More on Quantum Gravity

Physics in the 20th century was dominated by two great revolutions in the way we think about the nature of the universe at the most fundamental level: quantum theory and relativity theory. Currently, they are physicists' best understanding of the gears and wheels behind how everything works; however, each has limitations and it remains an unfinished revolution.

Quantum Theory

Quantum theory is our understanding of how things work at the ultra-microscopic scale of atoms and subatomic particles. Indeed, quantum theory was developed, in large part, to understand how it is possible for atoms to exist in our universe. That process of discovery revealed laws of nature completely alien to the ways of thinking we all develop, based on our day-to-day experiences with the world. For instance, it was discovered that a single particle could behave as if it were in two places at once, and that a pair of particles, even a great distance apart, could behave in some ways as a single entity.

Over the course of the 20th century, these quirky quantum insights culminated in today's standard model of particle physics, which is by far the most detailed and reliable description of nature the world has ever seen. It explains, at a fundamental level, almost everything, with mind-boggling accuracy – from the colours of a peacock's feathers and the hardness of diamonds, to the magnetic field of an electron and the remarkable properties of the quantum vacuum. The theory continues to be subjected to ever more stringent tests - for instance, under the extreme conditions that existed during the first hundred microseconds of the Big Bang, when the universe was filled with a novel state of matter called a quark gluon plasma.

          

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A quark gluon plasma can be created by heating matter to a temperature of about a million million Kelvin [more].       

 

 

 

Relativity Theory

The only thing the standard model does not explain is why an apple falls, or any other phenomenon involving gravity. This is the domain of general relativity, Albert Einstein's theory of space, time, and gravity. In this theory, space and time are no longer treated as separate entities, as Galileo and Newton had conceived, but are intimately related aspects of a single, four-dimensional entity called spacetime. Moreover, rather than merely providing a background stage upon which the events of the universe unfold, Einstein's spacetime is a dynamical player in the universe's great dance:  matter causes spacetime to warp, and this warping, in turn, affects the way matter moves, the net result being a beautiful, purely geometrical explanation of the phenomenon we call gravity.

This new way of thinking about space, time, and gravity proved to be enormously successful. Without it, the Global Positioning System would fail in seconds (military accuracy). The Jet Propulsion Laboratory uses general relativity to predict the ephemerides of the planets with extreme accuracy, necessary to get spacecraft to their precise destinations. General relativity is essential to understanding a wide variety of incredibly energetic astrophysical processes such as gamma-ray bursts (GRBs), the most violent explosions in the universe since the Big Bang. In a matter of seconds, a GRB can release the amount of energy our Sun will radiate over its entire 10-billion-year lifetime! General relativity also provides the mathematical framework within which virtually all of modern cosmology is understood, from the Big Bang to the accelerated expansion of the universe.

Limitations

These two theories together – quantum and relativity – provide the tools to explain virtually everything we currently have the technology to test. In practice they have never failed despite nearly a century of intense efforts to push them to the breaking point. However, extreme situations, which are not yet accessible to experiments, reveal their limitations, and here both the quantum and relativity theories fail.

For example, when a quantity of mass is compressed into a sufficiently small region of space, as is believed to happen, for instance, during the core collapse of a high-mass star leading to a GRB, general relativity predicts that a black hole will form. The spacetime will become so warped – gravity so intense – that a region of space will be created from which nothing, not even light, can escape. Meanwhile, the matter inside continues to collapse until its density becomes infinite, the warping of spacetime becomes infinite, and time inside the black hole "ends". Similarly, general relativity-based models describing the evolution of our universe predict that the cosmos had a definite beginning – a "time zero" at which the density of matter and radiation, and the warping of spacetime were both infinite, with no information on what, if anything, might have preceded this.

For physicists, infinities like this are a warning sign. They indicate that our description of what is happening has reached the limit of its usefulness and has broken down. There is some key aspect of the nature of reality that our theory is failing to take into account.  For example, near "time zero" (during the Big Bang), the billions of galaxies worth of matter in the observable universe today (not to mention an even larger amount of dark matter) occupied a region of space much smaller than the nucleus of a single atom! To describe such a bizarrely extreme situation will require a theory that seamlessly combines our best understanding of the very small (quantum theory) with our best understanding of space, time, and gravity (general relativity). What general relativity fails to take into account is the quantum nature of space, time, and gravity.

Quantum theory, on the other hand, was originally developed in the context of space and time as envisioned by Newton and Galileo. It was later extended to the "flat" spacetime of Einstein's theory of special relativity, i.e. spacetime in the absence of matter, which formed the mathematical foundations upon which the standard model of particle physics is based. It was even extended to the warped spacetime of, for example, a black hole, which led to the prediction of Hawking radiation – that a black hole is not black, but rather glows like a hot coal. But in all of these cases, spacetime is still considered as a background stage, where matter and radiation alone are the animated players, contrary to the principle lesson of general relativity – that spacetime is dynamic. 

