This book is devoted to the problems of the growth of science. These prob lems, neglected for a long time by the philosophers of science, have become in the 60's and 70's a subject of vivid discussion. There are philosophers who stress only the dependence of science upon various sociological, psycho logical and other factors and deny any internal laws of the development of knowledge, like approaching the truth. The majority rejects such nihilism and searches for the laws of the (...) growth of science. However, they often overlook the role of the Correspondence Principle which connects the suc cessive scientific theories. On the other hand, some authors, while stressing the role of this principle, overlook logical difficulties connected with it, e. g. the problem of the incompatibility of successive theories, of the falsity of some of their assumptions, etc. I believe the Correspondence Principle to be a basic principle of the pro gress of contemporary physics and, probably, of every advanced science. How ever, this principle must be properly interpreted and the above-mentioned logical difficulties must be solved. Their solution requires, as it seems, revealing the idealizational nature of the basic laws of science, in any case of the quantitative laws of advanced sciences. This point has been recently emphasized by some Polish philosophers, especially in Poznan. (shrink)

We discuss the fate of the correspondence principle beyond quantum mechanics, specifically in quantum field theory and quantum gravity, in connection with the intrinsic limitations of the human ability to observe the external world. We conclude that the best correspondence principle is made of unitarity, locality, proper renormalizability (a refinement of strict renormalizability), combined with fundamental local symmetries and the requirement of having a finite number of fields. Quantum gravity is identified in an essentially unique way. (...) The gauge interactions are uniquely identified in form. Instead, the matter sector remains basically unrestricted. The major prediction is the violation of causality at small distances. (shrink)

A comprehensive look at the kinds of correspondence principle in physics.

Although Bohr’s Correspondence Principle (CP) played a central role in the first days of quantum mechanics, its original version seems to have no present-day relevance. The purpose of this article is to show that the CP, with no need of being interpreted in terms of the quantum-to-classical limit, still plays a relevant role in the understanding of the relationships between the classical and the quantum domains. In particular, it will be argued that a generic version of the CP (...) is very helpful in elucidating the physical meaning of the phenomenon of quantum decoherence. (shrink)

Several philosophers of science have claimed that the correspondence principle can be generalized from quantum physics to all of (particularly physical) science and that in fact it constitutes one of the major heuristical rules for the construction of new theories. In order to evaluate these claims, first the use of the correspondence principle in (the genesis of) quantum mechanics will be examined in detail. It is concluded from this and from other examples in the history of (...) science that the principle should be qualified with respect to its nature and relativized with respect to its scope of application. At the same time this conclusion implies a qualification and a relativization of the heuristic power of the principle. Generally speaking, intertheoretical correspondence is primarily of a formal-mathematical and empirical but not of a conceptual nature. Moreover, it only applies to certain parts of the theories involved. Finally, a number of philosophical justifications of the principle are discussed and some conclusions are drawn concerning the debates on theory reduction and on the discovery-justification distinction. (shrink)

One finds, even in texts by distinguished physicists, diverse enunciations of the correspondence principle. Typical is that quantum mechanics should agree with classical mechanics in some appropriate limit. Most commonly, the limit specified is that of high quantum numbers, or of large masses and orbits of large dimensions. But sometimes it is specified as mean behavior when large numbers quanta are involved, or sometimes even as just the average of quantum mechanical variables. Sometimes, the principle is even (...) taken as a prescription for replacing the classical dynamical observables with an appropriate mathematical operator. In 1918, however, Bohr proposed what he would later call the correspondence principle as a way of deriving amplitudes and polarizations of emitted and absorbed spectral lines. I will begin with Bohr's principle and trace the evolution of correspondence considerations through the 1920's, with a view as to whether in each case it is supposed to play the role of a theorem, an adequacy constraint, an inductive hypothesis or a heuristic. (shrink)

