Copenhagen Interpretation of Quantum Mechanics

哥本哈根量子力学诠释

First published Fri May 3, 2002; substantive revision Fri Dec 6, 2019

首次发布于2002年5月3日；实质性修订2019年12月6日星期五

As the theory of the atom, quantum mechanics is perhaps the most successful theory in the history of science. It enables physicists, chemists, and technicians to calculate and predict the outcome of a vast number of experiments and to create new and advanced technology based on the insight into the behavior of atomic objects. But it is also a theory that challenges our imagination. It seems to violate some fundamental principles of classical physics, principles that eventually have become a part of western common sense since the rise of the modern worldview in the Renaissance. The aim of any metaphysical interpretation of quantum mechanics is to account for these violations.

作为原子理论，量子力学也许是科学史上最成功的理论。它使物理学家，化学家和技术人员能够计算和预测大量实验的结果，并基于对原子物体行为的洞察力来创建新的先进技术。但这也是一种挑战我们想象力的理论。它似乎违反了古典物理学的一些基本原理，自从文艺复兴时期现代世界观崛起以来，这些原理最终已成为西方常识的一部分。量子力学的任何形而上学解释的目的都是为了解决这些冲突。

The Copenhagen interpretation was the first general attempt to understand the world of atoms as this is represented by quantum mechanics. The founding father was mainly the Danish physicist Niels Bohr, but also Werner Heisenberg, Max Born and other physicists made important contributions to the overall understanding of the atomic world that is associated with the name of the capital of Denmark.

哥本哈根的解释是理解原子世界的第一次一般尝试，因为这是量子力学所代表的。开国元勋主要是丹麦物理学家尼尔斯·玻尔，但维尔纳·海森堡，麦克斯·伯恩和其他物理学家也为对与丹麦首都名称相关的原子世界的整体理解做出了重要贡献。

In fact Bohr and Heisenberg never totally agreed on how to understand the mathematical formalism of quantum mechanics, and neither of them ever used the term “the Copenhagen interpretation” as a joint name for their ideas. In fact, Bohr once distanced himself from what he considered to be Heisenberg’s more subjective interpretation (APHK, p.51). The term is rather a label introduced by people opposing Bohr’s idea of complementarity, to identify what they saw as the common features behind the Bohr-Heisenberg interpretation as it emerged in the late 1920s. Today the Copenhagen interpretation is mostly regarded as synonymous with indeterminism, Bohr’s correspondence principle, Born’s statistical interpretation of the wave function, and Bohr’s complementarity interpretation of certain atomic phenomena.

实际上，玻尔和海森堡从未就如何理解量子力学的数学形式主义达成完全共识，而且他们俩都从未将“哥本哈根解释”一词用作其思想的统称。实际上，玻尔曾经与海森堡更为主观的解释相距甚远（APHK，第51页）。这个词是人们反对玻尔的互补性思想引入的标签，用以识别他们认为在1920年代末出现的玻尔－海森堡解释背后的共同特征。如今，哥本哈根解释已被广泛视为不确定性，玻尔的对应原理，波恩对波函数的统计解释以及玻尔对某些原子现象的互补解释的同义词。

1. The Background

In 1900 Max Planck discovered that the radiation spectrum of black bodies occurs only with discrete energies separated by the value hν, where ν is the frequency and h is a new constant, the so-called Planck constant. According to classical physics, the intensity of this continuous radiation would grow unlimitedly with growing frequencies, resulting in what was called the ultraviolet catastrophe. But Planck’s suggestion was that if black bodies only exchange energy with the radiation field in a proportion equal to hν that problem would disappear. The fact that the absorption and the emission of energy is discontinuous is in conflict with the principles of classical physics. A few years later Albert Einstein used this discovery in his explanation of the photoelectric effect. He suggested that light waves were quantized, and that the amount of energy which each quantum of light could deliver to the electrons of the cathode, was exactly hν. The next step came in 1911 when Ernest Rutherford performed some experiments shooting alpha particles into a gold foil. Based on these results he could set up a model of the atom in which the atom consisted of a heavy nucleus with a positive charge surrounded by negatively charged electrons like a small solar system. Also this model was in conflict with the laws of classical physics. According to classical mechanics and electrodynamics, one might expect that the electrons orbiting around a positively charged nucleus would continuously emit radiation so that the nucleus would quickly swallow the electrons.

1900年，马克斯·普朗克（Max Planck）发现黑体的辐射光谱仅在离散能量被值hν分开时出现，其中ν是频率，h是新常数，即所谓的Planck常数。根据经典物理学，这种连续辐射的强度会随着频率的增加而无限增加，从而导致所谓的紫外线灾难。但是普朗克的建议是，如果黑体仅与辐射场以等于hν的比例交换能量，那么这个问题就会消失。能量的吸收和发射是不连续的这一事实与经典物理学原理相冲突。几年后，爱因斯坦（Albert Einstein）在对光电效应的解释中运用了这一发现。他建议对光波进行量化，每个光量子可以传递给阴极电子的能量恰好是hν。下一步是1911年，欧内斯特·卢瑟福（Ernest Rutherford）进行了一些实验，将阿尔法粒子发射到了金箔中。根据这些结果，他可以建立一个原子模型，其中该原子由重核组成，重核带有正电荷，被带负电荷的电子包围着，就像一个小的太阳系。这个模型也与古典物理学定律相抵触。根据经典力学和电动力学，人们可能期望绕着带正电的原子核运行的电子将不断发射辐射，因此原子核将迅速吞下电子。

At this point Niels Bohr entered the scene and soon became the leading physicist on atoms. In 1913 Bohr, visiting Rutherford in Manchester, put forward a mathematical model of the atom which provided the first theoretical support for Rutherford’s model and could explain the emission spectrum of the hydrogen atom (the Balmer series). The theory was based on two postulates:

此时，尼尔斯·玻尔（Niels Bohr）进入了现场，并很快成为原子领域的领先物理学家。 1913年，玻尔访问曼彻斯特的卢瑟福，提出了原子的数学模型，这为卢瑟福的模型提供了第一个理论支持，并可以解释氢原子的发射光谱（巴尔默级数）。该理论基于两个假设：

1. An atomic system is only stable in a certain set of states, called stationary states, each state being associated with a discrete energy, and every change of energy corresponds to a complete transition from one state to another.

2. The possibility for the atom to absorb and emit radiation is determined by a law according to which the energy of the radiation is given by the energy difference between two stationary states being equal to hν.

原子系统仅在特定的一组状态（称为固定状态）下是稳定的，每个状态都与离散能量相关联，并且每次能量变化都对应于从一个状态到另一种状态的完整过渡。

原子吸收和发射辐射的可能性由定律确定，根据该定律，辐射的能量由等于hv的两个稳态之间的能量差给出。

Some features of Bohr’s semi-classical model were indeed very strange compared to the principles of classical physics. It introduced an element of discontinuity and indeterminism foreign to classical mechanics:

与古典物理学原理相比，玻尔的半经典模型的某些功能确实非常奇怪。它引入了不连续性的要素

1. Apparently not every point in space was accessible to an electron moving around a hydrogen nucleus. An electron moved in classical orbits, but during its transition from one orbit to another it was at no definite place between these orbits. Thus, an electron could only be in its ground state (the orbit of lowest energy) or an excited state (if an impact of another particle had forced it to leave its ground state.)

显然，并不是每个空间中的每个点都可以被围绕氢核移动的电子所接近。电子在经典轨道中运动，但是在其从一个轨道过渡到另一个轨道的过程中，它在这些轨道之间没有确定的位置。因此，电子只能处于其基态（能量最低的轨道）或受激态（如果另一个粒子的撞击迫使其离开基态）。

2. It was impossible to predict when the transition would take place and how it would take place. Moreover, there were no external (or internal) causes that determined the “jump” back again. Any excited electron might in principle move spontaneously to either a lower state or down to the ground state.

无法预测何时会发生过渡以及过渡如何发生。而且，没有外部（或内部）原因再次确定“跳跃”。原则上，任何受激电子都可以自发地移动到较低状态或下降到基态。

3. Rutherford pointed out that if, as Bohr did, one postulates that the frequency of light ν, which an electron emits in a transition, depends on the difference between the initial energy level and the final energy level, it appears as if the electron must “know” to what final energy level it is heading in order to emit light with the right frequency.

卢瑟福指出，如果像玻尔那样假设电子在跃迁中发射的光的频率ν取决于初始能级和最终能级之间的差异，就好像电子必须“知道”其前进的最终能量水平，以便以正确的频率发光。

4. Einstein made another strange observation. He was curious to know in which direction the photon decided to move off from the electron.

爱因斯坦又做了一个奇怪的观察。他很好奇，想知道光子决定从电子移向哪个方向。

Between 1913 and 1925 Bohr, Arnold Sommerfeld and others were able to improve Bohr’s model, and together with the introduction of spin and Wolfgang Pauli’s exclusion principle it gave a reasonably good description of the basic chemical elements. The model ran into problems, nonetheless, when one tried to apply it to spectra other than that of hydrogen. So there was a general feeling among all leading physicists that Bohr’s model had to be replaced by a more radical theory. In 1925 Werner Heisenberg, at that time Bohr’s assistant in Copenhagen, laid down the basic principles of a complete quantum mechanics. In his new matrix theory he replaced classical commuting variables with non-commuting ones. The following year, Erwin Schrödinger gave a simpler formulation of the theory in which he introduced a second-order differential equation for a wave function. He himself attempted a largely classical interpretation of the wave function. However, already the same year Max Born proposed a consistent statistical interpretation in which the square of the absolute value of this wave function expresses a probability amplitude for the outcome of a measurement.

从1913年到1925年，玻尔，阿诺德·索默费尔德（Arnold Sommerfeld）等人能够改进玻尔的模型，并结合自旋和沃尔夫冈·保利（Wolfgang Pauli）的排除原理，对基本化学元素进行了合理的描述。然而，当人们试图将其应用于除氢谱以外的光谱时，该模型仍存在问题。因此，所有领先的物理学家普遍认为，玻尔模型必须被更激进的理论所取代。 1925年，当时维尔在哥本哈根的助手维尔纳·海森堡（Werner Heisenberg）提出了完整量子力学的基本原理。在他的新矩阵理论中，他用非通勤变量代替了传统的通勤变量。次年，ErwinSchrödinger给出了一个更简单的理论表述，他为波动函数引入了二阶微分方程。他本人尝试对波动函数进行经典的解释。但是，在同一年，麦克斯·伯恩（Max Born）提出了一种一致的统计解释，其中该波动函数的绝对值的平方表示测量结果的概率幅度。

2. Classical Physics

Bohr saw quantum mechanics as a generalization of classical physics although it violates some of the basic ontological principles on which classical physics rests. Some of these principles are:

玻尔将量子力学视为经典物理学的概括，尽管它违反了经典物理学所依赖的一些基本本体论原理。其中一些原则是：

物理对象及其标识的原则：

· The principles of physical objects and their identity:

物理对象及其标识的原则：

o Physical objects (systems of objects) exist in space and time and physical processes take place in space and time, i.e., it is a fundamental feature of all changes and movements of physical objects (systems of objects) that they happen on a background of space and time;

物理对象（对象系统）在空间和时间中存在，物理过程在时空中发生，即，它是物理对象（对象系统）在空间背景下发生的所有变化和运动的基本特征和时间；

o Physical objects (systems) are localizable, i.e., they do not exist everywhere in space and time; rather, they are confined to definite places and times;

物理对象（系统）是可本地化的，即它们在空间和时间上并不处处存在；相反，它们仅限于确定的地点和时间；

o A particular place can only be occupied by one object of the same kind at a time;

一个特定的位置一次只能被一个相同种类的物体占据；

o Two physical objects of the same kind exist separately; i.e., two objects that belong to the same kind cannot have identical location at an identical time and must therefore be separated in space and time;

两种同类型的物理对象分开存在；即，属于同一种类的两个对象不能在同一时间具有相同的位置，因此必须在空间和时间上分开；

o Physical objects are countable, i.e., two alluded objects of the same kind count numerically as one if both share identical location at a time and counts numerically as two if they occupy different locations at a time;

物理对象是可数的，即，如果两个相同类型的暗指对象一次共享相同的位置，则它们在数值上就算为一个，而如果它们一次占据不同的位置，则在数值上是2。

· The principle of separated properties, i.e., two objects (systems) separated in space and time have each independent inherent states or properties;

分离属性的原理，即在空间和时间上分离的两个对象（系统）具有各自独立的固有状态或属性；

· The principle of value determinateness, i.e., all inherent states or properties have a specific value or magnitude independent of the value or magnitude of other properties;

价值确定性原则，即所有固有状态或属性都有特定的值或大小，而与其他属性的值或大小无关；

· The principle of causality, i.e., every event, every change of a system, has a cause;

因果关系原则，即每个事件，系统的每次更改都有原因；

· The principle of determination, i.e., every later state of a system is uniquely determined by any earlier state;

确定原则，即系统的每个较新状态由任何较早状态唯一地确定；

· The principle of continuity, i.e., all processes exhibiting a difference between the initial and the final state have to go through every possible intervening state; in other words, the evolution of a system is an unbroken path through its state space; and finally

连续性原则，即所有在初始状态和最终状态之间表现出差异的过程都必须经历所有可能的介入状态；换句话说，系统的演化是贯穿其状态空间的一条不间断的道路。

· The principle of the conservation of energy, i.e., the energy of a closed system can be transformed into various forms but is never gained, lost or destroyed.

最后节约能量的原理，即封闭系统的能量可以转换成各种形式，但永远不会获得，损失或破坏。

Due to these principles it is possible within, say, classical mechanics, to define a state of a system at any later time with respect to a state at any earlier time. So whenever we know the initial state consisting of the system’s position and momentum, and know all external forces acting on it, we also know what will be its later states. The knowledge of the initial state is usually acquired by observing the state properties of the system at the time selected as the initial moment. Furthermore, the observation of a system does not affect its later behavior or, if observation somehow should influence this behavior, it is always possible to incorporate the effect into the prediction of the system’s later state. Thus, in classical physics we can always draw a sharp distinction between the state of the measuring instrument being used on a system and the state of the physical system itself. It means that the physical description of the system is objective because the definition of any later state is not dependent on measuring conditions or other observational conditions.

