Lorentz–Fitzgerald Contraction and The Ad Hoc Defense of Theories

While reading Conjecture and Refutations (p. 333) Popper noted that initially Newtonian physics was defended from the results of the Michelson and Morley experiment — the famous experiment where they found the speed of light to be constant regardless of the direction the earth was moving from the sun — via something known as Lorentz-Fitzgerald Contraction. Prior to reading this, I wasn’t aware of Lorentz-Fitzgerald Contraction.

Newtonian physics predicts that there is no maximum speed, yet here we had an experiment that showed light’s speed unchanged whether you were moving towards the light or away from it. Lorentz and Fitzgerald solved this problem by hypothesizing that objects moving in a direction contract but only in the direction of motion.

Wikipedia says that Lorentz and Fitzgerald actually came up with this explanation to save Lorentz’s theory of stationary ether.

In other words, this theory was entirely ad hoc as a means of saving the theory of ether but also “saved” Newtonian physics using the same explanation.

This is a good example of how a single observation that runs counter to a theory can never truly falsify it due to the Duhem-Quine thesis. Newtonian physics was incorrect, but at the time of Lorentz you couldn’t have known that only via the Michelson and Morley experiment (even though it contradicted Newtonian physics) because Lorentz-Fitgerald contraction might turn out to be correct.

This is also a good example of why ad hocs explanations are bad explanations. An ad hoc conjecture that entities contract in the direction of motion leaves a large explanation gap. Why do they contract? And how does Newtonian physics explain it? These two problems make it a bad explanation. As Popper put it:

…a good theory is not ad hoc. The ideas of adhocness and it’s opposite, which may perhaps be termed ‘boldness,’ are very important. Ad Hoc explanations are explanations which are not independently testable; independently, that is, of the effect to be explained. They can be had for the asking, and are therefore of little theoretical interest.

Objective Knowledge, p. 15-16

I’ve used this argument in various forms in the past when ad hoc explanations are advanced against my arguments. [1] Deutsch suggests that ad hoc explanations are research projects rather than explanations. They are possible ways to solve the problem if you can turn it into a good (non-ad hoc) explanation in the future. They are not themselves good explanations. Deutsch says:

But in any case, the existence of a problem with a theory has little import besides, as I said, informing research programmes – unless both the new and the old explicanda are well explained by a rival theory. In that case the problem becomes grounds for considering the problematic theory tentatively refuted. Therefore, to meet criterion (iii) above [i.e. “it could easily be adapted to account for anything (so it explains nothing)], it must not be protected from such a refutation by declaring it ad hoc to be unproblematic. Instead any claim that its apparent flaws are not real must be made via scientific theories and judged as explanations in the same way as other theories.

The Logic of Experimental Tests, Particularly of Everettian Quantum Theory, p. 10

Note how this makes ad hoc explanations bad explanations because they fail against the hard-to-vary criteria. So ad hoc explanations are directly related to the hard-to-vary criteria.

This implies that we need to take our ad hoc explanations seriously and not use them simply as ways to dismiss ideas we don’t agree with. If we are forced to use an ad hoc explanation we are, in a sense, admitting to the existence of a problem with our preferred theory. Further, we need to not stop at merely making the ad hoc explanation, but instead follow it up with how to turn it into a full explanatory theory that can be tested against it’s competitors.

In fact, this is what happened with Lorentz–Fitzgerald Contraction! Einstein’s Theory of General Relativity incorporated (and entirely subsumed) Lorentz-Fitzgerald contraction into that theory such that it was no longer an ad hoc explanation. But did so by replacing Newtonian physics altogether.

This is an example of how ad hoc explanations are bad explanations, but not necessarily false explanations.


[1] I do not have permission to quote the discussion in question, but it was regarding this post that I made about face blindness. I claimed that face blindness was a problem (though presumably soluble one) for the idea that the existence of Universal Explainers means brains do not have ‘parts’ because if we learn to recognize faces via our “Universal Explainer” module, then we should be able to relearn how to recognize faces if that module is lost due to physical damage.

The following arguments were made to show that I was incorrect and that this was not even a problem:

  1. Perhaps adults just have a hard time creatively reconstructing modules they previously had.
  2. Perhaps some adults do relearn face recognition but do so quickly such that we think they never lost it.

Both of these are ad hoc explanations in that they are meant to reduce testability and are not themselves testable. In addition, they aren’t predicted by our current understanding of Universal Explainer theory (that is to say, they aren’t explained by Universal Explainer theory) and they each have large explanation gaps. For example, why do adults have a hard time re-learning abilities they gained as a child when children do not? And why do adults either never re-learn face recognition or re-learn face recognition so quickly that we can’t tell they lost it? It’s not hard to tell these explanations were only meant to save the preferred theory and weren’t being put forward as true testable alternatives.

The ad hoc nature of these arguments makes them bad explanations because they are easy-to-vary. As Popper put it, ad hoc explanations can be had for the asking. So the mere fact that you can think of one means basically nothing. But they may very well be good research projects.

The important thing is that you never allow an ad hoc explanation to simply be a final rebuttal to a problem or no problem will ever be a problem. This would make all our theories easy-to-vary. You must always take your own ad hoc explanation seriously and think about how it could be tested and integrated into the full theory.

One could imagine a future theory of Universal Explainers that is far more developed where it becomes obvious why adults can’t relearn face recognition and it just follows from the explanation.

I should also note that my own proposed solution to the problem (that face recognition is not part of the Universal Explainer module) is itself ad hoc at this point and is really a research project too. We have to start somewhere.

Ad hoc explanations, if taken seriously, actually can be improved upon and eventually make interesting predictions that allow them to move forward. For example, my conjecture predicts that we’ll find that Universal Explainer modules are less efficient learners compared to some non-explanatory Machine Learning-like modules. (Something that is not true today!) More likely, my conjecture was just wrong.

But the problem I was advancing really is an existing problem and the ad hoc nature of the responses demonstrates this.

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