In this blog post, we examine the misunderstandings arising from interpretations of quantum mechanics through The Quantum Story. We unravel the complex logic of quantum mechanics, focusing on the concept of wave-particle duality.
It is no exaggeration to say the 21st century is the era of quantum mechanics. Quantum mechanics provides the theoretical foundation for technologies that profoundly impact society, such as explaining the principles of semiconductors. Consequently, physicists introduce quantum mechanics in public lectures and columns, and many science students begin studying it from their undergraduate years.
Whether in general physics textbooks or popular science columns, the ‘Copenhagen interpretation’ is mentioned when introducing quantum mechanics. Why mention this ‘interpretation’ specifically? Because physical theories are composed of mathematical structures and semantics. Since physical theories describe the world, it must be clearly established how symbols appearing in the mathematical structure correspond to real physical quantities, and how operations between symbols correspond to real-world interactions. In classical mechanics, discussions about interpretation were not particularly active. This is because the absolute interpretation of spacetime and the causal interpretation of events, which are the premises of classical mechanics, align well with everyday experience and are naturally accepted. However, quantum mechanics is far removed from empirical intuition, making the interpretation of its mathematical structure crucial. Reflecting this importance, physicists mention the Copenhagen interpretation, accepted as the mainstream interpretation, when introducing quantum mechanics.
When understanding physical theories, interpreting mathematical results is as important as understanding the mathematical structure itself. Especially in science lectures covering quantum mechanics at a general knowledge level, grasping the physical meaning is crucial. However, interpretations of quantum mechanics are often misunderstood by the public and many science students. Here, “interpretation of quantum mechanics” refers to the mainstream Copenhagen interpretation. Numerous studies and tools have been developed internationally to measure misunderstandings and comprehension of quantum mechanics concepts, including the Quantum Mechanics Concept Inventory (QMCI) (Falk, 2004) and the Quantum Physics Conceptual Survey (QPCS) (Wuttiprom et al., 2009). Domestically, Lim et al. (2012) used the QPCS developed by Wuttiprom et al. (2009) to investigate the understanding of fundamental quantum mechanics concepts among physics majors. The results showed an average correct answer rate of 56.5%, a standard deviation of 22.2%, and a minimum score of 9.7%. The correct answer rate was particularly low on questions testing physical concepts. This indicates that many people find the interpretation of quantum mechanics extremely difficult and misunderstand it. This article aims to discuss why many people misunderstand the interpretation of quantum mechanics and how this problem can be overcome. It focuses particularly on the wave-particle duality and complementarity concepts, which are the most contentious issues in the philosophy of quantum mechanics and also had the highest error rates among university students. It should be noted upfront that this article does not argue for or against the validity of complementarity.
According to Bohr, for concepts to be complementary, they must satisfy the following four conditions: 1. They describe different properties, 2. Together they provide a complete description of the object, 3. They are mutually exclusive, and 4. They must be applied diachronically, not synchronically. The particle model and wave model of light embody different properties of light. Both models are necessary to explain all phenomena, they hold equal status, and they cannot be applied simultaneously to a single phenomenon; thus, they are complementary.
The Copenhagen interpretation posits that physical objects possess wave-particle duality ‘complementarily’. Suppose an object exhibits particle-like properties in one experiment and wave-like properties in a second. This necessitates acknowledging that the object possesses both wave-like and particle-like properties, termed wave-particle duality. The problem lies in how to interpret these seemingly contradictory experimental results. If a realist interpretation is adopted, we face the paradoxical situation where an object that was literally a particle must transform into a wave, and we must be able to describe the mechanism of such a causal process. Bohr argued that introducing a complementary framework could resolve this paradox. According to Bohr, the very nature of the world inherently possesses a complementary framework. Indeed, Bohr believed every concept has a complementary counterpart. Wave nature and particle nature are complementary pairs; it is by observing phenomena differently that wave nature and particle nature are observed, not that light actually shifts between wave and particle states.
A significant misunderstanding frequently arises in people’s understanding of the complementary duality of wave-particle nature. The first misunderstanding is as follows: light is both a wave and a particle, but when humans observe light, it reveals itself only in one form, either as a wave or as a particle. This misunderstanding is akin to the expression that when one property of wave-like or particle-like nature is observed, the other property disappears. To draw an analogy, light is like a coin possessing both a front and back simultaneously, yet when humans see the coin, they can only perceive one side at a time. This is because, due to the limitations of our cognitive abilities, we can only observe one characteristic at a given moment. However, Bohr’s complementarity is not this interpretation. Within the complementary framework, the particle model and the wave model cannot coexist synchronously.
