Bohr’s Como Argument: Complementarity and the Problem of Causality

Dirac’s contributions to the discovery of nonrelativistic quantum mechanics and quantum electrodynamics, prior to his discovery of the relativistic wave equation, are described.

The quantum uncertainty principle stipulates that when one observable is predictable there must be some other observables that are unpredictable. The principle is viewed as holding the key to many quantum phenomena and understanding it deeper is of great interest in the study of the foundations of quantum theory. Here we show that apart from being restrictive, the principle also plays a positive role as the enabler of non-classical dynamics in an interferometer. First we note that instantaneous action at a distance should not be possible. We show that for general probabilistic theories this heavily curtails the non-classical dynamics. We prove that there is a trade-off with the uncertainty principle that allows theories to evade this restriction. On one extreme, non-classical theories with maximal certainty have their non-classical dynamics absolutely restricted to only the identity operation. On the other extreme, quantum theory minimizes certainty in return for maximal non-classical dynamics.

A history of the discovery of `new' quantum mechanics and theparadoxes of its probabilistic interpretation are brieflyreviewed from the modern point of view of quantum probabilityand information. Modern quantum theory, which has beendeveloped during the last 20 years for the treatment of quantum opensystems including quantum noise, decoherence, quantum diffusionsand spontaneous jumps occurring under continuous in timeobservation, is not yet a part of the standard curriculum ofquantum physics. It is argued that the conventional formalism ofquantum mechanics is insufficient for the description of quantumevents, such as spontaneous decays say, and the new experimentalphenomena related to individual quantum measurements, but theyhave all received an adequate mathematical treatment in quantumstochastics of open systems.Moreover, the only reasonable probabilistic interpretation ofquantum mechanics put forward by Max Born was, in fact, inirreconcilable contradiction with traditional mechanical realityand causality. This led to numerous quantum paradoxes, some ofthem due to the great inventors of quantum theory such asEinstein and Schrödinger. They are reconsidered in thispaper from the modern point of view of quantum stochastics and information.The development of quantum measurement theory, initiated by vonNeumann, indicated a possibility for resolution of thisinterpretational crisis by divorcing the algebra of thedynamical generators and the algebra of the actual observables,or Bell's beables. It is shown that within this approachquantum causality can be rehabilitated in the form of asuperselection rule for compatibility of the actual historieswith the potential future. This rule, together with theself-compatibility of the measurements ensuring the consistencyof the histories, is called the nondemolition, or causalityprinciple in modern quantum theory. The application of this rulein the form of dynamical commutation relations leads to thederivation of the von Neumann projection postulate, and also tothe more general reductions, instantaneous, spontaneous, andeven continuous in time. This gives a dynamical solution, in theform of the quantum stochastic filtering equations, of thenotorious measurement problem which was tackled unsuccessfullyby many famous physicists starting with Schrödinger andBohr.It has been recently proved that the quantum stochastic modelfor the continuous in time measurements is equivalent to a Diractype boundary-value problem for the secondary quantized input`offer waves from future' in one extra dimension, and to areduction of the algebra of the consistent histories of pastevents to an Abelian subalgebra for the `trajectories of theoutput particles'. This supports the corpuscular-wave duality inthe form of the thesis that everything in the future arequantized waves, while everything in the past are trajectories of therecorded particles.

From the point of view of classical theory and our everyday experience, quantum phenomena are surprising and the concepts of quantum mechanics are incomprehensible. Since the beginning of quantum theory scientists questioned its very basic concepts, such as locality, reality, and complementarity, and proposed gedankenexperiments, or thought experiments, to probe its foundations. In the light of new optical technology we have been able to realize some of these experiments. This chapter will focus on three of them: (1) EPR-Bohm-Bell correlation and Bell’s inequality; (2) Scully’s quantum eraser; (3) Popper’s experiment. The results of these experiments are very interesting. On one hand, the experimental observations confirm the predictions of EPR-Bell, Scully, and Popper. On the other hand, the calculations from quantum theory perfectly agree with the experimental data. Moreover, apparently, the experimental observations do not lead to any “violations” of the principles of quantum mechanics. One important conclusion we may draw from these optical tests is that all the observations are the results of multi-photon interference: a group of photons interferes with the group itself at distance. The nonlocal multi-photon interference phenomena may never be understood in classical theory, however, it is legitimate in quantum mechanics. The superposition principle of quantum theory supports the superposition of multi-photon amplitudes, whether the photons are entangled or randomly grouped and despite the distances between these individual photodetection events.

Exact predictions for most quantum systems are computationally inaccessible. This is the so-called many body problem, which is present in most common interpretations of quantum mechanics. Therefore, predictions of natural quantum phenomena have to rely on some approximations (assumptions or simplifications). In the literature, there are different types of approximations, ranging from those whose justification is basically based on theoretical developments to those whose justification lies on the agreement with experiments. This last type of approximations can convert a quantum theory into an “unfalsifiable” quantum theory, true by construction. On the practical side, converting some part of a quantum theory into an “unfalsifiable” one ensures a successful modeling (i.e. compatible with experiments) for quantum engineering applications. An example of including irreversibility and dissipation in the Bohmian modeling of open systems is presented. On the ontological level, however, the present-day foundational problems related to controversial quantum phenomena have to avoid (if possible) being contaminated by the unfalsifiability originated from the many body problem. An original attempt to show how the Bohmian theory itself (minimizing the role of many body approximations) explains the transitions from a microscopic quantum system towards a macroscopic classical one is presented.

