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The Problem of Subjectivity and Objectivity in Physics
Masahiro Sano
- The Establishment of Objectivity as a Result of Excluding Subjective Elements
Physics is generally considered the most rigorous science, an archetype of an objective and universal science. The practical successes brought about by physics, such as nuclear energy and space exploration, are regarded as proof of the objectivity of physics. The objectivity of physics is guaranteed by its experimental basis and quantitative methods; in other words, it is claimed that physics captures nature as it is through experiments. Because physics is formed from facts derived from experiments without prejudice or preconception, it is considered objective.
Objectivity in physics is understood as capturing the objective reality “as it is,” meaning the exclusion of various subjective elements such as biases and preconceptions. This basis for asserting the objectivity of physics by excluding subjective elements from recognition was provided by Galileo. He believed that “the universe is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures.” Galileo also distinguished between primary qualities and secondary qualities, considering the latter as subjective elements that should be explained through the former.
As a result, Galileo viewed qualities like “smell, taste, and sound” as secondary qualities that should be excluded from the real world and focused on primary qualities like “size, shape, number, and motion” as the objective properties that should be studied. Thus, discovering the true structure of the physical world and reading the “book of nature” through mathematics became the objective of science according to Galileo. It came to be believed that the objectivity of physics is established as a result of excluding subjective elements.
In this paper, we will examine the problem of subjectivity and objectivity in physics from the second perspective, using the thoughts of physicists themselves as a clue.
- Subjective Elements Explained Even by Naive Objectivism
In naive objectivism, subjective elements are not completely excluded from the entire process of physical research to maintain objectivity. For example, because physicists are also human, subjective elements such as the motivations for research naturally become one of the elements constituting the research process. There might be physicists who conduct research with thoughts such as “I want to win a Nobel Prize.” Historically, under the leadership of Nazism, there was an attempt to deny relativity theory and quantum mechanics in favor of “Aryan physics.” However, such social motives that physicists may have are external to the content of physics itself and have no direct relevance to the essential research process of physics.
Now, is there no room for subjective elements to enter into physics itself? In reality, this is not the case. Here, I will discuss the issues of hypotheses and the arbitrariness of the expression forms of physical theories, which are subjective elements acknowledged even by naive objectivism.
(1) Hypotheses
Since we cannot know a priori what constitutes a correct physical theory or what the objective nature of reality is, it is indispensable to formulate hypotheses in research. That is, “physics without hypotheses” is impossible. For example, Poincaré stated, “Anyone who has reflected a little has noticed how wide a place hypotheses occupy; the mathematician can no more do without them than the experimenter.” Hypotheses are clearly subjective because they are “invented” to explain observed facts rather than being derived from them.
However, hypotheses do not threaten naive objectivism. This is because hypotheses are thought to be immediately tested experimentally, revealing their truth or falsehood. Hypotheses found to be false by experiments are discarded as errors. In contrast, hypotheses proven true are no longer hypotheses but are treated as true, objective theories. Thus, subjective conjectures are ultimately excluded from physics through experimental testing. In naive objectivism, the issue of hypotheses is explained as the process of eliminating subjective elements and establishing objectivity. According to naive objectivism, nature, as a book, is read exactly as it is through experiments, and hypotheses represent subjective motives for which part of nature to read. Like personal motives such as “wanting to win a Nobel Prize,” hypotheses are necessary when starting physical research but are not components of true physical theories as descriptions of nature as it is.
(2) The Arbitrariness of the Expression Forms of Theories
With the advancement of mathematization in physics, it has become possible to express physical theories in various forms. For example, the equations of motion in classical mechanics can be expressed in multiple forms, such as Newton’s equation of motion (F = ma), Lagrange’s equations of motion, and Hamilton’s canonical equations. Additionally, space can be represented using three-dimensional Cartesian coordinates (x, y, z) or spherical coordinates (r, θ, φ). Regardless of the expression form used, the same physical theory is being represented due to mathematical equivalence, making it the same physical theory.
In naive objectivism, it is believed that among the various expression forms of a theory, one represents nature as it is, while the others are considered mathematical constructs used for computational convenience. For instance, in classical mechanics, Newton’s equations of motion are generally thought to represent nature as it is. Therefore, according to naive objectivism, the arbitrariness of the expression forms does not negate the fact that the physical theory represents nature as it is.
In practice, there are cases where it is not immediately understood that the theories are the same. This was the case with the two formulations of quantum mechanics: “matrix mechanics” and “wave mechanics.” Due to differences in the underlying concepts of nature and a lack of understanding of their mathematical equivalence, they were initially considered opposing theories. Naive objectivism would explain this as a temporary misunderstanding by physicists. Schrödinger proved the mathematical equivalence of both formulations, resolving this misunderstanding.
However, does mathematical equivalence truly mean the theories are identical as physical theories? The naive objectivist interpretation of physical theories runs into difficulties when answering this question affirmatively. Let’s take electromagnetism as an example to examine this point.
Electromagnetism can be expressed using the electric field (E) and the magnetic field (H) as fundamental physical quantities or using the electromagnetic potentials (A) and (φ) as fundamental physical quantities. Both systems are mathematically equivalent and are considered the same theory. However, since the theoretical concepts that form the basis of both systems differ, they cannot both be considered a description of nature as it is. The claim that the same physical object can be both an electromagnetic field and an electromagnetic potential is contradictory. Thus, according to naive objectivism, one of the systems represents nature as it is, while the other is a mathematical tool. Just as in classical mechanics, where quantities like force, mass, and acceleration are considered real, and the “generalized coordinates” and “generalized forces” in the Lagrangian equations are considered mathematical constructs, the same applies here.
