The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [211]
9. More precisely, gravity can be canceled in a region of space by going into a freely falling state of motion. The size of the region depends on the scales over which the gravitational field varies. If the gravitational field varies only over large scales (that is, if the gravitational field is uniform, or nearly so), your free-fall motion will cancel gravity over a large region of space. But if the gravitational field varies over short-distance scales—the scales of your body, say—then you might cancel gravity at your feet and yet still feel it at your head. This becomes particularly relevant later in your fall because the gravitational field gets ever stronger ever closer to the black hole’s singularity; its strength rises sharply as your distance from the singularity decreases. The rapid variation means there is no way to cancel the effects of the singularity, which will ultimately stretch your body to its breaking point since the gravitational pull on your feet, if you jump in feetfirst, will be ever stronger than the pull on your head.
10. This discussion exemplifies the discovery, made in 1976 by William Unruh, that links one’s motion and the particles one encounters. Unruh found that if you accelerate through otherwise empty space, you will encounter a bath of particles at a temperature determined by your motion. General relativity instructs us to determine one’s rate of acceleration by comparing with the benchmark set by free-fall observers (see Fabric of the Cosmos, Chapter 3). A distant, non-free-fall observer thereby sees radiation emerging from a black hole; a free-fall observer does not.
11. A black hole forms if the mass M within a sphere of radius R exceeds c2R/2G, where c is the speed of light and G is Newton’s constant.
12. In actuality, as the matter collapsed under its own weight and a black hole formed, the event horizon would generally be located within the boundary of the region we’ve been discussing. This means that we would not have so far maxed out the entropy that the region itself could contain. This is easily remedied. Throw more material into the black hole, causing the event horizon to swell out to the region’s original boundary. Since entropy would again increase throughout this somewhat more elaborate process, the entropy of the material we put within the region would be less than that of the black hole that fills the region, i.e., the surface area of the region in Planck units.
13. G. ’t Hooft, “Dimensional Reduction in Quantum Gravity.” In Salam Festschrift, edited by A. Ali, J. Ellis, and S. Randjbar-Daemi (River Edge, N.J.: World Scientific, 1993), pp. 284–96 (QCD161:C512:1993).
14. We’ve discussed that “tired” or “exhausted” light is light whose wavelength is stretched (redshifted) and vibrational frequency reduced by virtue of its having expended energy climbing away from a black hole (or climbing away from any source of gravity). Like more familiar cyclical processes (the earth’s orbit around the sun; the earth’s rotation on its axis, etc.), the vibrations of light can be used to define elapsed time. In fact, the vibrations of light emitted by excited Cesium-133 atoms are now used by scientists to define the second. The tired light’s slower vibrational frequency thus implies that the passage of time near the black hole—as viewed by the faraway observer—is slower too.
15. With most important discoveries in science, the pinnacle result relies on a collection of earlier works. Such is the case here. In addition to ’t Hooft, Susskind, and Maldacena, the researchers who helped blaze the trail to this result and develop its consequences include Steve Gubser, Joe Polchinski,