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CRC Press eBooks

Chapter Nine

L I Ponomarev

Published Nov 11, 2021• 0 citations
Publisher

Abstract

The more scientists learned about the atom, the less categorical became the questions they put to nature. The uncertainty relation is a strict law of nature, which is in no way related to some imperfections of our devices. The uncertainty relation is directly opposed to intuition and everyday experience. Heisenberg explained the matter by discarding still another idealization of classical physics — the concept of observation. It turned out that in quantum mechanics it had to be revised, along with the concept of motion. The concepts of “phenomenon”, “measurement”, and “observation” are closely related to one another but they are by no means identical. Any measurement is essentially interaction between the instrument and the object to be studied. The principle that Bohr named complementarity is one of the most fundamental philosophical and scientific ideas of our time, which can only be compared to the principle of relativity and the concept of a physical field.

DOI
10.1201/9781003062950-11

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The more scientists learned about the atom, the less categorical became the questions they put to nature. The uncertainty relation is a strict law of nature, which is in no way related to some imperfections of our devices. The uncertainty relation is directly opposed to intuition and everyday experience. Heisenberg explained the matter by discarding still another idealization of classical physics — the concept of observation. It turned out that in quantum mechanics it had to be revised, along with the concept of motion. The concepts of “phenomenon”, “measurement”, and “observation” are closely related to one another but they are by no means identical. Any measurement is essentially interaction between the instrument and the object to be studied. The principle that Bohr named complementarity is one of the most fundamental philosophical and scientific ideas of our time, which can only be compared to the principle of relativity and the concept of a physical field.
Abstract One of the foundational principles of quantum mechanics is Heisenberg’s uncertainty relation. According to this relation, no one can measure both the position of a particle and how fast it is moving simultaneously no matter how precise the measuring instruments. Heisenberg’s uncertainty relation and the associated Bohr’s principle of complementarity are explained using simple examples. The idea that measurement disturbs the system is a source of the uncertainty. The philosophical question whether the uncertainty represents only our inability to measure the properties precisely or it has much deeper consequences related to the question of reality is also discussed.
For over nine decades, quantum mechanics has profoundly shaped our understanding of nature, offering explanations for the stability of atoms, the formation of mole cules, the properties of materials, and phenomena such as light or radioactivity. It is essential to modern technologies—from microchips to lasers—and underpins the physics of elementary particles. Yet, despite its successes, it remains a deeply mysterious theory, confronting a central enigma: why does the quantum world behave so differently from everyday reality? Elements such as superposition and quantum entanglement—which allow particles to exist simultaneously in multiple states or remain interconnected regardless of distance—contradict classical world intuitions. This gap between microscopic and macroscopic behavior has given rise to what is known as the “measurement problem,” raising fundamental questions about the nature of reality. Diverging interpretations have led to two major schools of thought: anti-realism, promoted by Niels Bohr, which holds that reality depends on the observer and their interaction with measurement instruments; and realism, supported by Albert Einstein, which argues that quantum mechanics is incomplete and that eality exists independently of observation. Bohr’s complementary philosophy and Heisenberg’s uncertainty principle were central to the formulation of the “Copenhagen interpretation,” which became dominant in the 20th century. However, the persistent opposition of scientists like Einstein and Schrödinger inspired generations of physicists to seek a unification between quantum mechanics and relativity, culminating in new theories such as loop quantum gravity and string theory. Thus, the debate between realism and anti-realism remains alive, and philosophy continues to play a crucial role in exploring the new foundations of physics.
The two most important areas in modern physics are quantum mechanics and the theory of relativity. Unlike classical physics, where Newton's mechanics dominates, these two areas change human beings' fundamental view of the universe. One of the theories that build up the base of quantum mechanics is Heisenberg's Uncertainty Principle. Starting from a thought experiment, Heisenberg's microscope in the setting of classical physics, Werner Heisenberg built a bridge between classical and quantum physics by presenting a counterintuitive outcome in the thought experiment. Since then, the observer of a physics phenomenon is no longer a bystander. The behavior of observation became a part of the physical experiment. To come up with a mathematical expression that can describe such a new discovery, Heisenberg came up with matrix mechanics and the concept of complementary variables. There is a trade-off between a pair of complementary variables. When one of them is measured precisely, meaning the information of that variable is known on a large scale, the other variable can not be measured precisely, meaning there is no way to know enough information about the other variable. The principle indicates a fundamental limit on what human beings can know about the unknown variables. The discoveries of other complementary variables help physicists know the new image of the physics world under new rules.
Chapter 2 explains how in constructing quantum mechanics, old ideas had to be discarded and well-established principles had to be modified or even abandoned. First it was necessary to be convinced of the physical reality of the atomic structure of matter; then to show that Newtonian mechanics is not directly applicable to the study of the atom; later to show that Maxwell’s electrodynamics alone does not describe all the elementary processes of interaction between an atom and other quantum particles. The chapter takes us from Planck’s energy quantum to Einstein’s quantization as a universal phenomenon, from Bohr’s quantum atom model, and the early quantization rules, to de Broglie’s waves associated with corpuscles in motion. It ends with a corollary on the electrodynamic nature of quantum mechanics.
Niels Bohr, as is well known, introduced the notion of complementarity into physics, as a fundamental principle of quantum mechanics. It holds that objects have complementary properties that cannot be measured accurately at the same time. For example, the particle and wave aspects of physical objects are such complementary phenomena. Both concepts are borrowed from classical mechanics, where it is impossible to be both, a particle and a wave at the same time. Particle and Wave represent the complementarity of the Discrete and the Continuous. Humans reason by means of concepts (meanings) and language, as well as, by means of logical or arithmetic symbolism. Meanings are continua, whereas logic and arithmetic are based on relations of identity and difference.
One of the various interpretations of quantum mechanics occupies a privileged position in the opinion of the majority of physicists. This is the Copenhagen view, which owes its fame and popularity not only to historical reasons but also to its simplicity and practical efficiency. As is well known, the Copenhagen outlook was elaborated collectively. Nevertheless, Niels Bohr's and W. Heisenberg's contributions should be singled out as particularly outstanding. This chapter describes two principles, which are in fact the two pillars on which Bohr's doctrine is built. These are: The working of measuring instruments must be accounted for in purely classical terms . Another one is quantum systems that should not even be thought of as possessing individual properties independently of the experimental arrangement. In the particular case of the pair of observables "position" and "momentum," the Heisenberg uncertainty relations can be considered as a generalization of the complementarity principle.