          

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In the "collapsar" model for the production of gamma-ray bursts [more].  Figure courtesy Weiqun Zhang (NYU) and Stan Woosley (UCSC).

Unification

At a fundamental level, general relativity and quantum theory are thus seen to be contradictory, and mutually incompatible, which becomes evident in situations where both of these aspects of nature become equally important, for instance near the Big Bang or black hole singularities. This is the reason why we are not yet satisfied with the enormous achievements of the relativity and quantum theories, and is why the revolution they started remains unfinished. It is necessary to combine these two ways of thinking into a single, even more fundamental theoretical framework that has been called quantum gravity.

Indeed, they must be unified if we are to have any hope of answering a host of interesting and profound questions, including: Can we travel backwards in time?  Is information lost when something falls into a black hole? What is the nature of the matter-spacetime singularity inside a black hole? Finally, perhaps the biggest of all:  What is the origin of our universe? How did it come into existence? Was there something before the Big Bang? How might there not have been?

The history of physics has taught us again and again that successful unifications of seemingly disparate theories result in great leaps of progress, invariably leading to deeper insights into – and more profound questions about – the workings of our mysterious universe. Because the search for a theory of quantum gravity strongly challenges the entire foundation of our current understanding of the universe, it is not very likely to be a simple mix of quantum and relativity ideas, but rather a significant paradigm shift. It might be as completely alien to our current mindsets as the quantum and relativity theories once were. This is exciting.

The Heart of the Problem

As emphasized above, the central lesson of general relativity is that spacetime is not fixed. It is a dynamical physical entity in its own right, on the same footing as matter.  To start with, matter does not simply move around in an inert, static spacetime, according to how that spacetime is warped; it also warps the very spacetime it is moving around in. For example, two black holes orbiting each other will emit gravitational waves (see figure): ripples in the geometry of spacetime, in some ways similar to light or other electromagnetic waves; in particular, both carry energy. They are as real a physical entity as light from the Sun, which carries energy that warms the Earth. Warped spacetime is physics, not just mathematics. This has profound consequences that are not fully understood even classically. 

What about the quantum nature of such a dynamical warping? Just as the quantum nature of electromagnetism (i.e., photons) was necessary to understand how light and matter interact, it is widely believed that dynamical spacetime geometry should similarly be "quantized". The heart of the problem is that our traditional understanding of quantum theory is deeply rooted in fixed spacetimes: either Newton’s absolute space and time (original quantum mechanics of the atom), or the flat absolute spacetime of special relativity (standard model of particle physics), or the fixed warped spacetime of, for example, a black hole (Hawking radiation). What we are attempting to understand is the quantum nature of the very structure we traditionally rely on to understand quantum theory. It is a self-referential enigma of profound depth and exquisite subtlety. For example, attempting to apply ideas that proved so incredibly successful in particle physics (with its fixed background spacetime) has failed dramatically. We need new ways of thinking.

          

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As two black holes orbit around each other. they emit gravitational waves that carry away energy [more]       

© AEI, ZIB and LSU.  Click here to view video.

New Ways of Thinking

A number of approaches to quantum gravity have emerged, the two most studied being string theory and loop quantum gravity. The former is discussed here. The latter starts with a reformulation of general relativity that highlights its mathematical similarity to electromagnetism. Attempting to quantize general relativity in this new formulation while respecting the main lesson of general relativity – not to presuppose any fixed background spacetime – led to a new loop quantization method, which has been validated in the more familiar setting of electromagnetism.

The result of this mathematical construction is called loop quantum gravity, in which space can be imagined to be filled with a dense spin network with quantized geometric properties. Each edge in such a network carries an abstract quantity called "spin". A 2-dimensional surface slicing through such a network – e.g., the surface of a black hole – acquires area in proportion to the total amount of spin in the edges penetrating the surface (see figure). Like the quantized energy levels of the hydrogen atom, the admissible values of area are quantized.  Volumes of space, as well as its warping and bending, are also quantized. Thus space is not smooth, but rather granular; like atoms of ordinary matter, there are "atoms" of space. Such spin networks evolve over time in discrete steps.

Other important approaches to quantum gravity include:

Causal sets, introduced by Rafael Sorkin, in which spacetime points (events) are assumed to be discrete, like sprinkles on a cake. Its starting point is relativity's basic rules about which events can influence other events, and where such influence is impossible: something here and now can influence something there and then only by signals respecting the universal speed of light limit.

Triangulation approaches, in which space or spacetime are "triangulated" like a geodesic dome.  Curvature (warping) arises in the way the (higher dimensional) "triangles" fit together.