由于这些原理，例如在经典力学中，有可能相对于任何较早时间的状态在任何较晚时间定义系统的状态。因此，只要我们知道由系统的位置和动量组成的初始状态，并且知道作用在该系统上的所有外力，我们也就会知道其后续状态是什么。通常通过观察在选定为初始时刻的系统的状态属性来获取初始状态的知识。此外，对系统的观察不会影响其以后的行为，或者，如果观察会以某种方式影响该行为，则总是有可能将影响合并到对系统的后继状态的预测中。因此，在经典物理学中，我们总是可以在系统上使用的测量仪器的状态与物理系统本身的状态之间进行清晰的区分。这意味着系统的物理描述是客观的，因为任何后续状态的定义都不取决于测量条件或其他观察条件。

Much of Kant’s philosophy can be seen as an attempt to provide satisfactory philosophical grounds for the objective basis of Newton’s mechanics against Humean scepticism. Kant thus argued that classical mechanics is in accordance with the transcendental conditions for objective knowledge. Kant’s philosophy undoubtedly influenced Bohr in various ways, as many scholars in recent years have noticed (Hooker 1972; Folse 1985; Honner 1987; Faye 1991; Kaiser 1992; and Chevalley 1994). Bohr was definitely neither a subjectivist nor a positivist philosopher, as Karl Popper (1967) and Mario Bunge (1967) have claimed. He explicitly rejected the idea that the experimental outcome is due to the observer. As he said: “It is certainly not possible for the observer to influence the events which may appear under the conditions he has arranged” (APHK, p.51). Not unlike Kant, Bohr thought that we could have objective knowledge only in case we can distinguish between the experiential subject and the experienced object. It is a precondition for the knowledge of a phenomenon as being something distinct from the sensorial subject, that we can refer to it as an object without involving the subject’s experience of the object. In order to separate the object from the subject itself, the experiential subject must be able to distinguish between the form and the content of his or her experiences. This is possible only if the subject uses causal and spatial-temporal concepts for describing the sensorial content, placing phenomena in causal connection in space and time, since it is the causal space-time description of our perceptions that constitutes the criterion of reality for them. Bohr therefore believed that what gives us the possibility of talking about an object and an objectively existing reality is the application of those necessary concepts, and that the physical equivalents of “space,” “time,” “causation,” and “continuity” were the concepts “position,” “time,” “momentum,” and “energy,” which he referred to as the classical concepts. He also believed that the above basic concepts exist already as preconditions of unambiguous and meaningful communication, built in as rules of our ordinary language. So, in Bohr’s opinion the conditions for an objective description of nature given by the concepts of classical physics were merely a refinement of the preconditions of human knowledge.

康德的大部分哲学思想都可以看作是为牛顿反对Humean怀疑主义的机制的客观基础提供令人满意的哲学基础的尝试。康德因此认为古典力学符合客观知识的先验条件。正如近年来许多学者所注意到的那样，康德的哲学无疑以各种方式影响了玻尔（Hooker 1972; Folse 1985; Honner 1987; Faye 1991; Kaiser 1992; and Chevalley 1994）。正如卡尔·波普（Karl Popper，1967）和马里奥·邦奇（Mario Bunge，1967）所宣称的那样，玻尔绝对既不是主观主义者也不是实证主义者。他明确拒绝实验结果归因于观察者的想法。正如他所说：“观察者当然不可能影响在他所安排的条件下可能发生的事件”（APHK，第51页）。与康德不同，玻尔认为只有在我们能够区分经验主体和经验主体的情况下，我们才能拥有客观知识。作为一种现象的知识，它与感觉对象有所不同是一个前提，我们可以将其称为对象而不涉及对象对对象的体验。为了使对象与主体本身分离，经验主体必须能够区分其经历的形式和内容。这仅在主体使用因果关系和时空概念来描述感官内容，将现象置于时空因果关系中的情况下才有可能，因为正是我们感知的因果时空描述构成了他们的现实标准。 。因此，玻尔认为，使我们有可能谈论一个物体和客观存在的现实的是那些必要概念的应用，并且“空间”，“时间”，“因果关系”和“连续性”的物理等价物是他将其称为“位置”，“时间”，“动量”和“能量”的概念称为经典概念。他还认为，上述基本概念已经作为明确和有意义的交流的先决条件而存在，并以我们的普通语言规则为基础。因此，在玻尔看来，古典物理学概念给出的客观描述自然的条件仅仅是人类知识前提的改进。

3. The Correspondence Rule

The guiding principle behind Bohr’s and later Heisenberg’s work in the development of a consistent theory of atoms was the correspondence rule. The full rule states that a transition between stationary states is allowed if, and only if, there is a corresponding harmonic component in the classical motion (CW Vol. 3, p. 479). Bohr furthermore realized that according to his theory of the hydrogen atom, the frequencies of radiation due to the electron’s transition between stationary states with high quantum numbers, i.e. states far from the ground state, coincide approximately with the results of classical electrodynamics. Hence in the search for a theory of quantum mechanics it became a methodological requirement to Bohr that any further theory of the atom should predict values in domains of high quantum numbers that should be a close approximation to the values of classical physics. The correspondence rule was a heuristic principle meant to make sure that in areas where the influence of Planck’s constant could be neglected the numerical values predicted by such a theory should be the same as if they were predicted by classical radiation theory.

玻尔和后来的海森堡在发展一致的原子理论中所遵循的指导原则是对应规则。完全规则规定，当且仅当经典运动中存在相应的谐波分量时，才允许在稳态之间进行转换（CW第3卷，第479页）。玻尔进一步认识到，根据他对氢原子的理论，由于电子在具有高量子数的稳态（即远离基态的状态）之间跃迁而产生的辐射频率与经典电动力学的结果大致相符。因此，在寻找量子力学理论时，玻尔提出了方法学上的要求，即原子的任何进一步理论都应预测高量子数域中的值，该值应与经典物理学的值非常接近。对应规则是一种启发式原理，旨在确保在可以忽略普朗克常数影响的区域中，这种理论所预测的数值应该与经典辐射理论所预测的数值相同。

The Bohr-Sommerfeld core model of the atomic structure came into trouble in the beginning of the 1920s due to the fact that it couldn’t handle an increasing number of spectroscopic phenomena. In 1924 Wolfgang Pauli introduced a new degree of freedom according to which two electrons with the same known quantum numbers could not be in the same state. A year later, in 1925, Ralph Kronig, Georg Uhlenbeck and Samuel Goudsmit explained this new degree of freedom by introducing the non-classical concept of electron spin. It has been suggested, however, that Pauli’s proposal meant a lethal blow not only to the Bohr-Sommerfeld model, but also to the correspondence principle because “how to reconcile the classical periodic motions presupposed by the correspondence principle with the classically non-describable Zweideutigkeit of the electron’s angular momentum?” (Massimi 2005, p. 73)

原子结构的Bohr-Sommerfeld核心模型在1920年代初陷入困境，原因是它无法处理越来越多的光谱现象。 1924年，沃尔夫冈·保利（Wolfgang Pauli）引入了新的自由度，根据该自由度，两个具有相同已知量子数的电子不能处于同一状态。一年后的1925年，拉尔夫·克罗尼格（Ralph Kronig），乔治·乌伦贝克（Georg Uhlenbeck）和塞缪尔·古德斯密特（Samuel Goudsmit）通过引入非经典的电子自旋概念，解释了这一新的自由度。但是，有人提出，Pauli的提议不仅给Bohr-Sommerfeld模型带来致命的打击，而且对对应原理也造成了致命的打击，因为“如何将对应原理所预设的经典周期性运动与经典不可描述的Zweideutigkeit进行协调”电子的角动量？” （Massimi 2005，第73页）

Although the exclusion rule and the introduction of spin broke with the attempt to explain the structure of the basic elements along the lines of the correspondence argument (as Pauli pointed out in a letter to Bohr) Bohr continued to think of it as an important methodological principle in the attempt to establish a coherent quantum theory. In fact, he repeatedly expressed the opinion that Heisenberg’s matrix mechanics came to light under the guidance of this very principle. In his Faraday Lectures from 1932, for instance, Bohr emphasizes: “A fundamental step towards the establishing of a proper quantum mechanics was taken in 1925 by Heisenberg who showed how to replace the ordinary kinematical concepts, in the spirit of the correspondence argument, by symbols referring to the elementary processes and the probability of their occurrence” (CC, p. 48). Bohr acknowledged, however, that the correspondence argument failed too in those cases where particular non-classical concepts have to be introduced into the description of atoms. But he still thought that the correspondence argument was indispensable for both structural and semantic reasons in constructing a proper quantum theory as a generalised theory from classical mechanics.

尽管排除规则和自旋的引入打破了尝试按照对应论点来解释基本元素的结构的方式（正如保利在给玻尔的一封信中指出的那样），但玻尔仍将其视为重要的方法论原理。试图建立一个连贯的量子理论。实际上，他反复表达了这样的观点，即海森堡的矩阵力学是在这一原理的指导下曝光的。例如，玻尔在1932年的法拉第演讲中强调：“海森堡在1925年迈出了建立适当的量子力学的基本步骤，他展示了如何根据对应论证的精神替换普通的运动学概念，表示基本过程及其发生概率的符号”（CC，第48页）。然而，玻尔承认，在必须将特定的非经典概念引入原子描述的情况下，对应论点也失败了。但是他仍然认为，在构造适当的量子理论作为经典力学的广义理论时，从结构和语义两方面来说，对应论证都是必不可少的。

Indeed, spin is a quantum property of the electrons which cannot be understood as a classical angular momentum. Needless to say, Bohr fully understood that. But he didn’t think that this discovery ruled out the use of the correspondence rule as guidance to finding a satisfactory quantum theory. A lengthy quotation from Bohr’s paper “The Causality Problem in Atomic Physics” (1938) gives evidence for this:

实际上，自旋是电子的量子性质，不能理解为经典角动量。毋庸置疑，玻尔完全理解这一点。但是他并不认为这一发现会排除使用对应规则作为寻找令人满意的量子理论的指导。玻尔的论文“原子物理学中的因果问题”（1938年）中有一长篇引述提供了以下证据：

Indeed, as adequate as the quantum postulates are in the phenomenological description of the atomic reactions, as indispensable are the basic concepts of mechanics and electrodynamics for the specification of atomic structures and for the definition of fundamental properties of the agencies with which they react. Far from being a temporary compromise in this dilemma, the recourse to essentially statistical considerations is our only conceivable means of arriving at a generalization of the customary way of description sufficiently wide to account for the features of individuality expressed by the quantum postulates and reducing to classical theory in the limiting case where all actions involved in the analysis of the phenomena are large compared with a single quantum. In the search for the formulation of such a generalization, our only guide has just been the so called correspondence argument, which gives expression for the exigency of upholding the use of classical concepts to the largest possible extent compatible with the quantum postulates. (CC, p.96)

的确，在原子反应的现象学描述中，只要有足够的量子假设，对于说明原子结构以及与之反应的机构的基本性质的定义，必不可少的是力学和电动力学的基本概念。在此困境中，这绝不是暂时的折衷，而是求助于基本统计上的考虑，这是我们得出的一种通用的描述方式的概括方法，它足以广泛地解释量子假设所表达的个性特征并将其简化为经典，这是我们唯一可以想到的方法。在极限情况下的理论，即与单个量子相比，现象分析所涉及的所有动作都很大。在寻求这种概括的表述时，我们的唯一指南就是所谓的对应论点，该论点表达了在最大程度上保持与量子假设相容的坚持使用经典概念的迫切性。 （CC，第96页）

This shows that, according to Bohr, quantum mechanics, as formulated by Heisenberg, was a rational generalization of classical mechanics when the quantum of action and the spin property were taken into account.

The correspondence rule was an important methodological principle. In the beginning it had a clear technical meaning for Bohr. It is obvious, however, that it makes no sense to compare the numerical values of the theory of atoms with those of classical physics unless the meaning of the physical terms in both theories is commensurable. The correspondence rule was based on the epistemological idea that classical concepts were indispensable for our understanding of physical reality, and it is only when classical phenomena and quantum phenomena are described in terms of the same classical concepts that we can compare different physical experiences. It was this broader sense of the correspondence rule that Bohr often had in mind later on. He directly mentioned the relationship between the use of classical concepts and the correspondence principle in 1934 when he wrote in the Introduction to Atomic Theory and the Description of Nature:

这表明，根据玻尔的观点，海森堡提出的量子力学是经典力学的合理概括，其中考虑了作用量子和自旋特性。

对应规则是重要的方法论原则。最初，它对玻尔具有明显的技术意义。但是，很明显，将原子理论的数值与经典物理学的数值进行比较是没有意义的，除非两种理论中物理术语的含义是可比的。对应规则基于认识论思想，即经典概念对于我们对物理现实的理解是必不可少的，只有当用相同的经典概念描述经典现象和量子现象时，我们才能比较不同的物理经验。玻尔后来常常想到的就是这种对通信规则的广泛理解。 1934年他在《原子理论导论和自然描述》中写道，他直接提到了古典概念的使用和对应原理之间的关系：

[T]he necessity of making an extensive use … of the classical concepts, upon which depends ultimately the interpretation of all experience, gave rise to the formulation of the so-called correspondence principle which expresses our endeavours to utilize all the classical concepts by giving them a suitable quantum-theoretical re-interpretation (ATDN, p. 8)

Bohr’s practical methodology stands therefore in direct opposition to Thomas Kuhn and Paul Feyerabend’s historical view that succeeding theories, like classical mechanics and quantum mechanics, are incommensurable. In contrast to their philosophical claims of meaning gaps and partial lack of rationality in the choice between incommensurable theories, Bohr believed not just retrospectively that quantum mechanics was a natural generalization of classical physics, but he and Heisenberg followed in practice the requirements of the correspondence rule. Thus, in the mind of Bohr, the meaning of the classical concepts did not change but their application was restricted. This was the lesson of complementarity.

