Translational Invariance and Newton’s God

Tim Maudlin is writing a two-volume introduction to the philosophy of physics, and I was fortunate enough to get a peek at a draft of Volume One, about space and time. There is one anecdote in there about Leibniz’s objections to Newtonian physics that is worth passing along. This came up in the course of the Leibniz-Clarke correspondence.

Leibniz was quite fond of proclaiming overarching a priori principles. Perhaps the most famous/infamous is the Principle of Sufficient Reason, which states that everything that happens does so for some good reason. But there was also the Principle of Identity of Indiscernibles, which states that if two things have all the same properties, they are really the same thing. Sounds reasonable enough (although one might worry what qualifies as a “property”), but it can get you in trouble if you take it too far.

Remember that Newton believed in absolute space — a rigid three-dimensional set of points that forms the arena in which physics takes place. Leibniz, on the other hand, claimed that space should be thought of purely in terms of relations between different points, without any metaphysical baggage of “absoluteness.” (From a modern perspective, Leibniz was closer to correct, given Galilean relativity; but once we allow for spacetime curvature in general relativity, the relational view becomes less useful.)

So far, so good. The weird part, to modern ears, comes in when we consider Newtonian cosmology. In order to explain matter in the universe, Newton departed from the strict consequences of his Laws of Motion. Instead, he imagined that empty space existed for an infinite period of time, before eventually God decided to create matter in it.

That’s the part Leibniz couldn’t go along with. He didn’t believe God would work that way, for reasons that amount to what we would now call the translational invariance of space. If God is going to create all this matter in empty space, Leibniz reasons, He has to put it somewhere. But where? Every point is equally good! Therefore there can’t be any “sufficient reason” to create it in one place rather than in some other place. Therefore there must be a deep metaphysical flaw at the heart of Newton’s theory. Interestingly, he didn’t go for “matter has been around forever,” but instead came down on the side of “there is no such thing as absolute space.”

Maybe he was worried about Boltzmann Brains?