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Quantum Mechanics

Bohr's complementarity principle:

different factual aspects of truth are not contradictory but complementary as we need all views to form a complete picture of reality 



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Complementarity And The World: Niels Bohr’s Message In A Bottle, by Wavefunction on Monday, November 29, 2021

Werner Heisenberg was on a boat with Niels Bohr and a few friends, shortly after he discovered his famous uncertainty principle in 1927. A bedrock of quantum theory, the principle states that one cannot determine both the velocity and the position of particles like electrons with arbitrary accuracy. Heisenberg’s discovery foretold of an intrinsic opposition between these quantities; better knowledge of one necessarily meant worse knowledge of the other. Talk turned to physics, and after Bohr had described Heisenberg’s seminal insight, one of his friends quipped, “But Niels, this is not really new, you said exactly the same thing ten years ago.”

In fact, Bohr had already convinced Heisenberg that his uncertainty principle was a special case of a more general idea that Bohr had been expounding for some time – a thread of Ariadne that would guide travelers lost through the quantum world; a principle of great and general import named the principle of complementarity.

Complementarity arose naturally for Bohr after the strange discoveries of subatomic particles revealed a world that was fundamentally probabilistic. The positions of subatomic particles could not be assigned with definite certainty but only with statistical odds. This was a complete break with Newtonian classical physics where particles had a definite trajectory, a place in the world order that could be predicted with complete certainty if one had the right measurements and mathematics at hand. In 1925, working at Bohr’s theoretical physics institute in Copenhagen, Heisenberg, Bohr’s most important protégé, had invented quantum theory when he was only twenty-four. Two years later came uncertainty; Heisenberg grasped that foundational truth about the physical world when Bohr was away on a skiing trip in Norway and Heisenberg was taking a walk at night in the park behind the institute.

When Bohr came back he was unhappy with the paper Heisenberg had written, partly because he thought the younger man seemed to echo his own ideas, but, more understandably, because Bohr – a man who was exasperatingly famous for going through a dozen drafts of a scientific paper and several drafts of even private letters – thought Heisenberg had not expressed himself clearly enough. The 42-year-old kept working on the 26-year-old until the latter admitted that “the uncertainty relations were just a special case of the more general complementarity principle.”

So what was this complementarity principle? Simply put, it was the observation that there are many truths about the world and many ways of seeing it. These truths might appear divergent or contradictory, but they are all equally essential in representing the true nature of reality; they are complementary. As Bohr famously put it, “The opposite of a big truth is also a big truth”. Complementarity provided a way to reconcile the paradoxes that seemed to bedevil quantum theory’s interpretation of reality.

The central scientific paradox was what is called wave-particle duality. In 1803, the British polymath Thomas Young had proposed that light, contrary to Isaac Newton’s view of it, consists of waves; an experiment like diffraction makes this wave nature clear. A hundred years later, in 1905, Einstein proposed that light in fact consists of particles, an idea he invoked in order to explain the photoelectric effect and which won him a Nobel Prize; these particles were later called photons.

Soon it was found through other experiments that all subatomic particles and not just photons could display wave and particle behavior. In 1924, the French physicist and aristocrat Louis de Broglie saw a way through the impasse when he came up with a simple equation that related the momentum of a particle – a particle property – inversely to its wavelength – a wave property.

In spite of de Broglie’s insight, particles clearly don’t look like waves and waves don’t look like particles in real life. In fact the very names seem to put them at odds with one another. It was Bohr who saw both the problem and the solution. Particles and waves both exist and are equally valid and essential ways of interpreting the quantum world. Depending on what experiment you do you might see one or the other and never both, but they are not contradictory, they are complementary. Most crucially, you simply cannot make sense of reality without having both in hand. It was a powerful insight that cut through the complexities of intuition and language; it was not too different in principle from other counterintuitive truths that science has uncovered, for instance the truth that both lighter and heavier bodies fall at the same rate. Complementarity rationalized opposing tendencies of the physical world and indicated that they were one. It was what had made Bohr subsume the opposing quantities in Heisenberg’s uncertainty principle under the same rubric...

As we approach what seem to be novel problems in the 21st century, Bohr’s complementarity is a message in a bottle from one fraught world to another, telling us that seeing these new problems through the lens of an old principle can be most rewarding. We seem to live in a time when many see social and political problems through a binary, black-or-white, zero sum lens. Either my viewpoint is right or yours, but not both. Complementarity bridges that division....

even flawed visions may contain snatches of truth that should be acknowledged as potential building blocks in our view of reality

If we accept the idea of complementarity, we are in essence accepting the validity of all ways of looking at the world, and not just one. This does not mean that all ways are equally right – we can’t accept the germ theory of disease and the “theory” of diseases as a punishment from God on equal terms – but it is precisely through placing them on a level playing field and letting them play out their logical flow that we can even know how much of which view is right. In addition, Bohr realized that the world is indeed gray, that even flawed visions may contain snatches of truth that should be acknowledged as potential building blocks in our view of reality. But ultimately, Bohr’s plea for complementarity was a plea for what he called an “open world”, an ideal that for him was the highest that the peoples of the world could aspire to, an ideal that arose naturally from the democratic republic of science.