Generally, the electric and magnetic fields are considered real theoretical concepts, while the electromagnetic potential is regarded as a non-existent mathematical construct. This is because the electromagnetic field was considered an observable quantity, whereas the electromagnetic potential was not. However, recently, the quantum effects of electromagnetic potentials (Aharonov-Bohm effect) have been experimentally verified, and electromagnetic potentials are now increasingly considered observable, acknowledging their reality.
As a result, naive objectivism, which regards electromagnetic potentials as mathematical constructs, faces significant difficulties. For the same physical object, two different theoretical concepts can be applied, and both are considered real, leading to a contradiction. If various expression forms of a theory are considered to have equal status, it leads to the denial of naive objectivism.
The negative implications of the arbitrariness of the expression forms of theories against naive objectivism were already pointed out by L. Boltzmann. Evaluating H.R. Hertz’s attempt at a new formulation of classical mechanics, Boltzmann stated, “Hertz has made physicists keenly aware of what philosophers have been saying all along: that no theory can ever be something that actually coincides with nature.”
- Instrumentalism as a Counter-Ideology to Naive Objectivism
In section 2, I discussed the issues of subjective elements acknowledged even by naive objectivism. However, these subjective characteristics do not completely negate naive objectivism. It is still possible to explain the existence of these elements within the framework of naive objectivism. Therefore, here, I will consider a more systematic critique of naive objectivism.
First, let’s consider instrumentalism, which emerged around the same time as naive objectivism. Instrumentalism regards theoretical concepts merely as tools for calculation and denies their reality.
(1) Instrumentalism — Theories and Theoretical Concepts as Tools for Calculation
Copernicus proposed the heliocentric theory, asserting that the Earth actually revolves around the Sun. In contrast, some critics of the heliocentric theory took the position that it was merely a tool for calculation and not a true description of the world. For example, Andreas Osiander, in the preface to Copernicus’s major work On the Revolutions of the Heavenly Spheres, wrote, “It is not necessary that these hypotheses should be true or even probable; it is sufficient if they provide a calculus consistent with the observations.” This statement criticized the naive objectivist understanding of the heliocentric theory.
Instrumentalism, which positioned physical theories as mathematical tools for calculation and prediction, was inherited by thinkers like Berkeley. Berkeley argued that force “does not actually exist in nature but should be seen as a mathematical hypothesis” and that while it is “useful for reasoning and calculations concerning motion or bodies in motion, it is of no use for understanding the true nature of
motion itself.” He further noted that “regarding gravity, it is clear that Newton did not introduce it as a true physical property but merely as a mathematical hypothesis.” These statements criticized the naive objectivist understanding of Newtonian mechanics.
Instrumentalism continues to be supported by many physicists even today. For example, Schrödinger, one of the founders of wave mechanics, initially regarded the wave function as an existing wave, maintaining a naive objectivist stance. However, he later shifted to an instrumentalist position. In an article titled “The Present Situation in Quantum Mechanics,” Schrödinger stated that with the establishment of quantum mechanics, “one has to abandon naive realism and rely directly on the indubitable proposition that, in the end, there is only observation and measurement. Henceforth, all our physical thoughts are fundamentally based on or directed toward the results of measurements that are, in principle, feasible. … The wave function is nothing more than a means to predict the probabilities of measurement outcomes.” This statement reflects an instrumentalist interpretation of quantum mechanics.
Moreover, Dirac, who significantly contributed to the development of quantum mechanics, said, “Physicists know how to calculate and compare the results with experiments. If the results agree with the experiments, they are satisfied, and that’s all physicists need.”
Thus, many modern physicists (especially those researching quantum mechanics) take an instrumentalist stance. Just as the emergence of non-Euclidean geometry in mathematics led to the denial of a naive objectivist understanding of mathematics, the development of quantum mechanics in physics can be seen as having broken naive objectivism. This is because the fundamental concept of quantum mechanics, the wave function, cannot be interpreted as representing an actual wave in nature. There are several reasons why the wave function is considered non-real. The most decisive reason is the probabilistic interpretation of the wave function. Since the wave function represents probabilities, it cannot be considered a real wave. Additionally, for many-particle systems, the wave function is expressed not in three-dimensional space but in multi-dimensional configuration space. Since real space is three-dimensional, the wave function cannot be said to exist within real space. Furthermore, while nature is considered to have a real-number structure, the wave function is expressed in complex numbers, which is another reason.
Quantum mechanics cannot be explained from a naive objectivist perspective. That is, the wave function, the fundamental concept of quantum mechanics, is not considered a description of nature as it is. So, is instrumentalism, which regards the wave function merely as a tool for calculation, correct? Next, I will critically examine the claims of instrumentalism.
(2) Criticism of Instrumentalism
Instrumentalism argues that theoretical concepts are tools for prediction and calculation. However, naive objectivists would likely also accept this. The point of contention between naive objectivism and instrumentalism was whether theories are descriptions of nature as it is. With the advent of quantum mechanics, naive objectivism encountered difficulties on this point. However, this does not mean that the claims of instrumentalism are correct. Instrumentalism argues more than just that theories are not descriptions of nature as it is; it claims that theories are subjective constructs that have no connection to nature.
