Complementarity Principle

Complementarity is an interesting concept that was introduced by Neils Bohr in the year 1928. Neils Bohr introduced the complementarity principle or the concept of complementarity in one of the famous Como lectures. The concept of complementarity was not precisely descriptive in Bohr’s work, but whenever he elaborated the concept of complementarity it was fitting the explanation profoundly. Neils Bohr recognized the need for the mathematical formalism of quantum mechanics to be constructed in a rationally coherent conceptual framework if it were to serve as the core of an acceptable scientific theory.

Explain The Principle of Complementarity

As we already know, 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, where the distributions in position and in momentum are related by Fourier transformation. 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. The essence of atomic physics may be expressed in the so-called quantum postulate, which attributes to any atomic process an essential discontinuity, or rather individuality, completely new to classical theories and symbolized by Planck’s quantum of action. The quantum postulate implies that any observation of atomic phenomena will involve an interaction with the agency of observation not to be neglected.  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.

Bohr's Complementarity Principle

Now let us explain the principle of complementarity or Bohr’s complementarity principle. 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 can not precisely describe the dual nature of light. Now suppose that an experiment is constructed in such a way that it is designed to measure the particle nature of the matter. This implies that, during this experiment, errors of measurement of both position and the time coordinates must be zero or absent, this in turns explains that the momentum, energy and the wave nature of the matter are completely unknown. Similarly, if an experiment is designed for measuring the wave nature of the particle, then the errors in the measurement of the energy and the momentum will be zero, whereas the position and the time coordinates of the matter will be completely unknown. 

From the above explanation, we can conclude that, 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. It was first explained by Niels Bohr in the year 1928 and hence it is familiarly known as the Bohr’s Complementarity principle.

What Bohr explained or Bohr 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. 

Did You Know?

The introduction of quantum mechanics was one of the most controversial scenarios in physics history as it was about to violate many classical aspects. The correspondence principle is one such discovery. It was probably Einstein's new derivation of Planck's black-body radiation law (1916-17) that most directly inspired Bohr's formulation of the Correspondence Principle around 1918, which thereafter played such a large role in his attempts to understand quantum phenomena. Bohr's reliance on the correspondence principle seems to have been a principal motive for his distrust of the photon concept and related willingness to give up energy-momentum conservation to save the classical wave picture of electromagnetic radiation.