Archive for September, 2010

Recognizing limitations: mathematics and the classical world

Posted in Uncategorized on September 4, 2010 by quantummoxie

It’s close enough for horseshoes and hand grenades.

Or so the saying goes.  Yet, apparently, we seem to think classical physics is an exact science.  As Peter Byrne says in his book on Hugh Everett,

Quantum mechanics differs from classical physics in this: if you can exactly record and reproduce the initial conditions of a classical experiment (dropping a cannonball from a tower, say), then, every time you exactly repeat the set-up of that experiment, the results will be exactly the same.

I suppose the word ‘exactly’ is his caveat.  Nevertheless, we often fall back on this theoretical certainty as actually achievable.  But is it?  No, because increasing the accuracy (and repeatability) of classical experiments necessarily pushes them closer to the quantum domain!  The most accurate physical theory is not Newtonian mechanics or Maxwellian electrodynamics, it’s quantum electrodynamics (QED) which (as the name suggests) is a quantum theory, not a classical one (the theory matches experiment to within ten parts per billion (10−8)).  But when thinking classically, we’re used to allowing a bit of room for error.

Or maybe, as I’ve railed about on this blog before, we’ve fallen into the trap of assuming that mathematics is somehow a perfect model of reality.  Or, rather, it’s not even a model at all, it simply is reality.  This is not just a problem in physics, by the way.  This is a problem – and a growing one – in many areas.  Some would say it is what led to the recent economic meltdown – an over-reliance on the “reality” of mathematics.  As the aforementioned Hugh Everett once said,

[W]hen a theory is highly successful and becomes firmly established, the model tends to become identified with ‘reality’ itself, and the model nature of the theory becomes obscured [see Byrne’s book, p.72].

Once we have granted that any physical theory is essentially only a model for the world of experience, we much renounce all hope of finding anything like ‘the correct theory.’  There is nothing which prevents any number of quite distinct models from being in correspondence with experience (i.e. all ‘correct’), and furthermore no way of ever verifying that any model is completely correct, simply because the totality of all experience is never accessible to us [see Byrne, p. 92].

This does not mean we should accept crackpot theories with no basis in real science.  Nor does it mean science is necessarily subjective.  As noted above, QED is incredibly accurate.  What it does mean, is that we need to stop arrogantly believing that ‘our’ theories (and thus no one else’s!) are how the world really works.  As Aage Peterson summarized regarding Bohr’s ideas (who Everett ironically tried to counter),

It is wrong to think that the task of physicists is to find out how nature is.  Physics concerns what we can say about nature [Byrne, p.89].

In other words, the limits of physics are ultimately the limits of humanity.  Physics – and mathematics – are human constructs.  They are highly accurate and predictive, but nevertheless they are just models (for the most part).  This should not be used as an excuse to disregard science, however.  As I said, science is extraordinarily accurate and predictive (when done right) and the evidence should speak for itself.  But don’t arrogantly assume it corresponds to reality.

(And, yes, I am in the midst of reading Byrne’s book, if you couldn’t tell…)