1. B. G. Sidharth, of the Centre for Applicable Mathematics and Computer Sciences at India’s B. M. Birla Science Centre, is a prolific author and researcher on topics of modern physics.
   Sidharth has hypothesized about the fractal structure of the universe, about holistic cosmology, and about dualities and linkages between the microworld and the macro-universe.
   He has studied Earth’s magnetic field—geomagnetism—and looked to temperature effects on electrons in Earth’s solid core to explain puzzling reversals in our planet’s magnetic field. He has studied the magnetic field about Jupiter and astronomical links connecting early civilizations of the Indus Valley in India with Mayan Central America and Easter Island. He has studied the origin of life on Earth, and extraterrestrial chemical sources for some of life’s ingredients.
   Sidharth notes two recent important discoveries of physics—the confirmation that neutrinos have nonzero mass, and the confirmation that the universe is ever-expanding, perhaps at an accelerating pace—and he discusses how these discoveries create the need for new physics models beyong the big bang and beyond the standard model of particle physics.
   Quantum black holes are a central concept of Sidharth’s analyses, leading to new frameworks for understanding particle physics and astrophysics, for unifying physics’ forces, and for reconciling quantum physics and general relativity.
   

   Quantized Fractal Spacetime

   Sidharth has explored the implications of quantized spacetime—space and time being granular, not continuous, at its smallest scales. He discusses how the quantization of time—the existence of the chronon as time’s smallest quantum—leads to an explanation of the arrow of time. And quantized spacetime leads to extended particles—elementary particle building blocks that aren’t just dimensionless points, but that have extended dimensions, as string theory postulates.
   Quantized spacetime is fuzzy spacetime, exhibiting the fractional dimensionality of complexity theory’s fractal geometry. This leads to quantized fractal spacetime, a framework in which Sidharth places, and expands upon, quantum superstring theory.
   Quantized fractal spacetime’s geometry is not our familiar geometry, the geometry dating back to Archimedes and other ancients. Quantized fractal spacetime is non-Archimedean, or ultrametric: lengths and distances cannot be measured as in our familiar Archimedean geometry. Quantized fractal spacetime is also noncommutative: its geometry, its spacetime, is not flat or ordered according to our usual formulas of geometry and algebra.
   Sidharth uses a different form of mathematics—p-adic mathematics—to describe the physics of his quantized fractal spacetime, his fuzzy noncommutative spacetime. We’ll save the details of p-adic mathematics for Chapter 38, where we’ll be discussing Pitkänen’s extensive and central use of p-adic mathematics within topological geometrodynamics. For now, we’ll just mention that other physicists, too, have found applications of p-adic mathematics to their work, and—as we’ll be detailing further in Chapter 38—mathematicians have demonstrated that p-adic numbers have a unique place alongside real numbers as the only two complete mathematical systems.
   Sidharth refers to his quantized fractal spacetime, his fuzzy noncommutative spacetime, as “a new paradigm for a new century.” It is a paradigm that explains some of physics’ longstanding mysteries, such as how the elusive magnetic monopole comes to exist and why it is so hard to detect. And much more generally, through quantized fractal spacetime Sidharth has proposed a unification of electromagnetism with gravity, and in addition brought physics’ strong force into this unification.
   

   Quantum Black Holes

   Quantum black holes are a central mechanism for Sidharth’s unification of physics’ forces, and ultimately for a unification of quantum physics and general relativity. Sidharth’s quantum black holes are based on the Kerr-Newman black hole that would result from the collapse of a spinning massive star, not the earlier-modeled Schwarzschild black hole, which derives from the collapse of a stationary star.
   Sidharth identifies matter particles—fermions—with quantum black holes. This is, arguably, the key to all of Sidharth’s theories. The horizon of the black hole—the dividing surface from inside of which nothing, not even light, will ever overcome the black hole’s gravitational force—corresponds to a critical quantum wavelength, called the Compton wavelength. The Compton wavelength is based on the work for which Arthur Compton won a share of the 1927 Nobel Prize for physics, for his demonstration of X-rays’ dual wave/particle nature. In Sidharth’s fractal universe, Sidharth characterizes the Compton wavelength as comparable to the thickness of the brushstrokes with which all of Nature is painted. And quantized spacetime solves a problem that must be addressed in models that incorporate black holes, preventing the model from reducing to the naked singularity that appears deep inside a black hole.
   All of Sidharth’s modeling—quantized fractal spacetime, fuzzy spacetime, ultrametric and noncommutative mathematics—is brought to bear here. As he moves away from conventional spacetime, Sidharth generalizes the Heisenberg Uncertainty Principle and challenges conventional notions of scale. He looks at recent experimental suggestions of variation in the fine structure constant, which determines the smallest relevant quanta of space and time, and concludes that dimensionality is not absolute, but depends critically on the scale of resolution, from the Planck scale to cosmological distances. And then the next leap: to quantum effects at multiple macro scales, universally.
   