因此，玻尔的实用方法论与托马斯·库恩（Thomas Kuhn）和保罗·费耶拉本德（Paul Feyerabend）的历史观点直接相反，后者认为诸如经典力学和量子力学之类的成功理论是无与伦比的。与对意义鸿沟和在无与伦比的理论之间进行选择时部分缺乏理性的哲学主张相反，玻尔不仅仅回顾性地认为量子力学是经典物理学的自然概括，而且他和海森堡在实践中遵循了对应规则的要求。因此，在玻尔看来，古典概念的含义没有改变，但其应用受到了限制。这是互补的教训。

4. Complementarity

After Heisenberg had managed to formulate a consistent quantum mechanics in 1925, both he and Bohr began their struggle to find a coherent interpretation for the mathematical formalism. Heisenberg and Bohr followed somewhat different approaches. Where Heisenberg looked to the formalism and developed his famous uncertainty principle or indeterminacy relation, Bohr chose to analyze concrete experimental arrangements, especially the double-slit experiment. In a way Bohr merely regarded Heisenberg’s relation as an expression of his general notion that our understanding of atomic phenomena builds on complementary descriptions. At Como in 1927 he presented for the first time his ideas according to which certain different descriptions are said to be complementary.

4.互补性

在海森堡（Heisenberg）在1925年设法制定出一致的量子力学之后，他和玻尔（Bohr）便开始努力寻找数学形式主义的连贯解释。海森堡和玻尔采取了一些不同的方法。海森堡着眼于形式主义并发展了他著名的不确定性原则或不确定性关系的地方，玻尔选择分析具体的实验安排，尤其是双缝实验。玻尔只是以某种方式将海森堡的关系视为他对我们对原子现象的理解建立在互补描述基础上的一般观念的一种表达。 1927年，他在科莫（Como）首次提出了自己的想法，根据该想法，某些不同的描述被认为是互补的。

Bohr pointed to two sets of descriptions which he took to be complementary. On the one hand, there are those that attribute either kinematic or dynamic properties to the atom; that is, “space-time descriptions” are complementary to “claims of causality”, where Bohr interpreted the causal claims in physics in terms of the conservation of energy and momentum. On the other hand, there are those descriptions that ascribe either wave or particle properties to a single object. How these two kinds of complementary sets of descriptions are related is something Bohr never indicated (Murdoch 1987). Even among people, like Rosenfeld and Pais, who claimed to speak on behalf of Bohr, there is no agreement. The fact is that the description of light as either particles or waves was already a classical dilemma, which not even Einstein’s definition of a photon really solved since the momentum of the photon as a particle depends on the frequency of the light as a wave. Furthermore, Bohr eventually realized that the attribution of kinematic and dynamic properties to an object is complementary because the ascription of both of these conjugate variables rests on mutually exclusive experiments. The attribution of particle and wave properties to an object may, however, occur in a single experiment; for instance, in the double-slit experiment where the interference pattern consists of single dots. So within less than ten years after his Como lecture Bohr tacitly abandoned “wave-particle complementarity” in favor of the exclusivity of “kinematic-dynamic complementarity” (Held 1994).

玻尔指出了两组描述，他认为这些描述是相辅相成的。一方面，有些原子将运动学或动力学特性归因于原子；另一方面，原子能将动力学或动力学特性归因于原子。就是说，“时空描述”是对“因果关系的主张”的补充，在玻尔中，玻尔从能量和动量守恒的角度解释了物理学中的因果关系。另一方面，有些描述将波或粒子属性归因于单个对象。玻尔从未指出过这两种互补的描述是如何关联的（默多克，1987年）。即使在声称代表玻尔讲话的罗森菲尔德和佩斯等人之间也没有达成共识。事实是，将光描述为粒子或波已经是一个经典的难题，因为光子作为粒子的动量取决于波的光的频率，所以甚至爱因斯坦对光子的定义也没有真正解决。此外，玻尔最终意识到运动和动态属性归因于对象是互补的，因为这两个共轭变量的归属都基于互斥实验。但是，粒子和波的属性归因于一个对象可能会发生在单个实验中；例如，在双缝实验中，干涉图样由单个点组成。因此，在他的科莫演讲之后不到十年的时间里，玻尔就默契地放弃了“波粒互补”，而转向了“运动-动力学互补”（Held 1994）。

It was clear to Bohr that any interpretation of the atomic world had to take into account an important empirical fact. The discovery of the quantization of action meant that quantum mechanics could not fulfill the above principles of classical physics. Every time we measure, say, an electron’s position, the apparatus and the electron interact in an uncontrollable way, so that we are unable to measure the electron’s momentum at the same time. Until the mid-1930s when Einstein, Podolsky and Rosen published their famous thought-experiment with the intention of showing that quantum mechanics was incomplete, Bohr spoke as if the measurement apparatus disturbed the electron. This paper had a significant influence on Bohr’s line of thought. Apparently, Bohr realized that speaking of disturbance seemed to indicate—as some of his opponents may have understood him—that atomic objects were classical particles with definite inherent kinematic and dynamic properties. After the EPR paper he stated quite clearly: “the whole situation in atomic physics deprives of all meaning such inherent attributes as the idealization of classical physics would ascribe to such objects.”

玻尔很清楚，对原子世界的任何解释都必须考虑到一个重要的经验事实。作用量化的发现意味着量子力学无法满足上述经典物理学原理。每次我们测量一个电子的位置时，设备和电子都会以无法控制的方式相互作用，因此我们无法同时测量电子的动量。直到1930年代中期，爱因斯坦，波多尔斯基和罗森发表了著名的思想实验，目的是证明量子力学是不完整的，玻尔的讲话似乎使测量设备干扰了电子。这篇论文对玻尔的思路产生了重大影响。显然，玻尔意识到，说到扰动似乎表明（正如他的一些反对者所理解的那样），原子物体是具有确定的固有运动学和动力学性质的经典粒子。在EPR论文发表后，他非常清楚地指出：“原子物理学的整体情况剥夺了所有涵义，例如古典物理学的理想化将这些固有属性归因于这些对象。”

Hence, according to Bohr, the state of the measuring device and the state of the object cannot be separated from each other during a measurement but they form a dynamical whole. Bohr called this form of holism “the individuality” of the atomic process. Thereby, he had in mind not only that the interaction is uncontrollable but also that the system-cum-measurement forms an inseparable unity due to the entanglement – although Bohr’s did not use this term (Faye 1991, 1994; Howard 1994, 2004).

因此，根据玻尔，测量装置的状态和物体的状态在测量期间不能彼此分离，而是形成动态整体。玻尔称这种整体主义为原子过程的“个性”。因此，他不仅考虑到交互作用是不可控的，而且还考虑到系统和测量由于纠缠而形成了密不可分的统一体，尽管玻尔没有使用该术语（Faye 1991，1994; Howard 1994，2004）。

Also after the EPR paper Bohr spoke about Heisenberg’s “indeterminacy relation” as indicating the ontological consequences of his claim that kinematic and dynamic variables are ill-defined unless they refer to an experimental outcome. Earlier he had often called it Heisenberg’s “uncertainty relation”, as if it were a question of a merely epistemological limitation. Furthermore, Bohr no longer mentioned descriptions as being complementary, but rather phenomena or information. He introduced the definition of a “phenomenon” as requiring a complete description of the entire experimental arrangement, and he took a phenomenon to be a measurement of the values of either kinematic or dynamic properties.

在EPR论文发表后，玻尔也谈到了海森堡的“不确定性关系”，这表明他声称运动学和动态变量的定义不明确，除非它们涉及实验结果，否则会带来本体论后果。 此前，他经常称其为海森堡的“不确定性关系”，就好像这只是一个认识论上的局限性问题一样。 此外，玻尔不再提到描述是互补的，而是现象或信息。 他介绍了“现象”的定义，因为它需要对整个实验装置进行完整的描述，并且他认为一种现象是对运动学或动力学特性值的度量。

Bohr’s more mature view, i.e., his view after the EPR paper, on complementarity and the interpretation of quantum mechanics may be summarized in the following points:

玻尔较为成熟的观点，即他在EPR论文发表后对互补性和量子力学解释的观点，可以归纳为以下几点：

1. The interpretation of a physical theory has to rely on an experimental practice.

2. The experimental practice presupposes a certain pre-scientific practice of description, which establishes the norm for experimental measurement apparatus, and consequently what counts as scientific experience.

3. Our pre-scientific practice of understanding our environment is an adaptation to the sense experience of separation, orientation, identification and reidentification over time of physical objects.

4. This pre-scientific experience is grasped in terms of common categories like thing’s position and change of position, duration and change of duration, and the relation of cause and effect, terms and principles that are now parts of our common language.

1.对物理理论的解释必须依靠实验实践。

2.实验实践以某种特定的科学前实践为前提，该实践建立了实验测量仪器的规范，因此也算作科学经验。

3，我们对环境的科学认识实践是对随着时间的流逝而发生的分离，定向，识别和重新识别的感官体验的一种适应。

4.这种先科学的经验是根据常见类别（例如事物的位置和位置的变化，持续时间和持续时间的变化，以及因果关系，术语和原则）构成的，这些常见类别现在已成为我们通用语言的一部分。

5. These common categories yield the preconditions for objective knowledge, and any description of nature has to use these concepts to be objective.

6. The concepts of classical physics are merely exact specifications of the above categories.

7. The classical concepts—and not classical physics itself—are therefore necessary in any description of physical experience in order to understand what we are doing and to be able to communicate our results to others, in particular in the description of quantum phenomena as they present themselves in experiments;

8. Planck’s empirical discovery of the quantization of action requires a revision of the foundation for the use of classical concepts, because they are not all applicable at the same time. Their use is well defined only if they apply to experimental interactions in which the quantization of action can be regarded as negligible.

5，这些共同的类别为获得客观知识提供了前提，对自然的任何描述都必须使用这些概念来达到客观。

6.经典物理学的概念仅是上述类别的精确规范。

7.因此，在任何物理经验的描述中，古典概念（而不是古典物理学本身）都是必需的，以便理解我们在做什么并且能够将结果传达给其他人，尤其是在描述量子现象时，在实验中展示自己；

8，普朗克对行动量化的经验发现，需要修改使用经典概念的基础，因为它们不能同时适用。仅当将它们应用于可以忽略作用量化的实验相互作用时，它们的使用才得到很好的定义。

9. In experimental cases where the quantization of action plays a significant role, the application of a classical concept does not refer to independent properties of the object; rather the ascription of either kinematic or dynamic properties to the object as it exists independently of a specific experimental interaction is ill-defined.

10. The quantization of action demands a limitation of the use of classical concepts so that these concepts apply only to a phenomenon, which Bohr understood as the macroscopic manifestation of a measurement on the object, i.e. the uncontrollable interaction between the object and the apparatus.

11. The quantum mechanical description of the object differs from the classical description of the measuring apparatus, and this requires that the object and the measuring device should be separated in the description, but the line of separation is not the one between macroscopic instruments and microscopic objects. It has been argued in detail (Howard 1994) that Bohr pointed out that parts of the measuring device may sometimes be treated as parts of the object in the quantum mechanical description.

12. The quantum mechanical formalism does not provide physicists with a ‘pictorial’ representation: the ψ-function does not, as Schrödinger had hoped, represent a new kind of reality. Instead, as Born suggested, the square of the absolute value of the ψ-function expresses a probability amplitude for the outcome of a measurement. Due to the fact that the wave equation involves an imaginary quantity this equation can have only a symbolic character, but the formalism may be used to predict the outcome of a measurement that establishes the conditions under which concepts like position, momentum, time and energy apply to the phenomena.

9，在动作量化起着重要作用的实验情况下，经典概念的应用并不指物体的独立属性;确切地说，对象的运动或动态特性归因于它的存在，因为它独立于特定的实验相互作用而存在是不确定的。

10，行动的量化要求限制经典概念的使用，因此这些概念仅适用于现象，玻尔将其理解为对物体进行测量的宏观表现，即物体与设备之间不可控制的相互作用。

11，物体的量子力学描述与测量仪器的经典描述不同，这要求物体和测量设备在描述中应该分开，但是分开的线不是宏观仪器和微观仪器之间的一条线对象。有人曾详细论证过（霍华德1994年），玻尔指出，在量子力学描述中，有时会将测量装置的某些部分视为物体的一部分。

12，量子力学形式主义并不能为物理学家提供“图形化”的表述：ψ函数并不像薛定er所希望的那样代表着一种新的现实。相反，正如博恩（Born）所建议的那样，ψ函数的绝对值的平方表示测量结果的概率幅度。由于波动方程涉及虚数，因此该方程只能具有符号性质，但是可以使用形式主义来预测测量结果，该测量确定了应用位置，动量，时间和能量等概念的条件现象。

13. The ascription of these classical concepts to the phenomena of measurements rely on the experimental context of the phenomena, so that the entire setup provides us with the defining conditions for the application of kinematic and dynamic concepts in the domain of quantum physics.

14. Such phenomena are complementary in the sense that their manifestations depend on mutually exclusive measurements, but that the information gained through these various experiments exhausts all possible objective knowledge of the object.

13.这些经典概念对测量现象的归属取决于现象的实验环境，因此整个设置为我们提供了将运动学和动力学概念应用于量子物理学领域的定义条件。

14，这种现象是互补的，因为它们的表现取决于相互排斥的测量结果，但是通过这些各种实验获得的信息耗尽了对物体的所有可能的客观知识。

Bohr thought of the atom as real. Atoms are neither heuristic nor logical constructions. A couple of times he emphasized this directly using arguments from experiments in a very similar way to Ian Hacking and Nancy Cartwright much later. What he did not believe was that the quantum mechanical formalism was true in the sense that it gave us a literal (‘pictorial’) rather than a symbolic representation of the quantum world. It makes much sense to characterize Bohr in modern terms as an entity realist who opposes theory realism (Folse 1986; Faye 1991).