Twistor theory, introduced by Roger Penrose, in which rays of light, rather than spacetime points, are taken as the most primitive elements of spacetime. This novel way of thinking about spacetime gives a powerful new description of how fundamental particles and forces act on each other.

These and other approaches all have interconnections with each other, to some degree or other, and together represent one of the greatest intellectual adventures of all time.

          

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Spin network in loop quantum gravity, some edges of which penetrate the surface of a black hole.       

Reprinted by permission from Macmillan Publishers Ltd: Nature, 421, 702-703, 13 February 2003. 

Are We There Yet?

 How might we know?  One way is theoretical. Some physicists hope that there exists only one mathematically self-consistent "theory of everything", in which case the universe is the way it is because nothing else is possible.  However, this seems increasingly unlikely. The other is experimental, which may allow us to distinguish between the various candidate theories. 

The challenges are enormous. Consider that ordinary matter, like a chair made of atoms, cannot exist in Newton’s non-quantum universe, and yet the quantum nature of the chair is not evident unless we "zoom in" to the scale of atoms – about 10-10 metres.  The quantum nature of space, time, and gravity may be similarly essential to the very existence of the universe itself, yet it is believed that quantum gravity effects become evident only if we zoom in to the Planck scale, about 10-35 meters. Considering that we are currently able to zoom in (using high energy particle accelerators) to only about 10-18 meters – a hundred million billion times short of the mark – it seems hopeless that we will ever directly observe quantum gravity effects. 

However, indirect tests may be possible. For example, if space is in some way granular, then photons of different wavelength (colour) may "feel" this granularity to different degrees, affecting their speed differently. Such an effect would be very slight, but fortunately it would also be cumulative. For instance, differently coloured photons emitted at the same time from a GRB, travelling at slightly different speeds over a distance of cosmic scale, may arrive at the Earth at measurably different times.  See figure. As another example, one of the candidate theories might yield a reliable model for the earliest phase of cosmic evolution, the Big Bang, and thus testable predictions about the Big Bang’s observable consequences. Notice that in both examples, we are using the universe itself as a cosmic-sized "magnifying glass" to conduct experiments on the almost unimaginably small Planck scale!

          

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In loop quantum gravity, a photon occupies a (large) number of edges at each instant [more].  From Atoms of Space Time, Lee Smolin. Copyright © January 2004 by Scientific American, Inc. All rights reserved.

To learn more about quantum gravity at Perimeter Institute and the researchers, please click here

Perimeter Institute Resources

Public Lectures

The following selection of Perimeter Institute multi-media presentations by leading scientists is particularly relevant to quantum gravity. Click on the link to read a full description of each talk and choose your viewing format.

Specially for Teachers and Students

These multi-media talks by Perimeter Institute researchers and visiting scientists were presented to youth and educators during Perimeter Institute's ISSYP, EinsteinPlus or other occasions.

Suggested External Resources

  • Einstein Online:  Relativity and the Quantum (basic)
  • The official string theory website (basic to advanced)
  • Website for Brian Greene’s The Elegant Universe (basic)
  • Stanford Encyclopedia of Philosophy: Quantum Gravity
  • Baez, John. The Quantum of Area?  Nature, 2003. Vol. 421, page 702. (basic)
  • Barbour, Julian. The End of Time: The Next Revolution in Physics. Oxford University Press, 2001. (intermediate)
  • Callender, Craig, and Huggett, Nick (Eds.). Physics Meets Philosophy at the Planck Scale:  Contemporary Theories in Quantum Gravity. Cambridge University Press, 2001. (intermediate)
  • Greene, Brian. The Elegant Universe. Vintage Books, 2000. (basic)
  • ---.  The Fabric of the Cosmos. Knopf, 2004.  (basic)
  • Hawking, Stephen. The Universe in a Nutshell. Bantam, 2001. (basic)
  • ---. A Brief History of Time. Bantam, 1998. (basic)
  • Penrose, Roger.  The Road to Reality.  Vintage, 2007.  (basic to advanced)
  • Smolin, Lee.  Three Roads to Quantum Gravity.  Basic Books, 2002. (basic)
  • ---. Atoms of Space and Time. Scientific American, January, 66-75. (basic)
  • ---. How Far Are We from the Quantum Theory of Gravity, http://arxiv.org/abs/hep-th/0303185. (intermediate to advanced)
  • ---. Loop Quantum Gravity  http://www.edge.org/3rd_culture/smolin03/smolin03_index.html. (basic)
  • Welcome to Quantum Gravity. Special section. Physics World, November 2003.  Vol. 16, No. 11, page 27. (basic)

The 20th century was dominated by two great revolutions in the way we think about the nature of the universe – but each has limitations and remain unfinished revolutions.