   Fluctuational Cosmology

   The logical result of Sidharth’s thinking is a framework of fluctuational cosmology. In this framework, the universe was created as a phase transition, a fluctuation in the background zero-point field. Dark energy—the mysterious force fighting gravity, pulling the universe outward—is one consequence. And more generally, fluctuational cosmology describes the emergence—from a chaotic universe at the Planck scale—of quantized spacetime, the cosmology we inhabit, and all of the laws of physics.
   Sidharth’s work, summarized only briefly here, is of great intellectual breadth and depth. His applications of p-adic mathematics will be reflected in our #1 Hidden Radical Theory of New Physics, which intertwines the real physical world and the p-adic world of the mind.
   First, though, our #2 theory, a theory of thought space, the world of the mind.
   

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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.
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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.
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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.
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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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Why Is This So Hard?

Why is it so difficult to construct a complete theory of quantum gravity?
If your junior high school or high school science courses were anything like mine, somewhere along the line you had a lesson on Galileo dropping objects from the Leaning Tower of Pisa. You were fooled into saying that a heavy ball would fall more quickly than a lighter ball, at which point your science teacher told you that, no—they’d both hit the ground at the same time. This bothered you, because it seemed so counterintuitive. Then you were stunned into silence by the claim that—in a vacuum, without air resistance—even a feather would fall at the same pace as a lead ball.
Rather than this being something that fourteen-year-olds should feel foolish about not understanding, this is actually an important mystery of physics. We expect, when we have more of a force-generating quantity, to have greater force. A big light shines more brightly than a small light. A nucleus with lots of protons has more strong force holding it together than a nucleus with few protons. So why would a more massive block of matter not fall faster than a less massive block—doesn’t more mass mean more gravitational force?
The answer, in its general form, has to do with the precisely offsetting phenomenon of inertia: the larger the mass, the more force it takes to accelerate it. This question—the question of why inertial mass is equivalent to gravitational mass—is not at all a trivial question of physics, and in fact remains one of the mysteries of gravity. Attempts to solve this mystery have led to some strange hypotheses, such as University of California physicist Shu-Yuan Chu’s recent work suggesting that this involves forward- and backward-in-time interactions between objects on earth and all of the other matter in the universe.
And this mystery about the nature of gravity is just one element of why it is so hard to establish a theory of quantum gravity. Also noted as sources of difficulty in successfully modeling quantum gravity are:
• Gravity is so weak that the effects of quantum gravity are noticeable only at the smallest scales of distance.
• Gravitons interact with everything—all forms of matter, all forms of energy (remember: matter and energy are equivalent, through E = mc2), even with other gravitons.
• As we’ve mentioned, spacetime plays an active, dynamic role in gravity, unlike the passive role it plays as the stage on which the other forces act.
In the meantime, experimental physicists aren’t standing still while the theoreticians work this out. At both subatomic and astronomical lengths, physicists continue the search for evidence of the graviton and quantum gravity.
A 2001 progress report on contemporary approaches to quantum gravity notes: “Work along these lines has not yet led to any physical breakthroughs, but perhaps that is too much to ask, given that more conventional approaches have not been terribly successful either.” But the analysis continues: “It is safe to say that most people working in quantum gravity expect that the theory will eventually lead to radical changes in our understanding of space and time.”
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NEW PHYSICS AND THE MIND, although aimed at the general reading public, is intensively researched and sourced. See NEW PHYSICS AND THE MIND for the endnotes associated with this excerpt, as well as for a complete bibliography of the works referenced throughout NEW PHYSICS AND THE MIND.

NEW PHYSICS AND THE MIND: mind physics + new physics = the 21st century's theory of everything

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