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fluids_ch1

# fluids_ch1 - Chapter 1 Pressure Potentials And The Gradient...

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Chapter 1 Pressure, Potentials, And The Gradient 1.1 Field Theories in Physics You are already familiar with the physics of forces, and you understand that an object can only be accelerated if a force acts on it. We have however avoided the fundamental questions of exactly how one object places a force upon an other object. You may respond, "How silly, a force is placed upon an object when another object pushes or pulls it." But there are forces for which the bodies do not need to be in contact, for example, gravity where it is possible for one planet to attract another even though the two are separated by a very large distance. This "action at a distance" has stymied many of the great minds, and the full understanding of this problem has come only within the last forty years. Unlike other theories, it is not the work of an isolated genius, but is the culmination of centuries of work by many people. The question we will answer is how can one object place a force upon another without any apparent contact between the two whatsoever? Something must go between the two objects to carry the force, and we'll call it the field. We will direct our attention from the forces to the fields themselves. Note that this raises the level of abstraction considerably, but you should not forget that the reason for obtaining the field is to find the force. Always ask your self, "Now that I have found this field, what force would this field place upon my system." This course is the study of classical field theories. What properties must the fields have, and how do we describe these field? It turns out, as you will see, that classical field theories do not fundamentally answer the question posed because one cannot touch or feel a classical electric field. More importantly, the electromagnetic fields are not conserved at all! They can be created and destroyed. Well, if they cannot be seen or felt and they are not conserved, do they exist? Might they be nothing more than a mathematical trick? There is no way yet devised to tell whether the classical electromagnetic fields in fact do exist, but in any case, the question is not relevant because a modern theory with the unwieldy name of Quantum Electrodynamics (referred to as QED) has combined field theory, relativity, and quantum mechanics into a powerful theory that agrees with experiment to 14 decimal places! In QED the electric and magnetic field are combined to form discreet packets or quanta called photons. These photons sometimes behave as particles and they can be seen and counted by machines. In fact under special circumstances, it is possible for the human eye to "see" one photon. In relativity mass and energy are equivalent, and it is possible, therefore, to create mass from photons, and conversely, to annihilate matter and antimatter to produce photons. This is done Classical Fluids, Chapter 1 -1- quite easily in modern particle accelerators. Relativity gives us a general conservation law called

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fluids_ch1 - Chapter 1 Pressure Potentials And The Gradient...

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