and energy it has swallowed. Hawking demonstrated that black holes have a temperature (requiring the emission of Hawking radiation from a black hole’s surface). Since black holes are basically nothing more than pure gravity, describing them in terms of the thermodynamic properties of entropy and temperature hinted at deeper links between gravity and thermodynamics.
A further hint to that link came from the Dutch Nobel physics laureate Gerard ’t Hooft. In 1993 he proposed that reality shares common features with holograms, like the flashy images embedded in credit cards that store apparently three-dimensional information on a flat surface. In a similar way, ’t Hooft asserted, information about the contents in three-dimensional space might be stored on two dimensions, sort of the way 2-D mirrors covering the walls of a room record information about all the objects within the room’s 3-D space.
’t Hooft’s conjecture, known as the holographic principle, and its later elaboration by Stanford physicist Leonard Susskind built on Bekenstein’s work on black hole entropy. Bekenstein had found that a black hole’s entropy is proportional to the surface area of its outer boundary, known technically as the event horizon. In other words, the information about a black hole’s interior is stored on its surface, just as with a hologram.
A black hole’s “surface,” of course, is not like a soap bubble or globe of Plexiglas. It’s an imaginary sphere surrounding a black hole’s center, a boundary defined by the distance marking the point of no return for anything that gets too close. Such a boundary, or “screen” as Verlinde calls it, could be imagined in other regions of space, and that is what he does to deduce the roots of gravity. Holographic screens enclosing regions of space encode information about the contents of that space, he says, just as a black hole’s horizon encodes what it has swallowed, or the mirrors on the walls reflect the contents of the room.
Such information stored on the screen gives it a temperature — not in the everyday thermometer sense, but rather something analogous to the Hawking radiation temperature on the surface of a black hole. Temperature differences between the screen and the space outside of it create the cosmic analog of an entropy gradient, driving masses outside the screen to move just as Newton’s laws prescribe. Rather than a mysterious attraction at a distance, gravity simply expresses the tendency of masses to move under the impetus of a gradient driving them to a state of higher entropy.
“By making natural identifications for the temperature and the information density on the holographic screens, … the laws of gravity come out in a straightforward fashion,” Verlinde writes.
He is careful to emphasize that his ideas are tentative and not to be taken too literally. Increasing an object’s entropy does not make it more massive, for instance, and temperature on a spacetime surface storing bits and bytes wholly beyond human perception is not the same thing as the temperature of a hot day or a cold drink. (Gravity would not disappear if ordinary temperature dropped to absolute zero.) But the analogous thermodynamic formulas connect the underlying concepts of temperature and entropy and gravity in ways that just might lead to a deeper understanding of the cosmos — eventually. “The ideas will and are being developed further, and along the way may evolve, be refined or even slightly altered,” Verlinde commented via e-mail. “This is what science is about.”
Entropy in action
Verlinde takes a first step toward further development in his paper by extending his analysis to general relativity, which depends on the equality of inertia (the tendency of a mass to retain its state of motion) and the gravitational mass (proportional to the force of attraction between objects). Verlinde shows that inertia’s declaration that a body at rest stays at rest simply reflects the absence of entropic gradients.
Applying the entropic gravity idea to general relativity puts it to a severe test. Any new explanation for gravity would have to reproduce the large-scale history of the cosmos, including such phenomena as the expansion of the universe and its recent acceleration. Physicists Damien Easson, Paul Frampton and Nobel laureate George Smoot, for instance, suggest that entropic gravity would remove the need for the unidentified “dark energy” in space that most cosmologists believe to be responsible for the cosmic acceleration. If gravity is entropy in action, then acceleration would occur with no need for dark energy, Easson, Frampton and Smoot calculate in a paper posted online in March (arXiv.org/abs/1002.4278). They simply assume that the holographic principle is at work on the two-dimensional surface encompassing the entire visible 3-D universe. If all the information about the universe is encoded on a holographic screen coinciding with the horizon of the visible universe, the temperature on the screen would create an entropy gradient driving accelerated expansion. Their calculated acceleration matches the observed acceleration as inferred by its effects on the relative brightness of distant supernova explosions.
With holographic information storage on the universe’s horizon, dark energy no longer is needed to explain the supernova observations. “The acceleration of the universe simply arises as a natural consequence of the entropy of the universe, via the holographic principle,” the physicists write.