玻尔认为原子是真实的。原子既不是启发式结构也不是逻辑结构。几次之后，他都直接使用实验中的论点来强调这一点，这与后来的Ian Hacking和Nancy Cartwright极为相似。他不相信量子力学形式主义是正确的，因为它给了我们量子世界的文字（“绘画”）而非符号表示。用现代术语将玻尔描述为反对理论现实主义的实体现实主义者是很有意义的（Folse 1986； Faye 1991）。

It is because of the imaginary quantities in quantum mechanics (where the commutation rule for canonically conjugate variable, p and q, introduces Planck’s constant into the formalism by qp − pq = ih/2π that quantum mechanics does not give us a ‘pictorial’ representation of the world. Neither does the theory of relativity, Bohr argued, provide us with a literal representation, since the velocity of light is introduced with a factor of i in the definition of the fourth coordinate in a four-dimensional manifold (CC, p. 86 and p. 105). Instead these theories can only be used symbolically to predict observations under well-defined conditions. Therefore, many philosophers have interpreted Bohr as an antirealist or an instrumentalist when it comes to theories. However, Bohr’s reference to the use of imaginary number in quantum mechanics as an argument for his rejection of a pictoral representation may seem misplaced. The use of imaginary numbers is more a question about the conventional choice of scale whether measurements should be represented in terms of imaginary or real number than an indication of a certain magnitude expressed in terms of these numbers is not real. Dieks (2017) gives a nuanced discussion of Bohr’s argument, and he concludes that in the context of quantrum mechanics Bohr saw imaginary numbers to be associated with incompatible physical quantities.

正是由于量子力学中的虚量（其中典范共轭变量p和q的交换规则通过qp−pq = ih /2π将普朗克常数引入形式主义中，量子力学才没有给我们提供``图形表示''表示）玻尔认为，相对论也没有为我们提供文字表示，因为在四维流形（CC，p （第86页和第105页），这些理论只能象征性地用于在定义明确的条件下预测观测结果，因此，许多哲学家将玻尔视为理论的反现实主义者或工具主义者。在量子力学中使用虚数作为拒绝接受图形表示的论点似乎是错误的。无论是用虚数还是实数表示测量结果，而不是用这些数字表示一定幅度的表示结果，都是不现实的。 Dieks（2017）对玻尔的论点进行了细致的讨论，他得出结论，在量子力学的背景下，玻尔认为虚数与不相容的物理量有关。

In general, Bohr considered the demands of complementarity in quantum mechanics to be logically on a par with the requirements of relativity in the theory of relativity. He believed that both theories were a result of novel aspects of the observation problem, namely the fact that observation in physics is context-dependent. This again is due to the existence of a maximum velocity of propagation of all actions in the domain of relativity and a minimum of any action in the domain of quantum mechanics. And it is because of these universal limits that it is impossible in the theory of relativity to make an unambiguous separation between time and space without reference to the observer (the context) and impossible in quantum mechanics to make a sharp distinction between the behavior of the object and its interaction with the means of observation (CC, p. 105).

通常，玻尔认为，量子力学中互补性的要求在逻辑上与相对论中的相对性要求是同等的。他认为，这两种理论都是观察问题的新颖方面的结果，也就是说，物理学中的观察是与上下文有关的事实。这又是由于相对论域中所有作用的最大传播速度和量子力学域中任何作用的最小传播。由于这些普遍性的限制，相对论中不可能在不参考观察者（上下文）的情况下在时间和空间之间进行明确的分离，而在量子力学中则不可能在光子的行为之间做出清晰的区分。物体及其与观测手段的相互作用（CC，第105页）。

Complementarity is first and foremost a semantic and epistemological reading of quantum mechanics that carries certain ontological implications. Bohr’s view was, to phrase it in a modern philosophical jargon, that the truth conditions of sentences ascribing a certain kinematic or dynamic value to an atomic object are dependent on the apparatus involved, in such a way that these truth conditions have to include reference to the experimental setup as well as the actual outcome of the experiment. This claim is called Bohr’s indefinability thesis (Murdoch 1987; Faye 1991). Hence, those physicists who accuse this interpretation of operating with a mysterious collapse of the wave function during measurements haven’t got it right. Bohr accepted the Born statistical interpretation because he believed that the ψ-function has only a symbolic meaning and does not represent anything real. It makes sense to talk about a collapse of the wave function only if, as Bohr put it, the ψ-function can be given a pictorial representation, something he strongly denied.

互补首先是对量子力学的语义和认识论解读，具有某些本体论意义。玻尔的观点是，用现代哲学术语来表述，将某个运动学或动态值赋予一个原子物体的句子的真实条件取决于所涉及的装置，以这种方式，这些真实条件必须包括对实验设置以及实验的实际结果。这种说法被称为玻尔的不可定义论点（Murdoch 1987; Faye 1991）。因此，那些物理学家指责这种解释是在测量过程中波函数发生了神秘的坍塌，这是不正确的。玻尔接受了伯恩（Born）统计解释，因为他认为ψ函数仅具有象征意义，并不代表任何真实含义。只有如Bohr所说，只有给ψ函数赋予一个图形表示形式，才可以谈论波动函数的崩溃，但他坚决否认了这一点。

Indeed, Bohr, Heisenberg, and many other physicists considered complementarity to be the only rational interpretation of the quantum world. They thought that it gave us the understanding of atomic phenomena in accordance with the conditions for any physical description and the possible objective knowledge of the world. Bohr believed that atoms are real, but it remains a much debated point in recent literature what sort of reality he believed them to have, whether or not they are something beyond and different from what they are observed to be. Henry Folse argues that Bohr must operate with a distinction between a phenomenal and a transcendental object. The reason is that this is the only way it makes sense to talk about the physical disturbance of the atomic object by the measuring instrument as Bohr did for a while (Folse 1985, 1994). But Jan Faye has replied that Bohr gave up the disturbance metaphor in connection with his discussion of the EPR thought-experiment because he realized that it was misleading. Moreover, there is no further evidence in Bohr’s writings indicating that Bohr would attribute intrinsic and measurement-independent state properties to atomic objects (though quite unintelligible and inaccessible to us) in addition to the classical ones being manifested in measurement (Faye 1991).

确实，玻尔，海森堡和许多其他物理学家认为互补性是对量子世界的唯一理性解释。他们认为，它使我们能够根据任何物理描述的条件和对世界的可能客观认识来理解原子现象。玻尔认为原子是真实的，但是在最近的文献中仍然有很多争论点，他认为原子具有什么样的现实，它们是否超出了所观察到的范围并且与所观察到的有所不同。亨利·佛斯（Henry Folse）认为，玻尔必须在现象性对象与先验对象之间进行区分。原因是，这是唯一的一种谈论测量对象对原子物体的物理扰动的方法，就像玻尔在一段时间内所做的那样（Folse 1985，1994）。但是扬·费耶（Jan Faye）回答说，玻尔在讨论EPR思想实验时放弃了干扰隐喻，因为他意识到这是一种误导。而且，玻尔的著作中没有进一步的证据表明玻尔将把固有的和不依赖于测量的状态属性归因于原子对象（尽管对我们来说是很难理解和难以接近的），而不是在测量中表现出经典的状态（Faye 1991）。

5. The Use of Classical Concepts

A central element in the Copenhagen Interpretation is Bohr’s insistence on the use of classical concepts both with respect to describing experimental results and endowing quantum formalism with an empirical interpretation. The special cognitive status ascribed to the classical concepts is something Bohr stressed from the very beginning. Here is a quotation from 1934:

哥本哈根诠释的中心要素是玻尔在描述实验结果和通过经验解释赋予量子形式主义方面都坚持使用经典概念。玻尔从一开始就强调归因于古典概念的特殊认知状态。以下是1934年的报价：

No more is it likely that the fundamental concepts of the classical theories will ever become superfluous for the description of physical experience. … It continues to be the application of these concepts alone that makes it possible to relate the symbolism of the quantum theory to the data of experience (ATDN, p.16).

对于身体经验的描述，古典理论的基本概念不再是多余的。 ……仅凭这些概念的应用，就可以将量子理论的象征意义与经验数据联系起来（ATDN，第16页）。

Later he expressed the same view in an often quoted passage:

后来，他在经常引用的段落中表达了相同的观点：

It is decisive to recognize that, however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word ‘experiment’ we refer to a situation where we can tell to others what we have done and what we have learned and that, therefore, the account of the experimental arrangement and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics (APHK, p. 39).

可以果断地认识到，无论现象超出经典物理解释的范围，所有证据的说明都必须用经典术语表述。争论仅是通过“实验”一词来指一种情况，在这种情况下，我们可以告诉他人我们所做的事情和所学的知识，因此，对实验安排和观察结果的说明必须可以用明确的语言表达，并适当应用古典物理学的术语（APHK，第39页）。

Bohr saw the classical concepts as necessary for procuring unambiguous communication about what happens in the laboratory. Classical concepts are indispensable, because they enable physicists to describe observations in a clear common language, and because they are the ones by which the physicists connect the mathematical formalism with observational content.

Over the years, different authors have come up with different explanations of why Bohr thought that classical concepts were unavoidable for the description of quantum phenomena. Here we shall group those explanations in relation to five different philosophical frameworks: 1) Empiricism, 2) Kantianism, 3) Pragmatism, 4) Darwinianism, and 5) Experimentalism.

玻尔认为，经典的概念对于进行实验室中发生的事情进行明确的交流是必不可少的。古典概念是必不可少的，因为它们使物理学家能够以一种清晰的通用语言描述观测结果，并且因为它们是物理学家将数学形式主义与观测内容联系起来的依据。

多年以来，不同的作者对玻尔为什么认为量子概念的描述不可避免地使用了经典概念提出了不同的解释。在这里，我们将针对五种不同的哲学框架对这些解释进行归类：1）经验主义； 2）康德主义； 3）实用主义； 4）达尔文主义； 5）实验主义。

Empiricism. This view is represented by the logical positivists. They believed that the interpretation of any scientific theory should be grounded in empirical observations. No theory, according the positivists, is cognitively meaningful unless its terms can be connected to terms that are able to express results that would verify that theory. Observational terms refer directly to observable things or observable properties of physical objects, whereas theoretical terms are explicitly defined by correspondence rules connecting them with the observational terms. Hence classical terms, like position and momentum, are exactly such terms that enable physicist to ascribe a physical meaning to quantum mechanics.

经验主义。这种观点由逻辑实证主义者代表。他们认为，任何科学理论的解释都应基于经验观察。实证主义者认为，除非理论的术语可以与能够表达将验证该理论的结果的术语相关联，否则任何理论都没有认知意义。观察术语直接指的是物理对象的可观察事物或可观察特性，而理论术语则由将它们与观察术语相连接的对应规则明确定义。因此，诸如位置和动量之类的经典术语正是使物理学家能够将物理意义归因于量子力学的术语。

Kantianism. Many philosophers and physicists have recognized a strong kinship between Kant and Bohr’s thinking or a direct Kantian influence on Bohr. In the thirties C.F. von Weizsäcker and Grete Hermann attempt to understand complementarity in the light of neo-Kantian ideas. As von Weizsäcker puts it many years later, “The alliance between Kantians and physicists was premature in Kant’s time, and still is; in Bohr, we begin to perceive its possibility”. A series of modern scholars (Folse 1985; Honner 1982, 1987; Faye 1991; Kaiser 1992; Chevalley 1994; Pringe 2009; Cuffaro 2010; Bitbol 2013, 2017; and Kauark-Leite 2017) has also emphasized the Kantian parallels. Although these scholars find common themes, they also disagree to what extent Kantian or neo-Kantian ideas can be used as spectacles through which we may vision Bohr’s understanding of quantum mechanics. On the other hand, Cuffaro (2010) holds that any proper “interpretation of Bohr should start with Kant”, and that “complementarity follows naturally from a broadly Kantian epistemological framework.” Kant’s assumption was that our forms of intuition and our categories of thoughts constitute the transcendental conditions for the possibility of any objective experience. Thus, space and time are referred to as the forms of intuition, and the categories of understanding such as causation, unity, plurality, and totality are the a priori concepts which the mind imposes on the sense impressions that appear in our intuition. In a similar way, it is argued that Bohr saw concepts like space, time, causation, unity, and totality as a priori categories that was necessary for any objective description of quantum phenomena, and that classical physics was an explication and operationalization of these a priori concepts.

康德主义。许多哲学家和物理学家已经认识到康德和玻尔的思想之间有着很强的血缘关系，或者康德对玻尔的直接影响。三十年代冯·魏兹泽克和格里特·赫尔曼试图根据新康德思想来理解互补性。就像冯·魏兹萨克（vonWeizsäcker）多年后所说的那样：“康德人与物理学家之间的联盟在康德时代还为时过早，现在仍然如此；在玻尔，我们开始意识到它的可能性。”一系列现代学者（Folse 1985; Honner 1982，1987; Faye 1991; Kaiser 1992; Chevalley 1994; Pringe 2009; Cuffaro 2010; Bitbol 2013，2017;和Kauark-Leite 2017）也强调了康德的相似之处。尽管这些学者发现了共同的主题，但他们也不同意康德式或新康德式的思想可以在多大程度上用作眼镜，从而使我们可以了解玻尔对量子力学的理解。另一方面，卡法罗（Cuffaro，2010）认为，任何适当的``对玻尔的解释都应从康德开始''，并且``互补性自然地源于广泛的康德认识论框架''。康德的假设是，我们的直觉形式和思想类别构成了产生任何客观经验的先决条件。因此，空间和时间被称为直觉的形式，诸如因果关系，统一性，多元性和整体性之类的理解类别是先验概念，大脑将其强加于出现在我们直觉中的感官印象上。有人以类似的方式认为，玻尔将空间，时间，因果关系，统一性和整体性等概念视为对量子现象进行任何客观描述所必需的先验类别，并且古典物理学是对这些现象的解释和可操作性。先验的概念。

Pragmatism. Some scholars have advocated for a more pragmatic explanation of Bohr’s thesis concerning the indispensability of classical concepts. Here the interpretation focuses on how we experimentally get to know something about atoms. We find out about atoms by interacting with atomic systems, not by picturing them, and the interaction are accounted for in terms of experiential categories. The pragmatists typically reject the a priori status of the mind’s categories as they take them to be contingent. From a physical perspective it is a simple matter of facts that we need classical language to understand our scientific practise; it does not require any philosophical justification (Dieks 2017). Likewise, Dorato (2017) compares Bohr’s indispensable thesis to Peter Strawson’s descriptive metaphysics according to which we all share a common conceptual scheme about the experiential world which cannot be given a further justification. Also Folse notes, in a comparison between Bohr and I.C. Lewis, that classical concepts reflect our empirical needs and shared interests and may eventually change if these needs and interests change (Folse 2017). The common language together with the development of a physical clarification of some basic empirical concepts gave us the classical physics because such an improved language enables us to communicate in an unambiguous and objective manner about our observations. As Bohr puts it: “... even when the phenomena transcend the scope of classical physical theories, the account of the experimental arrangement and the recording of observations must be given in plain language, suitably supplemented by technical physical terminology. This is a clear logical demand, since the very word ”experiment“ refers to a situation where we can tell others what we have done and what we have learned.” (APHK, p. 71). The use of classical concepts to grasp the world is beneficial for understanding each other. Such empirical concepts provide us with an objective description of the function and outcome of physical experiments.

