When can we treat certain experimental parameters as free variables?
Consider trying to figure out whether or not a certain drug is efficacious. We design an experiment that proceeds as follow:
- Break a collection of experimental subjects up into two groups randomly.
- To one of the groups give the drug, and to the other give a sugar pill.
- Record how the different groups respond to their different conditions.
- Analyze the results using some kind of statistical method. If the group that took the drug has a significantly better response than the group that didn’t, then tentatively conclude that the drug was effective. Otherwise conclude that the drug was ineffective.
Obviously this is a toy example; I’ve gone into none of the details, and in particular I do not claim that this exhausts our ability to design better experiments. But it will serve as an example for our purposes.
The reason why we might think something like this method would work is that the experimenters intervene on the system, and give different treatments to different groups. By comparing the results, we are trying to infer something about the causal structure of this situation. Whatever the virtues of the particular statistical test and experimental design we end up using, one of the key parts of this situation is that we think this intervention is independent in some some sense from the rest of the situation.
Consider the following case. Suppose we do this experiment, and we get perfect results. By this I mean that everyone who takes the drug gets completely better (or the drug has the maximum intended effect), and the group that takes the sugar pill has no change. Suppose we do this as many times as you like. You can probably feel the pull to the conclusion that the drug is efficacious.
However, suppose I instead offer this hypothesis. There were aliens that were watching Earth, and wanted to mess with us earthlings. So the aliens, using advanced technology, came down, invisible to us, and healed about half of the people that had been chosen for the experiment. They then hacked the brain of the scientists and the randomization process used to divide the group so that the different groups were divided such that the group given the drug was composed of the people the aliens healed, and the people the aliens didn’t heal were in the sugar pill group. Furthermore, anytime we ran another experiment of this drug on Earth the aliens did the same thing.
This hypothesis also explains the data perfectly. However, it is clear that in this case we cannot make the inference that the drug works. The drug itself could be totally ineffective.
Now, at this moment a word might come to mind.
In this case, the experimental parameters were not free variables, since they were determined by the aliens. Thus, the inference we wanted to draw was undermined.
Now this might seem silly. Again, conspiratorial. No one in their right mind would have this as a viable hypothesis for the situation. Not just because of the aliens, mind you, but because the hypothesis the drug works does not seek to describe the rest of the world. Thus, baring any additional information about aliens and what have you, the kind of hypothesis we care about is not one that lends itself to conspiratorial analysis.
How about in the case of physics? Unlike the drug case, physics seeks to describe the whole world. The world includes the experimenters. When we are evaluating a physical theory, can we treat the experimental parameters as free variables?
This is one of the central questions of physicist John S. Bell’sFree variables and local causality.
***The original paper can be found here.***
In Epistemological Letters Bell had argued that quantum mechanics is not locally causal. By this he means that quantum mechanics allows for distant physical systems to affect each other. This violates the locality constraints of special relativity.
His argument relies on treating some experimental parameters as free variables. In particular, you need two humans (or at the very least measuring devices) at physically separated conditions who can choose which quantity of a physical system to measure (x as opposed to y spin, for example). If this condition (more technically specified, and with the correct way of setting up the experiment) is satisfied then, Bell showed, quantum mechanics is non-local.
In Free variables and local casuality Bell is responding to critics of his argument. In particular, Clauser, Horne, and Shimony (CHS) in Epistemological Letters disagree that we can treat the experimental parameters as free variables.
In the context of this thought experiment (the one in which Bell argues quantum mechanics violates local causality) a free variable is one of which there is no record. We can see what this means in the context of the alien experiment. In that case, there are certainly records. In particular, the most relevant record of choice of which person goes in which group is the set of people whom the aliens healed. It is because of this particular record that we cannot make the inference that the drug was effective. Similarly, in order for Bell’s argument to work there has to be no kind of “common hidden mechanism” (p. 1) correlating the results of the experiment for the spatially separated physical systems. Otherwise, in Bell’s words, “the apparent non-locality could be simulated” (p. 1).
Of course, in this case the idea is not that something like aliens might be the common hidden mechanism, but rather something in the nature of physics itself. Perhaps, for example, the starting conditions of the universe are such that whenever someone makes a choice of which quantity to matter, there will be no case in which non-locality occurs; it would be only simulated.
In order to defend this assumption, the one that rules out these kind of physical conspiracies, Bell appeals to a distinction betwen “analyzing various physical theories, on the one hand, and philosophizing about the unique real world on the other hand” (p. 2). He points out that when it comes to the actual physical world we can never in reality see what would have happened had we done something different. This is a problem of counterfactuals. In particular, we cannot ever repeat the same experiment twice. In Bell’s poetic words, “the hands of the clock will have moved, and the moons of Jupiter” (p. 2). Using the theory, in this case of quantum mechanics, we calculate the consequences of changing different free parameters in a hypothetical physical situation. We can then evaluate the theory partially on what it predicts will happen under these different hypothetical conditions.
Thus, on Bell’s picture of how we do theoretical physics, it is part of the methodology to see what the theory dictates in different physical setups. Thus, for the purposes of doing theoretical physics, we must be able to treat certain things in certain contexts as free variables.
The paper is short, and rewards reading. In particular, it is an interesting investigation of the methodology of theoretical physics. If Bell is right, then we must avoid such conspiratorial thinking in physics, for the sake of effective methodology.