A history and drama of the development of quantum probability theory is outlined starting from the discovery of the Plank's constant exactly a 100 years ago. It is shown that before the rise of quantum mechanics 75 years ago, the quantum theory had appeared first in the form of the statistics of quantum thermal noise and quantum spontaneous jumps which have never been explained by quantum mechanics. Moreover, the only reasonable probabilistic interpretation of quantum theory put forward by Max Born was in fact in irreconcilable contradiction with traditional mechanical reality and classical probabilistic causality. This led to numerous quantum paradoxes, some of them due to the great inventors of quantum theory such as Einstein and Schroedinger. They are reconsidered in this paper from the modern quantum probabilistic point of view.
A history and drama of the development of quantum probability theory is outlined starting from the discovery of the Plank's constant exactly a 100 years ago. It is shown that before the rise of quantum mechanics 75 years ago, the quantum theory had appeared first in the form of the statistics of quantum thermal noise and quantum spontaneous jumps which have never been explained by quantum mechanics. Moreover, the only reasonable probabilistic interpretation of quantum theory put forward by Max Born was in fact in irreconcilable contradiction with traditional mechanical reality and classical probabilistic causality. This led to numerous quantum paradoxes, some of them due to the great inventors of quantum theory such as Einstein and Schroedinger. They are reconsidered in this paper from the modern quantum probabilistic point of view.
A history of the discovery of `new' quantum mechanics and the paradoxes of its probabilistic interpretation are briefly reviewed from the modern point of view of quantum probability and information. Modern quantum theory, which has been developed during the last 20 years for the treatment of quantum open systems including quantum noise, decoherence, quantum diffusions and spontaneous jumps occurring under continuous in time observation, is not yet a part of the standard curriculum of quantum physics. It is argued that the conventional formalism of quantum mechanics is insufficient for the description of quantum events, such as spontaneous decays say, and the new experimental phenomena related to individual quantum measurements, but they have all received an adequate mathematical treatment in quantum stochastics of open systems. Moreover, the only reasonable probabilistic interpretation of quantum mechanics put forward by Max Born was, in fact, in irreconcilable contradiction with traditional mechanical reality and causality. This led to numerous quantum paradoxes, some of them due to the great inventors of quantum theory such as Einstein and Schrödinger. They are reconsidered in this paper from the modern point of view of quantum stochastics and information. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for resolution of this interpretational crisis by divorcing the algebra of the dynamical generators and the algebra of the actual observables, or Bell's be ables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection rule for compatibility of the actual histories with the potential future. This rule, together with the self-compatibility of the measurements ensuring the consistency of the histories, is called the nondemolition, or causality principle in modern quantum theory. The application of this rule in the form of dynamical commutation relations leads to the derivation of the von Neumann projection postulate, and also to the more general reductions, instantaneous, spontaneous, and even continuous in time. This gives a dynamical solution, in the form of the quantum stochastic filtering equations, of the notorious measurement problem which was tackled unsuccessfully by many famous physicists starting with Schrödinger and Bohr. It has been recently proved that the quantum stochastic model for the continuous in time measurements is equivalent to a Dirac type boundary-value problem for the secondary quantized input `offer waves from future' in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the `trajectories of the output particles'. This supports the corpuscular-wave duality in the form of the thesis that everything in the future are quantized waves, while everything in the past are trajectories of the recorded particles.
A history of the discovery of quantum mechanics and paradoxes of its interpretation is reconsidered from the modern point of view of quantum stochastics and information. It is argued that in the orthodox quantum mechanics there is no place for quantum phenomenology such as events. The development of quantum measurement theory, initiated by von Neumann, and Bell's conceptual critics of hidden variable theories indicated a possibility for resolution of this crisis. This can be done by divorcing the algebra of the dynamical generators and an extended algebra of the potential (quantum) and the actual (classical) observables. The latter, called beables, form the center of the algebra of all observables, as the only visible (macroscopic) observables must be compatible with any hidden (microscopic) observable. It is shown that within this approach quantum causality can be rehabilitated within an extended quantum mechanics (eventum mechanics) in the form of a superselection rule for compatibility of the consistent histories with the statistically predictable future. The application of this rule in the form of the nondemolition principle leads to the statistical inference of the von Neumann projection postulate, and also to the more general quantum information dynamics for instantaneous events, spontaneous localizations (i.e. quantum jumps), and state diffusions (i.e. continuous trajectories). This gives a dynamical solution, in the form of a Dirac boundary value problem and reduced filtering equations, of the notorious decoherence and measurement problems which was tackled unsuccessfully by many famous mathematicians and physicists starting with von Neumann, Schroedinger and Bohr.
