Rob Spekkens is a theoretical physicist who works on the foundations of quantum mechanics, which means that he thinks a lot about the meaning of experiments in quantum mechanics: what experiments are for, their relationship to theory, and how to build better ones. In a recent talk (June 2017, ETH Zurich) he distinguished between the three best reasons for doing experiments in physics:
- don’t know what we’ll find (e.g. in cosmology)
- adjudicate between competing theories
- identify phenomena that resist explanation in current theoretical paradigm
and two less good (but still valid) reasons:
- doing it improves our own understanding
- helps us develop technology based on the theory
I understand Rob’s reason for distinguishing the two sets of reasons (he thinks many experiments in quantum physics are unnecessary, since all they do is confirm the standard theory), but for the purposes of this post I won’t distinguish between the two sets. A gold-standard physics experiment should satisfy all five reasons, and they all reflect some pragmatic aspect of “what an experiment is”.
Speaking of pragmatics, Rob also has a wonderful little diagram illustrating how the different aspects of physics—realist, empiricist, and pragmatist—interact in quantum mechanics. There’s the realists, dominated by theoreticians, who construct all those pretty interpretations of physics and claim, “this is how the real world works”. There’s the empiricists, who analyze the data, come up with all the probability tables and say “whatever ‘real’ means, these are the probability tables that work; when you do A, you get B back (this percent of the time)”. And finally there’s the pragmatists: whatever the probability tables or Hilbert spaces or diagrams are telling me, they should help me propose a concrete experiment or solve a concrete engineering problem.
How different traditions in physics interact to produce (the field of) physics. Courtesy of Rob Spekkens.
I love this diagram! First, let’s recognize what it is: it is a structural, pragmatic account of physics research. It’s structural because it decomposes physics into these three different traditions, and tells us about their interaction. It’s pragmatic because it talks about how to understand and build actual experiments, and because it has a giant atomic symbol to represent all the other practical stuff! To be clear, I don’t think Rob would say that only pragmatists design experiments, only that experiments in the lab are ultimately ground in complex stuff like lasers, beam splitters, and measurement devices that go beep; “axiomatization from pragmatic principles” means taking the complex stuff in the lab and operationalizing it into abstract stuff like probability measures, unitary operators, and even “observers”. In return, a list of the abstract stuff can be converted directly into laboratory procedures.
In this post (adapted from a recent talk I gave at the Rethinking Workshop), I’d like to spend some time thinking about the following question: how can we build a “higher-order” model not only of the physical theories but of the physical experiments which test those theories, so that we can ground out “physical interpretations of theories” (e.g. interpretations of quantum mechanics) in terms of their pragmatics, i.e. the experiments they suggest?
(This post is currently in progress!)
Thought experiments ∩ real experiments
The foundations of quantum mechanics concerns itself with interpretations of quantum mechanics. Examples of interpretations include (in rough order from realist to idealist) the Everett “many-worlds” interpretation, the Copenhagen interpretation, a variety of models involving decoherence, the “new” Copenhagen intepretation, the relational interpretation of Rovelli, and quantum Bayesianism aka QBism. Two things to note: (1) most, if not all, of these interpretations stem from the measurement problem in quantum mechanics—how does a continuous wave function that outputs a superposition of probabilities at all times always give rise to a discrete, “pure” output when measured in an experiment?—and (2) every interpretation agrees on the “quantum mechanics” part, meaning all the experiments and all the predictions of quantum theory. (As one physicist told me, quantum field theory is a non-interacting theory or “black box” theory: it predicts outputs based on inputs, and says nothing about the interactions between particles).
Statement (2) above implies that it is very difficult to design and run real experiments that can distinguish between different interpretations of quantum mechanics. On the other hand, there are some classic thought experiments that can illustrate their differences, e.g. Schrodinger’s cat, Wigner’s friend, and extensions thereof. However, none of them completely rule out any interpretation—they are ways of refining our intuitions about different interpretations, and testing the consistency of our theory (in this case, quantum theory) across the full range of possible experimental scenarios, not merely the ones that we see. These experimental scenarios often go like, “suppose the universe had no mass,” “ignore all fluctuations in the system,” “suppose we apply a unitary evolution to Wigner’s friend,” or “suppose all cows were perfect spheres.”
I want to make pragmatic distinction between thought experiments and real experiments. Typically, theoretical physicists construct thought experiments and write papers about thought experiments; these papers go like […]. Typically, experimental physicists construct real experiments and write papers about real experiments; these papers go like […]. Note that this is a pragmatic distinction.
Thought
I believe (though I accept that it could be argued otherwise).
if only at the level of what goes into . There is no avoiding the operational perspective; real experiments are embedded within vastly more complicated engineering environments, and we can’t hope to model all of the decisions that go into constructing a laboratory.
but at the end of the day each real experiment does something: confirms or denies some isolated feature of a theory. I want to consider the functional role of experimentation in the verification of theories and in the construction and revision of mathematical models.
… TBC!
Correspondences
Fix a theory. A simple experiment tests some isolated feature of that theory. More complicated experiments (like the LHC) can be used to test many different features of that theory. Is there a way of composing many simple experiments into a more complicated experiment? Dually, is there a way of decomposing a complicated experiment into many simple experiments?
In what follows, I will call an ensemble of experiments a correspondence. This post is as much about defining ensembles of experiments as it is about defining experiments, since constructing correspondences, to me, is a generalization of another question of immediate interest: how does one combine different learning algorithms?
A higher-order model of the form above should suggest, among other things, a way to not only design single experiments for isolated features of physical theories, but to “co-design” entire ensembles of different experiments based on different interpretations.
% experiments set constraints on interpretations, but they also help us “practice” in the real world. The real world suggests new “laws” and “axioms” based on what works in the lab, while theory suggests new sorts of experiments to run.
Experiment as intervention
% Bayesian inference, do-calculus, Judea Pearl
What is a statistical model?
% McCullaugh