Introduction: The Epistemological Revolution of Quantum Mechanics

Quantum mechanics is one of the most successful physical theories that human intellect has ever achieved. From semiconductors, lasers, and MRIs to modern quantum computers, the technological foundation of our modern society is built upon the mathematics of quantum mechanics. However, behind its overwhelming practical success, the philosophical and epistemological questions that quantum mechanics poses to us about “what reality is” remain a subject of deep controversy even a century after its birth.

At the center of this controversy stands the Danish physicist Niels Bohr (1885–1962) and the “Copenhagen Interpretation” he led. The naive materialistic picture of “objective reality existing independently of the observer,” which classical physics had assumed, completely breaks down in the microscopic world of quantum mechanics. Bohr proposed the “Complementarity Principle” to integrate the seemingly contradictory phenomenon of wave-particle duality and asserted the indivisibility of the measuring apparatus and the observed object.

In this article, we will thoroughly unravel from a highly detailed and academic perspective how Bohr’s complementarity principle was born, how it was forged in the great dispute of the century with Albert Einstein, and what legacy it leaves for modern quantum information theory and the philosophy of science. This is not a mere retrospective of the history of physics, but a journey to the root of epistemology asking “what does it mean for us to perceive the world.” Let us unfold the intellectual struggle between Bohr and Einstein in search of the truth hidden in the depths of nature.

Chapter 1: The Storm of the Genesis of Quantum Mechanics

1.1 The Limits of Classical Physics and Bohr’s Atomic Model

From the end of the 19th century to the early 20th century, classical mechanics and classical electromagnetism were facing numerous “unexplainable phenomena.” The spectrum problem of black-body radiation (ultraviolet catastrophe), the photoelectric effect, and above all, the stability of atoms. The solar system-type atomic model proposed by Ernest Rutherford in 1911 featured a heavy atomic nucleus with a positive charge at the center, surrounded by light electrons with negative charges orbiting it. However, according to the laws of classical electromagnetism (Maxwell’s equations), electric charges undergoing accelerated motion such as circular motion must emit electromagnetic waves (bremsstrahlung) and lose energy. According to calculations, it had a fatal flaw that electrons would crash into the nucleus in an instant of 10 to the minus 11 seconds. The very fact that our bodies exist stably was a strong counter-evidence to classical physics.

What saved this severe crisis was the “Bohr model of the atom” by Niels Bohr in 1913. Bohr boldly introduced Max Planck’s quantum hypothesis (quantization of energy) and Albert Einstein’s light quantum hypothesis, and posited the following two epoch-making assumptions:

1. The assumption of stationary states: Electrons can only exist in certain discrete energy states (orbits), and as long as they are in this state, electrons do not emit electromagnetic waves even if they are in accelerated motion. These permissible orbits are determined by the quantum condition $L = mvr = n\hbar$, where the angular momentum $L$ is an integer multiple of Planck’s constant $\hbar = h/2\pi$.
2. The frequency condition: Only when an electron transitions from one stationary state (energy $E_i$) to another stationary state (energy $E_f$) (this is called a “quantum leap”), it emits or absorbs a photon with energy equal to that energy difference. That is, $E_i - E_f = h\nu$ (where $\nu$ is the frequency of light).

Bohr’s theory theoretically derived the Balmer series of the hydrogen atom (emission spectrum in the visible light region) and the Rydberg constant with astonishing accuracy, shocking the physics community. However, the Bohr model at this point was a transitional one called the “old quantum theory,” which forcibly patched discontinuous quantum conditions onto the framework of continuous spatial orbits of classical mechanics, and had the limitation that it could not explain the extension to multi-electron atoms or the intensity distribution of spectral lines. The construction of a deeper and more universal theory was urgently required.

1.2 Heisenberg’s Matrix Mechanics and Non-commutative Algebra

In 1925, quantum mechanics experienced a dramatic paradigm shift. The young genius Werner Heisenberg, who had been conducting research at Bohr’s institute, made the radical decision to completely banish the visual and classical concept of “unobservable electron orbits” from physics. He constructed a completely new mechanics based only on actually observable physical quantities (the frequency of spectral lines and the amplitude of transition probabilities).

Completed with the cooperation of Max Born and Pascual Jordan, this theory was called “Matrix mechanics.” Here, physical quantities (position $x$ and momentum $p$) are not simply real numbers, but are treated as infinite-dimensional matrices (or operators). And the most shocking feature of this mechanics was its “Non-commutativity,” meaning that changing the order of multiplication of position and momentum changes the result.

