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As I further my study on the history of quantum theory in an attempt to grapple

the various non-intuitive concepts, if not thoroughly, at least qualitatively, I come

across the so called concept of complementarity. It is part of the Copenhagen Interpretation proposed by Bohr and his colleagues.

Complementarity aims to reconcile two seemingly contradictory properties of matter, namely its wave and particle nature at the microscopic world. Irrefutable scientific evidences have been provided to support both the argument for light behaving as particles and behaving as waves. (e.g. Young's double slit experiment, and photoelectric effect.) Some of the most brilliant minds of the 20th century, such as Einstein, Plank, Heisenberg, had spent timeless effort trying to unveil nature's secret. And indeed, some great contributions had been made.

Schrodinger had proposed a wave function (psi) to describe the behaviour of a particle in an arbitrary potential. His theory worked quite well in that it predicted experimental outcomes with reasonable accuracy. However, the exact physical interpretation of his function was not exactly known. Schrodinger himself had expressed an opinion that his function represents amplitude of actual physical wave in 3 dimensional space, despite the function being a complex one. But his argument was quickly disproved: based on his theory, a two particle system should be interpreted as representing two waves in the same 3 dimensional space if the wave equation represents physical waves, but it turned out that the wave function represented 1 wave in 6 dimensional space, rendering his wave function a merely mathematical one. Later, another great physicist Born found that the square of the modulus of the wave function represented the probability of finding the particle at a particular location. This discovery revealed the probabilistic nature of quantum system.

Heisenberg in 1920’s published his famous paper on uncertainty principle, suggesting that momentum and position can not be measured with arbitrary precision at the same time; the increase in the precision of measurement of one of these observables will result reduction in the precision of measurement of another.

Because of the probabilistic nature of finding a particle, prior to a measurement, we do not know exactly where a particle is. However, as we measure it, we would locate the particle in a range of locations as governed by the uncertainty principle. Therefore, we have, in a way, disturbed the system: after the measurement the system is no longer the previous one precisely because the particle, instead of could be found anywhere, is now confined within a range of locations as a result of our measurement. If we extend this argument: prior to a measurement, we do not know if a particle, say a photon, behaves like a wave or like a particle. But as we measure it, our measurement would reveal it is either a wave or a particle, but never both. Similarly, in a way, we have disturbed the system because the system now, rather then being either a wave or a particle (we don't know), is now definitely a wave or a

particle (we know).

This notion of "if the system is measured, then it is disturbed" had been taken for adopted by the public and even numerous physics introductory texts.

The concept of complementarity pegs the notion of disturbance to be a mere misconception. The argument of disturbance is implicitly a result of our classical mind model. In classical physics, we consider the result obtained from an experiment to be merely the reflection of the observed quantities.

For example, if we are trying to find out what the colour of an apple is, we would look at it with our bare eyes. In this case, the apple is the observed, and our eyes are the observing instrument. With our bare eyes, we would see that the apple is red, and thus conclude that red is the colour of the apple. However, if we observe the apple, not with our bare eyes, but with some other instrument, say for example, a pair of sunglasses, we would conclude that brown is the colour of the apple. Now, similar to the wave-particle duality, apple has a red-brown colour duality. Obviously, in the above case we had forgotten the effect of instrument. (In quantum systems, the instrument could actually interact with the observed. The observed could be affected by the observing instrument beyond the superficial way in the apple case.)

The core idea of complementarity is based on arguments similar to the one above. Essentially, complementarity argues that the result of a measurement must not only be associated with the observed(e.g. the apple), but should be considered as a manifestation of the whole system of observing instrument (e.g. our eyes, or sun glasses) and the observed (e.g. the apple). Along this argument, a measurement is thus specific to the system of (observing instrument + observed). In a sense, the observed is not, in essence, disturbed by the action of a measurement. The fact that the observed manifests itself differently (show different result, e.g. sometimes red, sometimes brown for apple, and sometimes wave and sometimes particle for matter) over a range of measurement is a result of using different observing instrumentations.

The attachement picture is a thought experiment I produced to elucidate this concept.