The claim that theories and theoretical concepts are subjective constructs only makes sense in contrast to the objectivity of observations or measurement results. Theoretical concepts are merely products of thought and are subjective, whereas observations or measurement results are not mere products of thought and are considered objective.
As evident from the previous citations related to instrumentalism—such as “in reality, there is only observation and measurement” or “the only basis for all our physical thoughts is … the results of measurements”—instrumentalism assumes the reality (objectivity) of observations or measurement results. Even Mach, an instrumentalist who denied the reality of atoms by regarding them as “mere symbols of complexes of sensory elements,” stated that “sensory facts are the starting point and goal of all adaptations in the thoughts of a physicist.” Thus, observations or measurement results are considered certain, as something to be explained by theories or theoretical concepts. In other words, the objectivity of observations or measurement results supports the instrumentality of theories and theoretical concepts. The assumption of an absolute separation between theory and observation was used to contrast the objectivity of measurement results with the subjectivity of theories.
However, as argued by N.R. Hanson, observational facts are theory-laden. In other words, observations are guided by theories, and theories underlie observations. There is no such thing as pure observation without theory. At the very least, the observational statements that form the basis of physical theories contain theoretical concepts. Observational results without theoretical concepts are meaningless. For physical theory, for instance, the visual position of a needle in an ammeter itself is not the issue; what matters is what this visual position signifies for the physical theory. In other words, in physics, it is not the “visual position of the needle in the ammeter” but the “value of the electric current” that constitutes the observational result.
Even observable physical quantities like velocity, acceleration, current, and voltage are theoretical concepts. The meanings of these terms are given in relation to theories such as mechanics and electromagnetism. As is evident from this discussion, the absolute separation of observation and theory, which is the fundamental premise of instrumentalism, should be rejected. Since there is no “pure observational fact without theory,” instrumentalism is incorrect.
Furthermore, if we acknowledge the theory-laden nature of observational facts, then both observational facts and theories can be said to have the same existential status. If observational facts are considered real, then theories are also real in the same way. One cannot claim that only theories are subjective constructs. The instrumentalist claim that pianos are real but that the atoms said to compose the pianos are not real is incorrect. As argued by Shozo Omori, “The everyday world of appearances and the world depicted by scientists with atoms, molecules, and electromagnetic fields are one and the same.” “Objects as collections of atoms and perceptual images with colors and smells are actually one and the same thing.” The perceptual description and the physical description overlap. The claim that observational facts and theories have equivalent existential status serves as both a critique of instrumentalism and of naive objectivism. Naive objectivism considers only “primary qualities” like size and motion to be objective, while “secondary qualities” like color and sound are purely subjective. However, if we recognize the theory-laden nature of observational facts or “overlapping depictions,” then “secondary qualities” must also be considered objective in some sense.
Against instrumentalism, I have thus far presented critiques from two perspectives, but there are also various critiques from other perspectives. If instrumentalism is to be rejected, as argued thus far, then a different perspective will be needed for a critique of naive objectivism. Next, I will explore a more general critique of naive objectivism from the perspective of the historical change of theories, rather than its relation to quantum mechanics.
- Theory Change and the Constancy of Nature
The fact that physics changes historically presents a significant difficulty for naive objectivism. Naive objectivism assumes that nature exists independently of the changes in physical theories. For example, in the transition from the geocentric model to the heliocentric model, nature itself remains unchanged and constant. That is to say, no one claims that “suddenly, the Earth started revolving around the Sun” after the heliocentric model was proposed by Copernicus and established as the true theory. Even in the era of Aristotelian cosmology, it is considered today that the Earth was orbiting the Sun, independent of the theory change from geocentric to heliocentric.
If one takes a naive objectivist stance and argues that physical theories are descriptions of nature as it is, then one must also claim that theories should not change as long as nature remains constant. If nature is unchanging, then the theories describing it should not change either. So, why do theories change historically?
Naive objectivism explains this process of theory change as the rejection of false theories (like the geocentric model) and the acceptance of true theories (like the heliocentric model). However, not all theory changes can be understood as a shift from a false theory to a true one. The historical shift from Newtonian mechanics to relativity theory or from classical mechanics to quantum theory is generally not considered a change from a false theory to a true one. To illustrate this point more concretely, let us consider the debate over the nature of light. Newton proposed the particle theory of light. In contrast, Hooke advocated the wave theory. The debate between the particle theory and the wave theory eventually concluded with the wave theory being accepted, due to experiments such as measuring the speed of light in water. Light was then considered to be a wave. However, in 1905, based on phenomena such as the photoelectric effect, Einstein proposed the quantum theory of light. After the experimental confirmation of the Compton effect, the quantum theory of light was regarded as correct. Once again, light was considered a particle. And then another change occurred: by treating electromagnetic fields quantum mechanically, light came to be seen as “photons.” Although opinions differ on what exactly photons are, they are generally considered to possess both particle-like and wave-like properties. In such cases, the position of naive objectivism, which insists that all prior theories were wrong, is overly simplistic because each preceding theory can be considered correct within certain limits.
