Analysis of the laws which form, direct universe and of the interacting elements in the interactions emerging by these laws. Forming the theoretical, philosophical infrastructure of the some physical concepts and phenomena such as kinetic energy, uncertainty, length contraction, relative energy transformations, gravity, time and light speed to understand universe better manner as well as possible. Almost any physical subject takes us easily to the same point by visiting the other subjects because of the creation type of matter as there is no alternative. Every mathematical equation is a production of a thinking; so it does not have to be right always as it may has different meanings for different minds and because of wrong thinking, assembly elements even if it may has a certain information sometimes or usually. If our portion is, our portion is as we took some pickaxes and shovels, starting for science mining as the below to understand universe better manner, if it is possible especially by strong evidences by thinking first as simple as possible. Only one pencil and one paper are enough. At this situation, the biggest problem is to be one of them exists and the other does not of them.
Analysis of the laws which form, direct universe and of the interacting elements in the interactions emerging by these laws. Forming the theoretical, philosophical infrastructure of the some physical concepts and phenomena such as kinetic energy, uncertainty, length contraction, relative energy transformations, gravity, time and light speed to understand universe better manner as well as possible. Almost any physical subject takes us easily to the same point by visiting the other subjects because of the creation type of matter as there is no alternative. Every mathematical equation is a production of a thinking; so it does not have to be right always as it may has different meanings for different minds and because of wrong thinking, assembly elements even if it may has a certain information sometimes or usually. If our portion is, our portion is as we took some pickaxes and shovels, starting for science mining as the below to understand universe better manner, if it is possible especially by strong evidences by thinking first as simple as possible. Only one pencil and one paper are enough. At this situation, the biggest problem is to be one of them exists and the other does not of them.
More than a hundred years ago, a series of discoveries, especially in physics, began to subtly (or maybe not) reveal some mysterious properties of matter, properties that in some fashion or other were not acceptable to our established way of perceiving Reality. Strangely enough, these properties were not taken seriously by science because they pointed to a reality that seemed too fantastical to be true, a reality that seemed to have no substance or permanence. These so called mysterious properties matter, for lack of a better word, turn out to be fundamentally related to the following discoveries: The ambiguous wave-particle duality. As in de Broglie matter-waves and the Compton properties of particles. The ubiquitous appearance of the cycle constant (τ=2π=C⁄r) in physical mathematical relations. The general applicability of the Fourier Transform to represent/model physical motion and other natural processes. The Heisenberg Uncertainty Principle and its mysterious constraint between conjugate variables, momentum and position for example. Quantum Mechanics and its collapse of the wavefunction. The surprising mass-energy equivalence. As in Einstein’s E=mc^2. The perplexing isotropy of the speed of light. The mind boggling time dilation and length contraction of Einstein’s Special Relativity (SR). The contradictory fabric of SR/GR’s spacetime and its assignment of properties to the void. The surprisingly discrete nature of atomic properties. As in Quantum Mechanics (QM). Needless to say, no matter what science has tried in order to fit the above discoveries into our physical world, their implications continue to elude an intuitively acceptable explanation in material terms. This monograph, although not necessarily in chronological order, is a recapitulation of previous monographs written by the author in an attempt at a single-source theoretical explanation/clarification for the above mentioned list of “mysterious” properties of matter, in terms of one fundamental set of properties, the motional geometry of matter.
COGNITIVE ASPECTS OF THE HEISENBERG PRINCIPLE I T HE Heisenberg uncertainty principle, like its rival theory of relativity/ has been one of the truly crucial phases in the physics of our day~ It did not, like the discovery of a new element or the Maxwell equations, simply indent the story of classical physics for a new paragraph. It was not only a new chapter but a new book. Detected, in the words of Heisenberg himself, when physics became self-critical, the principle is a statement of what is observable-like its contemporary, the theory of relativity. It was anew advance in method, so revolutionary indeed that physics has virtually lost meaning as content and become synonymous , as logical empiricism amply indicates, with mere rules of procedure. That science is developing into a system of logic, combining the Cartesian stress on clearness with the Kantian regulative idea, actually confirms a contention of traditional philosophy. It reveals that once we deny the colors and sounds, the life, lights, and purpose in our universe-as pure scientific method actually does-we are fated to deny much more than quality. Quality is in the order of form, substance, and being. The moment quality is banished from the real world, by the same 1 That all is not as peaceful and unified in physics as the layman sometimes believes can be seen in the deep cleavage between quantum and relativity mechanics. For the first, the exact specification of space (position) and time (velocity, momentum) has no meaning, while in relativity theory such exact description is the only meaning that can be had. Despite the efforts 'of leading physicists, including Dirac, to unite the two theories, the contradiction is so profound that one of these systems must eventually be abandoned or, more probably, both of them will be superseded. The recent work .of Schroedinger and apparently also of Einstei~ himself are directed to extend the general theory of relativity, making the current theory a special case just as Newtonian physics is a special case of present relativity mechanics. 474 COGNITIVE ASPECTS OF THE HEISENBERG PRINCIPLE 475 decree being itself-because it is an immediate, non-inertial (formal) thing like quality-is driven into its only possible exile, nothingness. It is not surprising then that, after modern physics· has finished its task, the universe should not only be emptied of its lights, its fragrance, its sweetness, and its music but should also be without being and without existence. The uncertainty principle has been much debated in modern thought. Its impact has brought a sad end to the pride of 19th century science since it prevents a complete knowledge of anything at all by shading into the darkness at least one of the two major factors that specify it. Shortly after the principle was born it was hailed by various authors as a proof of free will, of the possibility of religion, and of non-mechanistic concepts in biology. In a more consistent and challenging sense, it has often been taken to refute what the physicist calls causality and what the philosopher calls the order of nature. The fact of the matter is that if the senses alone supply knowledge, truly only one thing at a time can be apprehended. If Hume was right in philosophy, so is Heisenberg. But when sensism yields to an intellectual insight into reality, it is easy to refute the scientist's claim to dethrone the doctrine of nature's order which he could never detect, even in classical physics, by pointerreadings .2 But whatever the fate of the Heisenberg principle in cosmology , it has had a most fruitful career in the field of physics. To Heisenberg himself, the principle was a point of departure for an original development of quantum mechanics based on the " uncertainty " of position and momentum,.: 3 If, for example, measurements are made, under a microscope, of the position of an electron, the photon (light-particle), which impinges on the eye and thus conveys the required knowledge to the physicist, has had to collide with the electron, thus imparting an impact known as the Compton recoil. When • For ·a discussion of the order of nature, cf. J. Marling: The...
