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Physics + MathPhysics & Math

Why Quantize Gravity?

The Nature of RealityThe Nature of Reality

A good question is one that you know has an answer—if only you could find it. What’s her name again? Where are my keys? How do I quantize gravity? We’ve all been there.

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Science is the art of asking questions. Scientists often have questions to which they would like an answer, yet aren’t sure there is one. For instance, why is the mass of the proton 1.67 x 10 -27 kilograms? Maybe there is an answer—but then again, maybe the masses of elementary particles are what they are, without deeper explanation. And maybe the four known forces are independent of each other, not aspects of one unified “Theory of Everything.”

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Without a full theory of quantum gravity, physicists cannot understand what happens inside a black hole. Artist's conception of a black hole. Credit: By XMM-Newton, ESA, NASA (Public domain), via Wikimedia Commons

The quest for a theory of quantum gravity is different. To remove contradictions in the known laws of nature, physicists need a theory that can resolve the clash between the laws of gravity and those of quantum mechanics. Gravity and quantum mechanics have been developed and confirmed separately in countless experiments over the last century, but when applied together they produce nonsense. A working theory of quantum gravity would resolve these contradictions by applying the rules of quantum mechanics to gravity, thereby endowing the gravitational field with the irreducible randomness and uncertainty characteristic of quantization. We know there must be a way: if only we could find it.

Take the double-slit experiment : In quantum mechanics an electron is able to pass through two slits at once, creating a wave-like interference pattern on a detection screen. Yet the electron is neither a wave nor a particle. Instead, it is described by a

wave-function —a mathematical in-between of particle and wave—that allows it to act like a particle in some respects and a wave in others. This way, the electron can exist in a quantum superposition: It can be in two different places at once and go through both the right and the left slit. It remains in a superposition until a measurement forces it to “decide” on one location. This behavior of the electron, unintuitive as it seems, has been tested and verified over and over again. Strange or not, we know it’s real.

But what about the electron’s gravitational field? Electrons have mass, and mass creates a gravitational field. So if the electron goes through both the left and the right slit, its gravitational field should go through both slits, too. But in general relativity the gravitational field cannot do this: General relativity is no quantum theory, and the gravitational field cannot behave like a wave-function. Unlike the electron itself, the electron’s gravitational field must be either here or there, which means that electrons don’t always have their gravitational pull in the right place. We must conclude then that the existing theories just cannot describe what the gravitational field does when the electron goes through a double-slit. There has to be an answer to this, but what?

At first theorists thought there would be a simple fix: Just modify general relativity to allow the gravitational field to be in two places at once. Physicists Bryce DeWitt and Richard Feynman developed just such a theory in the 1960s, but they quickly realized that it worked only at small energies, whereas at high energies, when space-time becomes strongly curved, it produces nonsensical infinite results . This straightforward quantization, it turned out, is only an approximation to a more complete theory, one which should not suffer from the problem of infinities. It is this complete, still unknown, theory that physicists refer to as “quantum gravity.”

These first attempts at quantization break down when the gravitational force becomes very strong. This happens when large amounts of energy are compressed into a small regions of space-time. Without a full theory of quantum gravity, thus, physicists cannot understand what happens in the early universe or inside black holes.

Indeed, the black hole information loss problem is another strong indication that we need a theory of quantum gravity. As Stephen Hawking demonstrated in 1974, quantum fluctuations of matter fields close to a black hole’s horizon lead to the production of particles, now called “Hawking radiation,” that make the black hole lose mass and shrink until nothing is left. Today, the amount of radiation leaking out of the black holes in the Milky Way other galaxies is minuscule; they gain more mass from swallowing matter and gas around them than they can lose by Hawking radiation. But once the universe has cooled down sufficiently, which will inevitably happen, black holes will begin to evaporate. It will take hundreds of billions of years, but eventually they will be gone, leaving behind nothing but radiation.

This radiation does not carry any information besides its temperature. All the information about what fell into the black hole is irretrievably destroyed during the evaporation. The problem? In quantum mechanics, all processes are reversible, at least in principle, and information about the initial state of any process can always be retrieved. The information might be very scrambled and unrecognizable, such as when you burn a book and are left with smoke and ashes, but in principle the remains still contain the book’s information. Not so for a black hole. A book that crosses the horizon is gone for good, which conflicts with quantum mechanics, which demands that information always be conserved. The information loss problem is not a practical concern that affects observational predictions, but it is a deep conceptual worry about the soundness of our theories. It’s the kind of problem that keeps physicists up at night, and it shows once again that leaving gravity unquantized results in a conundrum which has to be resolved by quantum gravity.

Black holes and the Big Bang pose another problem for unquantized gravity because they lead to singularities , locations in space-time with a seemingly infinite energy density. Similar singularities appear in other theories too, and in these cases physicists understand that singularities signal the theories’ breakdown. The equations of fluid dynamics, for example, can have singularities. But these equations are no longer useful on distances below the size of atoms, where they must be corrected by a more fundamental theory. Physicists therefore interpret the singularities in general relativity as signs that the theory is no longer applicable and must be corrected.

Many physicists believe that a theory of quantum gravity will also shed light on other puzzles, such as the nature of dark energy or the unification of the other three known forces, the strong, electromagnetic, and weak force.

Given that thousands of the brightest minds have tried their hands at it, 80 years seems a long time for a question to remain unanswered. But physicists are not giving up. They know there must be an answer—if only they could find it.

Go Deeper
Author’s picks for further reading

arXiv: Conceptual Problems in Quantum Gravity and Quantum Cosmology
An in-depth, technical-level look at the problem of quantum gravity and its potential solutions.

Scientific American: Why Is Quantum Gravity So Hard? And Why Did Stalin Execute the Man Who Pioneered the Subject?
Gennady Gorelik, a historian of science at Boston University, on the 100-year history of the quest for quantum gravity and the promising young Russian physicist Matvei Bronstein, who predicted the need for a “radical reconstruction” of general relativity.

Three Roads to Quantum Gravity
Theoretical physicist Lee Smolin’s popular book on the quest to reconcile gravity and quantum mechanics.

This project/research was supported by grant number FQXi-RFP-1822 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.