Quantum mechanics has given scientists valuable lessons in how science works. Unfortunately, it has also been misinterpreted and misrepresented by pseudoscientists and portrayed as an antipode of classical physics. As a result, the majority of the educated public is confused about both the quantum theory and classical Newtonian physics and the relation between the two. We postpone the examination of the misrepresentation of the quantum theory in pseudoscience until Chapter 35. This chapter concentrates, in part, on the characteristics of the theory and how it is similar to (and different from) the classical theory.
Quantum mechanics has given scientists valuable lessons in how science works. Unfortunately, it has also been misinterpreted and misrepresented by pseudoscientists and portrayed as an antipode of classical physics. As a result, the majority of the educated public is confused about both the quantum theory and classical Newtonian physics and the relation between the two. We postpone the examination of the misrepresentation of the quantum theory in pseudoscience until Chapter 35. This chapter concentrates, in part, on the characteristics of the theory and how it is similar to (and different from) the classical theory.
The behavior of classical macroscopic particles – from baseballs to planets – is governed by Newtonian mechanics as we have described in the first chapters of this book. The behavior of very small particles, on the other hand, is governed by an entirely different collection of equations and rules that go under the name of “quantum mechanics” and these particles are referred to as quantum particles. These rules have analogies to classical mechanics, but are fundamentally different and somewhat mysterious as we discussed in Chapter 8. The fundamental principles of quantum mechanics cannot be proven to be correct. They were developed based on the results of experimental observation, by analogy with classical mechanics, and through the consideration of logical implications of the formalisms used. There is no way to derive the fundamental elements of quantum mechanics, any more than one could predict from first principles that Newtonian forces should add as vectors. On the other hand, quantum mechanics is among the most rigorously tested theories in science, and the predictions of quantum mechanics have, so far, always been in agreement with experiment. In this chapter, we will present quantum mechanics as a series of postulates and examine their implications in application to simple one-dimensional systems. In the next chapter we will examine quantum effects in real systems including atoms, molecules, crystals, and artificially engineered nano-structures. Postulates of quantum mechanics QM Postulate 1: A quantum particle is described by a wave function Ψ( x , y , z , t ) which is a function of spatial coordinates and time. All physically determinable quantities can be derived from the wave function Ψ( x , y , z , t ) ; quantities which cannot be found from the wave function are not physically meaningful. Note that some things that one could ask about a quantum particle, for example the exact position and simultaneous exact momentum of a particle, are not derivable from the wave function and are therefore considered indeterminate (or uncertain ). These are things which cannot ever be known about a particle, and, as such, they are meaningless to contemplate.
Despite its status as a core part of contemporary physics, there is no consensus among physicists on the question of what, if anything, the success of quantum theory is telling us about the physical world. This gives rise to the collection of debates and discussions known as "the interpretation of quantum mechanics". Describing quantum mechanics is complicated by there being so many interpretations of it. In text books, classical mechanics is an approximation of the quantum mechanics when ℏ → 0. In a first part, we recall the fundamental differences between the classical mechanics in different formalisms: Newtonian, Lagrangian and Hamiltonian (Jacobi). A second part is dedicated to the deep similarities and differences between classical and quantum mechanics. The third part deals with the misunderstanding between scientific communities about the meaning ℏ → 0. The last part deals with the porous frontier between classical and quantum physics to the light of the algebraic topology illustrated by two major theorems: Borsuk Ulam and Non squeezing Gromov's theorem.
This paper re-opens the debate on the failure of quantum mechanics to provide an understandable view of micro-reality. A critique is offered of the commonly accepted ‘Copenhagen Interpretation’ of a theory that is only a mathematical approach to the level of reality characterized by atoms and electrons. This critique is based on the oldest approach to thinking about nature for over 2500 years, known as Natural Philosophy. Quantum mechanics (QM) was developed over the first quarter of the 20th Century, when scientists were enthralled by a new philosophy known as Positivism, whose foundations were based on the assumption that material objects exist only when measured by humans – this central assumption conflates epistemology (knowledge) with ontology (existence). The present critique rejects this human-centered view of reality by assuming material reality has existed long before (and will persist long after) human beings (“Realism”). The defensive view that the micro-world is too different to understand using regular thinking (and only a mathematical approach is possible) is rejected totally. At least 12 earlier QM interpretations are critically analyzed, indicating the broad interest in “what does QM mean?” The standard theory of quantum mechanics is thus constructed on only how the micro-world appears to macro measurements - as such, it cannot offer any view of how the foundations of the world are acting when humans are not observing it - this has generated almost 100 years of confusion and contradiction at the very heart of physics. Significantly, we live in a world that is not being measured by scientists but is interacting with itself and with us. QM has failed to provide explanations: only recipes (meaningless equations), not insights. Physics has returned to the pre-Newtonian world of Ptolemaic phenomenology: only verifiable numbers without real understanding. The focus needs to be on an explicit linkage between the micro-world, when left to itself, and our