This seemingly bizarre commutation relation is precisely the ultimate law governing the quantum world, and later becomes the mathematical foundation deriving the uncertainty principle. Heisenberg’s theory rejected any visual imagery and attempted to describe nature purely through algebraic relationships.

1.3 Schrödinger’s Wave Mechanics and Its Frustration

While physicists were perplexed by the obscure and abstract mathematics of matrix mechanics, Erwin Schrödinger presented a completely different approach in 1926. He developed the concept of “matter waves (electrons also have properties as waves)” proposed by Louis de Broglie, and derived the partial differential equation that matter waves should obey, namely the “Schrödinger equation.”

This “Wave mechanics” used differential equations familiar to physicists and derived the energy levels of the hydrogen atom much more clearly than matrix mechanics. Later, Schrödinger himself and Paul Dirac proved that matrix mechanics and wave mechanics are mathematically perfectly equivalent.

Schrödinger initially attempted a “realistic interpretation” that this wave function $\psi$ represented waves of charge density (wave packets) of an electron in actual three-dimensional space. He loathed the discontinuous and eerie concept of quantum leaps and expected that nature could once again be pulled back into a continuous and deterministic mechanics of waves. However, this attempt ended in failure. Calculations revealed that even if an electron is represented as a localized wave packet, the wave packet would diffuse throughout space as time passed. The fact that the electron as a particle would spread out in space and disappear was contrary to experimental facts.

1.4 Born’s Probability Interpretation and the Collapse of Causality

How should Schrödinger’s wave function $\psi$ be interpreted? It was Max Born’s “probability interpretation (Born’s rule)” in 1926 that gave a definitive answer to this question.

Born proposed that the wave function itself is a complex wave (probability amplitude) that cannot be directly observed, and that the square of its absolute value $|\psi(x, t)|^2$ represents the “probability density” of finding a particle at position $x$ at time $t$.

This interpretation fundamentally overturned the paradigm of physics. The deterministic causality (Laplace’s demon) that dominated classical physics, stating that “if the initial conditions and equations of motion are completely determined, the future state is uniquely determined,” collapsed, showing that “fundamental probability (objective probability)” is inherent in the deepest part of nature. Where the electron will appear is left to the roll of the dice known only to God. This probabilistic and indeterministic worldview became the foundation of the philosophy of the Copenhagen school centered around Bohr, and at the same time became the spark that caused fierce resistance from Einstein and others.

Chapter 2: The Birth of the Complementarity Principle

2.1 The Declaration at the Como Conference in 1927

In the autumn of 1927, as the mathematical formulation of quantum mechanics (matrix mechanics and wave mechanics) was nearing completion, Bohr finally publicly declared the “Complementarity principle” at the International Physics Conference commemorating the 100th anniversary of the death of Alessandro Volta, held on the shores of Lake Como in Italy. This was a monumental lecture that established the philosophical and epistemological foundation of quantum mechanics.

The greatest conundrum Bohr faced was the paradox of “Wave-particle duality.” Light and electrons behave as continuous “waves” that create interference fringes in certain experiments (such as the double-slit experiment), and as “particles,” which are localized chunks of energy and momentum, in other experiments (such as the photoelectric effect or Compton scattering). In classical intuition, waves that continuously spread throughout space and particles localized at a single point are completely mutually exclusive concepts that cannot logically coexist.

Physicists at the time were agonizing over the dichotomous question of whether an electron is actually a wave or a particle. However, in response to this paradox, Bohr achieved a Copernican revolution by not reducing it to one or the other, but accepting the conflict itself as a profound property of nature.

2.2 The Logical Structure and Philosophical Implications of Complementarity

The core assertion of the complementarity principle is as follows:

“In order to completely describe the phenomena of the microscopic world, two concepts that are classically mutually exclusive (wave and particle, or position and momentum) are actually required as complementary to each other.”

According to Bohr, the picture of a wave and the picture of a particle are never simultaneously applied to a single object. Which picture appears depends entirely on “what kind of experimental apparatus we choose.” If you set up an apparatus to measure interference fringes, it appears as a wave; if you set up an apparatus to measure trajectories, it appears as a particle. In other words, nature never shows us its “objective figure as a whole” all at once, but rather cuts out and shows only one of its aspects depending on our inquiry (macroscopic experimental setup).

