Counterfactuals

Asking about what might have been can be useful, but is often just a waste of time.

Our astronomer has just finished a popular-science book on physics, concentrating on the fundamentals of particle physics.  We won’t give a full review here, but only note that the author was fond of counterfactuals, that is, asking how things would change if certain aspects of the universe were different.  He mentioned basic constants in particular, like the speed of light (which you’ve heard of), Newton’s gravitational constant, Planck’s constant (which may be new to you), and things like the masses of the electron and proton.

Revising basic constants is a time-honored theme in popular science.  George Gamow famously showed the effect of a slow speed of light and a large Planck in his Mr. Tompkins series.  As a description of what actually happens in situations beyond what we normally experience, his books are remarkably effective.  As an actual description of what would happen if things were to change, they are inaccurate.  For one thing, any serious messing with basic constants would cause people to disappear immediately, so there would be no Mr. Tompkins to see these wonderful things (the stories are presented as dreams in the books).

Changing constants (yes, it’s an oxymoron) are also a subject of serious science.  Paul Dirac suggested a connection between the basic numbers and the age of the universe, a topic worked out in more detail by Sir Arthur Eddington and others.  The hypothesis implies that constants change over time as the universe ages.  Some of the specific numbers they used are now known to be wrong, so the patterns they saw are either not there or must be shifted, but the hypothesis has not actually been conclusively disproven.  Indeed, now and then our astronomer sees a paper reporting that some team of scientists has checked atomic line-ratios in distant objects to see if anything differs from our laboratories.  So far, no change has held up to scrutiny, and firm limits can be put on any variation.

But in the book our astronomer finds the repeated assertion that, if G or h or c were to instantly become something quite different we’d all disappear.  He finds it unedifying.  It doesn’t really make the physics any clearer or more understandable.  That it could actually happen is conceivable, but only somewhere out in the distant fields of untestable speculation.

One could draw the conclusion that, since humans are only possible in a universe where the basic constants are very close to their present numbers, we are either insanely lucky or something/someone has carefully adjusted things.  The hidden assumptions here are that the constants can take on any value, and the ones they have were chosen by a random process.  These are both, at best, just speculations.  Any suggestion about the unlikely universe we live in comes from a poorly-constructed attempt at probability.

We don’t want to discourage speculation as such; it can be remarkably fruitful.  But be careful of the conclusions you draw from it.