The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [77]
Whose Distance Is It, Anyway?
Before moving on to the next step, the determination of how fast the universe was expanding when each of these distant supernovae happened, let me briefly untangle a potential knot of confusion. When we’re talking about distances on such fantastically large scales, and in the context of a universe that’s continually expanding, the question inevitably arises of which distance the astronomers are actually measuring. Is it the distance between the locations we and a given galaxy each occupied eons ago, when the galaxy emitted the light we’re just now seeing? Is it the distance between our current location and the location the galaxy occupied eons ago, when it emitted the light we’re just now seeing? Or is it the distance between our current location and the galaxy’s current location?
Here’s what I consider the most insightful way of thinking about these and a whole slew of similarly confusing cosmological questions.
Imagine you want to know the distances, as the crow flies, among three cities, New York, Los Angeles, and Austin, so you measure their separation on a map of the United States. You find that New York is 39 centimeters from Los Angeles; Los Angeles is 19 centimeters from Austin; and Austin is 24 centimeters from New York. You then convert these measurements into real-world distances by looking at the map’s legend, which provides a conversion factor—1 centimeter = 100 kilometers—which allows you to conclude that the three cities are about 3,900 kilometers, 1,900 kilometers, and 2,400 kilometers apart, respectively.
Now imagine that the earth’s surface swells uniformly, doubling all separations. This would certainly be a radical transformation, but even so your map of the United States would continue to be perfectly valid as long as you made one important change. You’d need to modify the legend so that the conversion factor read “1 centimeter = 200 kilometers.” Thirty-nine centimeters, 19 centimeters, and 24 centimeters on the map would now correspond to 7,800 kilometers, 3,800 kilometers, and 4,800 kilometers across the expanded United States. Were the expansion of the earth to continue, your static, unchanging map would remain accurate, as long as you continually updated its legend with the conversion factor relevant at each moment—1 centimeter = 200 kilometers at noon; 1 centimeter = 300 kilometers at two p.m.; 1 centimeter = 400 kilometers at four p.m.—to reflect how locations were being dragged apart by the expanding surface.
The expanding earth proves a useful conceit because similar considerations apply to the expanding cosmos. Galaxies don’t move under their own power. Rather, like the cities on our expanding earth, they race apart because the substrate in which they’re embedded—space itself—is swelling. This means that had some cosmic cartographer mapped galaxy locations billions of years ago, the map would be as valid today as it was then.4 But, like the legend for the map of an expanding earth, the cosmic map’s legend must be updated to ensure that the conversion factor, from map distances to real distances, remains accurate. The cosmological conversion factor is called the universe’s scale factor; in an expanding universe, the scale factor increases with time.
Whenever you think about the expanding universe, I urge you to picture an unchanging cosmic map. Think of it as if it were any ordinary map lying flat on a table, and account for the cosmic expansion by updating the map’s legend over time. With a little practice, you’ll see that this approach vastly simplifies conceptual hurdles.
As a case in point, consider light from a supernova explosion in the distant Noa Galaxy. When we compare the supernova’s apparent