In the thought experiment, we can not say that the cube is either only orange or only blue. The cube is a combination of orange and blue and perhaps some other colour we could not observe. The colour blue and orange are said to be “mutually exclusive” as they are observed from different perspectives. Yet they (along with the other unseen colour) jointly complete the description of the cube.

Similarly, the wave-particle properties are complementary phenomena of a particle, just like the colour orange and colour blue seen above. Thus the gist of complementarity is “mutually exclusive, jointly completion”, as putted by Bohr himself.

One important fact that was missing in complementarity (or rather purposely evaded by Bohr) was that if deterministic reality exists prior to the measurement; in other words, if there pre-exist a definite property of the observable before the measurement takes place. Arguments from previous sections seem to suggest that the property (which we are trying to measure) of the observable is constructed by our measurement; since the manifestation of the observable is observing instrument specific. The probabilistic form of the location of the particle also suggests, in a way, that nature is non-deterministic. This is the understanding by Bohr.

Later on, another concept was proposed by a philosopher (who self-claimed to be a proponent of Bohr) named Murdoch. He suggests us to consider this: if, say that, we pick a view stance before we make a measurement, then what we will be observing should have a pre-existed property. This argument seems valid if we consider it within our previous thought experiment. Say, if we decide that we will observe the cube from perspective A, then we should always observe the colour blue. Therefore, the property of the cube is deterministic prior to the measurement because there pre-exist a definite property.

This is true, of course, if the cube under consideration is static (not moving). However, consider that if the cube is rotating randomly, then even if we pick our perspective beforehand, there still exists no definite property of the observable prior to the measurement. As a result, it seems that nature is a construction of our measurement after all.

This fundamental question of whether nature is deterministic or not had puzzled many great physicists and provoked lengthened debates. For instance, Einstein is so uncomfortable with the idea that nature is random and chaotic, and that no physical laws permit us to predict what reality really is, that later Einstein published the famous EPR paper. Later on, Schrodinger also published a paper on a thought experiment addressing this issue – the famous Schrodinger’s cat thought experiment. Which I do not yet fully comprehend.

the various non-intuitive concepts, if not thoroughly, at least qualitatively, I come

across the so called concept of complementarity. It is part of the Copenhagen Interpretation proposed by Bohr and his colleagues.

**Some background:**Complementarity aims to reconcile two seemingly contradictory properties of matter, namely its wave and particle nature at the microscopic world. Irrefutable scientific evidences have been provided to support both the argument for light behaving as particles and behaving as waves. (e.g. Young's double slit experiment, and photoelectric effect.) Some of the most brilliant minds of the 20th century, such as Einstein, Plank, Heisenberg, had spent timeless effort trying to unveil nature's secret. And indeed, some great contributions had been made.

Schrodinger had proposed a wave function (psi) to describe the behaviour of a particle in an arbitrary potential. His theory worked quite well in that it predicted experimental outcomes with reasonable accuracy. However, the exact physical interpretation of his function was not exactly known. Schrodinger himself had expressed an opinion that his function represents amplitude of actual physical wave in 3 dimensional space, despite the function being a complex one. But his argument was quickly disproved: based on his theory, a two particle system should be interpreted as representing two waves in the same 3 dimensional space if the wave equation represents physical waves, but it turned out that the wave function represented 1 wave in 6 dimensional space, rendering his wave function a merely mathematical one. Later, another great physicist Born found that the square of the modulus of the wave function represented the probability of finding the particle at a particular location. This discovery revealed the probabilistic nature of quantum system.

Heisenberg in 1920’s published his famous paper on uncertainty principle, suggesting that momentum and position can not be measured with arbitrary precision at the same time; the increase in the precision of measurement of one of these observables will result reduction in the precision of measurement of another.

**The disturbance of a measurement:**Because of the probabilistic nature of finding a particle, prior to a measurement, we do not know exactly where a particle is. However, as we measure it, we would locate the particle in a range of locations as governed by the uncertainty principle. Therefore, we have, in a way, disturbed the system: after the measurement the system is no longer the previous one precisely because the particle, instead of could be found anywhere, is now confined within a range of locations as a result of our measurement. If we extend this argument: prior to a measurement, we do not know if a particle, say a photon, behaves like a wave or like a particle. But as we measure it, our measurement would reveal it is either a wave or a particle, but never both. Similarly, in a way, we have disturbed the system because the system now, rather then being either a wave or a particle (we don't know), is now definitely a wave or a

particle (we know).

