The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [198]
9. Large flux values also tend to destabilize a given Calabi-Yau shape for the extra dimensions. That is, the fluxes tend to push the Calabi-Yau shape to grow large, quickly running into conflict with the criterion that extra dimensions not be visible.
Chapter 6: New Thinking About an Old Constant
1. George Gamow, My World Line (New York: Viking Adult, 1970); J. C. Pecker, Letter to the Editor, Physics Today, May 1990, p. 117.
2. Albert Einstein, The Meaning of Relativity (Princeton: Princeton University Press, 2004), p. 127. Note that Einstein used the term “cosmologic member” for what we now call the “cosmological constant”; for clarity, I have made this substitution in the text.
3. The Collected Papers of Albert Einstein, edited by Robert Schulmann et al. (Princeton: Princeton University Press, 1998), p. 316.
4. Of course, some things do change. As pointed out in the notes to Chapter 3, galaxies generally have small velocities beyond the spatial swelling. Over the course of cosmological timescales, such additional motion can alter position relationships; such motion can also result in a variety of interesting astrophysical events such as galaxy collisions and mergers. For the purpose of explaining cosmic distances, however, these complications can be safely ignored.
5. There is one complication that does not affect the essential idea I’ve explained but which does come into play when undertaking the scientific analyses described. As photons travel to us from a given supernova, their number density gets diluted in the manner I’ve described. However, there is another diminishment to which they are subject. In the next section, I’ll describe how the stretching of space causes the wavelength of photons to stretch too, and, correspondingly, their energy to decrease—an effect, as we will see, called redshift. As explained there, astronomers use redshift data to learn about the size of the universe when the photons were emitted—an important step toward determining how the expansion of space has varied through time. But the stretching of photons—the diminishment of their energy—has another effect: It accentuates the dimming of a distant source. And so, to properly determine the distance of a supernova by comparing its apparent and intrinsic brightness, astronomers must take account not just of the dilution of photon number density (as I’ve described in the text), but also the additional diminishment of energy coming from redshift. (More precisely still, this additional dilution factor must be applied twice; the second red shift factor accounts for the rate at which photons arrive being similarly stretched by the cosmic expansion.)
6. Properly interpreted, the second proposed answer for the meaning of the distance being measured may also be construed as correct. In the example of earth’s expanding surface, New York, Austin, and Los Angeles all rush away from one another, yet each continues to occupy the same location on earth it always has. The cities separate because the surface swells, not because someone digs them up, puts them on a flatbed, and transports them to a new site. Similarly, because galaxies separate due to the cosmic swelling, they too occupy the same location in space they always have. You can think of them as being stitched to the spatial fabric. When the fabric stretches, the galaxies move apart, yet each remains tethered to the very same point it has always occupied. And so, even though the second and third answers appear different—the former focusing on the distance between us and the location a distant galaxy had eons ago, when the supernova emitted the light we now see; the latter focusing on the distance now between us and that galaxy’s current location—they’re not. The distant galaxy is now, and has been for billions of years, positioned at one and the same spatial location. Only if it moved through space rather than solely ride the wave of swelling space