Real Particles in a Ghost Universe

I love imagination.  Ergo, I love thought experiments.

I was also inspired to become a physicist by Einstein.  Einstein was famous for his thought experiments.  Ergo, I love thought experiments.

My most recent thought experiment has been to try and flip on its head a way neutrino physicists have of making neutrinos sound as mystifying as they are to us as an object of study.  We call them “ghost particles” inundating our universe.  In fact, I once read an interesting estimate that in the one hour it would take you to read a popular science pamphlet on neutrinos, “about 100,000,000,000,000,000,000 [one hundred million billion] neutrinos [will have] zipped through your body unannounced” (pamphlet p.23).  Which does seem ghost like…and a little creepy.

But I wanted to break free of seeing things according to the usual narrative.  And it occurred to me that we don’t think of particles as ghosts, we think of mist-like people as ghosts.  At which point a thought experiment occurred to me:  supposing I tried to re-vision this weakly interacting state of neutrinos giving primacy to their perspective over mine?  In this case, we would be the ghosts, the mist-like people forms that could be passed right through, if I envision myself as a little neutrino being born in and careening out of a ghost-like sun and whizzing through a ghost-like earth.  Then neutrinos would appear to be “real particles” in a “ghost universe”.  Since neutrinos in the universe outnumber the number of known humans, the neutrino ghost universe is the majority view, compared to our ghost particle minority view.  Which begged the question, could this oddly anthropomorphic thought experiment help inspire me to discover something new?  Or was it the worst thought experiment ever?

Much to my delight, at around the time this idle thought popped into my head I was reading a paper about how Einstein made discoveries by historian of science J. D. Norton.  I wandered to Norton’s webpage and perused his articles when this title jumped right out at me: “The Worst Thought Experiment” in The Routledge Companion to Thought Experiments (there’s a book for that?!).  In it Norton dissects and demolishes a thought experiment by physicist Leo Szilard regarding “Maxwell’s demon” (itself a thought experiment that suggest the second of law of thermodynamics can be violated, i.e., that the entropy of an isolated system can decrease over time) and evolving to include information theory, which became the basis for a line of discussion and thought experiments continuing to today and with articles appearing in Nature and Scientific American.

Whether I agree or not with the particular physics assessment of this particular thought experiment is not important here.  What is of real value is Norton’s canny synthesis of a criteria by which good versus bad thought experiments can be distinguished:

GOOD THOUGHT EXPERIMENT

1. Thought experiment examines a specific behavior that illustrates a more general behavior.
2. Thought experiment idealizes away irrelevant behaviors to highlight relevant behaviors.

BAD THOUGHT EXPERIMENT

1. Thought experiment examines a common behavior that misrepresents general behavior.
2. Thought experiment idealizes away relevant behaviors as irrelevant behaviors.

Here at “The Insightful Scientist” my purpose is always to emphasize practice over philosophy.  So if good thought experiments can help to foster scientific discovery, as Einstein’s case of riding on light beams suggests, and even bad thought experiments can foster scientific activity, as Norton’s Szilard case suggests, then there’s a practice technique for thought experiments embedded in Norton’s criteria.

The technique might look something like this: step 1) come up with what you think is a good thought experiment in your area and do the calculations; step 2) come up with the correlated bad thought experiments, e.g., willfully make nuisance parameters central, use easy extreme cases that are atypical, etc. and do the calculations; step 3) see if your good thought experiment holds up in the face of your bad thought experiment.

To go one layer further, I suspect that the conceptual metaphor embodied mathematics idea I’ve previously mentioned in “The Re-Education of an Educated Mind” is partly at play in deciding good from bad thought experiments.  One key to the use of conceptual metaphor in mathematics is to import, in their entirety, the inferences embedded in the metaphorical source topic and apply them, consistently, to the target topic.  For example, in the Lakoff and Nunez book discussing conceptual metaphors and mathematics they define four grounding metaphors which form the basis of mathematicising sensory-motor experience into mathematics.  One of these is the “Arithmetic Is Object Collection” metaphor (p. 55), which goes like this:

Arithmetic is Object Collection Metaphor by G. Lakoff and R. Nunez

Source Domain (Object Collection)  → Target Domain (Arithmetic)

Collection of objects of the same size → Numbers

The size of the collection → The size of the number

Bigger → Greater

Smaller → Less

The smallest collection → The unit (one)

Putting collections together → Addition

Taking a smaller collection from a larger collection → Subtraction

If one takes their source topic as a kind of physics, like thermal fluctuations in Szilard’s case, and the target as the content of our thought experiment, which was the one-molecule gas machine for Szilard, then Norton’s discussion of Szilard seems to highlight that Szilard did not port over key inferences in a consistent way; hence Szilard’s thought experiment may be a bad one.

Another element of a good thought experiment worth adding to Norton’s focus is that it should not just attempt to visualize an experiment.  It should visualize an experiment where the outcome seems to violate a fundamental assumption or belief.  In other words, thought experiments are about testing conundrums, not just daydreaming.  A more illustrative example of a conundrum and a good thought experiment is the trolley problem from the philosophy of ethics, which tests the idea that “the good of the many outweighs the good of the few” by asking you to make a moral choice between two immoral options.

So back to my little neutrino thought experiment.  It’s easy to see now that it’s actually insufficiently formulated to be a thought experiment at all—there’s no idealized specific behavior as part of the thought.  Even more importantly I also have no concept of “how ghosts behave” to act as an inferential set to import into my thought.  It turns out, what I cited at the beginning of this log entry was just a good old-fashioned visual metaphor and not a thought experiment at all—so it’s an epic fail!  But as I said in “What You Fire Is What You Forge”, failure is key to improvement.  By trying to nail down a more systematic way to evaluate thought experiments I’ve stumbled upon some ideas for how to reformulate bad thought experiments into good ones by pinpointing what makes them bad and improving it.

So, the world of our little mercurial neutrinos, able to spontaneously change their identity at will, is indeed an interesting breeding ground for the pursuit of discovery.  And an epic failure of understanding proved to be a spark point for greater insight.  A team of researcher’s at the University of Chicago may be right: one of the greatest gifts we might be able to give ourselves is a repository of failed attempts.  It turns out that the worst thought experiment may prove to be our best starting point for meaningful insight.