There are a bunch of ways to “win the argument” or just clear up the students’ object-level confusion about mechanics:
Ask them to predict what happens if the experiment is repeated with the stand held more firmly in place.
Ask them to work the problems in their textbook, using whatever method or theory they prefer. If they get the wrong answer (according to the answer key) for any of them, that suggests opportunities for further experiments (which the professor should take care to set up more carefully).
Point out the specific place in the original on-paper calculation where the model of the pendulum system was erroneously over-simplified, and show that using a more precise model results in a calculation that agrees with the experimental results. Note that the location of the error is only in the model (and perhaps the students’ understanding); the words in the textbook describing the theory itself remain fixed.
Write a rigid body physics simulator which can model the pendulum system in enough detail to accurately simulate the experimental result for both the case that the stand is held in place and the case that it falls over. Reveal that the source code for the simulator uses only the principles of Newtonian mechanics.
Ask the students to pass the ITT of a more experienced physicist. (e.g. ask a physicist to make up some standard physics problems with an answer key, and then challenge the students to accurately predict the contents of the answer key, regardless of whether the students themselves believe those answers would make good experimental predictions.)
These options require that the students and professor spend some time and effort to clear up the students’ confusion about Newtonian mechanics, which may not be feasible if the lecture is ending soon. But the bigger issue is that clearing up the object-level confusion about physics doesn’t necessarily clear up the more fundamental mistakes the students are making about valid reasoning under uncertainty.
I wrote a post recently on Bayesian updating in real life that the students might be interested in, but in short I would say that their biggest mistake is that they don’t have a detailed enough understanding of their own hypotheses. Having failed to predict the outcome of their own experiment, they have strong evidence that they themselves do not possess an understanding of any theory of physics in enough mechanistic detail to make accurate predictions. However, strong evidence of their own ignorance is not strong evidence that any particular theory which they don’t understand is actually false.
The students should also consider alternatives to the “everyone else throughout history has been rationalizing away problems with Newtonian mechanics” hypothesis. That hypothesis may indeed be one possible valid explanation of the students’ own observations given everything else that they (don’t) know, but are they willing to write down some odds ratios between that hypothesis and some others they can come up with? Some alternative hypotheses they could consider:
they are mistaken about what the theory of Newtonian mechanics actually says
they or their professor made a calculation or modelling error
their professor is somehow trolling them
they themselves are trolls inside of a fictional thought experiment
They probably won’t think of the last one on their own (unless the rest of the dialogue gets very weird), which just goes to show how often the true hypothesis lies entirely outside of one’s consideration.
(Aside: the last bit of dialog from the students reminds me of the beginner computer programmer whose code isn’t working for some unknown-to-them reason, and quickly concludes that it must be the compiler or operating system that is bugged. In real life, sometimes, it really is the compiler. But it’s usually not, especially if you’re a beginner just getting started with “Hello world”. And even if you’re more experienced, you probably shouldn’t bet on it being the compiler at very large odds, unless you already have a very detailed model of the compiler, the OS, and your own code.)
There are a bunch of ways to “win the argument” or just clear up the students’ object-level confusion about mechanics:
Ask them to predict what happens if the experiment is repeated with the stand held more firmly in place.
Ask them to work the problems in their textbook, using whatever method or theory they prefer. If they get the wrong answer (according to the answer key) for any of them, that suggests opportunities for further experiments (which the professor should take care to set up more carefully).
Point out the specific place in the original on-paper calculation where the model of the pendulum system was erroneously over-simplified, and show that using a more precise model results in a calculation that agrees with the experimental results. Note that the location of the error is only in the model (and perhaps the students’ understanding); the words in the textbook describing the theory itself remain fixed.
Write a rigid body physics simulator which can model the pendulum system in enough detail to accurately simulate the experimental result for both the case that the stand is held in place and the case that it falls over. Reveal that the source code for the simulator uses only the principles of Newtonian mechanics.
Ask the students to pass the ITT of a more experienced physicist. (e.g. ask a physicist to make up some standard physics problems with an answer key, and then challenge the students to accurately predict the contents of the answer key, regardless of whether the students themselves believe those answers would make good experimental predictions.)
These options require that the students and professor spend some time and effort to clear up the students’ confusion about Newtonian mechanics, which may not be feasible if the lecture is ending soon. But the bigger issue is that clearing up the object-level confusion about physics doesn’t necessarily clear up the more fundamental mistakes the students are making about valid reasoning under uncertainty.
I wrote a post recently on Bayesian updating in real life that the students might be interested in, but in short I would say that their biggest mistake is that they don’t have a detailed enough understanding of their own hypotheses. Having failed to predict the outcome of their own experiment, they have strong evidence that they themselves do not possess an understanding of any theory of physics in enough mechanistic detail to make accurate predictions. However, strong evidence of their own ignorance is not strong evidence that any particular theory which they don’t understand is actually false.
The students should also consider alternatives to the “everyone else throughout history has been rationalizing away problems with Newtonian mechanics” hypothesis. That hypothesis may indeed be one possible valid explanation of the students’ own observations given everything else that they (don’t) know, but are they willing to write down some odds ratios between that hypothesis and some others they can come up with? Some alternative hypotheses they could consider:
they are mistaken about what the theory of Newtonian mechanics actually says
they or their professor made a calculation or modelling error
their professor is somehow trolling them
they themselves are trolls inside of a fictional thought experiment
They probably won’t think of the last one on their own (unless the rest of the dialogue gets very weird), which just goes to show how often the true hypothesis lies entirely outside of one’s consideration.
(Aside: the last bit of dialog from the students reminds me of the beginner computer programmer whose code isn’t working for some unknown-to-them reason, and quickly concludes that it must be the compiler or operating system that is bugged. In real life, sometimes, it really is the compiler. But it’s usually not, especially if you’re a beginner just getting started with “Hello world”. And even if you’re more experienced, you probably shouldn’t bet on it being the compiler at very large odds, unless you already have a very detailed model of the compiler, the OS, and your own code.)