Spekkens' 'Toy Theory'

I just read the paper about Spekkens' 'Toy Theory' of quantum mechanical phenomena. I had heard about this paper from the interview with Fuchs, where the paper is cited as being a support of the quantum bayesianism interpretation. I was not disappointed. This essay is awesome, and I think it is going to be seen as one of the most influential papers in in recent history. 

You should go read it here.

That's not to say that I think it is right in what it argues. Far from it, I think that the essay is fundamentally mistaken in many ways, though it is a smart and insightful fresh take on the subject. I think that there is much to learn from it, despite being at heart incorrect.

The paper's main goal is is argue that quantum states are epistemic and not ontic. Essentially, this is a claim against the realist interpretation of quantum mechanics. Ontic, here means that it is a theory which describes real objects in the world in a reliable way. The opposite of this is to claim that, though it enjoys predictive success, quantum mechanics at its base does not exactly describe the world. It is only a phenomenological theory, in a sense. It gives a scientist the means to predict how the world will behave, but it does so in a kind of incidental way. Phenomenological theories do not give causal accounts of why things behave the way they do, just a way to know what they will do. These types of theories are missing the causal mechanism that explains what happens.

Get it? Toy theory?

The alternative is epistemic, which is a version of non-realism that is plausible for quantum mechanics. Essentially, it claims that quantum states are not physical states, but are rather states of lack of information. Instead of encoding something about the world, the superposition of Schrödinger's cat just describes the information that we are lacking: the life or death state of the cat. Epistemic interpretations of quantum mechanics argue that quantum mechanics does not describe the real world, just a kind of lack of information about the world. Quantum Bayesianism is one of the more well known epistemic interpretations of quantum mechanics. 

This distinction between epistemic and ontic interpretations is a false dichotomy: it's not necessary that an interpretation fall into either of these categories. Furthermore, the dichotomy has a latent presupposition, but that is the subject of a later post.

Quantum states come in two different varieties: 'pure' and 'mixed' quantum states. A 'pure' q-state is essentially just a a quantum system described by one state vector in a superposition. 'Mixed' states are when a quantum system is described by multiple state vectors. A common view of many philosophers of science is that pure q-states are ontic, while mixed q-states are considered epistemic since they are just states of incomplete knowledge about what pure state a system is in. Spekkens argues that both pure and mixed q-states, however, are epistemic.

He claims that the epistemic view of q-states is superior to ontic view because certain phenomena like interference, noncommutivity, entanglement, no cloning, teleportation, etc. are mysterious in the ontic view seem natural in the epistemic view.

The success of this argument is a mixed one. On the one hand, this toy theory is useful for understanding some aspects of quantum phenomena. I think that it indeed is useful precisely because there is something true to it.

But I don't think Spekkens' claim is, strictly speaking, a fully true one. While it can be used for insight, the toy theory does not replace quantum mechanics in predictive power. This is why his argument is misleading: the toy theory cannot account for the list of phenomena above. For example, you cannot apply the toy theory alone to the situations which give rise to quantum interference phenomena. Quantum mechanics is capable of making empirical predictions, but the toy theory simply piggy-backs on those predictions.

This means that the toy theory is not a replacement of quantum mechanics in any way. This should be a red flag: scientific endeavors aim for predictive power. The 'toy theory' may be a strong philosophical aside, but it clearly requires another step backwards in understanding before we can go forwards.