实用主义。一些学者主张对玻尔有关古典概念必不可少的论点进行更务实的解释。在这里，解释着重于我们如何实验性地了解原子。我们通过与原子系统进行交互而不是通过描绘它们来了解原子，并且根据经验类别对交互进行了解释。实用主义者通常会拒绝心理类别的先验地位，因为他们认为它们是偶然的。从物理角度看，事实很简单，我们需要古典语言来理解我们的科学实践。它不需要任何哲学上的辩解（Dieks 2017）。同样，Dorato（2017）将玻尔的必不可少的命题与彼得·斯特劳森的描述形而上学作了比较，根据该形而上学，我们都对体验世界有一个共同的概念方案，无法给出进一步的论证。在Bohr和I.C.的比较中，也注意到了Folse。刘易斯（Lewis），古典概念反映了我们的经验需求和共同利益，如果这些需求和利益发生变化，最终可能会改变（Folse 2017）。通用语言以及对一些基本经验概念的物理澄清的发展为我们提供了古典物理学，因为这种改进的语言使我们能够以明确，客观的方式就我们的观察进行交流。正如玻尔所言：“ ...即使现象超越了古典物理理论的范围，实验安排和观测记录也必须以通俗的语言给出，并适当地辅以技术性的物理术语。这显然是合乎逻辑的要求，因为“实验”一词是指一种情况，在这种情况下，我们可以告诉他人我们所做的事情和所学到的知识。” （APHK，第71页）。使用古典概念来掌握世界有利于彼此理解。这样的经验概念为我们提供了对物理实验的功能和结果的客观描述。

Darwinism. In several places Bohr speaks about the classical concepts as embodied in our common language, which is adapted to account for our physical experiences. The selection of the word “adapted to” seems to indicate that Bohr relied on Darwin’s theory of natural selection in his search for an explanation. The classical concepts are indispensable for the description of our experience because we are forced by nature to use a common language that is adapted to reporting our visual experiences, which again is a result of humans’ adaptation to their physical environment (Faye, 2017). Apart from Bohr’s use of the word “adapted to”, Bohr’s former assistant Leon Rosenfelt, who was an ardent defender of Bohr’s complementarity, explicitly suggests that “the complementary logic” is due to human evolution: “I suspect the development of a computing and communication system like our brain demands about that complexity of organization which has been reached by our own species in the course of evolution” (Rosenfeld, (1961 [1979]), p.515). Natural selection installs certain permanent visual cognitive schemes in our predecessors, and this cognitive adaptation explains why these schemes, later reflected in our common language, gain a privileged epistemic status, and keep this status in physics in terms of refined classical concepts.

达尔文主义。玻尔在几个地方谈到了我们共同语言所体现的古典概念，这种语言适应了我们的身体经历。选择“适应于”一词似乎表明，玻尔在寻求解释时依赖于达​​尔文的自然选择理论。古典概念对于描述我们的经历是必不可少的，因为我们天生被迫使用一种适合于报告我们的视觉体验的通用语言，这也是人类适应其物理环境的结果（Faye，2017）。除了玻尔使用“适应于”一词外，玻尔的前助手莱昂·罗森费尔特曾是玻尔互补性的忠实拥护者，他明确暗示“互补逻辑”是由于人类的进化所致：“我怀疑计算机和计算机技术的发展。像我们大脑这样的交流系统要求我们自己的物种在进化过程中已经达到的组织的复杂性”（Rosenfeld，（1961 [1979]），第515页）。自然选择在我们的前辈中安装了某些永久性的视觉认知方案，这种认知适应性解释了为什么这些方案后来以我们的通用语言反映出来，为什么获得了特权的认识论地位，并根据精致的古典概念在物理学中保持了这种地位。

Experimentalism. Camilleri (2017) calls Bohr the philosopher of experiment. Others such as Perovic (2013) have also suggested that Bohr was more occupied by understanding the outcome of quantum experiments than by interpreting the quantum formalism. In his paper Camilleri proposes that the challenge Bohr was facing was that, on the one hand, experimental observation requires a sharp separation of the experiment and the observed object, and, on the other hand, because of what we today call entanglement, “it is no longer possible sharply to distinguish between the autonomous behaviour of a physical object and its inevitable interaction with other bodies serving as measuring instruments” (CC, p.84). So, according to Camilleri, Bohr solved this challenge by making a distinguish between the function and the structure of an experiment.

实验主义。 Camilleri（2017）称玻尔为实验哲学家。佩罗维奇（Perovic，2013）等其他人也认为，玻尔更多地是通过理解量子实验的结果而不是通过解释量子形式主义来完成的。 Camilleri在他的论文中提出，玻尔面临的挑战是，一方面，实验观察需要将实验和观察到的物体彻底分离，另一方面，由于我们今天所说的纠缠，“它不再能够清晰地区分一个物理对象的自主行为和它与作为测量工具的其他对象不可避免的相互作用之间的区别”（CC，第84页）。因此，根据卡米列里（Camilleri）的观点，玻尔通过区分实验的功能和结构来解决了这一难题。

Bohr’s central insight was that if a measuring instrument is to serve its purpose of furnishing us with knowledge of an object – that is to say, if it is to be described functionally – it must be described classically. Of course, it is always possible to represent the experimental apparatus from a purely structural point of view as a quantum-mechanical system without any reference to its function. However, any functional description of the experimental apparatus, in which it is treated as a means to an end, and not merely as a dynamical system, must make use of the concepts of classical physics (Camilleri, 2017, pp.30–31).

玻尔的中心见解是，如果一种测量仪器要达到其向我们提供物体知识的目的-也就是说，如果要对其进行功能描述-则必须经典地进行描述。 当然，总是可以从纯粹的结构角度将实验设备表示为量子力学系统，而无需对其功能进行任何参考。 但是，对实验设备的任何功能描述，只要将其视为达到目的的手段，而不仅仅是动力学系统，都必须利用经典物理学的概念（Camilleri，2017年，第30–31页） 。

This analysis explains not only why Bohr thought that classical concepts were indispensable for interpretational purposes, but also indicates why he thought that properties like momentum, position, and duration could be attributed only to an atom object in relation to a specific experimental arrangement. As Dieks (2017) mentions while denying any deeper philosophical motivation on Bohr’s part: the use of classical concepts is part of the laboratory life. “This classical description is basically just the description in terms of everyday language, generalized by the addition of physics terminology, and it is the one we de facto use to describe our environment” (Dieks 2017). But because of quantum of action, symbolized by Planck’s constant, the function of experiments that supply the physicists with exact information about space-time coordinations is incompatible with experiments whose function it is to supply them with exact information about energy and momentum.

该分析不仅解释了玻尔为什么认为古典概念对于解释目的是必不可少的，而且还表明了为什么他认为诸如动量，位置和持续时间之类的属性只能归因于与特定实验安排有关的原子对象的原因。正如Dieks（2017）提到的那样，他否认了玻尔的任何更深层次的哲学动机：经典概念的使用是实验室生活的一部分。 “这种经典的描述基本上只是日常语言的描述，通过添加物理术语来概括，这是我们事实上用来描述环境的描述”（Dieks，2017年）。但是由于用普朗克常数表示的作用量子，为物理学家提供时空配准的精确信息的实验功能与为他们提供有关能量和动量的精确信息的实验是不兼容的。

Indeed, there are both similarities and overlaps between some of the proposed explanations concerning the indispensability of classical concepts. Yet, not all of the suggested explanations can be true. Even though the aim of Bohr’s effort is to give an empirical interpretation of the quantum formalism, his empiricism is different from that of the logical positivists. He does not seek to reduce terms concerning theoretical entities to terms about sense-data or purely perceptual phenomena. He insists only that the empirical evidence physicists collect from their experiments on atomic objects has to be described in terms of the same concepts which were developed in classical mechanics in order for them to understand what the quantum theory is all about.

确实，关于古典概念必不可少的一些拟议解释之间既有相似之处，又有重叠之处。但是，并非所有建议的解释都是正确的。尽管玻尔努力的目的是对量子形式主义进行经验解释，但他的经验主义与逻辑实证主义者的经验主义是不同的。他并没有试图将有关理论实体的术语简化为有关感官数据或纯粹感知现象的术语。他仅坚持说，物理学家从原子物体实验中收集的经验证据必须以与经典力学中发展起来的相同概念来描述，以使他们了解量子理论的全部含义。

Nevertheless, the various explanations all give us some hints into the complexity of Bohr’s thinking concerning the description of physical experiments. At different times, he seems to put emphasis on one aspect rather than another, depending on the specific context of discussion. Sometimes he was occupied with the interpretation of experiments, sometimes with the relationship between actual experiments and the formulation of quantum mechanics. In emphasizing the necessity of classical concepts for the description of quantum phenomena, Bohr might have been influenced by Kantian-like ideas or neo-Kantianism (Hooker, 1994). But if so, he was a naturalized or a pragmatized Kantian. The classical concepts are merely explications of common-sense concepts that are already a result of our perceptual adaptation to the world. These concepts and the conditions of their application determine the conditions for objective knowledge. The discovery of the quantization of action has revealed to us, however, that we cannot apply these concepts to quantum objects as we did in classical physics. The use of classical concepts in the domain of quantum mechanics has to be restricted with respect to their use in classical mechanics. Now kinematic and dynamic properties (represented by conjugate variables) can be meaningfully ascribed to the object only in relation to some actual experimental results, whereas classical physics attributes such properties to the object regardless of whether we actually observe them or not. In other words, Bohr denied that classical concepts could be used to attribute properties to a physical world in-itself behind the perceptual phenomena, i.e. properties different from those being observed. In contrast, classical physics rests on an idealization, he said, in the sense that it assumes that the physical world has these properties in-itself, i.e. as inherent properties, independent of their actual observation.

尽管如此，各种解释都给我们一些暗示，以说明玻尔关于物理实验描述的思想的复杂性。在不同的时间，他似乎将重点放在一个方面，而不是另一方面，这取决于讨论的具体上下文。有时他忙于对实验的解释，有时则忙于实际实验与量子力学公式之间的关系。在强调描述量子现象的经典概念的必要性时，玻尔可能受到了类似康德式的思想或新康德主义的影响（Hooker，1994）。但是，如果是这样，他就是一个入籍的或实用的康德人。古典概念仅是常识性概念的解释，这已经是我们对世界的感知适应的结果。这些概念及其应用条件决定了客观知识的条件。然而，行动量化的发现向我们揭示了，我们不能像传统物理学那样将这些概念应用于量子物体。就经典力学中的使用而言，必须限制经典概念在量子力学领域的使用。现在，运动和动态属性（由共轭变量表示）只能与某些实际实验结果相关地有意义地归因于对象，而经典物理学将此类属性归因于对象，无论我们是否实际观察到它们。换句话说，玻尔否认可以使用经典概念将属性归因于感知现象本身的物理世界，即与观察到的属性不同的属性。相反，他说，古典物理学基于理想化，因为它假设物理世界本身具有这些属性，即作为固有属性，而与它们的实际观察结果无关。

6. The Interpretation of the Quantum Formalism

Classical concepts serve the important function of connecting the quantum mechanical symbolism with experimental observations. If one accepts that Bohr’s grasp of physics began with his understanding of the role of physical experiments, this understanding had strong implications for his empirical interpretation of the quantum formalism. The modern scholarly debate has taken Bohr to be an instrumentalist, an objective anti-realist (Faye 1991), a phenomenological realist (Shomar 2008), or a realist of various sorts (Folse 1985, 1994; Favrholdt 1994; MacKinnon 1994; Howard 1994, 2004; Zinkernagel 2015, 2016). But very often the various participants do not give an exact specification of how they understand these terms and how these terms apply to Bohr’s thinking. The whole discussion becomes confused because different authors use terms like “realism” and “antirealism” differently in relation to Bohr. For instance, Faye (1991) holds that Bohr is an entity realist but a non-representationalist concerning theories. Therefore he calls Bohr an objective antirealist. In contrast, Folse (1986) who also sees Bohr as both a entity realist and a theoretical non-representationalist calls him a realist. Moreover, Bohr himself would probably refuse to put any such labels on his own view.

古典概念起着将量子力学象征与实验观察联系起来的重要作用。如果有人接受玻尔对物理学的理解是从他对物理实验作用的理解开始的，那么这种理解就对他对量子形式主义的经验解释产生了深远的影响。现代学术辩论已使玻尔成为工具主义者，客观反现实主义者（Faye 1991），现象学现实主义者（Shomar 2008）或各种现实主义者（Folse 1985，1994; Favrholdt 1994; MacKinnon 1994; Howard 1994）。 ，2004； Zinkernagel 2015，2016）。但是很多时候，各种各样的参与者并没有给出他们如何理解这些术语以及这些术语如何适用于玻尔思想的确切说明。整个讨论变得混乱，因为不同的作者相对于玻尔使用不同的术语如“现实主义”和“反现实主义”。例如，费耶（Faye，1991）认为玻尔是一个实体现实主义者，但在理论上却是非代表主义者。因此，他称玻尔为客观反现实主义者。相比之下，也把玻尔既是实体现实主义者又是理论上的非代表主义者的福尔塞（Folse，1986）称他为现实主义者。此外，玻尔本人可能会拒绝在自己的观点上贴上任何这样的标签。

It is certain that Bohr regarded atomic objects as real (ATDN, p.93 and p.103). Their existence has been confirmed by countless experiments. Hence, phrased in a modern terminology Bohr might be classified as an entity realist in the sense that experiments reveal their classical properties in relation to an experimental set-up. Such a view does not fit traditional instrumentalism where the introduction of unobservable entities is a logical construction in order to classify various empirical observations together. But entity realism corresponds with objective anti-realism, phenomenological realist, and all other forms of realism because it does not indicate anything about one’s attitude towards theories. A further issue is then how to interpret a physical theory. Does or doesn’t the quantum formalism, according to Bohr, represent the world over and above being a tool for prediction?

