Encounters and disagreements between science, culture and language
Heisenberg’s so called uncertainty principle is one of the aspects of quantum physics that has enjoyed considerable cultural popularity for nearly a century. We will comment its meaning and shortcomings through a dialogue between a physicist and an artist, starting from a sample of the abusive interpretations to which this theme has given rise, in philosophy — from epistemology to metaphysics — but also in politics, economics, aesthetics, etc. We will then examine the reasons for the confusion that still surrounds this theme and discuss the terminological uncertainties it has encountered. Finally, we will assert that these ‘Heisenberg inequalities,’ as they have been more soberly renamed, not only cannot be interpreted as limiting scientific knowledge, but, when properly understood, actually open up specific modes of understanding quantum physics.
A., an artist, is exchanging here with his friend P., a physicist.
A. — You know how curious I am about quantum theory, which our many discussions have not yet satisfied. Today, I found a quote in an old art magazine that has prompted me to revisit the subject, as it suggests that one of your most famous ideas may not only apply to the microscopic physical world, but could also have implications in the field of aesthetics. Here it is: “When American author Michael Crichton studies contemporary American painter Jasper Johns, he refers to Werner Heisenberg’s “Uncertainty Principle”. In 1927, Heisenberg discovered that it was impossible to measure both the speed and position of an atomic particle (…). On a philosophical level, the realisation that certain aspects of the physical world could not be known — that they are an insoluble dilemma — came as a shock. The ambiguity of Jasper Johns’ works belongs to this school of thought.”[1] I do not understand the relationship between Jasper John’s work ambiguities and Heisenberg’s uncertainties, but I find the suggestion most stimulating. Perhaps you will explain it to me?
P. — I certainly cannot, as I find it completely nonsensical. In fact, I could provide you with a whole truckload of such quotations, attempting, since a century now, to apply what is wrongly called the Uncertainty Principle in all fields, from sociology to metaphysics, economics and politics. Here’s an example: “An atom is ‘free’ within the limits of Heisenberg’s uncertainty principle (…). So when a message of extrasensory perception, in the form of mindons, psitrons or whatever you like, touches a neuron in unstable equilibrium, it operates at the level of quantum uncertainty and can, if I may say so, work miracles.”[2] If I had to choose, I would prefer Dalí’s provocation: “And I, for one, the rabid paroxyst of imperialist precision, find nothing in the world as sweet, pleasant, restful and even graceful as the transcendental irony implied by Heisenberg’s uncertainty principle.”[3] However, in all these cases, it is simply a matter of misuse of language, shamelessly exploiting the authority attributed to the natural sciences.
A. — But the fact remains that it was physicists themselves who introduced this term, which you will agree is ambiguous in its generality and lends itself easily to such misuses.
P. — I readily plead guilty on behalf of my profession, which often lacks caution and precision in its statements, content to rely on its mathematical equations while neglecting their linguistic statements, which nevertheless carry meaning — good or bad. However, a few physicists had warned against this laxity from the very beginnings of quantum theory: “The immediate effect [of the uncertainty principle] will be to open the floodgates to a veritable deluge of intellectual licence and debauchery (…). [It will become] the basis for an orgy of rationalisation. [We will find in it] the substance of the soul, the principle of vital processes, the agent of telepathic communication. Some will find in the failure of the physical law of cause and effect the solution to the old problem of free will, while conversely atheists will see in it the justification of their conception of a world governed by chance.”[4]
A. — But isn’t this terminology quite natural for physicists, for whom taking into account the inevitable uncertainties of any measurement is a tool of their trade and one of their characteristic assets?
“In all these cases, it is simply a matter of misuse of language, shamelessly exploiting the authority attributed to the natural sciences.”
P. — Natural, perhaps, but not innocent. For you will agree that to speak of uncertainty about the position of an electron, for example, necessarily implies a limitation of our knowledge, implying that we cannot know exactly where the electron is.
