Pale Blue Dot - Carl Sagan [18]
If, on the other hand, the Universe has a finite age, why is it the way it is? Why wasn’t it given a very different character? Which laws of Nature go with which others? Are there meta-laws specifying the connections? Can we possibly discover them? Of all conceivable laws of gravity, say, which ones can exist simultaneously with which conceivable laws of quantum physics that determine the very existence of macroscopic matter? Are all laws we can think of possible, or is there only a restricted number that can somehow be brought into existence? Clearly we have not a glimmering of how to determine which laws of Nature are “possible” and which are not. Nor do we have more than the most rudimentary notion of what correlations of natural laws are “permitted.”
For example, Newton’s universal law of gravitation specifies that the mutual gravitational force attracting two bodies towards each other is inversely proportional to the square of how far they are apart. You move twice as far from the center of the Earth and you weigh a quarter as much; ten times farther and you weigh only a hundredth of your ordinary weight; etc. It is this inverse square law that permits the exquisite circular and elliptical orbits of planets around the Sun, and moons around the planets—as well as the precision trajectories of our interplanetary spacecraft. If r is the distance between the centers of two masses, we say that the gravitational force varies as 1/r2.
But if this exponent were different—if the gravitational law were 1/r4, say, rather than 1/r2—then the orbits would not close; over billions of revolutions, the planets would spiral in and be consumed in the fiery depths of the Sun, or spiral out and be lost to interstellar space. If the Universe were constructed with an inverse fourth power law rather than an inverse square law, soon there would be no planets for living beings to inhabit.
So of all the possible gravitational force laws, why are we so lucky as to live in a universe sporting a law consistent with life? First, of course, we’re so “lucky,” because if we weren’t, we wouldn’t be here to ask the question. It is no mystery that inquisitive beings who evolve on planets can be found only in universes that admit planets. Second, the inverse square law is not the only one consistent with stability over billions of years. Any power law less steep than 1/r3 (1/r2.99 or 1/r, for example) will keep a planet in the vicinity of a circular orbit even if it’s given a shove. We have a tendency to overlook the possibility that other conceivable laws of Nature might also be consistent with life.
But there’s a further point: It’s not arbitrary that we have an inverse square law of gravitation. When Newton’s theory is understood in terms of the more encompassing general theory of relativity, we recognize that the exponent of the gravity law is 2 because the number of physical dimensions we live in is 3. All gravity laws aren’t available, free for a Creator’s choosing. Even given an infinite number of three-dimensional universes for some great god to tinker with, the gravity law would always have to be the law of the inverse square. Newtonian gravity, we might say, is not a contingent facet of our universe, but a necessary one.
In general relativity, gravity is due to the dimensionality and curvature of space. When we talk about gravity we are talking about local dimples in space-time. This is by no means obvious and even affronts commonsense notions. But when examined deeply, the ideas of gravity and mass are not separate matters, but ramifications of the underlying geometry of space-time.
I wonder if something like this doesn’t apply generally to all anthropic hypotheses. The laws or physical constants on which our lives depend