PROBABILITY IN THE OLD QUANTUM THEORY Probability was connected to quantum theory right from the start, in 1900, through the derivation of Planck's radiation law. But not much attention has been paid to the concept of probability in quantized radiation, or in the ‘quantum jumps’ from one energy level to another in an atom, and related problems. A whole chapter or book, instead of a section, could be written on the background of quantum theory in statistical mechanics and spectral analysis with this aspect in mind. Probabilistic properties were included in very many of the most important papers dealing with radiation between 1900 and 1925. It became also clear in time that Planck's law could not be derived from classical physics. Einstein admits this around 1908. Later he said, in a work of 1917, that it is a weakness of the theory of photon emission that ‘it leaves to “chance” the time and direction of the elementary processes,’ thereby, according to Pais (1982, p. 412), making explicit ‘that something was amiss with classical causality.’ It remains somewhat open how the origins and shifting interpretations of probability in the old quantum theory affected the acceptance of the probabilistic interpretation of the new quantum mechanics of 1925–1926, and of the indeterminism that found its confirmation in Heisenberg's uncertainty relation in 1927.
Born’s probabilistic interpretation of quantum mechanics is commonly assumed to rely on classical probability theory in the sense of Kolmogorov. In this paper we argue that this assumption is methodologically unjustified. We show that quantum probabilities naturally arise from an analytic method fundamentally different from the synthetic approach underlying classical probability theory. In the analytic framework, the whole (the totality of alternatives) is primary, while probabilities of individual alternatives are derived quantities. Interference appears at the level of the realization probability of the whole, whereas conditional probabilities of alternatives remain additive within a given context. We demonstrate that many well-known quantum paradoxes originate from the inappropriate application of synthetic probabilistic reasoning. The proposed formulation is consistent with the Born rule, its extensions developed in our earlier works, and with Birkhoff–von Neumann quantum logic. Classical probability theory appears only as a degenerate formal limit and is not methodologically universal.
High Resolution Image Download MS PowerPoint Slide In July 1925, Werner Heisenberg submitted a paper to Zeitschrift für Physik entitled ‘On quantum-theoretical reinterpretation of kinematic and mechanical relationships’, thus giving birth to quantum mechanics. In the following year, building on de Broglie’s wave-particle duality, Erwin Schrödinger developed wave mechanics, and soon, Max Born provided a probabilistic interpretation of the wave function. The theory was further enriched by the exclusion principle of Wolfgang Pauli and the uncertainty principle of Heisenberg, which ultimately led to the development of relativistic quantum mechanics by Dirac. The Copenhagen Interpretation created a probabilistic framework for understanding the theory. Over the past century, quantum mechanics has paved the way for advances in quantum field theory, computing, and modern technologies. This historical narrative provides insights into the complex discovery process that led to the development of quantum mechanics, which can potentially guide novel breakthroughs amid challenging conceptual struggles, as seen in the field of artificial intelligence today.
Quantum mechanics is one of the great success stories of modern physics, making sense of the very small just as Einstein's theory of relativity made sense of the very large. But, for most students, the ideas that make quantum mechanics powerful can be confusing and counterintuitive. This volume in the Greenwood Guides to Great Ideas in Science series provides a history of quantum mechanics from the early breakthroughs of Planck and Einstein, at the beginning of the 20th century, to the present frontiers of quantum computing and quantum gravity. The approach is entirely non-technical, and is aimed at the general reader who may not have much mathematical background but who has a strong curiosity about some of the most important developments in modern science. Quantum Mechanics: A Historical Perspectivetraces the history of this powerful theory, including: ; The early discoveries by Max Planck and Albert Einstein regarding the quantization of radiation ; The early quantum theory, including Neils Bohr's theory of the atom ; The birth of modern quantum mechanics through the work of Heisenberg, Schrodinger, Born, Dirac and others ; Applications of quantum mechanics in chemistry, nuclear physics, electronics, and many other areas ; Recent work in quantum computation and quantum information theory The book emphasizes the fact that despite the great success of quantum mechanics, many exciting intellectual frontiers remain open for further researchers to explore. It includes a glossary, a timeline, and a bibliography of accessible resources for further research.