A. — Isn’t that the case?
P. — In general, yes, but for reasons much deeper than subjective ignorance or a limitation of our knowledge, as the usual formulation implies.
A. — What do you mean?
P. — Well, if we don’t know where the electron is, it is for the excellent reason that it’s not ‘somewhere’!
A. — You surprise me: you don’t mean to say that it’s nowhere! It is in space, and therefore has a location!
P. — Not a proper location, in any case. It certainly has spatiality, but it is not point wise. Moreover, this spatial extension is contingent, varying according to the circumstances that define the state of the electron.
A. — So it should be characterised by its spatial extension?
P. — Yes, but on condition that we do not conceive of it as fixed and unchanging: it is not a geometric dimension, but rather the size of the domain of space where the physical presence of the electron manifests itself, and which depends on the specific situation under consideration. Let us say that the electron is ‘extensible’.
“If we don’t know where the electron is, it is for the excellent reason that it’s not ‘somewhere’.”
A. — Why then not give the name ‘extension’ to the extent of this domain of localisation?
P. — That is indeed an excellent suggestion.
A. — And what are we going to call the Uncertainty Principle?
P. — First, it should be noted that this is not a fundamental principle, but simply a consequence of the formalism of quantum theory. Above all, there is no need to introduce the problematic words ‘uncertainty,’ ‘indeterminacy,’ or even ‘extension’ in order to understand what it is about. Some physicists, and not the least among them, have attempted, without much success, to clear things up, for example: “Such a mode of expression [’uncertainty relations‘] corresponds to the view that position and momentum have ’in reality” definite values but cannot be observed simultaneously; it is from this point of view that Heisenberg’s relations have been interpreted as uncertainty relations. But they have only served to hide the logical inconsistency resulting from the use of classical mechanics concepts outside their field of application.”[5] It would certainly be simpler and more accurate to talk about Heisenberg’s inequalities.
A. — How, then, would you state the best known of these inequalities in order to avoid erroneous and abusive interpretations?
P. — You would have to say something like: ‘the product of the spatial extension of a quanton by the width of its velocity spectrum has a lower bound’.
A. — That’s still somewhat esoteric, and less appealing than the traditional formulations.
P. — So, with a little less precision: ‘the narrower the location of a quanton, the wider its velocity spectrum’. Perhaps the most concise statement is still Bachelard’s lovely formula: ‘to enclose is to agitate’.
A. — But could you explain?
P. — Let me try. A quantum phenomenon is not generally characterised by a well-defined numerical value for its position, but by a spectrum (a plurality) of such values. The width of this spectrum is correlated with the characteristic span of velocities of the phenomenon. This correlation involves Planck’s constant, which clearly indicates its quantum nature. In other words, the more narrowly a quanton is localised, the broader its speed spectrum. Thus, rather than uncertainties, it is more appropriate to speak of spectral extensions or widths for physical quantities in the context of quantum theory.
A. — But what is the origin and history of the conventional terminology?
P. — I was curious to research its historical sources, which turned out to be more complex than a simple epistemological error.[6]
A. — Tell me about it.
P. — In the first article in which Heisenberg introduced, in 1927, the ‘principle’ that would later bear his name, an article obviously written in German…
“Far from constituting a limit to our knowledge […] Heisenberg’s inequalities give us a more adequate understanding of quantum objects, if only by preventing the use of invalid classical formulations.”
A. — Why ‘obviously’?
P. — Yes, you’re right, it’s no longer obvious today that at that time, which is not so long ago, it was possible to publish one’s work in one’s own language.
A. — Forgive me for interrupting, please continue.
P. — In this inaugural article, Heisenberg uses 30 times the word Ungenauigkeit, which can best be translated as ‘imprecision’ or “inaccuracy” and is the German term used to refer to what we traditionally call (experimental) ‘uncertainties’.
A. — But isn’t that what I was implying?
P. — Wait, it’s what comes next that’s interesting. In the same article, however, there are two occurrences of a new term in this context, Unbestimmtheit.
