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Leibniz & the Big Bang

Eric Kincanon says that Leibniz could have predicted the Big Bang in 1715.

The German philosopher and scientist Gottfried Leibniz (1646-1716) is best known to the general public for his independent development of calculus and the letter he wrote to Princess Caroline of Sweden in 1715. In this letter he challenged Isaac Newton’s statements about absolute time and space, arguing that they were heretical. Leibniz and Newton were long-time adversaries before the writing of this letter, and Leibniz was probably motivated by revenge. Still, this should not be a reason to dismiss his arguments. In fact, two hundred years before Einstein, Leibniz was arguing that time and space could not be absolute. Interestingly, the two philosophical laws that Leibniz used to challenge Newton’s concepts of space and time can also be used to argue for the Big Bang over the Steady State model of the Universe.

Leibniz’s first philosophical law was called the Principle of Sufficient Reason. Basically, it says that God does nothing without a sufficient purpose or reason. So since God created all things, all things must have been created for a sufficient purpose or reason. The important implication of this for the discussion of space and time is that it means that God is not whimsical or random in his actions; that is, everything must have sufficient reason for it being created as it is. Leibniz’s second philosophical law states that God does nothing twice. The second law can be seen as a consequence of the first. So for example, the Sun, being created by God, has a purpose: it provides warmth to the planets, determines their orbits, etc. Moreover, this purpose is fulfilled by the Sun, so there is no need for another Sun. Likewise each person is created with a unique purpose. God would not create another you, since your purpose is being fulfilled by you, and so the creation of another you would not have a purpose and, by the first law, would not be created by God.

Newton had argued that to be consistent with his law of inertia, space and time must be absolute – in other words, must exist independently of everything else, including God. If time and space are absolute, then, Newton reasoned, God must exist in time and space. This was what was seen as heretical by Leibniz, since God existing, and creating, in already-existing space and time would conflict with his first law. Consider the creation of the universe by a God in a space that already existed. As per his first law, Leibniz requires that God does things with sufficient reason. However, notice the problem God would have if space were absolute. Where would God put the Universe? With absolute space already existing, God would have to choose a particular spot to create the Universe in. But, to God each point in space would look the same, so how can there be any reason to choose one spot over another? There can’t be, Leibniz argues, so God cannot create in absolute space.

Existing in absolute time causes a similar problem. If Newton’s absolute time already exists, how does God decide when to create the Universe? God, under Newton’s thinking, must have picked a moment for creation. But, if God does everything with sufficient reason, how can he prefer one moment over another? Why would God prefer any particular moment to create the Universe rather than a different moment an hour earlier, or three thousand years later? According to Leibniz, God can’t just randomly pick a time, since that would mean God is acting without sufficient reason, and this would violate Leibniz’s first law.

Leibniz was of course unaware of the Big Bang theory – it was developed more than two centuries after his death. However, his philosophical laws could be used to argue for the Big Bang over its main competitor, the Steady State model. The Big Bang theory asserts that the Universe began as a point 13.8 billion years ago, and expanded to its current size. The Steady State model on the other hand has the Universe existing pretty much now as it always has, and at its start (if it had one), it was already infinite in size. Although some Steady State advocates argued for an infinitely old Universe, this would quickly be ruled out by Leibniz, since he always saw God as the Universe’s creator. More interestingly, Leibniz could also have argued against Steady State theory even if the Universe had had a finite past. If the Universe starts out as already being infinite in extent, God would have to give the objects he then creates particular positions and velocities. At first this might seem okay. Perhaps God could have created whatever stars existed a few billion years or however long ago it was, and given them positions and velocities such that everything would end up just where it is today. No, he could not, Leibniz would argue. Much like his argument against absolute space and time, Leibniz could argue that God (who of course follows Leibniz’s laws) could not choose one particular set of positions and velocities over the ones they would have had if they had been created (say) a few seconds later. So, Leibniz’s God, could not have created a Steady State Universe.

Notice how nicely these problems go away under the Big Bang. Under the Big Bang the Universe began as a point. A point has no internal structure; there is no way to have different arrangements of the interior of a point. This is also the only geometric possibility that has this character: a line segment, for example, must address size as well as how any material is distributed along it. A point has none of these issues. So, unlike the Steady State theory, Big Bang theory has a geometry at creation that is the only one acceptable to Leibniz’s laws. So Leibniz, I think, would have argued for the necessity of the Big Bang. It’s not just that the Big Bang theory doesn’t contradict Leibniz’s laws. Rather, it is the only way a God of purpose and reason could be a creator.

Eric Kincanon is in the Physics Department at Gonzaga University. Along with the physics, he teaches the metaphysics of time.