If we accept complementarity, we automatically become open to examining every single approach to a problem, every way of parsing reality. Most importantly, we become open to true, unfettered communication with our fellow human beings, a tentative but lasting step toward Bohr’s – and science’s – “gradual removal of prejudices”. That seems like an important message for today.



In physics, complementarity is a conceptual aspect of quantum mechanics that Niels Bohr regarded as an essential feature of the theory. The complementarity principle holds that objects have certain pairs of complementary properties which cannot all be observed or measured simultaneously. An example of such a pair is position and momentum. Bohr considered one of the foundational truths of quantum mechanics to be the fact that setting up an experiment to measure one quantity of a pair, for instance the position of an electron, excludes the possibility of measuring the other, yet understanding both experiments is necessary to characterize the object under study. In Bohr's view, the behavior of atomic and subatomic objects cannot be separated from the measuring instruments that create the context in which the measured objects behave. Consequently, there is no "single picture" that unifies the results obtained in these different experimental contexts, and only the "totality of the phenomena" together can provide a completely informative description…

Bohr publicly introduced the principle of complementarity in a lecture he delivered on 16 September 1927 at the International Physics Congress held in Como, Italy, attended by most of the leading physicists of the era, with the notable exceptions of Einstein, Schrödinger, and Dirac. However, these three were in attendance one month later when Bohr again presented the principle at the Fifth Solvay Congress in Brussels, Belgium.



… classical physics postulates that, at each instant of time, every elementary particle is located at some definite point or the position in space, and has a definite velocity, and hence corresponding definite momentum. On the other hand, in quantum physics, an elementary particle is represented by various distributions of possibilities... This consequence explains that localization at a point in position space demands a complete lack of localization in momentum space and vice versa.

Because of these contradictory theories regarding quantum motion Bohr came up with the complementarity principle. He explains that the very nature of quantum theory eventually forces us to regard the claim of space-time coordination and the claim of causality, the union of which characterizes the classical theories, as complementary but exclusive features of the description, symbolizing the idealization of observation and definition respectively.

Bohr further explains that the theories of quantum mechanics are characterized by the acknowledgement of a fundamental limitation in the classical physical ideas when applied to atomic phenomena… Accordingly, an independent reality in the ordinary physical sense can neither be ascribed to the phenomena nor to the agencies of observation. After all, the concept of observation is so far arbitrary as it depends upon which objects are included in the system to be observed. Ultimately, every observation can obviously be reduced to our sense perceptions…

We know that the consequence of the uncertainty principle is both the wave and particle nature of the matter can not be measured simultaneously. In other words, we cannot precisely describe the dual nature of light… when the particle nature of the matter is measured or displayed, the wave nature of the matter is necessarily suppressed and vice versa. The inability to observe the wave nature and the particle nature of the matter simultaneously is known as the complementarity principle…

What Bohr explained, or Bohr’s exact words were, “In a situation where the wave aspect of a system is revealed, its particle aspect is concealed; and, in a situation where the particle aspect is revealed, its wave aspect is concealed. Revealing both simultaneously is impossible; the wave and particle aspects are complementary.”

Compactly stated, the essential idea here is that in theories of quantum physics the information provided by different experimental procedures that, in principle cannot, because of the physical characteristics of the needed apparatus, be performed simultaneously, cannot be represented by any mathematically allowed quantum state of the system being examined. The elements of information obtainable from incompatible measurements are said to be complementary: taken together exhaust the information obtainable about the state. On the other hand, any preparation protocol that is maximally complete, in the sense that all the procedures are mutually compatible and are such that no further procedure can add any more information, can be represented by a quantum state, and that state represents in a mathematical form all the conceivable knowledge about the object that experiments can reveal to us.



Editor's last word:

Elsewhere on the WG site, we discussed the ancient Sufi-elephant parable. Ten blind men were handling different parts of the beast and each went away with a different opinion concerning the nature of elephants.

However, Bohr would say, these different aspects of the elephant – the truck, the leg, the tail, etc. – are not contradictory but complementary. We need the views of all ten men to gain a full picture of reality.

Bohr’s philosophical statement of “complementarity” issues as profound wisdom. See the “Cultism” page for a violation of what Bohr understands, each person claiming that his little part of “the elephant” represents the entire universe.