Moreover, even if we temporarily accept the naive objectivist explanation for the historical change in theories, this generates even more questions. One issue is why theories that were supposedly false were believed to be true in the first place. For example, why did so many people, for such a long time, consider the geocentric model to be true? Furthermore, how can we be sure that the theories currently regarded as “true” will
not be replaced by new theories? Like the geocentric model, could they not just be “believed to be true” but actually be “false”? It is difficult to answer these doubts logically.
In conclusion, recognizing the historical change of theories suggests that naive objectivism is untenable. Naive objectivism is not only rejected in specific cases, such as the arbitrariness of the expression forms of electromagnetic theory or the non-reality of the wave function in quantum mechanics, but it is also rejected from a general perspective, such as the historical change of theories.
Conclusion
Throughout this paper, we have critically examined two representative ideas concerning the problem of subjectivity and objectivity in physics: naive objectivism and instrumentalism. To summarize, naive objectivism asserts the objectivity of theories as descriptions of nature as it is, while instrumentalism claims the subjectivity of theories as mere tools for calculation. In this paper, we have critiqued naive objectivism from the perspective of the historical change of theories and instrumentalism from the perspective of the theory-laden nature of observational facts.
A new thought that transcends naive objectivism and instrumentalism is being developed through a re-examination of the definitions of subjectivity and objectivity. While this paper has only touched on this suggestively, it will be discussed in detail on another occasion.
References
- For example, Nobuharu Tanji’s “The Problem of Observation in Quantum Mechanics” (Shisou, August 1974 issue) and B. d’Espagnat’s Theory of Observation in Quantum Mechanics (translated by Shigeru Machida, Iwanami Shoten).
- The philosophical significance of Galileo’s scientific methodology is discussed in detail in E. Cassirer’s Philosophy and Exact Science (translated by Ken Oba, Kinokuniya Bookstore).
- The Assayer problem 6 (Masterpieces of the World Volume 21, “Galileo,” Chuo Koronsha, p. 308).
- The Assayer problem 48 (same source, p. 505).
- For further details, see A. D. Beyerchen’s Scientists Under Hitler (translated by Keiichi Tsunetomi, Iwanami Shoten).
- Regarding the importance of the hypothesis method and its historical development, see Laudan, L. (1981) Science and Hypothesis. Also, the famous phrase “I do not fabricate hypotheses” by Newton is discussed in Masao Watanabe’s “Newton and Hypotheses” (included in Newton’s Light and Shadow, Kyoritsu Shuppan).
- Poincaré’s Science and Hypothesis (translated by Isaburo Kono, Iwanami Bunko), p. 13.
- C. G. Hempel’s Philosophy of Natural Science (translated by Hiroshi Kurosaki, Baifukan), p. 23.
- Popper’s The Logic of Scientific Discovery (translated by Yoshikazu Onuchi and Hiroshi Mori, Hosei University Press), p. 48, p. 54.
- For further details on this point, see N.R. Hanson’s “Are Wave Mechanics and Matrix Mechanics Equivalent Theories?” in H. Feigl, G. Maxwell (eds.) Current Issues in the Philosophy of Science, pp. 401-428.
- Feynman, Leighton, and Sands’ The Feynman Lectures on Physics III, Electromagnetism (translated by Tatsuo Miyajima, Iwanami Shoten), p. 196.
- Hertz’s Principles of Mechanics (translated by Tomoyoshi Kamikawa, Tokai University Press).
- Boltzmann’s “Recent Developments in the Methods of Theoretical Physics” (included in Masterpieces of the World Volume 65, “Modern Science I”), p. 463.
- Masterpieces of the World Volume 66, “Modern Science II,” Chuo Koronsha, pp. 376-377.
- Dirac, “The Evolution of the Physicist’s Picture of Nature” (included in Science and Mathematics, Blue Backs), p. 49.
- There is also a rebuttal to this point arguing that nature is complex. R. Penrose, “Is Nature Complex?” (included in Encyclopedia of the Unknown [1] — The Frontiers of Physical Science, Britannica Japan).
- E. Mach’s Analysis of Sensations (translated by Gonojuke Sudo and Wataru Makabe, Hosei University Press), p. 254.
- E. Mach, same source, p. 266.
- N.R. Hanson’s Patterns of Discovery (translated by Yoichiro Murakami, Kodansha), Perception and Discovery Volumes 1 and 2 (translated by Keiichi Noya and Hiroshi Watanabe, Kinokuniya Bookstore).
- K.R. Popper’s Conjectures and Refutations (translated by Takashi Fujimoto, Juro Ishigaki, and Hiroshi Mori, Hosei University Press), p. 184.
- Shozo Omori’s The Structure of Knowledge and Learning (Obunsha), p. 12.
- Shozo Omori, same source, p. 165.
- Shozo Omori, same source, pp. 157-158, and K.R. Popper’s Conjectures and Refutations, p. 185.
- For a critique of instrumentalism from another perspective, see Yoichiro Murakami, “Nature and Humans” (included in Modern Science and Philosophy, Yushindo). Especially pp. 236-238, and K.R. Popper’s Conjectures and Refutations, Chapter 3 “Three Views on Knowledge.”
- A.F. Chalmers’ What is this thing called Science? (translated by Kiyoshi Takada and Masahiro Sano, Koseisha Koseikaku), p. 194.