This thought later became a profound epistemology that transcended the framework of physics and was discussed in analogy with biology, psychology, and even Eastern philosophy (yin-yang thought). When Bohr himself was later awarded the Order of the Elephant by the Danish royal family, he chose the Taijitu (symbol of yin and yang) as his coat of arms, bearing the Latin inscription “Contraria sunt complementa” (Opposites are complementary).

2.3 The Requirement of Classicality for Measuring Apparatus and Indivisibility

The most revolutionary and esoteric part of Bohr’s thought is the requirement for a “classical description of the measuring apparatus” and the “indivisibility of the measuring apparatus and the observed object.”

We humans are inhabitants of a macroscopic, classical world. In order for us to recognize measurement results, remember them, and communicate with other scientists using objective language, we inevitably have to use the concepts and language of classical physics, such as “clocks,” “rulers,” “position,” and “momentum.” Bohr strongly argued that “no matter what quantum mechanical experiment it is, the description of its results must be expressed in classical terms.”

However, once a specific measuring apparatus (for example, a high-resolution gamma-ray microscope to strictly measure the position of an electron) is set up, a quantum mechanical interaction occurs between the measuring apparatus (macro) and the object (micro). Because Planck’s constant $h$ has a finite, non-zero value, this interaction causes an uncontrollable and irreversible “disturbance.” Because of this, the measuring apparatus and the observed object can no longer be separated as two independent systems, and form one indivisible “whole phenomenon.”

For Bohr, asking “what state is the electron itself in when it is not being observed” was a scientifically meaningless question. The only meaningful object that physics can talk about is “the entire indivisible phenomenon, including its interaction with a specific macroscopic experimental apparatus.” Reality does not exist apart from observation. Here, classical realism was completely crushed.

Chapter 3: The Great Einstein-Bohr Debate

3.1 The 5th Solvay Conference (1927): The Clash of Giants and God’s Dice

Around the same time that the Copenhagen Interpretation was being established, Albert Einstein strongly objected to it. Even though Einstein was the very person who laid the foundation for quantum theory with his light quantum hypothesis, he resolutely rejected the probabilistic interpretation and anti-realist consequences of quantum mechanics.

“I cannot believe that God plays dice with the universe.”

This famous statement of his was a manifestation of his deep philosophical belief defending strict causality and the existence of objective physical reality independent of the observer. Einstein admitted that quantum mechanics correctly predicted experimental results, but he believed it was merely an “incomplete description (incomplete statistical theory)” of nature, and that there must be a deterministic true theory hidden behind it.

At the 5th Solvay Conference held in Brussels in 1927, the great debate that shines brilliantly in the history of science between Einstein and Bohr kicked off. Behind the scenes of the official sessions of the conference, they engaged in an exchange of fierce thought experiments from the hotel dining room in the morning to the lounge at night.

Every morning, Einstein presented clever and elaborate thought experiments showing the contradictions of the Copenhagen Interpretation (especially the violation of Heisenberg’s uncertainty principle), driving Bohr and his young disciples (Heisenberg, Pauli, Dirac, etc.) into a corner. But Bohr would think hard all day long, sometimes with a desperate expression, and by dinner time that day, he would always find the flaw hidden in Einstein’s thought experiment and perfectly prove the correctness of the uncertainty principle and complementarity.

3.2 Movable Double-Slit and Recoil Momentum

One of the representative thought experiments presented by Einstein is a double-slit experiment using a “movable first slit” that is not fixed to a screen.

Einstein’s argument: In a normal double-slit experiment, it is impossible to know which slit the electron passed through, slit A or slit B (which path information), so interference fringes of waves appear on the screen. However, the first slit (single slit) is suspended by a spring to make it movable. Depending on whether the electron passes through the first slit and heads for slit A above or slit B below, the direction of the “recoil momentum (kick)” given by the electron to the first slit will differ. Therefore, if the momentum of the first slit before and after the electron passes is precisely measured, it is possible to completely identify which path, A or B, the electron took. If the path can be identified, it means the electron behaved as a “particle.” But at the same time, since the structure of the slits themselves has not changed, the interference fringes on the screen (the nature of waves) should also continue to be observed. This means that the pictures of waves and particles hold true simultaneously, breaking down the complementarity principle!