This notion of "if the system is measured, then it is disturbed" had been taken for adopted by the public and even numerous physics introductory texts.

**Complementarity:**The concept of complementarity pegs the notion of disturbance to be a mere misconception. The argument of disturbance is implicitly a result of our classical mind model. In classical physics, we consider the result obtained from an experiment to be merely the reflection of the observed quantities.

For example, if we are trying to find out what the colour of an apple is, we would look at it with our bare eyes. In this case, the apple is the observed, and our eyes are the observing instrument. With our bare eyes, we would see that the apple is red, and thus conclude that red is the colour of the apple. However, if we observe the apple, not with our bare eyes, but with some other instrument, say for example, a pair of sunglasses, we would conclude that brown is the colour of the apple. Now, similar to the wave-particle duality, apple has a red-brown colour duality. Obviously, in the above case we had forgotten the effect of instrument. (In quantum systems, the instrument could actually interact with the observed. The observed could be affected by the observing instrument beyond the superficial way in the apple case.)

The core idea of complementarity is based on arguments similar to the one above. Essentially, complementarity argues that the result of a measurement must not only be associated with the observed(e.g. the apple), but should be considered as a manifestation of the whole system of observing instrument (e.g. our eyes, or sun glasses) and the observed (e.g. the apple). Along this argument, a measurement is thus specific to the system of (observing instrument + observed). In a sense, the observed is not, in essence, disturbed by the action of a measurement. The fact that the observed manifests itself differently (show different result, e.g. sometimes red, sometimes brown for apple, and sometimes wave and sometimes particle for matter) over a range of measurement is a result of using different observing instrumentations.

The attachement picture is a thought experiment I produced to elucidate this concept.

In the thought experiment, we can not say that the cube is either only orange or only blue. The cube is a combination of orange and blue and perhaps some other colour we could not observe. The colour blue and orange are said to be “mutually exclusive” as they are observed from different perspectives. Yet they (along with the other unseen colour) jointly complete the description of the cube.

Similarly, the wave-particle properties are complementary phenomena of a particle, just like the colour orange and colour blue seen above. Thus the gist of complementarity is “mutually exclusive, jointly completion”, as putted by Bohr himself.

**Is nature deterministic?**One important fact that was missing in complementarity (or rather purposely evaded by Bohr) was that if deterministic reality exists prior to the measurement; in other words, if there pre-exist a definite property of the observable before the measurement takes place. Arguments from previous sections seem to suggest that the property (which we are trying to measure) of the observable is constructed by our measurement; since the manifestation of the observable is observing instrument specific. The probabilistic form of the location of the particle also suggests, in a way, that nature is non-deterministic. This is the understanding by Bohr.

Later on, another concept was proposed by a philosopher (who self-claimed to be a proponent of Bohr) named Murdoch. He suggests us to consider this: if, say that, we pick a view stance before we make a measurement, then what we will be observing should have a pre-existed property. This argument seems valid if we consider it within our previous thought experiment. Say, if we decide that we will observe the cube from perspective A, then we should always observe the colour blue. Therefore, the property of the cube is deterministic prior to the measurement because there pre-exist a definite property.

This is true, of course, if the cube under consideration is static (not moving). However, consider that if the cube is rotating randomly, then even if we pick our perspective beforehand, there still exists no definite property of the observable prior to the measurement. As a result, it seems that nature is a construction of our measurement after all.

This fundamental question of whether nature is deterministic or not had puzzled many great physicists and provoked lengthened debates. For instance, Einstein is so uncomfortable with the idea that nature is random and chaotic, and that no physical laws permit us to predict what reality really is, that later Einstein published the famous EPR paper. Later on, Schrodinger also published a paper on a thought experiment addressing this issue – the famous Schrodinger’s cat thought experiment. Which I do not yet fully comprehend.