The Problem of Subjectivity and Objectivity in Physics
Masahiro Sano
Masahiro Sano
- The Establishment of Objectivity as a Result of Excluding Subjective Elements
Physics is generally considered the most rigorous science, an archetype of an objective and universal science. The practical successes brought about by physics, such as nuclear energy and space exploration, are regarded as proof of the objectivity of physics. The objectivity of physics is guaranteed by its experimental basis and quantitative methods; in other words, it is claimed that physics captures nature as it is through experiments. Because physics is formed from facts derived from experiments without prejudice or preconception, it is considered objective.
Objectivity in physics is understood as capturing the objective reality “as it is,” meaning the exclusion of various subjective elements such as biases and preconceptions. This basis for asserting the objectivity of physics by excluding subjective elements from recognition was provided by Galileo. He believed that “the universe is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures.” Galileo also distinguished between primary qualities and secondary qualities, considering the latter as subjective elements that should be explained through the former.
As a result, Galileo viewed qualities like “smell, taste, and sound” as secondary qualities that should be excluded from the real world and focused on primary qualities like “size, shape, number, and motion” as the objective properties that should be studied. Thus, discovering the true structure of the physical world and reading the “book of nature” through mathematics became the objective of science according to Galileo. It came to be believed that the objectivity of physics is established as a result of excluding subjective elements.
In this paper, we will examine the problem of subjectivity and objectivity in physics from the second perspective, using the thoughts of physicists themselves as a clue.
- Subjective Elements Explained Even by Naive Objectivism
In naive objectivism, subjective elements are not completely excluded from the entire process of physical research to maintain objectivity. For example, because physicists are also human, subjective elements such as the motivations for research naturally become one of the elements constituting the research process. There might be physicists who conduct research with thoughts such as “I want to win a Nobel Prize.” Historically, under the leadership of Nazism, there was an attempt to deny relativity theory and quantum mechanics in favor of “Aryan physics.” However, such social motives that physicists may have are external to the content of physics itself and have no direct relevance to the essential research process of physics.
Now, is there no room for subjective elements to enter into physics itself? In reality, this is not the case. Here, I will discuss the issues of hypotheses and the arbitrariness of the expression forms of physical theories, which are subjective elements acknowledged even by naive objectivism.
(1) Hypotheses
Since we cannot know a priori what constitutes a correct physical theory or what the objective nature of reality is, it is indispensable to formulate hypotheses in research. That is, “physics without hypotheses” is impossible. For example, Poincaré stated, “Anyone who has reflected a little has noticed how wide a place hypotheses occupy; the mathematician can no more do without them than the experimenter.” Hypotheses are clearly subjective because they are “invented” to explain observed facts rather than being derived from them.
However, hypotheses do not threaten naive objectivism. This is because hypotheses are thought to be immediately tested experimentally, revealing their truth or falsehood. Hypotheses found to be false by experiments are discarded as errors. In contrast, hypotheses proven true are no longer hypotheses but are treated as true, objective theories. Thus, subjective conjectures are ultimately excluded from physics through experimental testing. In naive objectivism, the issue of hypotheses is explained as the process of eliminating subjective elements and establishing objectivity. According to naive objectivism, nature, as a book, is read exactly as it is through experiments, and hypotheses represent subjective motives for which part of nature to read. Like personal motives such as “wanting to win a Nobel Prize,” hypotheses are necessary when starting physical research but are not components of true physical theories as descriptions of nature as it is.
(2) The Arbitrariness of the Expression Forms of Theories
With the advancement of mathematization in physics, it has become possible to express physical theories in various forms. For example, the equations of motion in classical mechanics can be expressed in multiple forms, such as Newton’s equation of motion (F = ma), Lagrange’s equations of motion, and Hamilton’s canonical equations. Additionally, space can be represented using three-dimensional Cartesian coordinates (x, y, z) or spherical coordinates (r, θ, φ). Regardless of the expression form used, the same physical theory is being represented due to mathematical equivalence, making it the same physical theory.
In naive objectivism, it is believed that among the various expression forms of a theory, one represents nature as it is, while the others are considered mathematical constructs used for computational convenience. For instance, in classical mechanics, Newton’s equations of motion are generally thought to represent nature as it is. Therefore, according to naive objectivism, the arbitrariness of the expression forms does not negate the fact that the physical theory represents nature as it is.
In practice, there are cases where it is not immediately understood that the theories are the same. This was the case with the two formulations of quantum mechanics: “matrix mechanics” and “wave mechanics.” Due to differences in the underlying concepts of nature and a lack of understanding of their mathematical equivalence, they were initially considered opposing theories. Naive objectivism would explain this as a temporary misunderstanding by physicists. Schrödinger proved the mathematical equivalence of both formulations, resolving this misunderstanding.
However, does mathematical equivalence truly mean the theories are identical as physical theories? The naive objectivist interpretation of physical theories runs into difficulties when answering this question affirmatively. Let’s take electromagnetism as an example to examine this point.
