Mechanics, classical

Author(s):  
Mark Wilson

Understood at its most general, ‘classical mechanics’ covers the approach to physical phenomena that dominated science from roughly the time of Galileo until the early decades of the twentieth century. The approach is usually characterized by the assumption that bodies carry an inherent mass and well-defined positions and velocities. Bodies subsist within a three-dimensional absolute space and influence one another through reciprocal forces. These objects obey the three laws of motion articulated by Isaac Newton in 1686 in a deterministic manner: once a mechanical system is assembled, its future behaviour is rigidly fixed. Such ‘classical’ assumptions were eventually rejected by Einstein’s theory of relativity, where the assumption of a three-dimensional Euclidean space is abandoned, and by quantum mechanics, where determinism and well-defined positions and velocity are eschewed. Classical mechanics is frequently characterized as ‘billiard ball mechanics’ or ‘the theory of mechanism’ on the grounds that the science treats its materials in the manner of colliding particles, or clockwork. Such stereotypes should be approached with caution because the basic framework of classical mechanics has long been subject to divergent interpretations that unpack the content of Newton’s ‘three laws’ in remarkably different ways. These differing interpretations provide incompatible catalogues of the basic objects that are supposed to comprise the ‘classical world’ – are they point masses, rigid bodies or flexible substances? Or, as many writers have suggested, should mechanics not be regarded as ‘about’ the world at all, but merely as a source of useful but fictitious idealizations of reality? These foundational disagreements explain why classical mechanics has often found itself entangled in metaphysics. Much of modern philosophy of science is characterized by attitudes that were originally articulated during the nineteenth century’s attempts to clarify the grounds of classical mechanics.

It is conventional to denote the physics of the period 1700-1900, from A the Principia to the advent of the relativity and quantum theories, as ‘classical’ or ‘Newtonian’ physics. These terms are not, however, very satisfactory as historical categories. The contrast between classical and ‘modern’ physics is perceived in terms that highlight the innovatory features of physics after 1900: the abandonment of the concepts of absolute space and time in Einstein’s theory of relativity, and of causality and determinism in quantum mechanics. ‘ Classical ’ physics is thus defined by ‘non-classical’ physics. The definitions and axioms of Principia , Newton’s exposition of the concepts of absolute space and time, and his statement of the Newtonian laws of motion, are rightly seen as fundamental to the 17th-century mechanization of the world picture.


Author(s):  
Yulia B. Melikh ◽  

The article examines the worldview of the 18th–19th centuries developed by three contemporaries. The philosophy of Immanuel Kant is placed at the center of the worldview, in relation to which the views of Alexander von Humboldt represent a return to Cartesianism, and the views of Carl Friedrich Gauss – an appeal to the future, to the theory of relativity of space and time. I. Kant taught that Euclidean space is, as the critique of pure reason asserts, the form of our contemplation, prescribed to every possible experience. For Humboldt, the world is fully measurable within three-dimensional Euclidean space. Gauss, on the other hand, thinks of Kant further, theoretically admitting and mathematically calculating the various possibilities of conceivability of space, thus the world for him is more relative, fiction, or a beautiful dream. Space is folded, curved and very strange. Cartesianism and the relativism of both scientists also extend to their ethical concepts: for Humboldt, man is a machine of “highest skill” designed to serve humanistic goals; for Gauss, human behavior admits of accidents and exceptions, although it did not reach the proper rationality and does not deserve attention, but yet, genius is possible. The personal characteristics of both scientists, as well as the connection with their epoch are revealed. Humboldt appears as a humanist, and Gauss as a misanthrope. It is concluded that the worldview is not one-dimensional, but includes the past, present, future of science, and also allows for mystery, chance, mystical elements present in culture.


Author(s):  
Leemon B. McHenry

What kinds of things are events? Battles, explosions, accidents, crashes, rock concerts would be typical examples of events and these would be reinforced in the way we speak about the world. Events or actions function linguistically as verbs and adverbs. Philosophers following Aristotle have claimed that events are dependent on substances such as physical objects and persons. But with the advances of modern physics, some philosophers and physicists have argued that events are the basic entities of reality and what we perceive as physical bodies are just very long events spread out in space-time. In other words, everything turns out to be events. This view, no doubt, radically revises our ordinary common sense view of reality, but as our event theorists argue common sense is out of touch with advancing science. In The Event Universe: The Revisionary Metaphysics of Alfred North Whitehead, Leemon McHenry argues that Whitehead's metaphysics provides a more adequate basis for achieving a unification of physical theory than a traditional substance metaphysics. He investigates the influence of Maxwell's electromagnetic field, Einstein's theory of relativity and quantum mechanics on the development of the ontology of events and compares Whitehead’s theory to his contemporaries, C. D. Broad and Bertrand Russell, as well as another key proponent of this theory, W. V. Quine. In this manner, McHenry defends the naturalized and speculative approach to metaphysics as opposed to analytical and linguistic methods that arose in the 20th century.


