COMMENT: CRITICAL POINT

Too confident about uncertaintyWhy is Heisenberg's uncertainty principle misused in popular culture, asks Robert P Crease

Werner Heisenberg has a lot to answer for.As one of the founders of quantum me-chanics, he left a huge legacy to physics. Asthe inventor of the uncertainty principle, healso left a huge legacy outside physics. AlbertEinstein may be more widely recognized bythe public - and his theory of relativity oftenappears in popular culture - but it is Hei-senberg who has had the greater impact onpublic discourse.

But then browse tfirough any bookshop's"new-age" section and you'll find peculiarstatements about the uncertainty principle,including the claims that its implications arepsychedelic and that it heralds cultural revo-lution. Strange interpretations turn up evenin academic circles, as in the following con-versation, published in American Theatre, be-tween the theatre director Anne Bogart andKristin Linklater, the noted vocal coach.

Linklater: "Some thinker has said that thegreatest spiritual level is insecurity."

Bogart: "Heisenberg proved that. Madi-ematically."

Linklater: "There you are."Some scientists and historians have ar-

gued that the word "uncertainty" is mislead-ing, and have debated other possible names.Nevertheless, that is only a part of the prob-lem. Some 75 years after the formulation ofthe uncertainty principle, why is its meaningstill so obscure?

Uncertainty and incompletenessConventionally, we expect a complete the-ory to say something about reality. Most the-ories that physicists teach and use, however,fall short. For example, what one of myphilosophy colleagues calls a "harmlesslyfudging theory", such as the ideal-gas law,ignores well understood things (van derWaals forces, hard-core repulsion) becausetalking about an ideal, rather than a real,object buys us something (ease of applica-tion). Meanwhile, a "harmlessly incompletedescriptive dieory" omits aspects of the sub-ject matter diat remain to be filled in. Suchtheories are harmless because these limita-tions do not threaten normal assumptionsabout the world.

The uncertainty principle is incomplete ina different sense. A mathematical relation, itis a feature of the statistical interpretation ofthe wavefunction in quantum mechanics. Itmakes no reference to any underlying phys-ical picture; there are no references to wavesor particles, nor to physical experiments. It isnot obvious what it refers to, except possiblythe clicks of a detector.

This is strange, but why? The strangenessof the uncertainty principle is not due to the

Weird stuff - quantum strangeness is hard to grasp

measurement process disturbing die objectmeasured, which would be a feature of anyNewtonian theory involving the exchangeof particles. Nor is die strangeness due tothe diings we observe being functions ofwhedier or not we observe die data pre-sented. Nor is it due to the fact diat it ad-dresses statistics. Radier, the strangeness ofquantum mechanics is that quantum for-mulations are not "about" a real object inthe conventional sense, or even what wetiiink of as an ideal object.

In classical physics, deviations of meas-ured quantities from ideal norms are treatedindependendy in a statistically based dieoryof errors. But the variations — statistical dis-tribution - of quantum measurements aresystematically linked in a single formalism.The wave formulae of quantum mechanicsare thus not about an ideal object, but aphysical situation in which die real objectis placed, which admits numerous potentialexperimental realizations.

The wavefunction thus describes a situ-ation diat is imperfect as a fact of die realworld. One needs to "make" or "bring" thatsituation into the real world in a specific con-text- and die choices diat one makes regard-ing what to measure and how to measure itaffect die "fact" that one is measuring. Or, ifone tries to think of die wavefunction as areal object - one of my physics colleagueslikes to think of it, for instance, as die squareroot of die charge density widi a phase - it'sstill not at all a visualizable one and behavesvery counterintuitively.

The search for picturesEinstein, famously, could not stomach that.In a complete dieory, he wrote in 1935 widiBoris Podolsky and Nadian Rosen, "everyelement of die physical reality must have acounterpart in die physical theory". Ein-stein tried to argue, unsuccessfully, diat die

incompleteness of quantum mechanics wasa flaw revealing diat diere had to be more tobe discovered: so-called hidden variables,die discovery of which will make its formu-lations refer direcdy to die real world.

Niels Bohr accepted the incompletenessof quantum mechanics, but argued diatposition and momentum were inherendyclassical concepts. While necessary for ushumans, diey were inapplicable to events indie microworld except in loose and, stricdyspeaking, inaccurate ways. Heisenberg ini-tially diought diat the right approach wasessentially to redefine die meaning of wordslike "position" and "momentum". How-ever, he later abandoned this effort, even-tually agreeing widi Bohr. Neverdieless, henever stopped trying to find imaginativephysical models for the uncertainty prin-ciple. Bohr, meanwhile, austerely and rigor-ously opposed diis.

The critical point"Everyone understands uncertainty. Ordunks he does," says die Heisenberg charac-ter in Michael Frayn's play Copenhagen. Theremark is ironic. Heisenberg himself some-times misrepresented the meaning of hisprinciple in his relendess quest to seek phys-ical, real-world models for it. In diat questlies much of die trouble.

But die quest is inevitable. Nobody under-stands a fact or principle nakedly, but onlyby connecting it with what else they alreadyknow. Scientists, whose minds are filled widimany different kinds of models, have aneasier time connecting die uncertainty prin-ciple with odier aspects of their training.This is much harder for non-scientists, dueto the "impedance mismatch" between thelanguage of the uncertainty principle anddie language in which non-scientists habitu-ally speak, with its heavy reliance on phys-ical analogies. Much information is lost indie process, and much distorted.

The challenge in explaining die meaningof die uncertainty principle to non-scientiststhus does not amount to hitting on die rightpicture or analogy, but in die seeminglyimpossible task of explaining die novel re-lation it involves between theory and theworld. But it is important to try, for other-wise there will continue to be informationloss and distortion in the public understand-ing of die uncertainty principle. Heisenbergproved diat. But not madiematically.

Robert P Crease is in the Department of Philosophy,

State University of New York at Stony Brook, and

historian at the Brookhaven National Laboratory,

US, e-mail rcrease@notes.cc.sunysb.edu

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