Electromagnetism can be expressed using the electric field (E) and the magnetic field (H) as fundamental physical quantities or using the electromagnetic potentials (A) and (φ) as fundamental physical quantities. Both systems are mathematically equivalent and are considered the same theory. However, since the theoretical concepts that form the basis of both systems differ, they cannot both be considered a description of nature as it is. The claim that the same physical object can be both an electromagnetic field and an electromagnetic potential is contradictory. Thus, according to naive objectivism, one of the systems represents nature as it is, while the other is a mathematical tool. Just as in classical mechanics, where quantities like force, mass, and acceleration are considered real, and the “generalized coordinates” and “generalized forces” in the Lagrangian equations are considered mathematical constructs, the same applies here.
Generally, the electric and magnetic fields are considered real theoretical concepts, while the electromagnetic potential is regarded as a non-existent mathematical construct. This is because the electromagnetic field was considered an observable quantity, whereas the electromagnetic potential was not. However, recently, the quantum effects of electromagnetic potentials (Aharonov-Bohm effect) have been experimentally verified, and electromagnetic potentials are now increasingly considered observable, acknowledging their reality.
As a result, naive objectivism, which regards electromagnetic potentials as mathematical constructs, faces significant difficulties. For the same physical object, two different theoretical concepts can be applied, and both are considered real, leading to a contradiction. If various expression forms of a theory are considered to have equal status, it leads to the denial of naive objectivism.
The negative implications of the arbitrariness of the expression forms of theories against naive objectivism were already pointed out by L. Boltzmann. Evaluating H.R. Hertz’s attempt at a new formulation of classical mechanics, Boltzmann stated, “Hertz has made physicists keenly aware of what philosophers have been saying all along: that no theory can ever be something that actually coincides with nature.”
- Instrumentalism as a Counter-Ideology to Naive Objectivism
In section 2, I discussed the issues of subjective elements acknowledged even by naive objectivism. However, these subjective characteristics do not completely negate naive objectivism. It is still possible to explain the existence of these elements within the framework of naive objectivism. Therefore, here, I will consider a more systematic critique of naive objectivism.
First, let’s consider instrumentalism, which emerged around the same time as naive objectivism. Instrumentalism regards theoretical concepts merely as tools for calculation and denies their reality.
(1) Instrumentalism — Theories and Theoretical Concepts as Tools for Calculation
Copernicus proposed the heliocentric theory, asserting that the Earth actually revolves around the Sun. In contrast, some critics of the heliocentric theory took the position that it was merely a tool for calculation and not a true description of the world. For example, Andreas Osiander, in the preface to Copernicus’s major work On the Revolutions of the Heavenly Spheres, wrote, “It is not necessary that these hypotheses should be true or even probable; it is sufficient if they provide a calculus consistent with the observations.” This statement criticized the naive objectivist understanding of the heliocentric theory.
Instrumentalism, which positioned physical theories as mathematical tools for calculation and prediction, was inherited by thinkers like Berkeley. Berkeley argued that force “does not actually exist in nature but should be seen as a mathematical hypothesis” and that while it is “useful for reasoning and calculations concerning motion or bodies in motion, it is of no use for understanding the true nature of
motion itself.” He further noted that “regarding gravity, it is clear that Newton did not introduce it as a true physical property but merely as a mathematical hypothesis.” These statements criticized the naive objectivist understanding of Newtonian mechanics.
Instrumentalism continues to be supported by many physicists even today. For example, Schrödinger, one of the founders of wave mechanics, initially regarded the wave function as an existing wave, maintaining a naive objectivist stance. However, he later shifted to an instrumentalist position. In an article titled “The Present Situation in Quantum Mechanics,” Schrödinger stated that with the establishment of quantum mechanics, “one has to abandon naive realism and rely directly on the indubitable proposition that, in the end, there is only observation and measurement. Henceforth, all our physical thoughts are fundamentally based on or directed toward the results of measurements that are, in principle, feasible. … The wave function is nothing more than a means to predict the probabilities of measurement outcomes.” This statement reflects an instrumentalist interpretation of quantum mechanics.
Moreover, Dirac, who significantly contributed to the development of quantum mechanics, said, “Physicists know how to calculate and compare the results with experiments. If the results agree with the experiments, they are satisfied, and that’s all physicists need.”
Thus, many modern physicists (especially those researching quantum mechanics) take an instrumentalist stance. Just as the emergence of non-Euclidean geometry in mathematics led to the denial of a naive objectivist understanding of mathematics, the development of quantum mechanics in physics can be seen as having broken naive objectivism. This is because the fundamental concept of quantum mechanics, the wave function, cannot be interpreted as representing an actual wave in nature. There are several reasons why the wave function is considered non-real. The most decisive reason is the probabilistic interpretation of the wave function. Since the wave function represents probabilities, it cannot be considered a real wave. Additionally, for many-particle systems, the wave function is expressed not in three-dimensional space but in multi-dimensional configuration space. Since real space is three-dimensional, the wave function cannot be said to exist within real space. Furthermore, while nature is considered to have a real-number structure, the wave function is expressed in complex numbers, which is another reason.
Quantum mechanics cannot be explained from a naive objectivist perspective. That is, the wave function, the fundamental concept of quantum mechanics, is not considered a description of nature as it is. So, is instrumentalism, which regards the wave function merely as a tool for calculation, correct? Next, I will critically examine the claims of instrumentalism.
(2) Criticism of Instrumentalism
Instrumentalism argues that theoretical concepts are tools for prediction and calculation. However, naive objectivists would likely also accept this. The point of contention between naive objectivism and instrumentalism was whether theories are descriptions of nature as it is. With the advent of quantum mechanics, naive objectivism encountered difficulties on this point. However, this does not mean that the claims of instrumentalism are correct. Instrumentalism argues more than just that theories are not descriptions of nature as it is; it claims that theories are subjective constructs that have no connection to nature.