Author(s):  
M. Suhail Zubairy

In this chapter, the Schrödinger equation is “derived” for particles that can be described by de Broglie waves. The Schrödinger equation is very different from the corresponding equation of motion in classical mechanics. In order to illustrate the fundamental differences between the two theories, one of the simplest problems of particle dynamics is solved in both Newtonian and quantum mechanics. This simple example also helps to show that quantum mechanics is the fundamental theory and classical mechanics is an approximation, a remarkably good approximation, when considering macroscopic objects. The solution of the Schrödinger equation is presented for a particle inside a box and the quantization condition is derived. The amazing possibility of quantum tunneling when a particle is incident on a barrier of height larger than the energy of the incident particle is also discussed. Finally the three-dimensional Schrödinger equation is solved for the hydrogen atom.


Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 659
Author(s):  
Gerrit Coddens

This paper aims at explaining that a key to understanding quantum mechanics (QM) is a perfect geometrical understanding of the spinor algebra that is used in its formulation. Spinors occur naturally in the representation theory of certain symmetry groups. The spinors that are relevant for QM are those of the homogeneous Lorentz group SO(3,1) in Minkowski space-time R4 and its subgroup SO(3) of the rotations of three-dimensional Euclidean space R3. In the three-dimensional rotation group, the spinors occur within its representation SU(2). We will provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra. We will then use the understanding that is acquired to derive the free-space Dirac equation from scratch, proving that it is a description of a statistical ensemble of spinning electrons in uniform motion, completely in the spirit of Ballentine’s statistical interpretation of QM. This is a mathematically rigorous proof. Developing this further, we allow for the presence of an electromagnetic field. We can consider the result as a reconstruction of QM based on the geometrical understanding of the spinor algebra. By discussing a number of problems in the interpretation of the conventional approach, we illustrate how this new approach leads to a better understanding of QM.


Author(s):  
E. T. Whittaker

In the “special” or “restricted” theory of relativity, for which the line-element ds of the “world” of space-time is given by , the geodesics of the world are straight lines, and the null geodesics (i.e. the geodesics for which ds vanishes) are the tracks of rays of light. When Einstein discovered the “general“ theory of relativity, in which the effects of gravitation are taken into account, he carried over this principle by analogy, and asserted its truth for gravitational fields; it was, in fact, the basis of his famous calculation of the deviation of light at the sun. The law was, however, not proved at the time: and indeed there is the obvious difficulty in proving it, that strictly speaking there are no “rays” of light—that is, electromagnetic disturbances which are filiform, or drawn out like a thread—except in the limit when the frequency of the light is infinitely great: in all other cases, diffraction causes the “ray” to spread out over a three-dimensional region.


Author(s):  
Serghey Stoilov Gherdjikov

Does science have any limits? Scientists say no. Philosophers are divided in their response. The humanities say that science is not "humanitarian," and thus not metaphysically deep. In response, scientists and some philosophers contend that science is the best knowledge we have about the world. I argue that science is limited by its form. Science has no object that derives from the human form. Everything that is incomparable to the dimension of the human body is reducible to notions that are commensurable to that body. This phenomenologically clarifies some of the most important discoveries in contemporary science. The Special Theory of Relativity shows the dependence of space and time on the accounting system. Quantum mechanics displays the limits of observation (Heisenberg) and logical indefiniteness by compelling the creation of a macropresentation of micro-objects and gets around logic (Feyerabend) through the principle of additionality. Experimental science has come out as an artificial projection of human expansion, not as a reflection of the transcendent order of the world itself. "The life world" successfully takes the place of "the objective world" of modern rationality.


Author(s):  
O. Faroon ◽  
F. Al-Bagdadi ◽  
T. G. Snider ◽  
C. Titkemeyer

The lymphatic system is very important in the immunological activities of the body. Clinicians confirm the diagnosis of infectious diseases by palpating the involved cutaneous lymph node for changes in size, heat, and consistency. Clinical pathologists diagnose systemic diseases through biopsies of superficial lymph nodes. In many parts of the world the goat is considered as an important source of milk and meat products.The lymphatic system has been studied extensively. These studies lack precise information on the natural morphology of the lymph nodes and their vascular and cellular constituent. This is due to using improper technique for such studies. A few studies used the SEM, conducted by cutting the lymph node with a blade. The morphological data collected by this method are artificial and do not reflect the normal three dimensional surface of the examined area of the lymph node. SEM has been used to study the lymph vessels and lymph nodes of different animals. No information on the cutaneous lymph nodes of the goat has ever been collected using the scanning electron microscope.


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