A. — That reminds me of my philosophy studies; it’s a term that has its origins in the Hegelian philosophical tradition. This word would correspond in English to ‘indeterminacy’ (in its more abstract sense, Hegel’s translators render it as ‘indeterminity’).
P. — ‘Indeterminacy’ was indeed used in English in the 1930’s, and is much preferable to ‘uncertainty’! It is not ideal, because the negative form of the word still too easily evokes an idea of failure or limitation of the theory, which completely misses the point; but ultimately, it refers to an effective characterisation: the position of the electron is generally not determined, at least in the usual sense of a point determination.
A. — But doesn’t it also refer to quantum ‘indeterminism’?
P. — Yes, unfortunately! Because this word is another of the evils that considerably affect the epistemological health of quantum theory. We can talk about it later, but it’s not exactly the same question. In any case, from 1929 onwards, it was this term (Unbestimmtheit) that generally prevailed, despite a brief appearance, in Heisenberg’s work and also in Weyl’s, of the word Unsicherheit, meaning ‘uncertainty’.
A. — But were you able to understand how, in French at least, ‘incertitude’ ended up dominating?
P. — It seems that the fault lies with a lazy adoption into French of a lax translation into English! Because in English, ‘uncertainty’ very quickly became the norm, as opposed to ‘indeterminacy’, and, unfortunately, imposed its equivalent in many other languages. Curiously, the term commonly used today in German to describe this indeterminate location of quantons is the adjective unschärfen, meaning ‘blunt’ or, better still, ‘fuzzy’. It should be noted, however, that Italian has remained faithful to ‘indeterminazione’.
A. — Allow me to be a little controversial. Because, after all, behind all your vocabulary quibbles, the fact remains that you don’t know where this damned electron is. Whether this is due to our own limitations, as some still believe, or, according to the modern point of view, if I understand you correctly, to the fault of the electron itself, which is incapable of satisfying itself of a well-defined position, you must agree that the result is indeed a defeat for the spirit of science, a renunciation of knowledge.
P. — I don’t agree at all, and in fact take the opposite view to such an assertion! Tell me: how much did your dreams weigh last night?
A. — What a stupid question!
P. — I couldn’t agree more. Just because a nonsensically phrased question does not receive an intelligible answer, you cannot conclude that our understanding is limited! You know the saying, ‘when you ask a stupid question, you get a stupid answer’. That’s exactly what happens when you force the electron to admit where it is exactly. At best, under duress, it ends up answering here, or there, or even there! The only difference with my little provocative question is that, in the case of material objects on our macroscopic scale, the mental reification of their properties has reached such a degree that we find it very difficult to conceive of the inappropriateness of ideas developed in a certain field of practice to account for reality in a radically new field.
A. — You would convince me more easily if, instead of criticising the negative descriptions of quantum objects, you showed me the positive effects of their new characterisations. But I suppose you are going to take refuge behind the technicality of the mathematical formalisms of quantum theory?
P. — The task is difficult, but perhaps not impossible. In any case, it is a fact that the so-called ‘uncertainties,’ when properly reinterpreted, are in fact sources of new certainties about the quantum world. Far from constituting a limit to our knowledge, as so many unfounded comments would have us believe, Heisenberg’s inequalities give us a more adequate understanding of quantum objects, if only by preventing the use of invalid classical formulations. Without going into the details of the formalism, we can thus understand, at an essentially heuristic level, the fruitfulness of quantum concepts themselves.[7] Let’s save this brief introduction to quantum theory for our next meeting, if you don’t mind.
Cover. Heisenberg’s uncertainty principle has undergone nearly a century of interpretations. Across science, philosophy, and culture, its popularity has sparked debates ranging from epistemology to politics, from economics to aesthetics.
(Source: Reproduction)
Jean-Marc Lévy-Leblond is a physicist and essayist, Professor Emeritus at the University of Nice and Director of the journal Alliage.
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