Bohr’s refutation: Bohr immediately pointed out that the measuring device, the movable slit itself, is also a physical entity and must obey the laws of quantum mechanics (the uncertainty principle). In order to measure the recoil momentum $p$ of the slit and identify the path, it is necessary to measure the change in momentum $\Delta p$ with extremely high precision. However, due to the uncertainty principle $\Delta x \Delta p \ge \hbar/2$, the more precisely one tries to measure the momentum $p$, the more the uncertainty $\Delta x$ of the slit’s position increases. If the initial position of the slit becomes uncertain, the “optical path difference” from the first slit through slits A and B to the screen also becomes uncertain. The moment the uncertainty of this optical path difference reaches the scale of the wavelength $\lambda$, the peaks and troughs of the interference fringes overlap, and as a result, the interference fringes on the screen completely blur and disappear (become a uniform distribution). In other words, the moment an “apparatus to obtain path information (particle nature)” is incorporated, the “interference fringes (wave nature)” are inevitably destroyed. Nature never permits contradictions. The complementarity principle was perfectly upheld.

3.3 The 6th Solvay Conference (1930): Bohr’s Miraculous Refutation and the “Photon Box”

At the 6th Solvay Conference in 1930, Einstein brought an even more refined and decisive thought experiment, the “Photon Box.” This was a terrifying trap aimed at directly breaking the time-energy uncertainty relation $\Delta E \cdot \Delta t \ge \hbar/2$.

Einstein’s proposal: Prepare a box filled with photons and a shutter controlled by a precise clock. The weight of the box is measured extremely accurately beforehand with a spring scale. At a specified time $t$, the clock operates, the shutter opens for a brief moment, and one photon escapes from the box. After that, the weight of the box is measured again. According to the formula for the equivalence of mass and energy $E=mc^2$ in the special theory of relativity, by measuring the decrease in the mass of the box $\Delta m$, the change in energy of the emitted photon $\Delta E = \Delta m c^2$ can be strictly calculated. On the other hand, the time at which the photon was emitted is strictly determined by the clock inside the box, so the uncertainty of time $\Delta t$ can be made zero. Therefore, both energy and time can be determined simultaneously with arbitrary precision, and the uncertainty principle breaks down. Quantum mechanics is incomplete!

Bohr was severely shocked by this brilliant argument and lost for words. Léon Rosenfeld, a participant in the conference, vividly recorded the situation at that time as follows: “Bohr paled and was extremely excited. He was running around trying to persuade everyone he met, muttering that Einstein could not be right. But he could not even find a clue to a refutation. In contrast, Einstein walked tall and majestically, with a quiet smile of victory on his face.”

However, the next morning, having stayed up all night thinking it through, Bohr presented a miraculous refutation that remains in history. The weapon he used was, ironically, Einstein’s own masterpiece, the “General Theory of Relativity.”

The Logical Structure of Bohr’s Miraculous Refutation:

1. In order to precisely measure the mass of the box, it is necessary to measure the displacement $q$ of the pointer of the spring scale. To perform this measurement, the box itself must be supported in a gravitational field, and the box experiences an uncertainty $\Delta p$ in momentum $p$ and an uncertainty $\Delta q$ in position. These obey Heisenberg’s uncertainty principle $\Delta q \Delta p \ge \hbar$.
2. When the box moves up and down by displacement $q$ in a gravitational field (acceleration $g$), the gravitational potential changes according to the general theory of relativity (the equivalence principle). The change in gravitational potential changes the “rate at which the clock runs” inside the box (gravitational redshift).
3. The uncertainty of this time dilation due to gravity $\Delta T$ is expressed using the measurement time $T$ as $\Delta T = T \frac{g \Delta q}{c^2}$.
4. On the other hand, the uncertainty of mass $\Delta m$ can be evaluated from the relationship of impulse as $\Delta p \approx g T \Delta m$.
5. Therefore, the uncertainty in position is $\Delta q = \frac{c^2 \Delta T}{g T}$, and the uncertainty in momentum is $\Delta p = g T \Delta m = g T \frac{\Delta E}{c^2}$.
6. Substituting these into the position-momentum uncertainty relation $\Delta q \Delta p \ge \hbar$, $$ \left(\frac{c^2 \Delta T}{g T}\right) \left(g T \frac{\Delta E}{c^2}\right) \ge \hbar $$ $$ \Delta T \Delta E \ge \hbar $$ Surprisingly, by incorporating the equations of Einstein’s own general relativity, the time-energy uncertainty relation was perfectly derived!