Quantum theory To conceptualize the molecular origins of thermodynamic equilibrium, one must first understand the elemental ways by which molecules interact. How does the world really work? What are the most fundamental principles that form the basis of reality as we know it? Currently our understanding of reality rests upon two principal concepts in physics: quantum theory and relativity. Both of these have been subjected to stringent experimental tests over the past century, and their combination has in part led to a deep understanding of elementary particles. There still remain some incompatibilities between the two, namely in understanding the nature of gravity, and there have been intense efforts to find new fundamental physical explanations. However, for the purposes of our discussion, we will focus solely on quantum theory since for nearly all of the models and systems that we will discuss one can safely avoid considerations of relativistic effects. Quantum mechanics describes the complete time evolution of a system in a quantum sense, in a manner analogous to what Newtonian mechanics does for classical systems. It is most easily described in terms of a system of fundamental particles, such as electrons and protons.
This paper presents a mathematical approach, based on the spectral analysis and Fourier transformation to derive the principle of uncertainty. The approach presented in this paper is found to be different from those appeared so far in the literature. It shows that the uncertainty principle is, in fact, an aliasing phenomenon and emerges merely from the quantization effect. The concept of ‘certainty’ is also introduced and discussed. It is shown that observation rates higher than the speed of a particle are the only possible approaches to the absence of uncertainty in the measurements of the observable quantities ofthe entity. This would imply that for particles travelling at the velocity of light, data acquisition rates higher than the speed of light should be required. Therefore, the uncertainty principle is related to the theory of relativity and exists so far as the velocity of light poses as an upperlimit universal constant. Otherwise, it would render to ‘certainty’ if our observation abilities could escalade at rates above the speed of light. This is to say that the uncertainty can be an inherent intrinsic property grounded in the universal speed limitation, which also subdues our observation abilities too; else demanding challenges on Einstein’s definition of simultaneity, and hence its consequences, has to be expected.
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.
This book is written with the graduate student in mind. I had in mind to write a text that would introduce my students to the basic ideas and concepts behind many-body physics. At the same time, I felt very strongly that I would like to share my excitement about this field, for without feeling the thrill of entering uncharted territory I do not think one has the motivation to learn and to make the passage from learning to research. Traditionally, as physicists we ask “what are the microscopic laws of nature?”, often proceeding with the brash certainty that, once revealed, these laws will have such profound beauty and symmetry that the properties of the universe at large will be self-evident. This basic philosophy can be traced from the earliest atomistic philosophy of Democritus to the most modern quests to unify quantum mechanics and gravity. The dreams and aspirations of many-body physics interwine the reductionist approach with a complementary philosophy: that of emergent phenomena . In this view, fundamentally new kinds of phenomena emerge within complex assemblies of particles which cannot be anticipated from an a priori knowledge of the microscopic laws of nature. Many-body physics aspires to synthesize, from the microscopic laws, new principles that govern the macroscopic realm, asking: What emergent principles and laws develop as we make the journey from the microscopic to the macroscopic? This is a comparatively modern and far less familiar scientific philosophy. Charles Darwin was perhaps the first to seek an understanding of emergent laws of nature. Following in his footsteps, Ludwig Boltzmann and James Clerk Maxwell were among the first physicists to appreciate the need to understand how emergent principles are linked to microscopic physics. From Boltzmann's biography [1], we learn that he was strongly influenced and inspired by Charles Darwin. In more modern times, a strong advocate of this philosophy has been Philip W. Anderson, who first introduced the phrase “emergent phenomenon” into physics. In an influential article entitled “More is different,” written in 1967 [2], he captured the philosophy of emergence, writing: The behavior of large and complex aggregations of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles.[…]