Not only can entropy explain the current acceleration of cosmic expansion, it also might explain the rapid burst of expansion, termed inflation, that occurred in a flash just after the Big Bang. In a paper posted in March (arXiv.org/abs/1003.4526), physicists at the Chinese Academy of Sciences in Beijing — Yi-Fu Cai, Jie Liu and Hong Li — suggest the need for two holographic screens: an outer screen at the universe’s horizon and an inner screen, something like the horizon of a black hole. In the early universe, entropies of the two screens generate the expansion of the universe. Further calculations involving quantum effects explain the universe’s early burst of inflation. Acceleration of the expansion, later in the life of the universe, would occur after the inner horizon evaporates away — just as black holes do by Hawking radiation.
As Verlinde notes, Hawking radiation is a quantum process: Quantum fluctuations in the space near a black hole’s surface allow some particles to escape, slowly draining the black hole of its mass and providing it with its “temperature” (until it evaporates entirely away). So a full analysis of the entropic-gravity idea will have to incorporate quantum mechanics, and that will alter the overall idea in subtle ways, says Verlinde, who is working on a paper that will probe those issues.
Ultimately, he says, the connection with quantum physics could help cement the long-sought unification between general relativity and quantum mechanics, possibly illuminating the role of string theory as well. For a quarter century, many physicists have favored string theory, which describes the basic particles of matter and force as tiny vibrating strands or loops called superstrings, as the best route for unifying quantum physics with gravity. The holographic principle plays an important role in string theory, and holographic screens bear resemblances to D-branes, multidimensional surfaces to which certain strings attach themselves. In Verlinde’s picture, strings are not fundamental entities, but emerge from processes on the screens just as gravity does.
The encoded universe
Underlying all this hoopla is a recurring theme at today’s physics frontiers: conceptualizing nature in terms of information. In Verlinde’s proposal, information stored on holographic screens is the prime source of the entropy underlying gravity. Similarly, in the cosmological scenario described by Easson and colleagues, information density on such screens drives accelerated cosmic expansion.
In yet another paper, Jae-Weon Lee of Jungwon University in South Korea and collaborators Jungjai Lee and Hyeong-Chan Kim develop this information-based reasoning more deeply, applying a famous principle from computer science formulated by the late IBM computer physicist Rolf Landauer. Landauer’s principle requires energy to be consumed — and therefore entropy to be increased — when a bit of information is erased.
Lee, Kim and Lee apply Landauer’s principle to the more complex “quantum” information possessed by a subatomic particle. In a different twist on Verlinde’s idea, they propose (arXiv.org/abs/1001.5445v2) that it is the erasure of quantum information when particles pass through a holographic screen that increases cosmic entropy. It’s just like what happens, they say, when a particle passing though a black hole’s event horizon is erased from the rest of the universe, increasing the black hole’s entropy in the process. Equations describing all this once again connect the thermodynamics of information erasure with gravity. “Putting it all together,” Lee, Kim and Lee write, “it is natural to imagine that gravity itself has a quantum informational origin.”
These are the sorts of papers that traditional experts rarely take seriously. Any one such paper would not make a ripple in physics Twitter traffic. And of course, all of these new ideas might turn out to be wrong. But despite their deviation from mainstream paths, these papers have attracted attention precisely because they hint at a way to solve riddles of gravity and quantum physics that traditional approaches, relying on particles and fields, have found intractable.
So it’s not necessarily crazy, even if still very speculative, to suppose that thermodynamics and information will serve as the bridge for bringing gravity and quantum physics together. As Lee, Kim and Lee write, Einstein’s equations link energy to matter and matter to gravity, and the new work connects matter and energy to information and entropy. These links imply that Einstein’s equations are more about information than energy, the physicists write. “In other words, information might be a more profound physical entity than matter or field.”Putting information theory and thermodynamics together in this way might very well have pleased Einstein, who failed to find the theory unifying gravity with the rest of physics despite three decades of effort. Einstein was a big thermodynamics fan. In his autobiographical notes, he acclaimed it as the one branch of science unlikely ever to be overturned. “Thermodynamics,” he wrote, “is the only physical theory of universal content concerning which I am convinced that, within the framework of the applicability of its basic concepts, … will never be overthrown.” It may be that thermodynamic concepts are more widely applicable than Einstein imagined, possibly able to solve the one problem he couldn’t conquer in his lifetime.