可以肯定的是，玻尔认为原子物体是真实的（ATDN，第93页和第103页）。它们的存在已被无数实验证实。因此，在现代术语中，玻尔可以被归类为实体实在论者，从某种意义上说，实验揭示了其与实验装置相关的经典特性。这种观点不适合传统的工具主义，在传统的工具主义中，引入不可观察的实体是一种逻辑构造，目的是将各种经验性观察归纳在一起。但是实体实在论与客观反实在论，现象学实在论以及所有其他形式的实在论相对应，因为它没有表明任何人对理论的态度。那么，另一个问题是如何解释物理理论。玻尔认为，量子形式主义是否代表了预测之外的世界？

Here are four statements which seem to show that Bohr was an instrumentalist concerning scientific theories in general and the quantum formalism in particular.

这里有四个陈述似乎表明玻尔是一个关于一般科学理论，特别是关于量子形式主义的工具论者。

1. The purpose of scientific theories “is not to disclose the real essence of phenomena but only to track down, so far as it is possible, relations between the manifold aspects of experience” (APHK, p.71).

2. “The ingenious formalism of quantum mechanics, which abandons pictorial representation and aims directly at a statistical account of quantum processes …” (CC, p. 152).

1.科学理论的目的“不是在揭示现象的实质，而是在可能的情况下尽可能地追踪各种经验之间的关系”（APHK，第71页）。

2.“量子力学的巧妙形式主义，放弃了图形表示，直接针对量子过程的统计解释……”（CC，第152页）。

3. “The formalism thus defies pictorial representation and aims directly at prediction of observations appearing under well-defined conditions” (CC, p. 172).

4. “The entire formalism is to be considered as a tool for deriving predictions of definite and statistical character …” (CC, p. 144).

3.“形式主义因此无视图形表示，而直接针对预测在明确条件下出现的观测结果”（CC，第172页）。

4.“应将整个形式主义视为推导确定和统计特性的预测的工具……”（CC，第144页）。

In these four statements Bohr mentions the absence of “pictorial representation” twice in relation to the quantum formalism. The term “pictorial representation” stands for a representation that helps us to visualize what it represents in contrast to “symbolic representation”. A pictorial representation is a formalism that has an isomorphic relation to the objects it represents such that the visualized structure of the representation corresponds to a similar structure in nature. Conversely, a symbolic representation does not stand for anything visualizable. It is an abstract tool whose function it is to calculate a result whenever this representation is applied to an experimental situation. With respect to the formalism of quantum mechanics it is particularly one’s interpretation of the wave function that determines whether one thinks of it symbolically as a tool for calculation of statistical outcomes or thinks of is as representing a real physical field.

在这四个陈述中，玻尔两次提到了与量子形式主义有关的“图形表示​​”的缺失。术语“图形表示​​”代表一种表示形式，与“符号表示”相比，它可以帮助我们形象地表示其表示形式。图形表示形式是一种形式主义，与它所表示的对象具有同构关系，因此表示形式的可视化结构与自然界中的相似结构相对应。相反，符号表示并不代表任何可可视化的内容。它是一种抽象工具，其功能是在将此表示形式应用于实验情况时计算结果。关于量子力学的形式主义，尤其是人们对波动函数的解释决定了人们是象征性地将其视为计算统计结果的工具还是认为其代表了真实的物理场。

In a close reading of the Como-paper, Dennis Dieks reaches the conclusion that “The notion that the lecture is meant to promulgate an instrumentalist interpretation of quantum theory according to which the whole formalism possesses only mathematical and no physical descriptive content is thus immediately seen to sit uneasily with the textual evidence.” (Dieks 2017, p.305). In other words, Dieks goes against the more general interpretation of Bohr according to which Bohr only believed that the wave function formalism is a mere tool for prediction. Just because Bohr writes off quantum formalism as a pictoral representation, it still gives us some insight into physical reality. First, Dieks points to another of Bohr’s argument against seeing Schödinger’s wave function as representing anything real. This argument concerns the fact that the wave function in quantum mechanics cannot represent a three-dimensional entity.

在仔细阅读Como论文时，丹尼斯·迪克斯（Dennis Dieks）得出这样的结论：“该演讲旨在传播对量子理论的工具主义解释的观念，据此，整个形式主义仅拥有数学上的内容，而没有物理上的描述性内容，因此立即可见。与文本证据不安地坐着。” （Dieks 2017，第305页）。换句话说，狄克斯违背了对玻尔的更一般的解释，玻尔只认为波函数形式主义仅仅是预测的工具。仅仅因为玻尔将量子形式主义作为一种绘画形式的表现而被废除，它仍然使我们对物理现实有了一定的了解。首先，迪克斯指出了玻尔的另一种论点，即反对将薛定er的波动函数表示为任何真实的东西。该论点涉及以下事实：量子力学中的波函数不能表示三维实体。

Bohr himself tells us that his second argument, about the dimensionality of configuration space, is the most important one: “above all there can be no question of an immediate connexion with our ordinary conceptions because... the wave equation is associated with the so-called co-ordinate space.” In other words, the Schrödinger wave in the case of a many-particle system cannot be a physical wave in three-dimensional space (which would be an “ordinary conception”) since it “lives” in a high-dimensional mathematical space (Dieks 2017, p.308).

玻尔本人告诉我们，关于配置空间维数的第二个论点是最重要的：“最重要的是，与我们的普通概念没有直接联系的问题，因为...波动方程与此相关。所谓的坐标空间。”换句话说，在多粒子系统的情况下，薛定ding波不能是三维空间中的物理波（这将是“普通概念”），因为它“存在”于高维数学空间中（狄克斯2017年，第308页）。

Then Dieks argues that even though this is an argument against wave function realism, it is not an argument that excludes the wave function from containing information about the quantum world. Dieks compares this argument to the one that denies phase space realism. “We can consistently deny the physical reality of phase space and still be realists with respect to particles. So we should not mistake Bohr’s argument for the symbolic character of the wave function for an argument in favor of instrumentalism tout court” (Dieks 2017, p. 308). The difference between classical many-particles system placed in a phase space and a system of quantum objects placed in the configuration space is, however, that the description of many particles in phase space can be decomposed into a description of single particles in three-dimensional physical space, whereas the sum of the quantum waves associated with many particles in configuration space yields yet another superimposed quantum wave, which cannot be decomposed into a description of single particles in three-dimensional space. Dieks then continues to show how the structural features of the quantum formalism guided Bohr in his interpretation of quantum mechanism. Likewise, he argues that Bohr’s pronouncements on the meaning of quantum mechanics should first of all be seen as responses to concrete physical problems, rather than as expressions of a preconceived philosophical doctrine. His analysis results in a finding that Bohr’s qualitative interpretation is in line with modern non-collapse theories.

迪克斯认为，即使这是反对波函数现实主义的论点，也不是排除了波函数不包含有关量子世界的信息的论点。迪克斯将这一论点与否认相空间现实主义的论点进行了比较。 “我们可以一贯否认相空间的物理现实，并且对于粒子仍然是现实主义者。因此，我们不应该将玻尔的论点误认为是波动函数的象征性，而将其视为有利于工具主义法庭的论点”（Dieks，2017年，第308页）。放置在相空间中的经典多粒子系统与放置在配置空间中的量子对象系统之间的区别是，相空间中的许多粒子的描述可以分解为三维中的单个粒子的描述物理空间，而与配置空间中许多粒子相关的量子波之和又产生了另一个叠加的量子波，无法分解成三维空间中单个粒子的描述。然后狄克斯继续展示了量子形式主义的结构特征如何指导玻尔对量子机理的解释。同样，他认为玻尔关于量子力学意义的声明首先应该被视为对具体物理问题的回应，而不是被视为一种先入为主的哲学学说。他的分析结果表明，玻尔的定性解释与现代非崩溃理论相符。

7. Misunderstandings of Complementarity

Complementarity has been commonly misunderstood in several ways, some of which shall be outlined in this section. First of all, earlier generations of philosophers and scientists have often accused Bohr’s interpretation of being positivistic or subjectivistic. Today philosophers have almost reached a consensus that it is neither. There are, as many have noticed, both typically realist as well as antirealist elements involved in it, and it has affinities with Kant or neo-Kantianism. The influence of Kant or Kantian thinking on Bohr’s philosophy seems to have several sources. Some have pointed to the tradition from Hermann von Helmholtz (Chevalley 1991, 1994; Brock 2003); others have considered the Danish philosopher Harald Høffding to be the missing link to Kantianism (Faye 1991; and Christiansen 2006).

互补性通常以几种方式被误解，其中一些将在本节中概述。首先，前几代哲学家和科学家经常指责玻尔对实证主义或主观主义的解释。今天，哲学家们几乎已经达成共识，那就是两者都不是。正如许多人所注意到的那样，它既涉及现实主义也涉及反现实主义元素，并且与康德或新康德主义有亲和力。康德或康德思想对玻尔哲学的影响似乎有多种来源。有人指出了赫尔曼·冯·亥姆霍兹的这一传统（Chevalley 1991，1994； Brock 2003）。其他人则认为丹麦哲学家哈拉尔德·霍夫丁（HaraldHøffding）是与康德主义的缺失环节（Faye 1991; and Christiansen 2006）。

But because Bohr’s view on complementarity has wrongly been associated with positivism and subjectivism, much confusion still seems to stick to the Copenhagen interpretation. Don Howard (2004) argues, however, that what is commonly known as the Copenhagen interpretation of quantum mechanics, regarded as representing a unitary Copenhagen point of view, differs significantly from Bohr’s complementarity interpretation. He holds that “the Copenhagen interpretation is an invention of the mid-1950s, for which Heisenberg is chiefly responsible, [and that] various other physicists and philosophers, including Bohm, Feyerabend, Hanson, and Popper, hav[e] further promoted the invention in the service of their own philosophical agendas” (p. 669).

但是，由于玻尔关于互补性的观点与实证主义和主观主义错误地联系在一起，因此哥本哈根的解释似乎仍然令人困惑。但是，唐·霍华德（Don Howard（2004））辩称，通常被称为代表哥本哈根统一观点的量子力学的哥本哈根解释，与玻尔的互补性解释有很大不同。他认为，“哥本哈根的解释是1950年代中期的发明，海森堡对此负有主要责任，[包括]鲍姆，费耶阿本德，汉森和波普尔等其他物理学家和哲学家，都进一步促进了这一运动的发展。为自己的哲学议程服务”（第669页）。

More recently, Mara Beller (1999) argued that Bohr’s statements are intelligible only if we presume that he was a radical operationalist or a simple-minded positivist. In fact, complementarity was established as the orthodox interpretation of quantum mechanics in the 1930s, a time when positivism was prevalent in philosophy of science, and some commentators have taken the two to be closely associated. During the 1930s Bohr was also in touch with some of the leading neopositivists or logical empiricists such as Otto Neurath, Philip Frank, and the Danish philosopher Jørgen Jørgensen. Although their anti-metaphysical approach to science may have had some influence on Bohr (especially around 1935 during his final discussion with Einstein about the completeness of quantum mechanics), one must recall that Bohr always saw complementarity as a necessary response to the indeterministic description of quantum mechanics due to the quantum of action. The quantum of action was an empirical discovery, not a consequence of a certain epistemological theory, and Bohr thought that indeterminism was the price to pay to avoid paradoxes. Never did Bohr appeal to a verificationist theory of meaning; nor did he claim classical concepts to be operationally defined. But it cannot be denied that some of the logical empiricists rightly or wrongly found support for their own philosophy in Bohr’s interpretation and that Bohr sometimes confirmed them in their impressions (Faye 2008).

最近，马拉·贝勒（Mara Beller，1999）辩称，只有当我们假设玻尔是激进的行动主义者或思想简单的实证主义者时，玻尔的言论才是可理解的。实际上，互补性被确立为1930年代对量子力学的正统解释，正值实证主义在科学哲学中盛行的时代，一些评论家已将二者紧密联系在一起。在1930年代，玻尔还与一些领先的新实证主义者或逻辑经验主义主义者保持联系，例如奥托·诺伊拉特（Otto Neurath），菲利普·弗兰克（Philip Frank）和丹麦哲学家约尔根·约根森（JørgenJørgensen）。尽管他们的反形而上学方法可能对玻尔产生了一定的影响（特别是在1935年左右，他与爱因斯坦就量子力学的完整性进行最后讨论时），但必须记住，玻尔始终将互补性视为对不确定性描述的必要回应。量子力学归因于作用量子。作用量子是经验发现，而不是某种认识论理论的结果，玻尔认为不确定性是避免自相矛盾的代价。玻尔从未诉诸于验证论者的意义理论。他也没有声称经典概念是在操作上定义的。但是不能否认的是，一些逻辑经验主义者在玻尔的解释中是对还是错找到了对自己哲学的支持，而且玻尔有时在他们的印象中证实了它们（Faye 2008）。

Second, many physicists and philosophers see the reduction of the wave function as an important part of the Copenhagen interpretation. This may be true for people like Heisenberg. But Bohr never talked about the collapse of the wave packet. Nor did it make sense for him to do so because this would mean that one must understand the wave function as referring to something physically real. Only if one can interpret a quantum measurement as an interaction between an instrument and an object, whose state is literally represented by Schrödinger’s wave function, and therefore taken to contain all potential values of observation, does it make sense to claim that the measurement forces the object to manifest one of these potential vales. Indeed, such a literal interpretation of the state vector implies that these values are somehow intrinsically present in the object with a certain probability all at once. In contrast, Bohr believed that particular kinematical and dynamical properties are relational because their attribution to a quantum system makes sense only in relation to a particular experimental set-up and therefore that these numerical properties could have a specific value only during a measurement.