Einstein was deeply impressed that his own thought experiment was refuted using his own general relativity, and he finally came to admit the “consistency (internal consistency)” of quantum mechanics. However, he never agreed for the rest of his life that quantum mechanics was a “complete description” of nature. Later, with the EPR paper (Einstein-Podolsky-Rosen paradox) in 1935, he pointed out the non-locality of “quantum entanglement,” moving the main battlefield of the debate to a deeper level.

Chapter 4: The Mathematical and Conceptual Framework of the Copenhagen Interpretation

Bohr’s philosophical arguments on complementarity were later given strict mathematical formulation on Hilbert space by John von Neumann, Paul Dirac, and others, and became established as the so-called “standard Copenhagen interpretation.”

4.1 Von Neumann’s Projection Postulate and the Collapse of the Wave Packet

In 1932, John von Neumann formulated in his masterpiece “Mathematical Foundations of Quantum Mechanics” that there are fundamentally two different processes (dynamical laws) for the time evolution of a quantum system.

1. $$ i\hbar \frac{\partial}{\partial t} |\psi(t)\rangle = H |\psi(t)\rangle $$

2. Process 2 (Projective Measurement, $R$-process): The moment an observation is made, the state vector discontinuously, irreversibly, and probabilistically “collapses (jumps)” to one of the eigenstates (eigenvectors) $|a_i\rangle$ of the observed physical quantity (Hermitian operator). This is called the collapse of the wave function or the projection postulate. The probability of the state collapsing to $|a_i\rangle$ is given by Born’s rule as $P_i = |\langle a_i | \psi \rangle|^2$.

This discontinuous change called “the collapse of the wave packet” is the greatest mystery in quantum mechanics, and the core of the infamous “Measurement Problem.” One can never derive this non-linear “collapse” from within the framework of a linear equation like the Schrödinger equation. Is the collapse not naturally derived from within the theory, but merely an ad hoc assumption demanded from the outside? Since measuring instruments are also collections of atoms, they should obey the Schrödinger equation; why does another physical law (Process 2) activate only at the moment of measurement? This paradox would forever haunt physicists.

4.2 Bohr’s Cut

While a quantum system (micro) falls into a superposition state according to the Schrödinger equation, a measuring apparatus (macro) possesses a clear single state obeying classical physics. Then, where on earth in this world does “the quantum system end and the classical measuring apparatus begin?” The problem of drawing this boundary line is called “Bohr’s cut” or the “Heisenberg cut.”

According to the standpoint of Bohr and others, where this cut is drawn is not uniquely determined by objective physical necessity, but is to some extent “arbitrary (mobile).” One may draw the cut between the observed electron and the microscope, treating the microscope as a classical system, or shift the cut so that the microscope is also a quantum system (in a superposition state), and draw the cut between the computer reading the microscope’s numbers and the human. Von Neumann proved mathematically that no matter where the cut is moved, the predicted probabilities of the observation results are perfectly identical (consistency).

What is important is the epistemological requirement that in order to describe a physical phenomenon with language, “one must inevitably draw a cut artificially somewhere and separate the observing subject (classical side) from the observed object (quantum side).” There is no absolute boundary in the world itself.

4.3 Wigner’s Friend Problem and the Observer’s Consciousness

Eugene Wigner pushed von Neumann’s “arbitrariness of the cut” to the extreme. If Bohr’s cut is gradually shifted further inside the observer, from the measuring apparatus to the computer, to the human retina, and to the optic nerve, ultimately the “cut” must reach the human brain, or the non-physical “Mind (consciousness).”

Wigner proposed the following thought experiment (Wigner’s friend). Inside a closed laboratory, Wigner’s “friend” performs a measurement on a quantum system (for example, measuring spin). From Wigner’s perspective outside the laboratory, since the friend inside is also an aggregate of atoms, right after the measurement, they must be in a massive quantum entanglement state, a superposition of “the state where the friend saw spin up” and “the state where the friend saw spin down.” When exactly does the collapse of the wave packet occur? Is it when the friend’s consciousness recognizes the result? Or does the entire universe collapse only at the moment Wigner opens the laboratory door, asks the friend for the result, and Wigner’s “consciousness” recognizes it?

This “von Neumann-Wigner interpretation” introduces an extremely subjective, non-physical, and occult element of “human consciousness” into physics, and was fiercely rejected by many physicists. However, this brought out the issue of “dependence on the observer” inherent in the Copenhagen interpretation in its most acute form, and it continues to be debated as an important paradox in modern foundations of quantum mechanics.

