I recently listened to an episode of the

Atheistically Speaking podcast on the subject of Einstein's and Gödel's belief (or lack thereof) in God. The podcast overall is quite enjoyable and going strong after more than 200 episodes; I've only started listening in the past few weeks and have been alternating between listening to new and archived episodes. At a point in this particular show, the host (Thomas) and his guest (Kurt) quite literally say: "Hey, if there's a physicist out there listening to this, let us know what you think..." So, this post is the result of taking them at their word, given that so much of the show had me shaking my head throughout. I should also mention that Thomas was kind enough to invite me to write to him directly, and the following is a slightly polished version of the e-mail I sent him. Here we go:

Quantum Mechanics (QM) is part of a core of
courses that all physicists take, no matter what their field. Obviously,
people who specialize in QM will get into it a lot deeper than those
that don't. There are some complicated areas of research going on right
now, and there's plenty of debate going on--but the "basics", if we
could call them that, are more than enough to refute just about
everything Kurt said on episode 242.

First, the easy point:
if you're going to take the approach "some smart guy believes X, so X
is true" your're already in trouble because, as Bertrand Russell said,
if you rely on an authority for your argument, there will always be
other authorities who disagree. So if we were to tally the John
Polkinghornes of the world as evidence that there could be a god hiding
somewhere in QM--or free will, or the soul, or whatever--, then we would have to be intellectually honest and tally all the other
guys who say he's full of shit as evidence that there's no such thing,
which is everybody else. People in this latter
camp include Sean Carroll, Lawrence Krauss, Richard Feynman, Tim
Maudlin, Steven Weinberg, and many others. Polkinghorne is a theologian,
so he's intellectually compromised by definition. This is not an

*ad-hominem*: this is a simple statement of the fact that he can't be
relied upon to be intellectually honest. If he were, he wouldn't be a
theologian.

Now, on to actual QM: Just as in high-school algebra
we had some complicated equation with numbers and letters, and we were
asked to solve for "x", so too in QM there's an equation to solve, only
mere algebra won't quite do the trick. This is the Schrödinger equation,
which looks something like this: \[ i \hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \Psi}{\partial x^2} + V\Psi. \]

It may look complicated, but the idea is the same as in high school algebra: solve for the

* wave function*, \(\Psi\) (greek letter "Psi"). After you do that, what you will get is an
equation for \(\Psi\) that tells you what its value is in terms of

*x* (position)
and

*t* (plain old time), plus some other physical constants and the
specifics of your system (these are included in the

*V* term above). Just
as "x" was uniquely determined by all the other variables in high-school
algebra, so too is \(\Psi\) determined--fully, for all time--by all the other
squiggles in the Schrödinger equation. This is a second-degree partial
differential equation and, with the right input, is fully deterministic.

The subtlety arises in the fact that \(\Psi\) is not a number, but a

*probability density*,
and that's where laymen get mixed up. Here is where an analogy will
help and, if you were to remember any part of this post as
particularly useful, this would be it. Imagine you have a fair die that
you can throw. For any given throw, it's pretty hard to know what number
is going to come up. Naively, one would think that the die coughs up a
random number between 1 and 6 each time. However, if you throw the die
many times, eventually you'll see a pattern: each number comes up
roughly 1/6 of the time. That 1/6 is determined by the

*geometry *of
the die. No matter what individual result you look
at--1,4,2,5,3,etc.--the 1/6 is always the same for every throw. That
1/6, roughly, is \(\Psi\). The geometry of the die is everything else in the
Schrödinger equation. So even though any given throw is undetermined,
the overall 1/6 is fixed for as long as the geometry is fixed.

*Every experiment ever done confirms that the above equation, or some version of it, is true.*
If Kurt (or Polkinghorne, or whoever) wants to say that god is
hiding somewhere in \(\Psi\), then they're making a claim that god can do no
better that to show up as what probability theory would predict anyway
without him, which seems like a pretty lame god to me.

As if that
weren't enough, there's an entire field of research on

hidden variable theory--the idea that there is a more fundamental, fully
deterministic physics underneath the probabilistic character of the wave
function. So the statement by Kurt, that it's just "a brute fact
that QM is this way" is not obviously true either. Anyway, on to Gödel:

First,
the necessary caveat: I'm a physicist, not a mathematician. With that
said,

Gödel's incompleteness theorems state that, for any given
mathematical system based on arithmetic and axioms, there will be one of
two inevitable outcomes: 1) there will be some theorems that will be
true but unprovable, or 2) all theorems will be provable, but some will
contradict others.

As an example, consider the sentence

"This statement is true".

Each
word there is well-defined and fits the usual syntax to create a
meaningful idea. You can think of each one of these words as an axiom (a
basic assumption that doesn't need to be proven), and the syntax is the
logic that is used to put them together and derive a theorem, which is a
conclusion--the meaning of the statement itself. However, we can follow
the same axioms and rules to construct a statement like this:

"This statement is false."

Each
word there is well-defined, and all the words are arranged properly,
but we can't decide on the meaning of the statement because the content of
the statement refutes its logical construction!

Now, even though
this is certainly important for the philosophy of mathematics, there is
no way that you can get from it to the claim made by Kurt that
some things are, and always will be, unknowable. That's a

*non-sequitur*
at worst, and a trivial argument from ignorance at best. A key
distinction to keep in mind is that

*unprovable* does not mean

*unknowable*: remember, item 1) for the incompleteness theorems says "

*true*, but not provable".
In a way, this is part of what theoretical physics is about: there are
some things we know are true (thanks to experiment) and we work to
explain them--that is, to prove why it must be the case that they are
true.

In any case, when people speak of god, they always mess up and fall into contradictions

*in the axioms themselves*.
Their conclusions are unsound because their premises are gibberish and
the arguments never get off the ground--there are no theorems to be
derived at all! This happens to all definitions of god that include
omnipotence, for example. Once they include that as a basic assumption,
the rest is white noise.

Thomas covered other many other areas of disagreement
with Kurt on the show itself, and some commenters on the episode site
have done so as well, so I'll leave it here for now. As a conclusion, I would say that people aren't smuggling contraband into QM (god, free will, the soul, consciousness) as much as they're smuggling it into their

*misunderstanding* of QM. Sometimes, these people even have PhD's and published peer-reviewed papers. Bad ideas in science are weeded out eventually, but someone has to actually get on the ground and

*do *it. This must be done by the experts, but it can be a slow, thankless process and so most of them just stay out of it and focus on their research; only a few jump in and get down and dirty. In the meantime, one has to be patient and wait it out.