The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [10]
Here’s how it goes. The gross overall content of a huge volume of space is characterized by how much “stuff” it contains; more precisely, the density of matter, or, more precisely still, the density of matter and energy that the volume contains. The equations of general relativity describe how this density changes over time. But without invoking the cosmological principle, these equations are hopelessly difficult to analyze. There are ten of them, and because each equation depends intricately on the others, they form a tight mathematical Gordian knot. Happily, Einstein found that when the equations are applied to a uniform universe, the math simplifies; the ten equations become redundant and, in effect, reduce to one. The cosmological principle cuts the Gordian knot by reducing the mathematical complexity of studying matter and energy spread throughout the cosmos to a single equation (you can see it in the notes).5
Not so happily, from Einstein’s perspective, when he studied this equation he found something unexpected and, to him, unpalatable. The prevailing scientific and philosophical stance was not only that on the largest of scales the universe was uniform, but that it was also unchanging. Much like the rapid molecular motions in your tea average out to a liquid whose appearance is static, astronomical motion such as the planets orbiting the sun and the sun moving around the galaxy would average out to an overall unchanging cosmos. Einstein, who adhered to this cosmic perspective, found to his dismay that it was at odds with general relativity. The math showed that the density of matter and energy cannot be constant through time. Either the density grows or it diminishes, but it can’t stay put.
Although the mathematical analysis behind this conclusion is sophisticated, the underlying physics is pedestrian. Picture a baseball’s journey as it soars from home plate toward the center field fence. At first, the ball rockets upward; then it slows, reaches a high point, and finally heads back down. The ball doesn’t lazily hover like a blimp because gravity, being an attractive force, acts in one direction, pulling the baseball toward earth’s surface. A static situation, like a stalemate in a tug-of-war, requires equal and opposite forces that cancel. For a blimp, the upward push that counters downward gravity is provided by air pressure (since the blimp is filled with helium, which is lighter than air); for the ball in midair there is no counter-gravity force (air resistance does act against a ball in motion, but plays no role in a static situation), and so the ball can’t remain at a fixed height.
Einstein found that the universe is more like the baseball than the blimp. Because there’s no outward force to cancel the attractive pull of gravity, general relativity shows that the universe can’t be static. Either the fabric of space stretches or it contracts, but its size can’t remain fixed. A volume of space 100 million light-years on each side today won’t be 100 million light-years on each side tomorrow. Either it will be larger, and the density of matter within it will diminish (being spread more thinly in a larger volume), or it will be smaller, and the density of matter will increase (being packed more tightly in a smaller volume).6
Einstein recoiled. According to the math of general relativity, the universe on the grandest of scales would be changing, because its very substrate—space itself—would be changing. The eternal and static cosmos that Einstein expected would emerge from his equations was simply not there. He had initiated the science of cosmology, but he was deeply distressed by where the math had taken him.
Taxing