The Nature of Matter and Black Holes

New controversy over whether a single theory can explain everything

By Leonard Mlodinow|Monday, October 24, 2005
RELATED TAGS: COSMOLOGY

Perhaps it was inevitable that two of the great mysteries of physics—the nature of matter and the nature of black holes—would come crashing into each other. Yet nobody anticipated the meeting or foresaw how fruitful it would be in generating novel ideas about the workings of the universe.

In 1996 Andrew Strominger and Cumrun Vafa of Harvard University were working on the mathematics of string theory, a physics model that describes all fundamental particles as vibrating strands of energy, when they realized that a key property of certain black holes can be predicted by string equations. The researchers recognized an opportunity. So far, string theory’s predictions have proved impossible to test with laboratory technology, but the analysis of black holes could help anchor it to the real world. Such work could also clarify what happened very early in the history of the universe. This conceptual breakthrough helped spawn a startling new field of study, string cosmology.

Stephen Hawking of the University of Cambridge and other like-minded researchers quickly found grand significance in the esoterica of string theory. For instance, the theory might explain why the expansion of the universe seems to be accelerating rather than diminishing. Most cosmologists latched on to an answer rooted in Einstein’s general theory of relativity, which states that gravity could be repulsive over long distances if the universe were permeated with an exotic form of energy. Now some theorists propose instead that the cosmos is speeding up because gravity grows weaker at huge distances due to a kind of leakage into the higher dimensions anticipated by string theory.

String theory may also offer an alternative picture of the first moments of existence. According to a leading cosmological model called inflation, the entire visible universe expanded wildly just after the Big Bang, growing almost instantaneously from a speck far smaller than a proton to a ball the size of a grapefruit, when the universe was 10-35 second old. No one has satisfactorily answered why inflation occurred. String theory has recently inspired a fresh approach. Paul Steinhardt of Princeton University and others speculate that our three-dimensional universe is part of a much larger, higher-dimensional reality and that the Big Bang is the result of a collision between our three-dimensional universe and another like it. The energy of this collision could account for many of the observed features of the universe without requiring an unexplained episode of inflation.

These developments make some physicists optimistic that string cosmology is coming close to realizing the hopes of 18th-century French philosopher Pierre-Simon Laplace, who believed there existed a theory from which we could derive everything there is to know about the universe. But Hawking has cast doubt on whether such a “theory of everything” is possible. His reasoning is based on quantum gravity, the information content of black holes, and especially on mathematician Kurt Gödel’s 1931 theorem that any formal mathematical system contains some statement that cannot be proved—it always remains somewhat incomplete.

In the spirit of Gödel’s proof, Hawking considers the following statement: This statement about the universe cannot be proved within the theory of everything. If the statement is true, then it cannot be proved within the theory; if the statement is false, then the theory of everything allows us to prove a false statement. Thus, the theory of everything must be either incomplete or inconsistent. Although such a statement may seem to have little to do with real physical processes, Hawking notes that the idea of a theory that governs the creators, and hence the creation, of the theory itself leads to logical problems.

Caltech string theorist John Schwarz shrugs off Hawking’s argument. “If there does not exist a simple description that captures the final theory in just one equation, we won’t let that stop us,” he says. “We would still try to use the patchwork of equations to describe all the things we want to know about the universe.”

Eyes on the sky
Next-generation observatories, some of them already under construction, will detect many different types of waves and particles, each of which contributes unique information about the workings of the universe.

Gamma-Ray Large Area Space Telescope
What: An orbiting observatory  50 times as sensitive as any existing gamma-ray telescope. It will open up new avenues of research into the nature of quasars, neutron stars, dark-matter particles, and the early history of the cosmos.
When: 2007
How much: $600 million

Constellation-X
What: NASA’s next-generation X-ray space observatory. It will employ four satellites operating in tandem as one enormous telescope. By gathering energetic X-rays, it will study the physics of black holes, the evolution of galaxy clusters, and the formation of heavy elements—crucial for life—in exploding stars.
When: 2016
How much: $800 million

Giant Magellan Telescope
What: A ground-based telescope incorporating seven mirrors, each 27.5 feet across, mated with mechanical actuators that cancel out atmospheric distortion. It will zero in on the birth of stars and planets, the origins of galaxies, and the evolution of cosmic structure.
When: 2016
How much: $400 million

James Webb Space Telescope
What: The successor to Hubble, built in collaboration with Europe and Canada. It will pick up the dim, highly reddened light emitted by the first stars in the universe and answer fundamental questions about galaxy formation, alien planets, and the geometry of the cosmos.
When: 2011
How much: $3 billion

Planck
What: A European Space Agency satellite that can detect slight fluctuations in the temperature of cosmic microwaves left over from the Big Bang. It will collect data on the conditions that gave rise to the observed mix of matter and energy in the cosmos, which will help explain the universe’s origin and fate.
When: 2007
How much: $500 million

Square Kilometer Array
What: The world’s largest radio telescope, with an array of 150 antennas, each 330 feet across. Built by a consortium of 15 countries. Goals include studying the Big Bang, probing the origin of galaxies, testing relativity near supermassive black holes, and searching for Earth-like planets.
When: 2020
How much: $1 billion

IceCube
What: A telescope like no other, consisting of 4,800 light detectors embedded into ultraclear ice at the South Pole. It will track neutrinos from supernova explosions and active galaxies, search for dark matter, and seek out so-called supersymmetric particles predicted by cutting-edge physics theories.
When: 2010
How much: $270 million

Laser Interferometer Space Antenna
What: A joint effort between NASA and the European Space Agency to build a trio of satellites, spaced 3 million miles apart, to search for gravity waves—ripples of space-time. In theory, such waves reverberated from the Big Bang during the first trillionths of a second of the universe’s life.
When: 2014
How much: $500 million


Stephen Hawking of the University of Cambridge has begun wondering where the ultimate limits of our knowledge lie.

Many leading physicists are searching for a single theory that explains all aspects of how the universe works. Will they succeed?
H:
Up to now, most people have implicitly assumed that there is an ultimate theory that we will eventually discover. Indeed, in the past I myself have suggested we might find it quite soon. However, we have recently realized that the two leading candidates for the ultimate theory—supergravity and string theory—are just part of a larger structure known as M-theory. Despite its name, M-theory isn’t a single theory. It is actually a network of theories, each of which works well in certain circumstances but breaks down in others. These theories have quite different properties. For instance, in some theories space has 9 dimensions while in others it has 10. Yet all these theories are on a similar footing—none can be said to be a better representation of the real world than the others. This has now made me wonder whether it is possible to formulate a single theory of the universe, at least in a finite number of statements.

Is the patchwork quality of M-theory merely a reflection of our ignorance?
H:
There are other, purely theoretical, reasons to believe that an ultimate theory of everything might not be possible. For instance, there is Gödel’s theorem, which says that you cannot formulate a finite system of axioms to prove every result in mathematics. A physical theory is a mathematical model, so if there are mathematical results that cannot be proved, there are physical problems that cannot be solved. But the real relevance of Gödel’s theorem is its connection to the fact that inconsistencies can arise if you try to prove statements that refer to themselves. One of the most famous of these is the assertion “This statement is false.” If the statement is true, then according to the statement itself, the statement is false. But if the statement is false, then the statement must be true. Since we are not angels who view the universe from the outside, we—and our theories—are both part of the universe we are describing, and hence our theories are also self-referencing. And so one might expect that they, too, are either inconsistent or incomplete.

Are you disturbed by the possibility that there is no single ultimate theory?
H:
Some people will be very disappointed if there is no ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I’ve changed my mind. I’m now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery. Without it, we would stagnate. 

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