Recognizing limitations: mathematics and the classical world

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…)

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One Response to “Recognizing limitations: mathematics and the classical world”

  1. Neil Bates Says:

    These are good points. As for the issue of quantum representation, note that MWI tries to bring back the lost determinism by saying that actually the wave function continues to evolve without “collapse”, but all superpositions are actualized. So to them there’s no failure to have a unique output from a given starting point (that starting point being a given WF distribution.) However they still can’t derive the Born Rule because with e.g. two splits you have to contrive to claim unequal probabilities like 64%:36%.

    However it’s worse than that, since the MWI idea doesn’t deal with the reallocation of amplitude cause by Renninger-style null measurements (the sort discussed in the E-V Bomb test downblog.) If a “good detector” (the very phrase already hints at further complications) makes no hit where the photon might be, then the photon perforce must be elsewhere. Hence the WF must suddenly rearrange to show full amplitude elsewhere, before a true measurement (click, the localization of cliche quantum measurement) even took place! (We presume the traditional superposition is of absorption at the obstruction v. absorption at the far detector – but neither took place when the reallocation occurred.)

    That ruins the idea of continued unitary evolution either in traditional QM (where UE continues until collapsed entirely by a definite “yes” measurement) or in MWI (where UE continues and the different outcomes always exist but somehow – how? – are separated.) That is since the WF is still spread out but has been concentrated in a different configuration. This is not the superposition of different measurements since actual detection hasn’t happened yet. Note further mischief comes from using unreliable detectors. What does a report or null result from them do to the WF?

    BTW regarding math as representation and per it’s use in thinking: see my latest post of how computational intelligences (like “AI”) wouldn’t even be able to represent substance versus conceptual models themselves. IOW, forced into MUH. (http://tyrannogenius.blogspot.com)

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