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Section 8: Gravity and Quantum Mechanics

Visualization of a stage in the quantum evolution of geometry, according to Loop Quantum Gravity.

Figure 25: Visualization of a stage in the quantum evolution of geometry, according to Loop Quantum Gravity.

Source: © T. Thiemann (Max Planck Institute for Gravitational Physics (Albert Einstein Institute)) & Mildemarketing Science Communication. More info

Despite the fact that there is no experimental evidence that conflicts with the predictions of general relativity, physicists have found compelling reasons to suspect that general relativity may be only a good approximation to a more fundamental theory of gravity. The central issue is reconciling general relativity with the demands of quantum mechanics. Well tested by experiment, quantum mechanics is the theory that describes the microscopic behavior of particles. Unit 5 of this course will delve into the details of quantum mechanics. In the quantum world, particles are also waves, the results of measurements are probabilistic in nature, and an uncertainty principle forbids knowing certain pairs of measurable quantities, such as position and momentum, to arbitrary precision. The Standard Model described in the previous two units provides a unified picture of the strong, weak, and electromagnetic forces within the framework of quantum mechanics. Nonetheless, theoretical physicists have found it to be extremely difficult to construct a theory of quantum gravity that incorporates both general relativity and quantum mechanics.

At the atomic scale, gravity is some 40 orders of magnitude weaker than the other forces in nature. In both general relativity and Newtonian gravity, the strength of gravity grows at shorter and shorter distances, while quantum effects prevent the other forces from similarly increasing in strength. At a distance of approximately 10-35 m, called the Planck length, gravity becomes as strong as the other forces. At the Planck length, gravity is so strong and spacetime is so highly distorted that our common notions of space and time lose meaning. Quantum fluctuations at this length scale produce energies so large that microscopic black holes would pop into and out of existence. A theory of quantum gravity is needed to provide a description of nature at the Planck length. Yet, attempts by researchers to construct such a theory, analogous to the Standard Model of particle physics, have lead to serious inconsistencies.

Theories of quantum gravity

A significant difference between a quantum theory of gravity and the Standard Model of particle physics is the role of spacetime in the theory. In the Standard Model, spacetime is a background in which the quantum particles interact. In quantum gravity, spacetime itself participates in the interactions and acquires quantum fluctuations. Theorists have proposed radically new ideas about spacetime at microscopic distances to serve as foundations for theories of quantum gravity. Loop Quantum Gravity is an approach in which spacetime itself arises from the theory as a grid of discrete (quantized) loops of gravitational field lines called "spin networks." In Causal Dynamical Triangulation, spacetime is two-dimensional at the Planck length scale and evolves into our four-dimensional spacetime at larger length scales.

Causal Dynamical Triangulation builds the spacetime in which we live from tiny triangles.

Figure 26: Causal Dynamical Triangulation builds the spacetime in which we live from tiny triangles.

Source: © Paul Coddington, University of Adelaide. More info

The most studied candidate for a theory of quantum gravity, string theory, posits that elementary particles are not points in spacetime but rather one-dimensional objects like open lengths or closed loops of string. Different modes of vibrations of the elementary strings give rise to the spectrum of particles in nature including the graviton, the particle that carries the gravitational force (analogous to the photon in electromagnetism). To provide a realistic theory of quantum gravity, string theories require extra spatial dimensions, each normally viewed as being finite in extent, such as a one-dimensional circle with a radius of the Planck length or larger. The presence of extra dimensions and new particles associated with gravity in string theories alters the gravitational inverse square law and the equivalence principle at very short distances. We will learn more about string theory and extra dimensions in Unit 4.

The small length scales and equivalently high energy scales at which quantum effects should modify gravity are far beyond the reach of current experimental techniques. A major challenge to finding the correct theory of quantum gravity is that it will be difficult to find experimental evidence to point us in the right direction.

Gravity at large distances

We can also wonder how well we know the behavior of gravity at very large lengths scales. As we have seen, the inverse square law of gravity has been verified over solar system distances, but the observable universe is 100 billion times larger than that. It requires a leap of faith to believe that our local laws of gravity hold everywhere. Some of the evidence for dark matter relies upon comparing the observed acceleration of objects far apart to that expected from the inverse square law. If the law of universal gravity is invalid for very small accelerations, as proposed in the MOND (Modified Newtonian Dynamics) theory, then our expectations for the interactions of distant objects would change.

Simulations of structure formation in the universe show the influence of gravity and dark energy.

Figure 27: Simulations of structure formation in the universe show the influence of gravity and dark energy.

Source: © Raul Angulo, Max Planck Institute for Astrophysics. More info

Dark energy, described in detail in Unit 11, has been proposed to explain why the expansion rate of the universe appears to be accelerating. The evidence for dark energy rests upon the comparison of observations with the predictions of general relativity applied to very large length scales. Theorists continue to explore a variety of ways to modify general relativity to circumvent the need for dark energy. As there is no direct experimental evidence one way or another, the behavior of gravity and very large length scales is still an open question.

The first unification in physics was Newton's law of universal gravitation that provided a common explanation for the motion of terrestrial and heavenly objects. It is ironic that for modern attempts to unify all of the forces in nature, gravity is the last and most difficult force to include. The theory of general relativity was a triumph of 20th century physics that revolutionized our concepts of space and time. Yet, even general relativity is not likely to be the ultimate theory of gravity. There is still much to be learned about gravity.