Those defile the purity of mathematical and philosophical truthy who confound real quantities with their relations and sensible measures. —ISAAC NEWTON, Principia Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size ), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).
Those defile the purity of mathematical and philosophical truthy who confound real quantities with their relations and sensible measures. —ISAAC NEWTON, Principia Before we say anything about quantum mechanics, let us take a quick look at the Newtonian (or ‘classical’) view of the physical universe. According to that view, nature consists of an enormous number of particles. When Newtonian physics is combined with the theory of the electromagnetic field, it becomes convenient to think of these particles as dimensionless (even if there is a kind of conceptual strain involved in trying to think of something as having a mass but not any size ), and as possessing electrical properties – negative charge, or positive charge, or neutrality. This leads to the well-known ‘solar system’ view of the atom – with the electrons whirling around the nucleons (neutrons and protons) just as the planets whirl around the sun. Out of atoms are built molecules; out of molecules, macroscopic objects, scaling from dust motes to whole planets and stars. These latter also fall into larger groupings – solar systems and galaxies – but these larger structures differ from the ones previously mentioned in being held together exclusively by gravitational forces. At every level, however, one has trajectories (ultimately that means the possibility of continuously tracing the movements of the elementary particles) and one has causality (ultimately that means the possibility of extrapolating from the history of the universe up to a given time to its whole sequence of future states).
The difficulties of the old quantum theory were largely dispelled by the development of quantum mechanics in the 1920s. First Heisenberg (1925) developed the rather abstract matrix mechanics and soon after Schro¨dinger (1926; see also Eckart, 1926) developed the physically more appealing wave mechanics. Subsequently he showed them to be mathematically equivalent. The physicists were greatly relieved; now they had once again a mathematical formalism that enabled the results of experiments to be calculated. It was possible to move forward. It is certainly a very elegant and indeed beautiful formalism, and does enable the results of many physical measurements to be calculated with great accuracy. It is used daily by atomic and nuclear physicists; there is no other way to make calculations. From the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything it is becoming more intense over the years. As Penrose has remarked, no one understands quantum mechanics. Feynman (1967; see also Sykes, 1994) also admitted that ‘nobody understands quantum mechanics’, and Einstein once remarked: ‘I have thought a hundred times as much about the quantum problems as I have about general relativity theory’ (Pais, 1994, p. 57). It should therefore be evident that the most that can be done here is to try to show where the real difficulties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. It is useful to ask what ‘understanding quantum mechanics’ actually means. Certainly it means being able to calculate the results of many measurements. The same applies to Newton’s theory of gravitation, which we understand in the sense that we can use it as a basis of calculation, although we do not really understand the gravitational force itself. Very often, especially in modern physics, the mathematical formalism does not give us the sort of intuitive physical feeling for what is going on that we often obtain from classical mechanics. Perhaps we can never achieve more than this for quantum mechanics. In classical mechanics we can assume that a property that is measured objectively exists prior to the interaction of the measuring apparatus with the observed system. Quantum mechanics, however, ‘is incompatible with the proposition that measurement discovers some unknown but pre-existing property’ (Peres, 1997, p. 14). There is an important distinction between mysteries and absurdities. We may be forced to live with mysteries, but there is no reason why we should put up with absurdities such as the wave-particle duality, tunnelling through potential barriers, acausal events and the collapse of the wave function. These are the quantum paradoxes that will be discussed later on. They arise within the Copenhagen interpretation of quantum mechanics and are solved by other interpretations. These alternative interpretations enable us to make conjectures about what is going on, even though we cannot understand it in detail. This is acceptable and a stimulus to further research. It is certainly difficult enough to understand quantum mechanics, but there is no need to try to visualize logical absurdities in the effort to do so. Quantum mechanics is a mathematical formalism that makes it possible to calculate the results of some experiments. Anything more than this, such as questions about the interpretation of what is measured and whether it tells us what is actually going on in the system being studied, belongs to philosophy. Thus we are concerned here with what is essentially a philosophical debate; if it were just a matter of physics the debate would have been settled long ago. One of the difficulties is that it invokes the results of experiments and uses the language of quantum mechanics. Inevitably this language uses philosophical terms and then it is easy to give the impression that the philosophical propositions are in some way entailed by the physical results. These in turn can influence theological thinking. In order to be quite clear which arguments are justified and which are not, it is essential to separate the three levels of discourse: physical, philosophical and theological. Our task is to relate these together, and this immediately raises the traditional problems of the philosophy of science, including the relation of experiment to theory, and of theory to explanation. We begin by discussing experiments, distinguishing between those that are real and those that are imaginary.
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.