Many still insist that light must have clearly defined physical quantities and seek a definitive answer to what light is. This leads to a second misconception: that whether light is a wave or a particle cannot be known until the act of observation occurs. Unlike the previous misconception, this one does not claim light is both a wave and a particle simultaneously, but it fundamentally fails to address the issue of complementarity. This discussion extends beyond the complementary framework itself. The complementary framework of the Copenhagen interpretation is the very nature of the world; the properties and meaning of an object cannot be well-defined prior to observation. Therefore, according to the Copenhagen interpretation, it is not that whether light is a wave or a particle cannot be known before observation, but rather that no discussion about light can occur before observation.
Thus far, we have examined the wave-particle complementarity duality and two common misunderstandings surrounding it. We will now explore the factors causing these misunderstandings, dividing them into two aspects: the characteristics of complementarity duality and modern physics education methods. These factors are as follows.
First, complementarity fails to resolve the logical difficulties that arise when quantum mechanics is expressed in classical language. While Bohr argued that the complementary framework represents the very nature of the world, it cannot be denied that complementarity is a metaphysical tool designed to avoid the paradox arising from duality by attributing both wave-like and particle-like properties to a single entity, light. That is, the logical situation developed in complementarity is one not found in the macroscopic world. Complementarity describes different attributes that, when combined, provide a complete explanation; it is exclusive and cannot be applied synchronously. While structurally well-established, it conflicts with basic logic, making it difficult for people to understand the Copenhagen interpretation.
Second, complementarity conflicts not only with logic but also with general notions about the development of scientific theories. According to Karl Popper, scientific theories must be falsifiable; when inconsistencies arise between existing theories and new experiments, the old theory must be modified into a new theory capable of explaining the new experiments. Einstein proposed the photon hypothesis to explain the photoelectric effect. Paradoxically, however, the photon hypothesis failed to explain the wave-like properties of particles described by existing theory. Consequently, no scientific theory emerged that could simultaneously account for both the wave-like and particle-like nature of particles. This is where Bohr’s tool of complementarity came into play. However, complementarity is merely a logical framework devised by Bohr; it is unfalsifiable and thus struggles to attain the status of a scientific theory. Consequently, a theory simultaneously explaining both wave and particle properties still does not exist. Yet, according to common perception, people naturally assume an advanced theory explaining both wave and particle properties must exist. This conflict between such perception and quantum mechanics leads people to misunderstand light as being like a coin.
Thirdly, modern physics education poses various mathematical questions within the theoretical framework but fails to raise conceptual questions about the framework itself. For example, a general physics textbook’s quantum mechanics section mentions duality only with the phrase “light possesses both wave and particle properties,” and among the 90+ practice problems included, not a single one asks about the concept of duality. Such superficial mention offers no help to students in accurately understanding the Copenhagen interpretation. The consequences of this teaching approach are starkly evident in surveys of quantum mechanics comprehension: among 25 questions with an average correct answer rate of 56.5%, the four questions testing the concept of particle-wave duality had a correct answer rate of 22.6%, while the two questions testing the concept of the uncertainty principle had a 30.7% correct answer rate. This is significantly lower than the remaining 19 questions, which involved substituting physical quantities into formulas to find values. Analysis of the four questions testing the wave-particle duality concept, based on response concentration indices and correct answer rates, revealed that students were relatively more likely to hold misconceptions about this concept. These issues are also evident in Mashhadi’s (1996) investigation of undergraduate students’ concepts regarding wave-particle duality. Taken together, this suggests that physics education methods that inadequately address philosophical aspects increase the likelihood of misunderstandings about quantum mechanics.
The discussion thus far can be summarized as follows. First, we examined the concept of complementarity pioneered by Bohr. We then clearly defined the complementary duality, the core tenet of the Copenhagen interpretation. Subsequently, we examined the misunderstandings arising from interpretations of duality and identified the factors contributing to these misunderstandings. The first factor—that complementarity conflicts with established logic—and the second factor—that complementarity conflicts with notions about the development of scientific theories—are both linked to the characteristics of complementary duality. The third factor, that physics education inadequately addresses philosophical aspects, relates to modern physics teaching methods.
What efforts are needed to resolve misunderstandings about duality? The most urgent aspect is education that gives significant weight to interpretations of quantum mechanics. While the above discussion focused only on physics textbooks and surveys of university students’ conceptual understanding, even in science lectures, clear communication of the Copenhagen interpretation is often lacking. Even in simplified lectures for the general public, analogies like comparing light to an elephant and humans to blind men, drawing parallels to proverbs, can potentially foster misunderstandings about complementarity. While concise metaphors are appealing because the logical structure of complementarity is difficult to describe using existing logic, they are undesirable as they obscure the essence of the interpretation and should be avoided. As Bohr stated, the complementary nature of truth is clarity. While we may never fully grasp the truth-based interpretation of quantum mechanics, I believe we should at least clearly understand what existing interpretations claim. I hope that philosophical interpretations of quantum mechanics receive significant attention throughout education and research.