mental models of this sphere of material reality, via the mechanism of measurement. This limits the role of measurement to confirming our mental models of reality but never confusing these with a direct image of ‘the thing in itself’. This implies a deep divide between reality and appearances, as Kant suggested. This paper includes an original analysis of several major assumptions that have been implicit in Classical Mechanics (CM) that were acceptable in the macroscopic domain of reality, demonstrated by its proven successes. Unfortunately, only a few of these assumptions were challenged by the developers of QM. We now show that these other assumptions are still generating confusions in the interpretation of QM and blocking further progress in the understanding of the microscopic domain. Several of these flawed assumptions were introduced by Newton to support the use of continuum mathematics as a model of nature. This paper proposes that it is the attempt to preserve continuum mathematics (especially calculus), which drives much of the mystery and confusion behind all attempts at understanding quantum mechanics. The introduction of discrete mathematics is proposed to help analyze the discrete interactions between the quintessential quantum objects: the electrons and their novel properties. A related paper demonstrates that it is possible to create a point-particle theory of electrons that explains all their peculiar (and ‘paradoxical’) behavior using only physical hypotheses and discrete mathematics without introducing the continuum mathematical ideas of fields or waves. Another (related) paper proves that all the known results for the hydrogen atom can also be exactly calculated from this new perspective with the discrete mathematics. * Surrey, B.C. Canada (604) 542-2299 spsi99@telus.net Version 2.015 08-05-2017 Begun 23-06-2008 {pp. 82, 70.2 Kw; 800 KB}
Introduction Chapter 1 dealt with one of the deepest mysteries in modern science: how to explain consciousness. This Part deals with another mystery: how to make sense of quantum mechanics. Both involve a problem of reconciliation with the classical worldview, which is one hint that the two mysteries might be related. A second is that, unlike classical physics, which makes no reference to or allowance for consciousness, quantum theory raises the issue of consciousness and its relationship to the physical world in a very direct way. These hints do not necessarily mean there is a connection between the two mysteries, but by the end of this Part I hope to have shown why it would be natural to look for one. My more immediate aim here is to give the social scientific reader an introductory understanding of the experimental findings of quantum theory, its key concepts, and the debates about its interpretation. The discussion assumes no prior knowledge of quantum physics and makes no use of mathematics. Quantum theory without equations might seem like an oxymoron, and certainly reading this Part will not enable anyone to use quantum theory. But to a perhaps surprising degree it is possible to understand quantum theory without being able to use it. Its findings can be communicated in ordinary language, and the same goes for its main concepts and interpretive debates. One consequence of this has been the emergence of a virtual cottage industry of books on quantum theory for a lay audience. Most are written by physicists, and many are quite good. However, it is not just popular treatments that do without equations: much of the professional philosophical literature does as well. (I draw on both kinds of literature below.) Philosophers of physics are trained to understand the math, of course, which is necessary for a full appreciation of the issues.
This chapter first takes up the claims the quantum mechanics make about themselves. It is devoted to some of the more popular aspects of quantum mechanics. The chapter looks at what quantum mechanics has to say about matter and energy and some of its major philosophical and scientific perplexities. There is sometimes confusion between the terms quantum mechanics and quantum mechanics. Before quantum mechanics, the discoveries of Sir Isaac Newton permeated every aspect of western thought for over 200 years—not just in science, but arts, literature, philosophy, and religion. Abandoning logic and scientific methodology, scientists began to concoct and follow new and mysterious theories that no one could understand, were unproveable, and yet were somehow intriguing enough to stick one’s attention. The early 1920s witnessed fundamental difficulties in quantum physics. Many physicists are unaware that the interpretation of modern quantum mechanics implies that energy and matter do not exist independently of the observer.
The odd concepts of quantum physics are nearly a century old. They may seem difficult and forbidding at first sight, but the barrier to understanding is not their difficulty but their differentness . Unlike classical models, quantum theory does not attempt to simulate Nature. It gives us information about observations of Nature. But it does contain a “theoretical entity” that claims to contain all information, observation notwithstanding, namely the quantum state vector in Hilbert space. Scientists routinely use the language of Hilbert space, and nonscientists do not use it at all, which is understandable but unfortunate. A sort of baby-talk has become the lingua franca for much of the popular journalism of quantum physics, an awkward patois that combines some of the early groping language of Bohr, de Broglie, Schrödinger, and Heisenberg with more modern words about symmetries and states. Earnest amateurs still ask me about the mystery of Bohr orbits. There is no mystery because there are no orbits, except as historical curiosities. Same for “wave–particle duality.” Same for “quantum jumps.” A friend once asked me to address a philosophy seminar about the “paradoxes of quantum mechanics.” He said he had approached C. N. Yang first, who replied “What paradoxes?” There are some mathematical and logical rough spots in our current best theory of matter, and perhaps some of them can be framed as paradoxes. But the theory is actually rather straightforward, and it has a perfectly clear interpretation linked to experiments that, in their simplest form, anyone can perform (and students do routinely in college laboratories). No empirical observations are known that are inconsistent with the quantum framework.