This article examines the problem of the origins of the correspondence principle formulated by Bohr in 1920 and intends to test the correctness of the argument that the essential elements of that principle were already present in the 1913 “trilogy”. In contrast to this point of view, moreover widely shared in the literature, this article argues that it is possible to find a connection between the formulation of the correspondence principle and the assessment that led (...) Bohr to abandon the search for a Planck-type theory. In fact, a thorough examination of Bohr’s works shows that the birth of this principle coincided with the depletion of a research program whose origins may date back to Bohr’s stay at the Rutherford’s laboratory (summer 1912). Finally, this article argues that original program of research was abandoned when it became clear that Planck’s quantum hypothesis for the harmonic oscillator was not an adequate support for the theoretical architecture of atomic physics; namely, there was evidence enough to justify a most drastic conclusion, according to Bohr: “I do not think that a theory of the Planck type can be made logical consistent”. (shrink)

Periodic systems are considered whose increments in quantum energy grow with quantum number. In the limit of large quantum number, systems are found to give correspondence in form between classical and quantum frequency-energy dependences. Solely passing to large quantum numbers, however, does not guarantee the classical spectrum. For the examples cited, successive quantum frequencies remain separated by the incrementhI −1, whereI is independent of quantum number. Frequency correspondence follows in Planck's limit,h → 0. The first example is that (...) of a particle in a cubical box with impenetrable walls. The quantum emission spectrum is found to be uniformly discrete over the whole frequency range. This quality holds in the limitn → ∞. The discrete spectrum due to transitions in the high-quantum-number bound states of a particle in a box with penetrable walls is shown to grow uniformly discrete in the limit that the well becomes infinitely deep. For the infinitely deep spherical well, on the other hand, correspondence is found to be obeyed both in emission and configuration. In all cases studied the classical ensemble gives a continuum of frequencies. (shrink)

No, but the paper argues that Bohr understood his correspondence principle, or at least an aspect of that principle expressed by the notion of rational generalization, as grounded in Hankel’s principle of permanence.

This paper presents a more clear formulation of the correspondence principle and explores its justification.

This book presents a history of the correspondence principle from a new perspective. The author provides a unique exploration of the relation between the practice of theory and conceptual development in physics. In the process, he argues for a new understanding of the history of the old quantum theory and the emergence of quantum mechanics. The analysis looks at how the correspondence principle was disseminated and how the principle was applied as a research tool during (...) the 1920s. It provides new insights into the interaction between theoretical tools and scientific problems and shows that the use of this theoretical tool changed the tool itself in a process of transformation through implementation. This process, the author claims, was responsible for the conceptual development of the correspondence principle. This monograph connects to the vast literature in the history of science, which analyzed theoretical practices as based on tacit knowledge, skills, and calculation techniques. It contributes to the historical understanding of quantum physics and the emergence of quantum mechanics. Studying how physicists used a set of tools to solve problems, the author spells out the ‟skillful guessing” that went into the making of quantum theoretical arguments and argues that the integration and implementation of technical resources was a central driving force for the conceptual and theoretical transformation in the old quantum theory. (shrink)

The correspondence principle states that the quantum system will approach the classical system in high quantum numbers. Indeed, the average of the quantum probability density distribution reflects a classical-like distribution. However, the probability of finding a particle at the node of the wave function is zero. This condition is recognized as the nodal issue. In this paper, we propose a solution for this issue by means of complex quantum random trajectories, which are obtained by solving the stochastic differential (...) equation derived from the optimal guidance law. It turns out that point set A, which is formed by the intersections of complex random trajectories with the real axis, can represent the quantum mechanical compatible distribution of the quantum harmonic oscillator system. Meanwhile, the projections of complex quantum random trajectories on the real axis form point set B that gives a spatial distribution without the appearance of nodes, and approaches the classical compatible distribution in high quantum numbers. Furthermore, the statistical distribution of point set B is verified by the solution of the Fokker–Planck equation. (shrink)

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles (...) as well as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity. (shrink)

The present paper is intended to take up the basic issue in Marxist epistemology: does the development of human cognition include mechanisms that ensure the attainment of, or approximation to, the absolute truth?But to take up this issue we have to define the concept of absolute truth. This is why the paper begins with comment on the assumptions we adopt. This is followed by explanations of the concept of the absolute truth and that of relative truth and some of derivative (...) concepts, too. Section 3 is concerned with the problem of whether the absolute truth is attainable, and with the role played in the process by the correspondence principle, which is reconstructed in a specified way. (shrink)

