This chapter shows how the concept of the trajectory of a quantum particle almost vanished in the battle between Werner Heisenberg’s matrix mechanics and Erwin Schrödinger’s wave mechanics. It took Niels Bohr and his complementarity principle of wave-particle duality to cede back some reality to quantum trajectories. However, Schrödinger and Einstein were not convinced and conceived of quantum entanglement to refute the growing acceptance of the Copenhagen Interpretation of quantum physics. Schrödinger’s cat was meant to be an absurdity, but ironically it has become a central paradigm of practical quantum computers. Quantum trajectories took on new meaning when Richard Feynman constructed quantum theory based on the principle of least action, inventing his famous Feynman Diagrams to help explain quantum electrodynamics.
This chapter shows how the concept of the trajectory of a quantum particle almost vanished in the battle between Werner Heisenberg’s matrix mechanics and Erwin Schrödinger’s wave mechanics. It took Niels Bohr and his complementarity principle of wave-particle duality to cede back some reality to quantum trajectories. However, Schrödinger and Einstein were not convinced and conceived of quantum entanglement to refute the growing acceptance of the Copenhagen Interpretation of quantum physics. Schrödinger’s cat was meant to be an absurdity, but ironically it has become a central paradigm of practical quantum computers. Quantum trajectories took on new meaning when Richard Feynman constructed quantum theory based on the principle of least action, inventing his famous Feynman Diagrams to help explain quantum electrodynamics.
How it all began In 1935, a decade after the invention of quantum theory by Heisenberg (1925) and Schrödinger (1926), three papers appeared, setting the stage for a new concept, quantum entanglement. The previous decade had already seen momentous discussions on the meaning of the new theory, for example by Niels Bohr (see his contribution to Albert Einstein: Philosopher-Scientist in Further reading); but these new papers opened up the gates for a new, very deep philosophical debate about the nature of reality, about the role of knowledge, and about their relation. Since the 1970s, it has become possible for experimenters to observe entanglement directly in the laboratory and thus test the counter-intuitive predictions of quantum mechanics whose confirmation today is beyond reasonable doubt. Since the 1990s, the conceptual and experimental developments have led to new concepts in information technology, including such topics as quantum cryptography, quantum teleportation, and quantum computation, in which entanglement plays a key role. In the first of the three papers, Einstein, Podolsky, and Rosen (EPR) realized that, if two particles had interacted in their past, their properties will remain connected in the future in a novel way, namely, observation on one determines the quantum state of the other, no matter how far away. Their conclusion was that quantum mechanics is incomplete and they expressed their belief that a more complete theory may be found. Niels Bohr replied that the two systems may never be considered independent of each other, and observation on one changes the possible predictions on the other. Finally, Erwin Schrödinger, in the paper which also proposed his famous cat paradox, coined the term “entanglement” (in German Verschränkung ) for the new situation and he called it “not one, but the essential trait of the new theory, the one which forces a complete departure from all classical concepts.”
Abstract This chapter examines some crucial experiments and basic principles of quantum mechanics that have strongly influenced the development of quantum theory in its modern form: starting from Planck’s law of black-body radiation and its derivation using the quantization of energy; Einstein’s photon hypothesis for the puzzle presented by the photoelectric effect and its test via the Millikan experiment; the Compton effect; Bohr’s theses for the structure of the hydrogen atom and the complementarity of waves and particles i.e., the wave-particle duality, culminating in de Broglie’s ideas for matter waves and their confirmation in the Davisson-Germer experiment for electron diffraction from a crystal; Heisenberg’s uncertainty principle for position and momentum as well as for energy an time; the famous double-slit experiment and Born’s probability interpretation, and finally the provocative thought experiment of Schrödinger’s cat
Abstract While the theory proved successful at describing a broad range experimental results, from the black body spectrum to the hydrogen atom, the question arose as to what the theory was telling us about the nature of physical reality. Schrödinger’s attempt to represent particles as wave packets failed because of the spreading of the wave packets. Max Born, investigating how the theory could be applied to scattering processes, was led to introduce the probability interpretation of the wave function. In an attempt to summarize the physical meaning of the theory, Heisenberg introduced the uncertainty principle. Niels Bohr and his Copenhagen school developed the philosophical position known as “complementarity.” There was a bitter dispute between Schrödinger and the “Copenhageners” over the necessity of quantum jumps in the theory.