其次，许多物理学家和哲学家将波函数的减小视为哥本哈根解释的重要组成部分。这对于像海森堡这样的人可能是正确的。但是玻尔从未谈论过波浪包的坍塌。对他来说这样做也没有意义，因为这意味着人们必须理解波函数是指物理上真实的东西。只有将量子测量解释为一种仪器与物体之间的相互作用时，其状态才真正由薛定ding的波函数表示，并因此被认为包含了所有潜在的观测值，才有理由断言测量力迫使反对表现出这些潜在价值之一。实际上，对状态向量的这种字面解释意味着这些值以某种概率一次全部地固有地存在于对象中。相比之下，玻尔认为特定的运动学和动力学性质是相关的，因为它们对量子系统的归属仅与特定的实验装置有关才有意义，因此这些数值性质仅在测量过程中才具有特定的值。

Third, Bohr flatly denied the ontological thesis that the subject has any direct impact on the outcome of a measurement. Hence, when he occasionally mentioned the subjective character of quantum phenomena and the difficulties of distinguishing the object from the subject in quantum mechanics, he did not think of it as a problem confined to the observation of atoms alone. For instance, he stated that already “the theory of relativity reminds us of the subjective character of all physical phenomena” (ATDN, p. 116). Rather, by referring to the subjective character of quantum phenomena he was expressing the epistemological thesis that all observations in physics are in fact context-dependent. There exists, according to Bohr, no view from nowhere in virtue of which quantum objects can be described.

第三，玻尔断然否认本体论的论点，即受试者对测量结果有任何直接影响。因此，当他偶尔提到量子现象的主观特征以及在量子力学中难以将物体与主体区分开时，他并不认为它只是局限于观察原子的问题。例如，他指出，“相对论使我们想起了所有物理现象的主观特征”（ATDN，第116页）。相反，通过提及量子现象的主观特征，他表达了认识论的论点，即物理学中的所有观察实际上都是与上下文相关的。根据玻尔的说法，从无处可寻，无法描述任何量子物体。

Fourth, although Bohr had spoken about “disturbing the phenomena by observation,” in some of his earliest papers on complementarity, he never had in mind the observer-induced collapse of the wave packet. Later he always talked about the interaction between the object and the measurement apparatus which was taken to be completely objective. Thus, Schrödinger’s Cat did not pose any riddle to Bohr. The cat would be dead or alive long before we open the box to find out. What Bohr claimed was, however, that the state of the object and the state of the instrument are dynamically inseparable during the interaction. Moreover, the atomic object does not posses any state separate from the one it manifests at the end of the interaction because the measuring instrument establishes the necessary conditions under which it makes sense to use the state concept.

第四，尽管玻尔在其有关互补性的最早论文中曾提到过“通过观察扰乱现象”，但他从未想到观察者会导致波包坍塌。后来他总是谈论对象与测量设备之间的相互作用，这被认为是完全客观的。因此，薛定ding的猫对玻尔没有构成任何谜语。在我们打开盒子找出来之前，这只猫可能已经死了或还活着。但是，玻尔声称，在交互过程中，对象的状态和仪器的状态在动态上是不可分割的。此外，原子对象不会具有与在交互结束时所显示的状态不同的任何状态，因为测量仪器会确定必要的条件，在该条件下使用状态概念才有意义。

It was the same analysis that Bohr applied in answering the challenge of the EPR-paper. Bohr’s reply was that we cannot separate the dynamical and kinematical properties of a joint system of two particles until we actually have made a measurement and thereby set the experimental conditions for the ascription of a certain state value (CC, p. 80). Bohr’s way of addressing the puzzle was to point out that individual states of a pair of coupled particles cannot be considered in isolation, in the same way as the state of the object and the state of the instrument are dynamically inseparable during measurements. Thus, based on our knowledge of a particular state value of the auxiliary body A, being an atomic object or an instrument, we may then infer the state value of the object B with which A once interacted (Faye 1991, pp. 182–183). It therefore makes sense when Howard (2004, p.671) holds that Bohr considered the post-measurement joint state of the object and the measuring apparatus to be entangled as in any other quantum interaction involving an entangled pair.

玻尔在回答EPR论文的挑战时也采用了同样的分析方法。玻尔的回答是，在我们进行实际测量并为特定状态值的归因设定实验条件之前，我们无法分离两个粒子的联合系统的动力学和运动学特性（CC，第80页）。玻尔解决难题的方法是指出，不能孤立地考虑一对耦合粒子的各个状态，就像物体的状态和仪器的状态在测量过程中是动态不可分割的一样。因此，根据我们对辅助物体A（是原子对象或仪器）的特定状态值的了解，然后我们可以推断出对象A曾经与之交互的对象B的状态值（Faye 1991，第182-183页）。 ）。因此，当霍华德（2004，p.671）认为玻尔认为对象和测量设备的测量后联合状态发生纠缠时，就像在涉及纠缠对的任何其他量子相互作用中一样，是有道理的。

Finally, when Bohr insisted on the use of classical concepts for understanding quantum phenomena, he did not believe, as it is sometimes suggested, that macroscopic objects or the measuring apparatus always have to be described in terms of the dynamical laws of classical physics. The use of the classical concepts is necessary, according to Bohr, because by these we have learned to communicate to others about our physical experience. The classical concepts are merely a refinement of everyday concepts of position and action in space and time. 

However, the use of the classical concepts is not the same in quantum mechanics as in classical physics. Bohr was well aware of the fact that, on pains of inconsistency, the classical concepts must be given “a suitable quantum-theoretical re-interpretation,” before they could be employed to describe quantum phenomena (ATDN, p. 8).

最终，当玻尔坚持使用古典概念来理解量子现象时，他并不相信，正如有时会建议的那样，宏观物体或测量仪器总是必须根据古典物理学的动力学定律来描述。玻尔认为，有必要使用经典概念，因为通过这些概念，我们学会了与他人交流我们的身体经验。古典概念仅仅是对时空中位置和动作的日常概念的完善。但是，在量子力学中，经典概念的使用与经典物理学中的使用不同。玻尔很清楚这样一个事实，即出于矛盾的痛苦，必须先对经典概念进行“适当的量子理论重新解释”，然后才能将其用于描述量子现象（ATDN，第8页）。

8. The Divergent Views

The Copenhagen interpretation is not a homogenous view. This insight has begun to emerge among historians and philosophers of science over the last ten to fifteen years. Both James Cushing (1994) and Mara Beller (1999) take for granted the existence of a unitary Copenhagen interpretation in their social and institutional explanation of the once total dominance of the Copenhagen orthodoxy; a view they personally find unconvincing and outdated partly because they read Bohr’s view on quantum mechanics through Heisenberg’s exposition. But historians and philosophers of science have gradually realized that Bohr’s and Heisenberg’s pictures of complementarity on the surface may appear similar but beneath the surface diverge significantly. Don Howard (2004, p. 680) goes as far as concluding that “until Heisenberg coined the term in 1955, there was no unitary Copenhagen interpretation of quantum mechanics.” The term apparently occurs for the first time in Heisenberg (1955). In addition, Howard also argues that it was Heisenberg’s exposition of complementarity, and not Bohr’s, with its emphasis on a privileged role for the observer and observer-induced wave packet collapse that became identical with that interpretation. Says he: “Whatever Heisenberg’s motivation, his invention of a unitary Copenhagen view on interpretation, at the center of which was his own, distinctively subjectivist view of the role of the observer, quickly found an audience” (p. 677). This audience included people like David Bohm, Paul Feyerabend, Norwood Russell Hanson, and Karl Popper who used Heisenberg’s presentation of complementarity as the target for their criticism of the orthodox view. However, it should also be mentioned that in later work, Feyerabend (1968, 1969) was one of the first philosophers who gave a painstaking analysis of complementarity in order to clear up the myth of it being unintelligible. Feyerabend urged philosophers and physicists to go back to Bohr and read him carefully.

Following up on Don Howard’s research, Kristian Camilleri (2006, 2007) points to the fact that complementarity was originally thought by Bohr (in his Como-paper) to exist between the space-time description and the causal description of the stationary states of atoms — and not between different experimental outcomes of the free electron. So the formulation of complementarity was restricted to the concept of stationary states because only there does the system have a well-defined energy state independent of any measurement. This observation deserves general recognition. But when Bohr rather soon thereafter began analysing the double slit experiment in his discussion with Einstein (1930), he had to extend his interpretation to cover the electron in interaction with the measuring apparatus.

Camilleri then shows how Heisenberg’s view of complementarity, in spite of Heisenberg’s own testimony, radically differs from Bohr’s. As Heisenberg understood complementarity between the space-time description and causal description, it holds between the classical description of experimental phenomena and the description of the state of the system in terms of the wave function. A quotation from Heisenberg (1958, p. 50) shows how much he misunderstood Bohr in spite of their previously close working relationship.

Bohr uses the concept of ‘complementarity’ at several places in the interpretation of quantum theory … The space-time description of the atomic events is complementary to their deterministic description. The probability function obeys an equation of motion as did the co-ordinates in Newtonian mechanics; its change in the course of time is completely determined by the quantum mechanical equation; it does not allow a description in space and time but breaks the determined continuity of the probability function by changing our knowledge of the system.

So, where Bohr identified the causal description with the conservation of energy, Heisenberg saw it as the deterministic evolution of Schrödinger’s ψ-function. In other words, Heisenberg, in contrast to Bohr, believed that the wave equation gave a causal, albeit probabilistic description of the free electron in configuration space. It also explains why so many philosophers and physicists have identified the Copenhagen interpretation with the mysterious collapse of the wave packet. The transition from a causal description in terms of the evolution of the ψ-function to a classical space-time description is characterized by the discontinuous change that occurs by the act of measurement. According to Heisenberg, these two modes of description are complementary.

In another study Ravi Gomatam (2007) agrees with Howard’s exposition in arguing that Bohr’s interpretation of complementarity and the textbook Copenhagen interpretation (i.e. wave-particle duality and wave packet collapse) are incompatible. More recently, Henderson (2010) has come to a similar conclusion. He makes a distinction between different versions of Copenhagen interpretations based on statements from some of the main characters. On one side of the spectrum there is Bohr who did not think of quantum measurement in terms of a collapse of the wave function (for a contrasting view see Jens Hebor 2005; and partly Zinkernagel 2016); in the middle we find Heisenberg talking about the collapse as an objective physical process but thinking that this couldn’t be analyzed any further because of its indeterministic nature, and at the opposite side Johann von Neumann and Eugene Wigner argued that the human mind has a direct influence on the reduction of the wave packet. Unfortunately, von Neumann’s dualistic view has become part of the Copenhagen methodology by people opposing this interpretation.

9. The Measurement Problem and the Classical-Quantum Distinction

Apparently, we are living in a quantum world since everything is constituted by atomic and subatomic particles. Hence classical physics seems merely to be a useful approximation to a world which is quantum mechanical on all scales. Such a view, which many modern physicists support, can be called quantum fundamentalism (Zinkernagel 2015, 2016). It can be defined as a position containing two components: (1) everything in the Universe is fundamentally of quantum nature (the ontological component); and (2) everything in the Universe is ultimately describable in quantum mechanical terms (the epistemological component). Thus, we may define quantum fundamentalism to be the position holding that everything in the world is essentially quantized and that the quantum theory gives us a literal description of this nature. The basic assumption behind quantum fundamentalism is that the structure of the formalism, in this case the wave function, corresponds to how the world is structured. For instance, according to the wave function description every quantum system may be in a superposition of different states because a combination of state vectors is also a state vector. Now, assuming that both the quantum object and the measuring apparatus are quantum systems that each can be described by a wave function, it follows that their entangled state would likewise be represented by a state vector. Then the challenge is, of course, how we can explain why the pointer of a measuring instrument enters a definite (and not a superposition) position, as experience tells us, whenever the apparatus interacts with the object. In a nutshell this is the measurement problem.

The Copenhagen interpretation is often taken to subscribe to a solution to the measurement problem that has been offered in terms of John von Neumann’s projection postulate. In 1932 [1996], von Neumann suggested that the entangled state of the object and the instrument collapses to a determinate state whenever a measurement takes place. This measurement process (a type 1-process as he called it) could not be described by quantum mechanics; quantum mechanics can only described type-2 processes (i.e., the development of a quantum system in terms of Schrödinger’s equation). In his discussion of the measurement problem, von Neumann then distinguished between (i) the system actually observed; (ii) the measuring instrument; and (iii) the actual observer. He argues that during a measurement the actual observer gets a subjective perception of what is going on that has a non-physical nature, which distinguishes it from the observed object and the measuring instrument. However, he holds on to psycho-physical parallelism as a scientific principle, which he interprets such that there exists a physical correlate to any extra-physical process of the subjective experience. So in every case where we have a subjective perception we must divide the world into the observed system and the observer. But where the division takes place is partly arbitrary. According von Neumann, it is contextual whether the dividing line is drawn between the description of the observed object (i) and the measuring instrument together with the observer (ii) + (iii), or it is drawn between the description of the observed object together with the measuring instrument, i.e., (i) + (ii), and the observer (iii). In other words, von Neumann argues that the observer can never be included in a type 2-process description, but the measuring instrument may sometime be part of a type 2-process, although it gives the same result with respect to the observed object (i). An important consequence of von Neumann’s solution to the measurement problem is that a type 1-process takes place only in the presence of the observer’s consciousness. Furthermore, even when von Neumann considers the situation in which the descriptions of (i) and (ii) are combined, he talks about the interaction between the physical system (i) + (ii) and an abstract ego (iii) (Neumann 1932 [1996], Ch VI). Therefore, the mind seems to play an active role in forming a type 1-process, which would be incompatible with psycho-physical parallelism.

Indeed, within philosophy of mind one cannot consistently maintain both psycho-physical parallelism and the existence of an interaction between the brain and the mind. So it is no wonder that Eugene Wigner (1967) followed up on the suggestion of the mind’s interaction by proposing that what causes a collapse of the wave function is the mind of the observer. But Wigner never explained how it was possible for something mental to produce a material effect like the collapse of a quantum system. The measuring problem led to the famous paradox of Schrödinger’s cat and later to the one of Wigner’s friend. Although von Neumann’s and Wigner’s positions are usually associated with the Copenhagen Interpretation, such views were definitely not Bohr’s as we shall see in a moment.

