The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [11]
It’s often said that Einstein blinked—that he went back to his notebooks and in desperation mangled the beautiful equations of general relativity to make them compatible with a universe that was not only uniform but also unchanging. This is only partly true. Einstein did indeed modify his equations so they would support his conviction of a static cosmos, but the change was minimal and thoroughly sensible.
To get a feel for his mathematical move, think about filling out your tax forms. Interspersed among the lines on which you record numbers are others you leave blank. Mathematically, a blank line signifies that the entry is zero, but psychologically it connotes more. It means you’re ignoring the line because you’ve determined that it’s not relevant to your financial situation.
If the mathematics of general relativity were arranged like a tax form, it would have three lines. One line would describe the geometry of spacetime—its warps and curves—the embodiment of gravity. Another would describe the distribution of matter across space, the source of gravity—the cause of the warps and curves. During a decade of ardent research, Einstein had worked out the mathematical description of these two features and had thus filled in these two lines with great care. But a complete accounting of general relativity requires a third line, one that is on an absolutely equal mathematical footing with the other two but whose physical meaning is more subtle. When general relativity elevated space and time into dynamic participants in the unfolding of the cosmos, they shifted from merely providing language to delineate where and when things take place to being physical entities with their own intrinsic properties. The third line on the general relativity tax form quantifies a particular intrinsic feature of spacetime relevant for gravity: the amount of energy stitched into the very fabric of space itself. Just as every cubic meter of water contains a certain amount of energy, summarized by the water’s temperature, every cubic meter of space contains a certain amount of energy, summarized by the number on the third line. In his paper announcing the general theory of relativity, Einstein didn’t consider this line. Mathematically, this is tantamount to having set its value to zero, but much as with blank lines on your tax forms, he seems to have simply ignored it.
When general relativity proved incompatible with a static universe, Einstein reengaged with the mathematics, and this time he took a harder look at the third line. He realized that there was no observational or experimental justification for setting it to zero. He also realized that it embodied some remarkable physics.
If instead of zero he entered a positive number on the third line, endowing the spatial fabric with a uniform positive energy, he found (for reasons I’ll explain in the next chapter) that every region of space would push away from every other, producing something most physicists had thought impossible: repulsive gravity. Moreover, Einstein found that if he precisely adjusted the size of the number he put on the third line, the repulsive gravitational force produced across the cosmos would exactly balance the usual attractive gravitational force generated by the matter inhabiting space, giving rise to a static universe. Like a hovering blimp that neither rises nor falls, the universe would be unchanging.
Einstein called the entry on the third line the cosmological member or the cosmological constant; with it in place, he could rest easy. Or, he could rest easier. If the universe had a cosmological constant of the right size—that is, if space were endowed with the right amount of intrinsic energy—his theory of gravity fell in line with the prevailing belief that the universe on the largest of scales was unchanging. He couldn’t explain why space would embody just the right amount of energy to ensure this balancing act, but at least he’d shown that general relativity, augmented with a cosmological constant of the right value, gave rise to the kind of cosmos he