Spacetime Foam

Spacetime is composed of a fluctuating arrangement of bubbles or loops called spacetime foam, or quantum foam. We use the holographic principle to deduce its structure, and show that the result is consistent with gedanken experiments involving spacetime measurements. We propose to use laserbased atom interferometry techniques to look for spacetime fluctuations. Our analysis makes it clear that the physics of quantum foam is inextricably linked to that of black holes. A negative experimental result, therefore, might have important ramifications for semiclassical gravity and black hole physics. Essay on Gravitation E-mail: [email protected] 0 Spacetime appears smooth on large scales. On small scales, however, it is bubbly and foamy due to quantum fluctuations. In this essay, we use the holographic principle to show that the fluctuations are much larger than what conventional wisdom leads us to believe. We alternatively derive the same results by carrying out gedanken experiments to measure distances and time intervals. Intriguingly, the fluctuations are large enough that they may soon be detectable with modern laser-based atom interferometers. From the holographic principle to spacetime foam The holographic principle grew out of the profound insights of Wheeler, Bekenstein, Hawking, ’t Hooft, and Susskind. [1] It states that the maximum number of degrees of freedom that can be put into a region of space is given by the area of the region in Planck units. To connect it to quantum foam, let us consider a region of space measuring R×R×R, and imgine partitioning it into cubes as small as physical laws allow. Into each small cube we put one degree of freedom. If the smallest uncertainty in measuring a distance R is δR, in other words, if the fluctuation in distance R is δR, then the smallest such cubes have volume (δR). (Otherwise, one could divide R into units each measuring less than δR, and by counting the number of such units in R, one would be able to measure R to within an uncertainty smaller than δR.) Thus the maximum number of degrees of freedom, given by the number of small cubes we can put into the region of space, is (R/δR). The holographic principle demands that (R/δR) <∼ (R/lP ) , where lP = ctP ≡ (h̄G/c ) is the Planck length. This yields δR > ∼ (Rl 2 P ) 1/3 = lP ( R lP )1/3 . (1) Thus quantum fluctuations from individual bubbles of spacetime add together to produce a (curious) 3 √ R-dependence and are much larger than the folklore [2] indicates (viz., δR > ∼ lP ). The corresponding metric fluctuation is given by δgμν > ∼ (lP/R) . Note that even for a macroscopic distance R, the fluctuation δR, though much larger than the Planck scale lP , is