Quantum theory confronts us with bizarre paradoxes which upset the logical edifice of classical physics. At the sub-atomic level, one particle seems to know what the others are doing (so-called 'non-locality'), and according to Heisenberg's 'uncertainty principle', there is a limit on how accurately nature can be observed. And yet the theory is amazingly accurate and widely applied, explaining all of chemistry and most of physics. This book takes us on a step-by-step tour with the key figures, including Planck, Einstein, Bohr, Heisenberg and Schrodinger. Each contributed at least one crucial concept to the theory. The puzzle of the wave-particle duality is here, along with descriptions of the two questions raised gainst Bohr's 'Copenhagen Interpretation' - the famous 'dead and alive cat' and the EPR paradox. Both remain unresolved at the beginning of the 21st century.
Wonderful news from Copenhagen Heisenberg and Schrödinger invented mathematical formalisms that provided correct answers to all the various problems of (non-relativistic) quantum theory. It was Bohr who uncovered the underlying significance of the theory; in particular he showed how the profound conceptual difficulties encountered as the theory developed – the so-called wave–particle duality, the totally unclassical nature of the uncertainty principle – could be neutralised by a revision, or more accurately a generalisation, of our use of physical concepts. Such was the generally accepted view of things from soon after 1927, when Bohr first put forward his ideas on complementarity at an international meeting of physicists at Como, through the 1930s, when it was felt that Bohr destroyed Einstein's contrary opinions, and certainly up to the time of Bohr's death in 1962. Bohr's analysis is usually spoken of as the Copenhagen interpretation of quantum theory, though it is instructive to realise that such a term was frowned upon by those closest to Bohr, since it appears to suggest that the interpretation is just one among (conceivably) many. Let us examine, for example, the words of Léon Rosenfeld, Bohr's disciple and long-term collaborator, as expounded at a conference in 1957 [52]. Rosenfeld maintained that any idea of ‘interpreting a formalism’ was a ‘false problem’, that in a good theory, the ‘ordinary language (spiced with technical jargon for the sake of conciseness)’ in which it is described, is ‘ inseparably united … with whatever mathematical apparatus is necessary’, that ‘we are here not faced with a matter of choice between two possible languages or two possible interpretations, but with a rational language intimately connected with the formalism and adapted to it, on the one hand, and with rather wild, metaphysical speculations … on the other’.
Prior to and into the first decade of Niels Bohr's 1913 atomic theory, physicists dealt with physical systems in which the usual space and time pictures of classical physics were assumed trustworthy and so could be extrapolated to any sort of matter in motion, for example, electrons move like billiard balls and light behaves analogously to water waves. In the German scientific milieu this visual imagery was accorded a reality status higher than viewing merely with the senses and was referred to as ‘ordinary intuition [ gewöhnliche Anschauung ]’. Ordinary intuition is the visual imagery abstracted from phenomena that we have actually witnessed in the world of sense perceptions. The concept of ordinary intuition was much debated during 1923–27 by physicists like Niels Bohr, Werner Heisenberg, Wolfgang Pauli and Erwin Schrödinger, all of whom used this term with proper Kantian overtones, and all of whom lamented its loss in the new quantum mechanics. Ordinary intuition is associated with the strong causality of classical mechanics. According to the law of causality, initial conditions (position and velocity or momentum and energy) can be ascertained with in-principle perfect accuracy. Consequently any system's continuous development in space and time can be traced with in-principle perfect accuracy using Newton's laws of motion and conservation of energy and momentum. Any limitations to the accuracy of measurements are assumed not to be intrinsic to the phenomena, that is they are interpreted to be systematic measurement errors that ideally can be made to vanish.