Chapter 5: Challengers to the Copenhagen Interpretation

While the Copenhagen Interpretation long reigned as the orthodox doctrine in the physics community and the pragmatism of “Shut up and calculate” dominated, physicists who were deeply in despair over its philosophical ambiguity and the unnaturalness of the “collapse of the wave packet” constructed various alternative interpretations and theories.

5.1 De Broglie-Bohm Pilot Wave Theory (Hidden Variable Theory)

Proposed by Louis de Broglie and refined by David Bohm in 1952, this theory is a prime example of a “Hidden-variable theory.” In this theory, it is considered that not only wave functions but also “actual particles (corpuscles)” with definite trajectories always exist simultaneously in the world.

In this interpretation, the universe is entirely deterministic, much like Newtonian mechanics. Even in the double-slit experiment, a particle always passes through only one of the slits, but the pilot wave passes through both slits and interferes, curving the trajectory of the particle to form interference fringes on the screen. The collapse of the wave packet is unnecessary, and the emergence of probability is said to simply result from our ignorance—our lack of exact knowledge of the “hidden variable,” which is the initial position of the particle.

However, a heavy price must be paid for this theory to hold. Since the quantum potential $Q$ does not decay with distance, a change in the state of a particle at the edge of the universe instantaneously affects the trajectories of other particles. In other words, one must fundamentally accept a severe “non-locality.” Moreover, it is extremely difficult to make it consistent with the special theory of relativity.

5.2 Everett’s Many-Worlds Interpretation (MWI)

In 1957, Hugh Everett III took a radical and beautiful approach to completely banish the greatest weakness of the Copenhagen interpretation, the “collapse of the wave packet (Process 2),” from theory. This is the Many-Worlds Interpretation (MWI).

Everett considered that there exists a single massive “Universal wave function” describing the entire universe, and it always continues to evolve deterministically according only to the Schrödinger equation (Process 1). When an observation is made, the wave packet does not collapse, but the observed object and the observer (as well as the environment) become entangled, and the entire world “branches” corresponding to each component of the superposition.

To put it in terms of the Schrödinger’s cat thought experiment, both “the world where the cat is alive” and “the world where the cat is dead” exist in parallel as physical realities and branch off. The observers in each branched world can only perceive one outcome due to the nature of entanglement, and cannot interfere with each other’s worlds. While the Many-Worlds Interpretation possesses the extremely refined simplicity of having only one mathematical formulation—the Schrödinger equation—it continually faces philosophical resistance because the ontological cost of the universe endlessly multiplying with every observation is far too massive.

5.3 Roger Penrose’s Objective Collapse Theory (OR)

While the Many-Worlds Interpretation denies the collapse of the wave function as an illusion, the Objective Collapse Theory asserts that “the collapse occurs objectively as a purely physical process, independent of human observation or consciousness.” Representative examples include the GRW theory.

Among these, the “gravitationally induced collapse model (Diósi-Penrose model)” proposed by Nobel laureate Roger Penrose is highly unique and grandiose. According to Penrose, when an object with mass exists in a superposition at different locations in space, from the standpoint of general relativity, this means a “superposition of different spacetime geometries.” However, a superposition of the spacetime structure itself is extremely unstable, and depending on the gravitational self-energy $E_G$ arising from the difference in mass distribution of the two states, once a certain time $\tau \approx \hbar / E_G$ elapses, it spontaneously (objectively) collapses into a single state. This is a profound approach directly linked to the unfinished problem of integrating quantum mechanics and general relativity (quantum gravity theory), and it also ties into attempts to explain human consciousness through microtubule quantum effects (Orch OR theory).

5.4 Quantum Decoherence Theory

Since the 1970s, the concept of “Quantum Decoherence” has been established through the research of Heinz-Dieter Zeh, Wojciech Zurek, and others. This is a theory that focuses on the fact that quantum systems are not isolated in a vacuum, but are always interacting with a massive external environment (photons, air molecules, thermal baths, etc.).

When a system interacts with the environment, entanglement occurs, and the “interference effects (phase information of the superposition)” peculiar to quantum systems leak into the environment in an extremely short time, diffuse, and are lost. Due to this decoherence phenomenon, macroscopic superposition states like Schrödinger’s cat instantaneously lose coherence and become virtually indistinguishable from classical probability distributions (mixed states). This provided a highly powerful and quantitative physical explanation for the problem of the transition to the classical limit, asking “why does our everyday world behave classically.”