In the present paper I aim to discuss the philosophical foundations of the early correspondence principle, by comparing the conceptual structure underlying the first correspondence principle with the procedure of analogy that Immanuel Kant introduced in the Critique of Judgment from 1790. On such a comparison, I will seek to demonstrate the consistency of the conceptual ratio according to which the correspondence principle is to the classical "concepts" of space and time, as these a (...) priori forms of intuition, in Kant, are related to the separate faculty of pure intuition. As a result, it will turn out that the conceptual structure of the correspondence principle suits to the Kantian doctrine of a separate faculty of pure intuition, which is divided from the faculty of understanding. The aim is to shed new light on the line of reasoning underlying Niels Bohr's analogical thinking in quantum physics. (shrink)

In an article by Margenau and Cohen various correspondence principles were described in connection with Weyl, Born-Jordan, and symmetrized ordering of quantum mechanical operators. In this article we make an interesting comparison between the aforementioned ordering process and our previous prescriptions.

In a recent revision (chapter 4 of Nowakowa and Nowak 2000) of an older article Leszek Nowak (1992) has attempted to rebut Niiniluoto’s 1990 critical suggestion that proponents of the Poznań idealizational approach to the sciences have committed a rather elementary logical error in the formal machinery that they advocate for use in the analysis of scientific methodology. In this paper I criticize Nowak’s responses to Niiniluoto’s suggestion, and, subsequently, work out some of the consequences of that criticism for understanding (...) the role that idealization plays in scientific methodology. (shrink)

Niels Bohr’s “correspondence principle” is typically believed to be the requirement that in the limit of large quantum numbers (n→∞) there is a statistical agreement between the quantum and classical frequencies. A closer reading of Bohr’s writings on the correspondence principle, however, reveals that this interpretation is mistaken. Specifically, Bohr makes the following three puzzling claims: First, he claims that the correspondence principle applies to small quantum numbers as well as large (while the statistical (...) agreement of frequencies is only for large n); second, he claims that the correspondence principle is a law of quantum theory; and third, Bohr argues that formal apparatus of matrix mechanics (the new quantum theory) can be thought of as a precise formulation of the correspondence principle. With further textual evidence, I offer an alternative interpretation of the correspondence principle in terms of what I call Bohr’s selection rule. I conclude by showing how this new interpretation of the correspondence principle readily makes sense of Bohr’s three puzzling claims. (shrink)

A vast amount of ink has been spilled in both the physics and the philosophy literature on the measurement problem in quantum mechanics. Important as it is, this problem is but one aspect of the more general issue of how, if at all, classical properties can emerge from the quantum descriptions of physical systems. In this paper we will study another aspect of the more general issue-the emergence of classical chaos-which has been receiving increasing attention from physicists but which has (...) largely been neglected by philosophers of science. (shrink)

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but in many ways superior to the well-known paper by Kramers and Heisenberg published the following year that is (...) widely credited to have led directly to Heisenberg's Umdeutung paper. As such, it clearly shows how strongly the discovery of matrix mechanics depended on earlier work on the application of the correspondence principle to the interaction of matter and radiation. (shrink)

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s (...) paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. (shrink)

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg’s Umdeutung paper. In telling this story, we have taken a 1924 paper by John H. Van Vleck in The Physical Review as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we derive is the Kramers dispersion formula, which played a key role in the thinking (...) that led to Heisenberg’s Umdeutung paper. We derive classical formulae for the dispersion, emission, and absorption of radiation and use Bohr’s correspondence principle to construct their quantum counterparts both for the special case of a charged harmonic oscillator (Sect. 5) and for arbitrary non-degenerate multiply-periodic systems (Sect. 6). We then rederive these results in modern quantum mechanics (Sect. 7). (shrink)

