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IN THE QUEST OF ELUSIVE QUANTUM GRAVITY

subhankar karmakar

Under general relativity theory, which is a classical not a quantum theory, the force of gravity is propagated by gravitational waves, which transmit the force of gravity at the speed of light.

Under a quantum theory of gravity, we focus on the quanta of gravity—gravitons, the elementary force particles that transmit gravity through a process of graviton exchange. Gravitons, never experimentally observed, are particles of zero mass which travel at the speed of light and have a quantum “spin” of 2.

Quantum gravity is of interest both to permit gravity to be unified with the other three forces, as well as to unify general relativity with quantum physics. Quantum gravity is at the heart of physics’ Theory of Everything.

Without migrating our understanding of gravity into the framework of quantum physics, general relativity will remain a theory of classical physics, of physics not reconciled with quantum theory. This seems inelegant, that these two major theories of modern physics—general relativity and quantum physics—are not unified into a single theory. The quest for a convincing theory of quantum gravity is physics’ search for the Holy Grail: quantum gravity will explain mysteries we’re aware of and also answer questions we don’t yet even know how to ask.

Some physicists, including Roger Penrose, who theorize about the connection between the brain and the mind, look for this connection at the intersection of general relativity and quantum physics. For these physicists, “everything”—in the Theory of Everything, for which quantum gravity is the centerpiece—must include not only force particles and matter particles, not only general relativity and quantum physics, but also a theory of consciousness.

Lee Smolin’s 2001 book Three Roads to Quantum Gravity draws from current approaches to propose his preferred approach to quantum gravity. We’ll start our discussion with Smolin’s approach to this central question of physics that remained unanswered as the new millennium began.

Background Independence

The three roads that Pennsylvania State University physicist and geometer Lee Smolin sees physicists taking toward quantum gravity are string theories, loop quantum gravity, and black hole thermodynamics. Smolin draws from these three approaches to recommend how quantum gravity is to be best understood.

String theorists are working very hard to create a theory of everything out of models in which strings are the elementary entity of physics. Today’s extradimensional string theories have proven remarkably robust in creating accurate models of physics’ particles and interactions. String theories provide a model for all four of physics’ forces and for the elementary particles of matter as well. Among string theories’ vibrational string patterns is a pattern that exactly produces the properties of the graviton. Thus, string theory is a quantum theory that incorporates gravity.

String theories’ detractors are concerned that new features seem to proliferate in order to respond to objections and to match the theory with observed reality. But it’s hard not to be impressed with how all-encompassing string theories are. Admittedly, there’s a “Christmas tree effect” as new features and twists embellish the theory to get it more accurate. But it’s a Christmas tree, not a national forest—it’s still a fairly compact theory considering the scope of the questions it’s addressing.

But string theories are background-dependent. The background is spacetime, and in string theories all of the forces—including gravity—operate against the background of spacetime. This seems to present a conceptual stumbling block in the way of using string theories to reconcile general relativity’s gravity with quantum physics’ other forces, because general relativity is a background-independent theory. Under general relativity, the force of gravity shapes spacetime—is spacetime.

So it’s hard to see how a string theory road to quantum gravity can be the whole road: even if string theory’s models provide extraordinary accuracy to the proposed structures of physics’ forces and matter, background-dependent theories will not give us the gravitational exceptionalism that we need. Gravity is not like the other forces. The other forces operate against the spacetime backdrop, in a spacetime grid. Gravity doesn’t. Gravity is the spacetime grid.

Theories of the nongravitational forces can be developed as background-dependent theories—the electromagnetic, weak, and strong forces operating against a background of a fixed spacetime grid. Theories of gravity also can (and have) been developed as background-dependent theories, but it’s hard to see how a background-dependent theory of gravity can be correct at the deepest levels. Gravity—the force being described—reshapes spacetime. How can a theory of gravity be validly constructed assuming fixed spacetime when we know there’s this recursive effect of gravity changing spacetime?

Smolin discusses the kind of radical rethinking that will be required to establish a complete theory of quantum gravity. The “three roads” of Smolin’s title will ultimately have to combine to produce a single more basic theory, and this more basic theory will have to be background-independent. In fact, there are string theorists today who are working to reformulate string theory to remove its inherent background dependence.