Quantum fundamentalists must indeed be ready to explain why the macroscopic world appears classical. An alternative to von Neumann’s projection postulate is the claim that the formalism should be read literally and that measurements (classical outcomes) do not describe the world as it really is. But there are ontological cost, which is significant to some. In one interpretation the world divides into as many worlds as there are possible measurement outcomes each time a system is observed or interacts with another system. Other fundamentalists had hoped that the decoherence program might come up with an appropriate explanation. The decoherence theory sees entanglement to exist not only between object and the measurement but also as something which includes the environment. If Bohr had known the idea of decoherence, he would probably have had no objection to it, as several authors have pointed to decoherence as a natural dynamical extension of his view that measurements is an irreversible amplification process (Schlosshauer and Camilleri 2015, 2017; Bächtold 2017, Tanona 2017; and Dieks 2017). However, it is generally agreed that decoherence does not solve the measurement problem (Bacciagaluppi 2016; Zinkernagel 2011). This might seems as if von Neumann’s projection postulate has to be reintroduced as a dynamical factor to explain why one and only one measurement result appears. However, as Dieks (2017) argues, Bohr’s interpretation could be understood as a non-collapse interpretation, since “the superposition does not have an empirical meaning independently of its interpretation via classically described experiments, so no replacement by another mathematical state is needed. We just have to interpret the formulas correctly.” In spite of that there is no general agreement to what extent Bohr opposed quantum fundamentalism.

Time and again Bohr emphasized that the epistemological distinction between the instrument and the object is necessary because this is the only way one can functionally make sense of a measurement. The epistemic purpose of a measuring instrument is to yield information about an object separated from the instrument itself. It is also generally agreed that Bohr didn’t treat the classical world of the measuring instrument as epistemically separated from quantum object along the line of a microscopic and macroscopic division. He sometimes included parts of the measuring instrument to which the quantum mechanical description should be applied. Don Howard (1994) therefore concludes that Bohr was not only an ontological quantum fundamentalist but in fact also a sort of an epistemological one. He believes that one can make Bohr’s requirement that measuring apparatus and the experimental results have to be described in ordinary language supplemented with the terminology of classical physics consistent with ontological quantum fundamentalism. According to him, Bohr never considered the measuring instrument as a classical object. Moreover, he thinks that this implies that Bohr had to understand the use of classical concepts differently from what scholars usually think. He reinterprets Bohr in terms of quantum states called “mixtures”. Howard believes that with respect to an experimental context in which an instrument interacts with an object, Bohr didn’t understand them as being in an entangled state but being separated in a mixture state. The consequence would be that the instrument and the object exist in a definite quantum state since such a state could be represented as a product of the wave function for the instrument and for the object.

But, as Maximilian Schlosshauer and Kristian Camilleri (2008 (Other Internet Resources), 2011) have pointed out, this does not solve the measurement problem. Howard does not explain under which circumstances one can move from a quantum system-cum-measuring apparatus being in a non-separable state to a mixture of separated states. Therefore one cannot be sure that the measuring apparatus is in a definite state and its pointer in a definite place. Some philosophers seem to argue that Bohr was an ontological but not an epistemological quantum fundamentalist. For instance, “Bohr believed in the fundamental and universal nature of quantum mechanics, and saw the classical description of the apparatus as a purely epistemological move, which expressed the fact that a given quantum system is being used as a measuring device” (Landsman 2007); and in a similar vein: “One is left with the impression from Bohr’s writings that the quantum-classical divide is a necessary part of the epistemological structure of quantum mechanics” (Schlosshauer and Camilleri 2008 (Other Internet Resources), 2015). So Klaas Landsman (2006, 2007) accepts Howard’s suggestion that Bohr is an ontological quantum fundamentalist but he rejects that Bohr should be considered an epistemological quantum fundamentalist. Landsman argues that Bohr held that the measuring instrument should be described in classical terms since the results of any measurement like in classical physics would always have a definite value. However, Landsman agrees that Bohr understood all objects as essentially quantum mechanical objects.

However, it may seem as if both Howard and Landsman miss the pragmatic nature of Bohr’s view on ontological issues. Bohr mentioned more than once that physics was not about finding the essence of nature but about describing the phenomena in an unambiguous way. In the foreground of Bohr’s thinking was the (1) the need of classical concepts for the description of measuring results; (2) non-separability due to the entanglement of the system and the measuring instrument; (3) the contextual nature of the measurements of complementary properties; and (4) the symbolic character of the quantum formalism. One has to take all four components into consideration if one wants to understand Bohr’s solution to the classical-quantum problem. According to Bohr, we are in quantum mechanics confronted with the “impossibility of any sharp separation between the behavior of atomic objects and the interaction with the measuring instruments which serve to define the very conditions under which the phenomena appear” (APHK, p. 210). This is definitely a non-classical feature which is described by quantum mechanics alone. In his response to the EPR-paper, Bohr strongly rejected that this form of interaction could be regarded as a mechanical influence. The influence was on the conditions of description, i.e. the experimental conditions under which it makes sense to apply classical concepts. But during a measurement we need to separate the system from the measuring instrument and the environment for pragmatic reasons. The pragmatic reasons seem to be reasonably clear. The outcomes of whatever experiment always yield a definite value, so the entanglement of object and the measurement instrument described by the quantum formalism only lasts until the interaction between object and instrument stops. The quantum formalism can predict the statistical outcome of these interactions but it cannot say anything about the trajectory of objects.

Bohr’s firmness about the use of classical concepts for the descriptions of measurement can be seen as his response to the measurement problem. This problem arises from the fact that quantum mechanics itself cannot account for why experiments on objects in a state of superposition always produce a definite outcome. Hence if one does not argue for spontaneous collapse of the wave function, hidden variables, or many worlds, one needs to supplement quantum mechanics with a classical description of measuring instruments in terms of clocks and rods. Henrik Zinkernagel (2015, 2016) may seem to get close to Bohr’s view when he argues that Bohr not so much solved the measuring problem as he dissolved it. According to his interpretation, Bohr believed in a quantum world, but only relative to a particular classical description and a certain classical world. The distinction between classical and quantum (both ontic and epistemic) is contextual. He thinks that the measurement problem is ultimately a consequence of ontological quantum fundamentalism (that everything is quantum). Because if everything is quantum – and correctly described by quantum formalism (what else would it mean to call everything quantum?) – then a measurement ends up in a superposition whether we describe the apparatus classical or not. One could say with Zinkernagel that Bohr believed all objects can be treated as quantum objects, but they cannot all be treated as quantum objects at the same time. Borrowing a conception from the two Russian physicists, Landau and Lifshitz, Zinkernagel claims that only some parts of the measuring device are entangled with the object in question, but those parts which are not entangled exists as a classical object. Depending on the context, objects cannot be treated as quantum objects in those situations in which they acts as measuring apparatuses. In these situations the classical treatment of the measuring device provides us with a frame of reference of space and time with respect to which an atomic object has a position, and, mutatis mutandis, with respect to which it has energy and momentum. Such a frame of reference is necessary for our ability to define and measure a particular property. In Bohr’s own words: “in each case [of measurement] some ultimate measuring instruments, like the scales and clocks which determine the frame of space-time coordination on which, in the last resort, even the definitions of momentum and energy quantities rest, must always be described entirely on classical lines, and consequently kept outside the system subject to quantum mechanical treatment” (CC, p. 104). What characterizes a frame of reference is that it establishes the conditions for the ascription of a well-defined position or a well-defined momentum, and treated classically measuring instruments act exactly as frames of reference. The implication is that Bohr did not exclude the application of quantum theory to any system. Every system can in principle be treated quantum mechanically, but since we always need a frame of reference to describe experimental outcomes, not all systems can be treated quantum mechanically at once.

In this debate Dorato (2017) stresses the fact that by making explicit reference to Einstein’s presentation of his special theory of relativity, Bohr regarded quantum mechanics as a theory of principle. This explains both Bohr’s epistemic reliance on the domain of classical physics and his ban of any attempt to construct classical objects from quantum objects. Despite this position Dorato argues that in order to justify his entity realism and anti-instrumentalist interpretations, Bohr also needed to postulate something ontologically distinct from the realm of quantum mechanics, a claim that creates the well-known problem of defining in a non-ambiguous and exact way the cut between the classical and the quantum realm. By following Zinkernagel, he claims that this problem is somewhat softened by Bohr’s contextualist theory of measurement. However, Bohr’s holism, according to which the measuring device and quantum object are in state of entanglement, is in objective tension with Bohr’s thesis of an ontological distinction, especially in virtue of the fact that by referring to the interaction between the quantum and the classical system as an irreversible physical process, Bohr seems to need a constructive approach to quantum mechanics that he wants to avoid.

Nonetheless, the question is to what extent Bohr really believed that the classical world is not only epistemically but also ontologically different from the quantum world? If he did not make an ontological distinction, there would be no contradiction between his epistemic view that the outcome of measurement needs to be described classically but that the apparatus ontologically is just as much a quantum object as the object under investigation. So when Bohr regarded quantum mechanics as a rational generalization of classical physics, he always thought of it as a way to secure the epistemic validity of quantum mechanics and not a way to save a classical ontology. Directly addressing Zinkernagel’s analysis, Dieks (2017) strongly argues that there can be little doubt that Bohr believed that quantum mechanics is universal in the sense that Heisenberg’s indeterminacy relation applies to both micro- and macroscopic systems due to the quantum of action. Classical mechanics is a mathematical approximation. Moreover, Bohr believed for epistemic reasons that we had to use classical language because this language is a refinement of our everyday language, which is adapted to describe our sensory experience and therefore the only language that can endow the quantum formalism with an empirical content. Hence, according to Dieks, Bohr assumed that it is only an epistemic necessity to describe “some systems classically in order to have a pragmatic starting point for the treatment of other systems.” Bohr’s demand of using classical concepts for epistemic reasons has no implications for his view that macroscopic objects are quantum objects. Measuring devices are not classical objects even though we need classical concepts to describe our general physical experiences and the outcome of quantum experiments. So Dieks concludes that the interaction between the measuring device and the quantum object determines, in the classical textbook examples, whether position or momentum talk can be carried over to the quantum object that is measured. The measuring device itself, if macroscopic and under ordinary circumstances (so that it really is a measuring device that can be used by us) allows both position and momentum talk in its own description. The measurement interaction determines which correlations are forged with the micro-world.

10. New Perspectives

After the 1950s a number of alternative interpretations to Bohr’s complementarity were articulated and they all found their proponents among physicists and philosophers of science. The Copenhagen interpretation started to lose ground to other interpretations such as Bohm’s interpretation, the many worlds interpretation, the modal interpretation and the decoherence interpretation, which have been more in vogue the last couple of decades. But parallel with the growing awareness of the essential differences between Bohr’s and Heisenberg’s understanding of quantum mechanics several philosophers of science have revitalised Bohr’s view on complementarity. Around the millennium a new recognition of the Copenhagen interpretation has emerged.

Rob Clifton and Hans Halvorson (1999, 2002) argue that Bohm’s interpretation of quantum mechanics can be seen as a special case of Bohr’s complementarity interpretation if it is assumed that all measurements ultimately reduce to positions measurement. Originally Jeffrey Bub and Clifton (1996) were able to demonstrate (given some idealized conditions) that Bohr’s complementarity and Bohm’s mechanics fall under their uniqueness theorem for no-collapse interpretations. Clifton and Halvorson improve this result by showing that Bohr’s idea of position and momentum complementarity can be expressed in terms of inequivalent representations in the C*-algebraic formalism of quantum mechanics. It turns out that either position or momentum are dynamically significant, but it is not permissible to assume that position and momentum are both dynamically significant in any single context. From these assumptions they conclude that Bohm’s hidden variables are none other than the “value states” that the complementarity interpretation postulates if position measurement were always dynamically significant, but this metaphysical restriction is not, as their results indicate, demanded by the physics. Rather, Clifton and Halvorson (1999) and Halvorson (2004) believe that complementarity may give us a realist interpretation of quantum field theory.

Philosophers have also started to explore the idea of decoherence in relation to Bohr’s view about “the inseparability of the behavior of the object and the interaction with the measuring instrument” or “the uncontrollable interaction between the atomic system and measurement apparatus.” (Schlosshauer and Camilleri 2011, 2017; Camilleri and Schlosshauer 2015; Bächtold 2017; and Tanona 2017). Although Bohr assumed that the measuring apparatus is altogether a quantum mechanical system, he nevertheless believed that the instrument could be approximately described by classical theory. Among the scholars just mentioned there is a general agreement that the notion of decoherent is coherent with Bohr’s view about the quantum-classical division and adds a dynamical explanation of quantum-to-classical transition which Bohr’s own exposition lacked. Also attempts to clear up the structural relationship between Bohr’s view and Hugh Everett’s “relative state”-interpretation have been carried out; a relationship which at some points is much closer than usually thought (Bacciagaluppi 2017).

Another insight into Bohr’s view of complementarity is due to Michael Dickson (2001, 2002). By using the contemporary theory of reference frames in quantum theory, he proves that Bohr’s response to the EPR thought-experiment was in fact the correct one. Moreover, he also maintains that Bohr’s discussions of spin, a property much less frame dependent than position and momentum, were very different from his discussions of the latter, and based on these differences he offers a Bohrian account of Bell’s theorem and its significance.

A re-assessment of Bohr’s philosophy of quantum mechanics is made by Whitaker (2004) on the basis of Clifton and Halvorson’s and Dickson’s works and in the light of quantum information theory. Besides these attempts to apply Bohr’s notion of complementarity to the contemporary discussions of the interpretation of quantum mechanics and quantum field theory there is an ongoing attempt to understand Bohr’s idea of symbolic representation (Tanona, 2004a, 2004b) and his notion of complementarity with respect to trends in post-modern philosophy and general epistemology such as poststructuralism, deconstructivism, feminism and cultural studies (Honner 1994; Plotnitsky 1994; Barad 2007; and Katsumori 2011).