Imagine that the universe consists of a billiard table. The moment I strike the first ball, I can calculate exactly how it will hit the other balls and exactly what speed and direction every part of the system will have. Now imagine that the universe is made up of particles whizzing about—some tightly packed together (like me), and some loosely floating about (like the air you breathe). These particles—tiny billiards themselves—bounce off each other in a predictable way. Anyone who knew the position and momentum of every particle in the universe at a given moment could calculate precisely the position and momentum of all of those particles in the next moment. Such an omniscient person could do the same at the next moment, and the moment after that until that person knew everything about all the particles at all the moments in the future. This process could have happened at any point in time, so that the whole timeline of the universe is completely determined by the past. This view is called determinism.
I was convinced by the logic of this argument until I knew about quantum mechanics. The uncertainty principle in quantum mechanics says that there can be no omniscient observer, not even hypothetically. This changed my views on determinism to the following: “The universe is overwhelmingly deterministic, with only small deviations afforded by quantum indeterminacy.”
Except that’s wrong too. While it’s true that quantum fuzziness obstructs any observer from knowing the precise position and momentum of any particle, the fact remains that Schroedinger’s Equation describes the evolution of any quantum mechanical system in time according to the deterministic mathematics of differential equations. The universe has a wavefunction (that is, the combination of all the wavefunctions of all the particles in the universe). While no one can determine the position and momentum of all the particles at any time, applying Schroedinger’s Equation to the wavefunction of the universe at one time yields the wavefunction of the universe at any later time. While no one can determine the future, the future itself is determined.
This, of course, can’t be right. It doesn’t seem like my choices are determined from billions of years before my birth. Yes, the genetic and social circumstances of my birth have determined many of the tendencies and opportunities available to me, but it seems like many of the particular details of my life are up to me. It seems like my conscious experience is not completely determined. Therefore, the convincing nature of the deterministic argument outlined above is an uncomfortable uncertainty for me.
The above deterministic picture rests on the idea that the entire universe is equivalent to the sum of everything in the universe. Any physical theory we have is a theory about the behavior of phenomena in the universe, and so one might argue that any such theory is inadequate to make statements about the universe at large. Maybe there are emergent properties of complex systems that can’t be described with reductionist techniques.
With these musings in mind, I look forward to reading Time Reborn by the physicist Lee Smolin. The book recognizes the classical arguments above, and sets out to “demolish” them. While most contemporary views of time state that time is relational—that is, time can only be defined as a relationship between different objects—Smolin argues that time is fundamental and absolute. Again, I am very convinced by the relational notion of time. Any motion defines a clock. If an object moves from here to there, you can define time as the thing that changed between here and there. In this way, time is just a statement of the fact that things change. We’ll see what Smolin has to say.