However, it must be noted that decoherence theory only explains “the vanishing of interference terms” (the apparent collapse), and does not resolve the ultimate mystery itself of “why this specific single outcome was realized” (Single outcome problem / Measurement problem) out of multiple classical possibilities. Therefore, today decoherence is generally operated in combination with other interpretations, such as being used to explain the mechanism of world branching in the Many-Worlds Interpretation.

Chapter 6: Bohr’s Legacy and the Epistemological Turn in the 21st Century

In modern physics, there is no single, clear dogma known as the “Copenhagen Interpretation.” While many physicists master quantum mechanics as a practical tool, they are diversely divided on interpretation into factions like the Many-Worlds faction and the hidden variables faction. However, the profound philosophical intuition presented by Bohr has by no means become a relic of the past. Rather, it has changed its guise and been resurrected at the forefront of 21st-century quantum information theory.

6.1 QBism (Quantum Bayesianism)

QBism (Quantum Bayesianism), proposed by Christopher Fuchs and others, is an approach that thoroughly pushes the “subjective and epistemological” aspect of the Copenhagen interpretation from the perspective of modern information theory.

In QBism, the wave function does not represent “objective physical reality” at all. It is nothing more than a user’s manual or a mathematical tool for individual agents (observers) to calculate their “degree of personal belief (probability prediction)” about future measurement results based on the information they possess. The collapse of the wave packet upon observation is not because any physical change occurred in the world, but simply because the agent obtained new information through measurement and updated their Bayesian probability (belief).

By taking this thoroughly anti-realist stance, the contradictions in the Wigner’s friend problem and the mystery of “non-local action (spooky action at a distance)” in the EPR paradox completely vanish. This is because what is updated is only the information and belief inside the agent’s head, and no physical influence is propagating across space. QBism can be said to be the purest and most radical successor to Bohr’s thought that “Physics is not about how nature is, but about what we can say about nature.”

6.2 Relational Quantum Mechanics (RQM)

Relational Quantum Mechanics (RQM), proposed by Carlo Rovelli, a pioneer in quantum gravity theory, also expands and relativizes the concepts of Bohr’s complementarity and indivisibility.

Just as Einstein’s theory of relativity stated that “absolute time and space do not exist, and velocity and time are always relative relationships to the observer,” Rovelli argues that an “absolute state of a system” does not exist in quantum mechanics either. The state of a physical system is defined only relatively, to another physical system (observer) with which it interacts. Therefore, even if observation is completed and the wave packet has collapsed for observer A, for another observer B who does not know about that interaction, the system and observer A could still be in a massive superposition state. Both descriptions are not contradictory. Sandwiched between realism and anti-realism, this approach views not the substance but the web-like “relations” of the world itself as fundamental reality, even carrying an Eastern philosophical resonance.

6.3 Conclusion: Bohr’s Epistemological Turn and Our Reality

The essence of the Copenhagen interpretation that Niels Bohr sought throughout his life was not merely an agreement on the mathematical rules of quantum mechanics, but lay in a philosophical “Epistemological turn.”

Once, Immanuel Kant stated in his “Critique of Pure Reason” that humans can only recognize “phenomena” constructed through the senses, and can never reach the “thing-in-itself (Ding an sich)” behind them. Bohr’s insight into the complementarity principle and the measurement problem can truly be called a Kantian turn in modern physics. We can never directly picture the “thing-in-itself” of the microscopic quantum using the classical concepts (position, trajectory, continuity) we use daily. What is allowed for us is only to integrate and understand the fragmentary phenomena that appear through the “window” of macroscopic measuring apparatuses within the complementary logical framework of waves and particles.

The following words left by Bohr continue to shine today as one of the deepest and most humble insights in the history of human thought regarding the fundamental questions of what science is and what reality is.

“It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.” (Niels Bohr)

Quantum mechanics taught us how strange and rich nature is, and how limited our human naive intuition is. The exploration surrounding the Copenhagen interpretation will continue to be a source of eternal philosophical contemplation, far transcending the framework of the academic discipline of physics, regarding how humans can recognize this vast universe and how they can speak about it in language. Forged through endless dialogues with Einstein, Bohr’s legacy will continue to live on as an inexhaustible inspiration for future scientists.

(The End)