FEATURE ARTICLE
Observing the Beginning of Time
New maps of the cosmic background radiation may display evidence of the quantum origin of space and time
Craig Hogan
The Holographic Principle
Inflationary cosmology assumes that basic spacetime is the way Einstein built it before quantum mechanics came along—a smooth and unbroken (if slightly perturbed) continuum, with quantum fields playing within it. At some level, though, we know this cannot be right. Quantum discreteness must come into play even in the structure of time and space. Perhaps the sky is painted with a pattern that contains clues to how this works.
Let's think about the information contained in such a pattern. Information content roughly corresponds to the size of the computer file needed to store, say, a picture or a sound. In standard inflation theory, the pattern on the sky is predicted to have an infinite amount of information, because in theory the variations in brightness are continuous noise. But a truly quantum cosmology may have a finite amount of information. If the amount of information during inflation is small enough, it may be smaller than the information content of the maps we make—in which case, the maps will show signs of quantum discreteness.
If your computer modem is new, it is very fast, and it carries so much information it sounds like random noise. With older, slower modems you could hear the pattern of tones, so it was obvious that the signals were discrete and carried a certain limited quantity of information.
If you look at a digital picture or an ancient mosaic up close you can see it break up into discrete elements. Each pixel (or each tile) has a uniform color and is selected from a limited inventory of choices. Similarly, although we have yet to find the pixelation of spacetime itself, we suspect that it is there at some level, and may first appear in the close-up view of quanta afforded by inflation.
Deep insights into the connection between quantum physics and spacetime physics come from the consideration of information flow in black holes. A black hole is made not of matter but of highly curved spacetime. Inside a roughly spherical, imaginary surface in space called an event horizon (with its size depending on the hole's mass), gravity (spacetime curvature) is so intense that no energy, not even light, can escape—except by quantum behavior. A quantum always has some spatial extent, so it always has some chance of being far enough away from the hole to escape its gravity. Thus a black hole actually radiates energy, and by doing so it converts pure "spacetime energy " (gravity itself) into other forms, such as light.The theory of black hole evaporation, developed by Stephen Hawking, Jacob Bekenstein and others, allows us to predict just how many particles are radiated by a black hole and what their energies are. It turns out that the maximum amount of information needed to completely describe everything that falls into a black hole is a very simple recipe. It is just one-quarter of the area A of the event horizon, expressed in Planck units (where G, the gravitational constant, h, the Planck constant, and c, the speed of light, are all equal to 1). Put another way, the state of a black hole—everything that could possibly be known about it, the result of any conceivable experiment—can be specified by a number that has n = A/4 ln 2 binary digits. (The natural logarithm of 2 factor is there if we measure information in bits rather than "natural" entropy units.)
We can think of spacetime itself as an active quantum object. In this view, Hawking radiation converts quanta of spacetime (gravity) into quanta of other forms of information-carrying energy. The beauty of this is that it gives us a precise handle on the numerical relationship between gravity and information, and therefore a quantitative estimate of the quantization of spacetime.
Based on such arguments, it has been argued, especially by Gerard 't Hooft of the University of Utrecht and Leonard Susskind of Stanford University, that physics must obey a "holographic principle"—the entire state of things in any three-dimensional volume can be specified by a finite quantity of information less than one-quarter of the area of a two-dimensional bounding surface (one that covers the three-dimensional volume). They conjecture that the world is like a hologram. In a conventional optical hologram an interference pattern generated by two laser beams is recorded on a two-dimensional piece of film. When the developed film is illuminated with another laser beam, the recorded information is reconstructed, projecting a three-dimensional image of the original object. 't Hooft and Susskind suggest that the universe seems to be three-dimensional to us, but at a deeper level it is "really" just happening on a two-dimensional projective surface (Figure 8). But there's more. The surface is not even continuous, but grainy—the hologram is made of discrete pieces like a mosaic. So there is vastly less information than one would have guessed from quantum mechanics and gravity considered separately.
Inflationary universes also have event horizons (they are rather like inside-out versions of black hole event horizons), and the maximum observable information is also one quarter of the area of the event horizon. This means that the range of different things that can happen during inflation is much less than predicted if one assumes that spacetime does not respond in a quantum way. In particular, the holographic constraint means that when the inflaton field fluctuates, it finds its options severely limited, in ways that may be observable. Thus the cosmic background radiation anisotropy may be our first example of a phenomenon yielding direct information on the operation of quantum gravity—whether that be something like string theory or another more fundamental set of ideas.
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