This chapter explores the intricate dynamics between medium-sized and large enterprises in EU candidate countries through the lens of Bohm's interpretation of Bohr's complementarity principle and Heisenberg's uncertainty principle which are two fundamental concepts in quantum theory. By drawing parallels between quantum mechanics and economic behavior, the research posits that the growth trajectories of these enterprises are interrelated, exhibiting complementary relationships under uncertainty that reflect the principles of quantum duality. Employing a robust research methodology, the chapter presents empirical evidence showcasing the correlation between capital concentration and growth rates of medium-sized and large enterprises across various regions. Statistical analyses, including Pearson coefficients, reveal significant relationships that support the hypothesis of a higher share of medium enterprises correlating with an increased presence of large enterprises revalidating complementariness. Furthermore, the findings highlight important policy implications for regional economic development, emphasizing the need for tailored strategies that foster the growth of both enterprise sizes under uncertain conditions. By integrating quantum theory with economic dynamics, this chapter contributes a novel perspective to the discourse on entrepreneurship and regional growth, encouraging further exploration of interdisciplinary approaches in econophysics research.

When the 5th Solvay conference on quantum theory took place in Brussels in 1927, the quantum community had undergone 2 years of rapid development and intense debate. Within the period from 1925 to 1927, matrix and wave mechanics had been developed independently of each other. The two theories were proven to be mathematically equivalent and turned out to be two formulations of an overarching quantum mechanical formalism. During this time, the new theories were applied to various problems that had long resisted solution and extended to new phenomena that were beyond their initial scope. Concurrently with this development, the proponents of wave mechanics and matrix mechanics, Erwin Schrodinger, Werner Heisenberg and the physicists from Gottingen and Copenhagen, first entered a heated debate on the meaning of quantum mechanics. At the heart of their discussion were the fundamental changes that the new quantum mechanics implied for physical theories in general. Basic elements of classical mechanics and the old quantum theory, such as the ability to visualize an abstract mathematical formalism in space and time, were missing in the developing theory. It was uncertain whether quantum mechanics in general could be understood in these terms, well established in classical mechanics. At first, the founders of matrix mechanics, Werner Heisenberg, Max Born and Pascual Jordan, found these questions rather unimportant. They believed, that the abstract mathematical formalism of quantum mechanics provided all that was required from a physical theory, and that the lack of physical models was unavoidable. Erwin Schrodinger and Louis de Broglie, on the other hand, were unwilling to accept the abandonment of the former aims of the physical theory and questioned whether progress within quantum mechanics was even possible without the most powerful tools for understanding natural phenomena.

The institutes of Arnold Sommerfeld in Munich, Niels Bohr in Copenhagen, and Max Born in Gottingen became the leading centers for the study of quantum theory in the first decades of the twentieth century. Although founded for a broader range of theoretical physics, the quantum became the major topic of research in Munich after the Bohr-Sommerfeld-model of the atom (1913–16). The heyday came in the 1920s, when Bohr's and Born's institutes started operation and became further attractive centers for ambitious theorists all over the world. The discovery of quantum mechanics (1925) should be regarded not only as the achievement of a few young geniuses (in particular Werner Heisenberg and Wolfgang Pauli) but also as the result of a collaborative effort emerging in the new social and intellectual environment of their teachers' schools in Munich, Gottingen and Copenhagen.