The purpose of the present paper is to develop kinematics of the special relativity with an anisotropy of the one-way speed of light. As distinct from a common approach, when the issue of anisotropy of the light propagation is placed into the context of conventionality of distant simultaneity, it is supposed that an anisotropy of the one-way speed of light is due to a real space anisotropy. In that situation, some assumptions used in developing the standard special relativity kinematics are (...) not valid so that the “anisotropic special relativity” kinematics should be developed based on the first principles, without refereeing to the relations of the standard relativity theory. In particular, using condition of invariance of the interval between two events becomes unfounded in the presence of anisotropy of space since the standard proofs drawing the interval invariance from the invariance of equation of light propagation are not valid in that situation. Instead, the invariance of the equation of light propagation, which is a physical law, should be taken as a first principle. A number of other physical requirements, associativity, reciprocity and so on are satisfied by the requirement that the transformations between the frames form a group. Finally, the correspondence principle is to be satisfied which implies that the coordinate transformations should turn into the Galilean transformations in the limit of small velocities. The above formulation based on the invariance and group property suggests applying the Lie group theory apparatus which includes the following steps: constructing determining equations for the infinitesimal group generators using the invariance condition; solving the determining equations; specifying the solutions using the correspondence principle; defining the finite transformations by solving the Lie equations; relating the group parameter to physical parameters. The transformations derived in such a way, as distinct from the transformations derived in the context of conventionality of distant simultaneity, cannot be converted into the standard Lorentz transformations by a coordinate change. The anisotropic nature of the presented transformations manifests itself in that they do not leave the interval invariant but only provide the conformal invariance of the interval. The relations that represent measurable effects include the conformal factor which depends on the relative velocity of the frames and the anisotropy degree. It is important to note the use of the correspondence principle as a heuristic principle which allows to relate the conformal factor to the anisotropy degree and thus completely specify the transformations and observable quantities. (shrink)

The basic dynamical quantities of classical mechanics, such as position, linear momentum, angular momentum and energy, obtain their fundamental epistomological content by means of their intimate relationship to the symmetries of the space-time manifold which is the arena of physics. The program of canonical quantization can be understood as a two stage process. The first stage is Bohr's Correspondence Principle, whereby the basic dynamical quantities of the quantum theory are required to retain precisely the same relationship to the (...) symmetries of the space-time manifold as do their classical counterparts, thereby preserving their epistemological, as well as measurement-theoretic, significance. Having so identified the basic dynamical variables, functions of these may now be used to identify the subtler symmetries of the proper canonical group. The second and determining stage of the quantization program requires the establishment of a correspondence between some of these subtler symmetries of the classical theory and related symmetries of the quantum theory, the relationship being determined by a common algebraic form for their defining functions. (shrink)

George Berkeley's two major works, A Treatise Concerning the Principles of Human Knowledge and Three Dialogues Between Hylas and Philonous, are presented here, together with perhaps the most searching examination his ideas received during his lifetime, that of the American Samuel Johnson, who corresponded with Berkeley during his stay in the country.

v. 1. The principles of moral philosophy -- v. 2. Christian philosophy.

The aim of this paper is to render a detailed analysis of the correspondence with Clarke in order to shed some light in the relationship between the Principle of Identity of Indiscernibles and the Principle of Sufficient Reason. Most of the secondary literature takes for granted that Leibniz derives the Principle of Identity of Indiscernible from the Principle of Sufficient Reason in at least some parts of the correspondence. This would render the Principle (...) of Identity of Indiscernibles a merely contingent truth and not a necessary principle. I will argue that this interpretation is misleading, and that Leibniz never abandoned the idea that the Principle of Identity of Indiscernibles is a necessary truth. Although he is continuously using the Principle of Sufficient Reason in his argumentation, he keeps in parallel a strong argumentation that entails the necessity of the Principle of Identity of Indiscernibles. To achieve this goal, it will be necessary to point out first some contextual facts that may determine a correct understanding of the correspondence. It will be also necessary to frame the discussion about the principles into the broader debate on the possibility of Newtonian space. Finally, it will be shown that the mentioned hypothesis is supported by textual evidence throughout the entire correspondence. (shrink)