In classical physics there is, in accordance with common sense, an objective world ‘out there’. That world evolves in a clear and deterministic way, being governed by precisely formulated mathematical equations. This is as true for the theories of Maxwell and Einstein as it is for the original Newtonian scheme. Physical reality is taken to exist independently of ourselves; and exactly how the classical world ‘is’ is not affected by how we might choose to look at it. Moreover, our bodies and our brains are themselves to be part of that world. They, also, are viewed as evolving according to the same precise and deterministic classical equations. All our actions are to be fixed by these equations - no matter how we might feel that our conscious wills may be influencing how we behave. Such a picture appears to lie at the background of most serious 1 philosophical arguments concerned with the nature of reality, of our conscious perceptions, and of our apparent free will. Some people might have an uncomfortable feeling that there should also be a role for quantum theory - that fundamental but disturbing scheme of things which, in the first quarter of this century, arose out of observations of subtle discrepancies between the actual behaviour of the world and the descriptions of classical physics. To many, the term ‘quantum theory’ evokes merely some vague concept of an ‘uncertainty principle’, which, at the level of particles, atoms or molecules, forbids precision in our descriptions and yields merely probabilistic behaviour. Actually, quantum descriptions are very precise, as we shall see, although radically different from the familiar classical ones. Moreover, we shall find, despite a common view to the contrary, that probabilities do not arise at the minute quantum level of particles, atoms, or molecules - those evolve deterministically - but, seemingly, via some mysterious larger-scale action connected with the emergence of a classical world that we can consciously perceive. We must try to understand this, and how quantum theory forces us to change our view of physical reality.
Quantum mechanics is our most successful physical theory. It underlies our very detailed understanding of atomic physics, chemistry, and nuclear physics, and the many technologies to which physical systems in these regimes give rise. Additionally, relativistic quantum mechanics is the basis for the standard model of elementary particles, which very successfully gives a partial unification of the forces operating at the atomic, nuclear, and subnuclear levels. However, from its inception the probabilistic nature of quantum mechanics, and the fact that “quantum measurements” in the orthodox formulation appear to require the intervention of non-quantum mechanical “classical systems,” have led to speculations by many physicists, mathematicians, and philosophers of science that quantum mechanics may be incomplete. Among the Founding Fathers of quantum theory, Einstein and Schrödinger were both of the opinion that quantum mechanics is in some way unsatisfactory, and this view has been amplified in more recent profound work of John Bell, among others. In an opposing camp, many others in the physics, mathematics, and philosophy communities have attempted to provide an interpretational foundation in which quantum mechanics remains a complete and self-contained system. Among the Founding Fathers, Bohr, Born, and Heisenberg maintained that quantum mechanics is a complete system, and a number of recent proposals have been made to improve upon or to provide alternatives to their “Copenhagen Interpretation.” The debate continues, and has spawned an enormous literature.
{N,n} QM contains two major parts: the Bohr formula-based part and the Schrodinger equation-based part. 1) For the Bohr formula-based part, after combining all results from the previous SunQM series papers, a {N,n//6} QM Structure (Master) Periodic Table (with N = -23..15, n = 1..12) is established. A summarized result of the {N,n//6} QM structure has been given for each region of this (Master) Periodic Table, including the cosmic {N,n//6} QM (at N > 5), the Solar {N,n//6} QM (at N= 5..-5), the chemical bond dominated world (at N= -2..-11), the atomic and nuclear {N,n//6} QM (at N= -12..-15), and the elementary particles and sub-quark {N,n//6} QM (at N ≤ -16). The common properties (that across all regions of the Master Period Table) has been discussed. For example, by adding many short-life intermediate states (n’ = 1..6^6) in between the major quantum state n=1..5, we can transform a quantum description (with n=1..5} into a (continuous) classical physics description (with n’ = 1..6^6). 2) For the Schrodinger equation-based part, we summarized that how to use {N,n//6} QM plus non-Born probability (NBP) plus Simultaneous-Multi-Eigen-Description (SMED) to describe a planet (or an atom in this planet) that orbiting around Sun, and a photon that propagating away (or towards to) a (Bohr) atom (and it can also be used for a 180° scattering). We further discussed the possibility to extend this description for any kind of movement (elliptical/parabolic/hyperbolic orbiting, scattering, etc.), with any inclination/eccentricity/precession. We also discussed how to use Schrodinger equation/solution for the N-body movement description. We pointed out that there is a conceptual difference between the {N,n} QM and the traditional QM in describing the H-atom’s electron orbit: while the probability (i.e., the Born probability) is the foundation of the traditional QM, the single trajectory (i.e., NBP peak’s time-dependent trajectory) is the foundation of the {N,n} QM (although this single trajectory will pick one of the many possible tracks based on the probability). 3) In the cosmic {N,n//6} QM, we explored the possibility that those super large cosmic “great walls” with distances ~ 9E+9 light-years from Earth are the (~ 9E+9 years old) self-images of our own Milky Way galaxy and be viewed at different angles. If this is correct, then our universe may should be a positive curved 3D space, with the circumference of ~ 9E+9 light-years. This means, just like we are practically living in the 2D spherical space on the surface of a 3D ball something (i.e., a planet), we may practically live in the 3D spherical space on the surface of a 4D ball something. 4) We pointed out that the wave mechanics is equally powerful as that of particle mechanics in solving a QM problem, and a particle mechanics based holographic-description and SMED is waiting to be developed. 5) Because the Bohr formula rn = r1 * n^2 correlates to the (free-fall) accelerated distance formula d = (1/2) *g *t^2 and Newton formula F = m * a, we believed that Bohr formula is the Number-One important formula in physics. We believed that all these results make {N,n} QM theory becomes one of the most (roughly) completed and (roughly) self-consistent theories in physics.