THE ATOMIC NUCLEUS1 In his recent address to the Fourth International Thomistic Congress, His Holiness Pope Pius XII stressed the need of philosophers acquainting themselves with the recent advances in nuclear science. This presents something of a problem for the professional philosopher. For at no time in the long history of science, have we ever witnessed anything comparable to the vast and intensified research, in great part Government subsidized, which is being brought to bear on the study of the atomic nucleus. The primary literature is vast and not always readily available in summary accounts. This survey of nuclear physics then may be of help to the philosopher and of interest to scientists in fields other than physics. The term nucleus was first introduced by Ernest Rutherford, the "father of nuclear physics", some forty years ago in connection with his most significant discovery, the conception of the atom as comprising a tiny but massive positively charged core surrounded by a very tenuous but relatively extensive electron structure. The development of Rutherford 's concept of the atom and its integration with Planck's quantum theory of radiation by men like Bohr, Heisenberg, Dirac and Schroedinger was the principal concern of atomic physics during the first three decades of this century. With its climax in the achievement of a unified theory of quantum mechanics, accounting for the physical and chemical behavior of the atom in both elementary and compound form, the center of the theoretical physicist's interest shifted from the extranuclear electron structure, the domain of atomic physics proper, to the nucleus and the score of "elementary" particles that are born of the heart of the atom. The last twenty years consequently, has witnessed the creation and development of a distinct branch of speculative science known as nuclear physics. Its present status is akin to that of atomic physics before the discovery of quantum mechanics. A great many nuclear phenomena have been studied and classified, but to date no satisfactory theory has been devised for integrating them. Such a theory, to be adequate, should account for what we know of elementary nuclear 1 Address given at the Fourth National Meeting of Franciscan Sisterhoods, Marian College, Indianapolis, Indiana, November 25—26, 1955. 350 The Atomic Nucleus351 particles, nuclear reactions and nuclear forces. And until such a theory appear, the material we intend to cover in this paper can be treated under these three topics even though the first and third overlap somewhat. i. Elementary Nuclear Particles It might be more exact to speak of the elementary particles of nuclear physics rather than elementary nuclear particles, since the first description implies nothing more than that such particles are objects of study in nuclear physics, whereas the latter designation intimates that the nucleus may be compounded of these elementary entities as a wall is of bricks or cinder-blocks. The latter is only partially correct, if true at all, in the sense that the physicist is wont to distinguish between the nucléons proper (the proton and neutron) which are assumed to retain their general identity within the nucleus as contrasted with neutrinos, electrons, gamma photons and mesons which have only a potential existence there and are created or annihilated in the course of changes of energy states of the nucléons in much the same way as photons are created or annihilated in connection with the energy changes of the electrons in the extranuclear structure of the atom. Even with this qualification the title is still misleading. For the term "elementary" is used in a purely relative sense. It does not imply invariable stability, for the elementary particles Usted by the nuclear scientist are almost all unstable and quickly decay into another elementary form. They are "elementary" only in as much as they do not seem to be composed in the ordinary physical or chemical sense of the word, as we would speak of an atom being composed of a nucleus and electron cloud, or a deutron being composed of a proton and a neutron, or an alpha particle of two neutrons and two protons, and so on. The term "particle" too may be misleading unless we keep in mind that all of...

It is well-known for a long time that quantum theory, although being extremely successful with respect to the correct description of experimental results, still involves conceptual problems of different kinds. The following three issues seem to be outstanding: they contain the basic problems to which numerous discussions in the field may be reduced. Interpretational problems which have lead to a variety of approaches presented and discussed, e.g., in Ref.[1]. Quantum theory of gravity, which is expected to provide the missing link between quantum theory and general relativity [2]. Quantum theory of measurement, an issue closely related to the question of irreversibility and the arrow of time [3].

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever. This definition itself does not rely on the formalism of quantum theory, avoiding many of the conceptual difficulties of usual definitions. We then derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems, as well as for the case of position and momentum. Our relations may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment. We also show that Englert's wave-particle duality relation [PRL 77, 2154 (1996)] can be viewed as an error-disturbance uncertainty relation.

Many attempts were made to derive with the old quantum theory structures for the hydrogen molecule, H_2, and the hydrogen molecule-ion, H_2^+, in agreement with the experimentally observed properties of these substances, in particular their energy contents. These were all unsuccessful, as were similar attempts to derive a satisfactory structure for the helium atom. It became increasingly evident that in these cases the straightforward application of the old quantum theory led to results definitely incompatible with the observed properties of the substances, and that the introduction of variations in the quantum rules was not sufficient to remove the disagreement. (For a summary of these applications see, for example, Van Vleck (1).) This fact was one of those which led to the rejection of the old quantum theory and the origination of the new quantum mechanics. The fundamental principles of the quantum mechanics were proposed by Heisenberg (2) in 1925. The introduction of the matrix algebra (3) led to rapid developments. Many applications of the theory were made, and in every case there was found agreement with experiment. Then the wave equation was discovered by Schrodinger (4), who developed,and applied his wave mechanics independently of the previous work. Schrodinger’s methods are often considerably simpler than matrix methods of calculation, and since it has been shown (5) that the wave mechanics and the matrix mechanics are mathematically identical, the wave equation is generally used as the starting point in the consideration of the properties of atomic systems, in particular of stationary states.

If nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum nonlocality. However, none of them can explain the set of quantum correlations arising in the simplest scenarios. In [Sci. Adv. 5, eaav8370] we have shown that generalized uncertainty relations, as well as a specific notion of locality, give rise to both familiar and new characterizations of quantum correlations. In particular, we have identified a condition, relativistic independence, which states that uncertainty relations are local in the sense that they cannot be influenced by other experimenters’ choices of measuring instruments. We proved that theories with nonlocal correlations stronger than the quantum ones do not satisfy this notion of locality, and therefore, they either violate the underlying generalized uncertainty relations or allow experimenters to nonlocally tamper with the uncertainty relations of their peers. In this talk I will discuss several implications of this work to multiplicative Bell inequalities, causality and networks. Finally, I will support the claim that locally consistent indeterminism should be understood as the enabler of most quantum phenomena (and possibly all of them).

Quantum mechanics, heredity and the origin of life

Approaches for improving students' understanding of quantum mechanics