The claim that theories and theoretical concepts are subjective constructs only makes sense in contrast to the objectivity of observations or measurement results. Theoretical concepts are merely products of thought and are subjective, whereas observations or measurement results are not mere products of thought and are considered objective.
As evident from the previous citations related to instrumentalism—such as “in reality, there is only observation and measurement” or “the only basis for all our physical thoughts is … the results of measurements”—instrumentalism assumes the reality (objectivity) of observations or measurement results. Even Mach, an instrumentalist who denied the reality of atoms by regarding them as “mere symbols of complexes of sensory elements,” stated that “sensory facts are the starting point and goal of all adaptations in the thoughts of a physicist.” Thus, observations or measurement results are considered certain, as something to be explained by theories or theoretical concepts. In other words, the objectivity of observations or measurement results supports the instrumentality of theories and theoretical concepts. The assumption of an absolute separation between theory and observation was used to contrast the objectivity of measurement results with the subjectivity of theories.
However, as argued by N.R. Hanson, observational facts are theory-laden. In other words, observations are guided by theories, and theories underlie observations. There is no such thing as pure observation without theory. At the very least, the observational statements that form the basis of physical theories contain theoretical concepts. Observational results without theoretical concepts are meaningless. For physical theory, for instance, the visual position of a needle in an ammeter itself is not the issue; what matters is what this visual position signifies for the physical theory. In other words, in physics, it is not the “visual position of the needle in the ammeter” but the “value of the electric current” that constitutes the observational result.
Even observable physical quantities like velocity, acceleration, current, and voltage are theoretical concepts. The meanings of these terms are given in relation to theories such as mechanics and electromagnetism. As is evident from this discussion, the absolute separation of observation and theory, which is the fundamental premise of instrumentalism, should be rejected. Since there is no “pure observational fact without theory,” instrumentalism is incorrect.
Furthermore, if we acknowledge the theory-laden nature of observational facts, then both observational facts and theories can be said to have the same existential status. If observational facts are considered real, then theories are also real in the same way. One cannot claim that only theories are subjective constructs. The instrumentalist claim that pianos are real but that the atoms said to compose the pianos are not real is incorrect. As argued by Shozo Omori, “The everyday world of appearances and the world depicted by scientists with atoms, molecules, and electromagnetic fields are one and the same.” “Objects as collections of atoms and perceptual images with colors and smells are actually one and the same thing.” The perceptual description and the physical description overlap. The claim that observational facts and theories have equivalent existential status serves as both a critique of instrumentalism and of naive objectivism. Naive objectivism considers only “primary qualities” like size and motion to be objective, while “secondary qualities” like color and sound are purely subjective. However, if we recognize the theory-laden nature of observational facts or “overlapping depictions,” then “secondary qualities” must also be considered objective in some sense.
Against instrumentalism, I have thus far presented critiques from two perspectives, but there are also various critiques from other perspectives. If instrumentalism is to be rejected, as argued thus far, then a different perspective will be needed for a critique of naive objectivism. Next, I will explore a more general critique of naive objectivism from the perspective of the historical change of theories, rather than its relation to quantum mechanics.
- Theory Change and the Constancy of Nature
The fact that physics changes historically presents a significant difficulty for naive objectivism. Naive objectivism assumes that nature exists independently of the changes in physical theories. For example, in the transition from the geocentric model to the heliocentric model, nature itself remains unchanged and constant. That is to say, no one claims that “suddenly, the Earth started revolving around the Sun” after the heliocentric model was proposed by Copernicus and established as the true theory. Even in the era of Aristotelian cosmology, it is considered today that the Earth was orbiting the Sun, independent of the theory change from geocentric to heliocentric.
If one takes a naive objectivist stance and argues that physical theories are descriptions of nature as it is, then one must also claim that theories should not change as long as nature remains constant. If nature is unchanging, then the theories describing it should not change either. So, why do theories change historically?
Naive objectivism explains this process of theory change as the rejection of false theories (like the geocentric model) and the acceptance of true theories (like the heliocentric model). However, not all theory changes can be understood as a shift from a false theory to a true one. The historical shift from Newtonian mechanics to relativity theory or from classical mechanics to quantum theory is generally not considered a change from a false theory to a true one. To illustrate this point more concretely, let us consider the debate over the nature of light. Newton proposed the particle theory of light. In contrast, Hooke advocated the wave theory. The debate between the particle theory and the wave theory eventually concluded with the wave theory being accepted, due to experiments such as measuring the speed of light in water. Light was then considered to be a wave. However, in 1905, based on phenomena such as the photoelectric effect, Einstein proposed the quantum theory of light. After the experimental confirmation of the Compton effect, the quantum theory of light was regarded as correct. Once again, light was considered a particle. And then another change occurred: by treating electromagnetic fields quantum mechanically, light came to be seen as “photons.” Although opinions differ on what exactly photons are, they are generally considered to possess both particle-like and wave-like properties. In such cases, the position of naive objectivism, which insists that all prior theories were wrong, is overly simplistic because each preceding theory can be considered correct within certain limits.