What this single theory will ultimately be based on will in all likelihood move us entirely away from a conceptualization that the universe consists of things occupying regions of space, toward instead a conceptualization that the universe consists of a network of relationships, of processes by which information is conveyed from one part of the universe to another.

Loop Quantum Gravity

String theories assume that space and time are granular, that there is a smallest granule of length (the Planck length, 10-33 centimeters) and a smallest granule of time (the Planck time, 10-43 seconds). Said another way, “quantum geometry is discrete.” Of course, these granules of space and time are so unimaginably small that there is no experimental verification that the geometry of spacetime is in fact discrete rather than continuous.

Loop quantum gravity, the second of Smolin’s “three roads to quantum gravity,” also assumes this granularity of space and time. But loop quantum gravity, of which Smolin is a key developer, sets out as its quest to remove background dependence. An earlier version, a lattice theory of gravity, was rejected, because the background dependence could not be eliminated. But loop quantum gravity does this by reducing spacetime to loops alone, with no background in which these loops reside. The loops interact in a network of “knots, links and kinks.” Taking the lead from work that Roger Penrose had done in the 1960s and 70s, the loop quantum gravity model is a spin network model, because the loops each have a value associated with the spin of physics’ elementary particles. The surface and volume of spacetime are built up at the edges and nodes of this spin network. Because spacetime at the Planck scale is not localized at a point, these spin networks have come to be called spin foam, and are currently a subject of exploration and theorizing among physicists across the world.

Smolin’s Resolution, and Its Critics

Smolin favors loop quantum gravity over string theories as the source of a theory of quantum gravity, due to loop quantum gravity’s inherent background independence. But Smolin also recognizes the power of string theory for describing forces and matter, even though this is accomplished against a classical spacetime background. For this reason Smolin views loop quantum gravity and string theory as complementary and ultimately reconcilable (with loops forming a more basic concept than strings). Perhaps, too, string theory will one day be successfully reformulated (as Grosse and Schlesinger propose) as a background-independent theory.

Smolin also discusses how both loop quantum gravity and string theories interrelate with black hole thermodynamics, the third of Smolin’s three roads to quantum gravity.

Smolin estimates that there are a billion billion (1018) black holes in the universe. Those looking to create a theory of quantum gravity from the study of black holes do so by incorporating concepts of the black hole’s entropy (degree of disorder, a key metric of thermodynamics) and the amount of information that a black hole—or any region of space—can contain.

For example, University of Oxford physicist Stephen Hawking theorizes (A Brief History of Time and elsewhere) that a quantum theory of gravity is needed to understand how the universe began: without a quantum theory of gravity, theories produce at the big bang an undesired collapse of all matter to zero volume, an undesired infinite density and infinite curvature of spacetime at the beginning of time. By drawing conclusions from studies of black holes, Hawking has proposed a theory of the universe, which includes quantum gravity, based on the concepts of imaginary time and the universe’s “multiple histories.”

These concepts—entropy, information, black holes, multiple universes, imaginary time—will be discussed in upcoming chapters. In his stab at reconciling this black hole thermodynamics “road” with the other two roads to quantum gravity, Smolin proposes that that the holographic principle—which quantifies how much information can be contained in any region of space—will be a basic principle that unites the three roads to quantum gravity. (Physicist Dennis Gabor won the 1971 Nobel Prize for physics for earlier work on the holographic method.) Under this unified approach, the universe is “a network of holograms,” a network of information.

Although we will be pursuing further elements of these concepts, it is probably not a surprise that the work of Smolin and colleagues studying quantum gravity is not universally accepted. For example, Michael Riordan—who teaches the history of physics at Stanford and at the University of California, Santa Cruz, and who has written the general-audience book The Hunting of the Quark—expresses a number of criticisms of this pursuit of quantum gravity. Principally, Riordan’s concern is the lack of experimental verifiability of these theories, the risk that “these imaginative theories of quantum gravity will remain rooted only in the misty realms of metaphysics.” In Riordan’s view, this contradicts four centuries of scientific method, and exposes physics to the “virulent attacks of postmodernist critics, who argue that that science has no special claim to objective reality.” Riordan asks, “Are these people really practicing science?”
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