Is the Universe Fundamentally Indeterministic?

My answer?  Yes!! 

What does that mean exactly?  Yeah, mumble mumble mumble.

Backing up,  I recently got a question from someone named Brian, who was commenting on the previous post.  I love this question - it goes straight to one of the most profound philosophical ideas that physics leads us to ponder.  The question was:


"I was just curious if you knew whether QM's being non-deterministic also rules out determinism at higher levels (like molecules, cells, etc)."

I'm not going to pretend that I can give a complete and totally satisfying answer to this question, but I will mumble at length about it!  It is going to take a couple of steps to get to the actual question.  So, here goes...me mumble my way through my own thoughts on the subject, in several steps

Step 1:  Quantum Mechanics and Determinism:

Quantum mechanics (the physics of very small systems like particles and atoms) is based on mathematical laws that are probabilistic in nature.  For example, these laws can tell you the probability that if you measure the location of an electron in an atom, you will find it at a particular place.  But, you can never predict exactly where the electron will be.  Hence, quantum mechanics is not a deterministic theory (it does not enable you to make exact predictions of the properties of particle systems).

Now, the question is:  is the probabilistic behavior fundamental, or is this just how we characterize what we observe because our theory is incomplete?  Maybe if we knew more about electrons, and we could measure extra properties of the electron or the atom, we could predict the exact location at any time.  Perhaps there are "hidden variables" describing the system of the electron in the atom, and our theory is just missing those.

This is a tempting way to rescue determinism, but it turns out to be impossible!  In 1964, a guy named Bell used a little bit of logic to come up with a straightforward way to test whether hidden variables could work.  Interestingly, you can test this experimentally without needing to specify what those hidden properties are.  Sure enough, experimental tests of particle behaviors prove that quantum mechanics isn't missing anything - the probabilistic description is complete.

As I discovered this spring (when I taught a class in Randomness), trying to explain Bell's theorem is really hard!  And, I should also mention that it's something that continues to be the subject of enormous discussion at the intersection between philosophy and physics (see, for example, the Stanford Encyclopedia of Philosophy article on Bell's Theorem).  As well as I understand it, the experimental tests of Bell's theorem lead you inescapably to pick one of the three following conclusions:
1) The universe is "fundamentally random", such that the behavior of something like an electron in an atom does not follow deterministic rules (whether or not we know those rules)
2) The universe does follow deterministic rules, but the behavior of a single particle is influenced by the location/behavior of every other particle in the universe (hence, even in principle it would be impossible to make exact predictions anyway).
3) Basic, simple logic is wrong.

If 3 were true, a whole lot of other stuff would make no sense.  But, depending on your philosophical preferences, you can pick option 1 or 2.  I'm perfectly happy with option 1, hence my resounding "yes" at the top of this post.

Step 2:  Macroscopic Determinism:

Ok, so let's just go forward with the assumption that particle behaviors can only be predicted probabilistically, and not deterministically.  Does that preclude deterministic behavior in macroscopic systems made up of many particles?  Not necessarily.

The rules of quantum mechanics, including the fuzzy, probabilistic behavior, really only operate for small systems.  Once you start to build up systems of many particles, their collective behavior becomes much more "classical" - governed by mathematics that is fully deterministic and allows exact prediction of behavior.  Probing the transition from probabilistic rules to deterministic rules is something physicists are currently doing (see some of the material in this previous post, for example).

It's not like one set of rules just turns off at a particular size scale and the other set of rules turns on.  Basically, the deterministic laws of classical physics (Newton's laws of motion, for example) can be viewed as only approximately true.  But the larger the system, the closer the approximation gets to being pretty perfect.  By the time you are operating with an object like a grain of dust, its behavior can be predicted with mathematics that is strictly deterministic, to a very very high accuracy.

So where does that leave the behavior of cells?  REALLY INTERESTING QUESTION!  I don't think anyone knows for sure, and a lot of the detailed physics of tiny biological systems is under study right now.  Cells are large enough objects that in terms of their physics, they probably could be described with deterministic mathematics.  But, at the same time, some of the processes within cells do take place at small enough scales that quantum mechanics could matter.  So, this is science to actively watch for in the coming decades - is anyone able to figure out whether the probabilistic nature of quantum mechanics measurably translates to randomness in the behavior of cells?

Step 3:  "Effective" Indeterminism:

There's one more step in how I think through all of this in my own head.  The underlying question to me (whether or not Brian had this in mind) is whether human brains are ultimately deterministic or not.  In other words, is every thought that I have a result of deterministic clockwork-like motions in my head?  Or is some of the apparent spontaneity ultimately due to the fundamental randomness of the universe (a lovely thought, in my opinion)?

This would seem to be a straightforward either-or situation:  either my brain is deterministic or it isn't.  But, I'd like to point out that even if it is deterministic, that doesn't necessarily mean we will ever actually be able to accurately predict what a system as complex as the brain will do.  This is not just a statement of the current limitations of science, but has to do with fundamental physics as well.

Even in fully deterministic systems, the interactions of many objects (particles, cells, etc.) can lead to a level of complexity such that the behavior appears to be random, and cannot ever be reduced in practice to deterministic laws.   It may be the case that to exactly predict the behavior of one neuron (even in a deterministic brain) you would need to know the positions and motions of so many particles that it would take a computer the size of the universe just to store the numbers.  If this is the case, the brain could still be "effectively" indeterministic - it could follow deterministic rules but involve such a level of complexity that no human instrument (present, or future, or even in science fiction) could ever determine what you're going to think next.