Moreover, even if we temporarily accept the naive objectivist explanation for the historical change in theories, this generates even more questions. One issue is why theories that were supposedly false were believed to be true in the first place. For example, why did so many people, for such a long time, consider the geocentric model to be true? Furthermore, how can we be sure that the theories currently regarded as “true” will
not be replaced by new theories? Like the geocentric model, could they not just be “believed to be true” but actually be “false”? It is difficult to answer these doubts logically.
In conclusion, recognizing the historical change of theories suggests that naive objectivism is untenable. Naive objectivism is not only rejected in specific cases, such as the arbitrariness of the expression forms of electromagnetic theory or the non-reality of the wave function in quantum mechanics, but it is also rejected from a general perspective, such as the historical change of theories.
Conclusion
Throughout this paper, we have critically examined two representative ideas concerning the problem of subjectivity and objectivity in physics: naive objectivism and instrumentalism. To summarize, naive objectivism asserts the objectivity of theories as descriptions of nature as it is, while instrumentalism claims the subjectivity of theories as mere tools for calculation. In this paper, we have critiqued naive objectivism from the perspective of the historical change of theories and instrumentalism from the perspective of the theory-laden nature of observational facts.
A new thought that transcends naive objectivism and instrumentalism is being developed through a re-examination of the definitions of subjectivity and objectivity. While this paper has only touched on this suggestively, it will be discussed in detail on another occasion.
References
- For example, Nobuharu Tanji’s “The Problem of Observation in Quantum Mechanics” (Shisou, August 1974 issue) and B. d’Espagnat’s Theory of Observation in Quantum Mechanics (translated by Shigeru Machida, Iwanami Shoten).
- The philosophical significance of Galileo’s scientific methodology is discussed in detail in E. Cassirer’s Philosophy and Exact Science (translated by Ken Oba, Kinokuniya Bookstore).
- The Assayer problem 6 (Masterpieces of the World Volume 21, “Galileo,” Chuo Koronsha, p. 308).
- The Assayer problem 48 (same source, p. 505).
- For further details, see A. D. Beyerchen’s Scientists Under Hitler (translated by Keiichi Tsunetomi, Iwanami Shoten).
- Regarding the importance of the hypothesis method and its historical development, see Laudan, L. (1981) Science and Hypothesis. Also, the famous phrase “I do not fabricate hypotheses” by Newton is discussed in Masao Watanabe’s “Newton and Hypotheses” (included in Newton’s Light and Shadow, Kyoritsu Shuppan).
- Poincaré’s Science and Hypothesis (translated by Isaburo Kono, Iwanami Bunko), p. 13.
- C. G. Hempel’s Philosophy of Natural Science (translated by Hiroshi Kurosaki, Baifukan), p. 23.
- Popper’s The Logic of Scientific Discovery (translated by Yoshikazu Onuchi and Hiroshi Mori, Hosei University Press), p. 48, p. 54.
- For further details on this point, see N.R. Hanson’s “Are Wave Mechanics and Matrix Mechanics Equivalent Theories?” in H. Feigl, G. Maxwell (eds.) Current Issues in the Philosophy of Science, pp. 401-428.
- Feynman, Leighton, and Sands’ The Feynman Lectures on Physics III, Electromagnetism (translated by Tatsuo Miyajima, Iwanami Shoten), p. 196.
- Hertz’s Principles of Mechanics (translated by Tomoyoshi Kamikawa, Tokai University Press).
- Boltzmann’s “Recent Developments in the Methods of Theoretical Physics” (included in Masterpieces of the World Volume 65, “Modern Science I”), p. 463.
- Masterpieces of the World Volume 66, “Modern Science II,” Chuo Koronsha, pp. 376-377.
- Dirac, “The Evolution of the Physicist’s Picture of Nature” (included in Science and Mathematics, Blue Backs), p. 49.
- There is also a rebuttal to this point arguing that nature is complex. R. Penrose, “Is Nature Complex?” (included in Encyclopedia of the Unknown [1] — The Frontiers of Physical Science, Britannica Japan).
- E. Mach’s Analysis of Sensations (translated by Gonojuke Sudo and Wataru Makabe, Hosei University Press), p. 254.
- E. Mach, same source, p. 266.
- N.R. Hanson’s Patterns of Discovery (translated by Yoichiro Murakami, Kodansha), Perception and Discovery Volumes 1 and 2 (translated by Keiichi Noya and Hiroshi Watanabe, Kinokuniya Bookstore).
- K.R. Popper’s Conjectures and Refutations (translated by Takashi Fujimoto, Juro Ishigaki, and Hiroshi Mori, Hosei University Press), p. 184.
- Shozo Omori’s The Structure of Knowledge and Learning (Obunsha), p. 12.
- Shozo Omori, same source, p. 165.
- Shozo Omori, same source, pp. 157-158, and K.R. Popper’s Conjectures and Refutations, p. 185.
- For a critique of instrumentalism from another perspective, see Yoichiro Murakami, “Nature and Humans” (included in Modern Science and Philosophy, Yushindo). Especially pp. 236-238, and K.R. Popper’s Conjectures and Refutations, Chapter 3 “Three Views on Knowledge.”
- A.F. Chalmers’ What is this thing called Science? (translated by Kiyoshi Takada and Masahiro Sano, Koseisha Koseikaku), p. 194.
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