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The Influence of the Liénard-Wiechert Retarded Potentials on the Electromagnetic Zero Point Waves of the Quantum Vacuum

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The Influence of the Liénard-Wiechert Retarded Potentials on the Electromagnetic Zero Point Waves of the Quantum Vacuum International Journal of Modern Theoretical Physics, 2013, 2(3): 153-183 International Journal of Modern Theoretical Physics ISSN: 2169-7426 Journal homepage:www.ModernScientificPress.com/Journals/ijmtp.aspx Florida, USA Article The Influence of the Liénard-Wiechert Retarded Potentials on the Electromagnetic Zero Point Waves of the Quantum Vacuum Claus Wilhelm Turtur University of Applied Sciences, Ostfalia, Germany, 38302 Wolfenbuettel, Salzdahlumer Strasse 46 – 48 E-mail: [email protected]; Phone: (+49) 5331-939-42220 Article history: Received 10 October 2013, Accepted 1 November 2013, Published 8 November 2013. Abstract: The fundament of this article is the retarded potential according to Liénard and Wiechert, as known in Electrodynamics. One of its consequences is the fact that alterations of the electrostatic field, as well alterations of the magnetic field, follow the propagation speed of electromagnetic waves, which also consists of field alterations. This is the vacuum speed of light, in agreement with the Theory of Relativity. Therefore, every Coulomb force, as well as every Lorentz force, acting over a non-zero distance, requires a well- defined amount of time, to propagate from one partner of interaction to the other one. The present paper describes, how the finite propagation speed of the interacting fields allows modifying the force of interaction between electrostatic charges or between magnets, due to an interaction with the electromagnetic zero point waves of the quantum vacuum. For the electrostatic case, a computation example of the field flux is demonstrated, which leads to an energy circulation, that can produce a perceptible Coulomb force. An analogous example for the magnetic field flux leads to a Lorentz force, not only perceivable but strong enough to be designated, to drive a real engine. The first mentioned example is already verified in experiment, the second example up to now is only available in theory. Keywords: Retarded potentials, Liénard-Wiechert, Quantum vacuum Copyright © 2013 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2013, 2(3): 153-183 154 1. Introduction The fundamental conception of the paper can be understood as the “Finite Propagation Speed of the Interacting Fields” (FPSIF), derived from the Liénard-Wiechert retarded potentials (see for instance [1][2]), as known from Electrodynamics: electrostatic as well as magnetic fields connect the partners of interaction with a certain delay in time, resulting from the propagation speed of the particles of interaction (photons). Their propagation speed is the speed of electromagnetic waves, which is the vacuum speed of light. This speed is also confirmed by the Theory of Relativity as a principle upper limit to every speed at all. There are few entities of physics which can reach this limit. The interacting particles and fields of the electromagnetic interaction are among them, namely the electrostatic field and the magnetic field. This fundamental conception of FPSIF allows us to define an energy circulation as being described in the first chapter; and furthermore it allows, to make benefit for later practical applications, of which the theoretical basis is developed in the further chapters of the paper. 2. An Energy Circulation According to the FPSIF-conception For example, the finite propagation speed of alterations of an electrostatic field can be illustrated according to Fig.1, where a metallic box, containing an electrostatic charge, can be used to emanate an electrostatic field, during the time interval when a metallic shutter is opened. Analogous models can be imagined for a thought model of an electromagnet being switched on and off, or for a permanent magnet inside a superconducting box. Field alterations can even be produced by a rotating permanent magnet (without box). The graphic of Fig.1 consists of eight lines, of which each represents a given moment of time, following the sequential order of t1 < t2 < t3 < … < t7 < t8 . At each moment, i.e. at each line, we observe the absolute value of the electrostatic field E as a function of the position x , so that we can see, how the field propagates through space and time. It is sufficient to treat the position one- dimensional in our principle illustration. Now we perform the following thought-experiment: At the position xa , we have an electrostatic charge “Q”, being mounted inside the mentioned metallic box, which shields the electrostatic field. On the right side of the metallic box, there is a window, which can be optionally opened or closed, by the use of a metallic shutter, drawn in blue colour. During the time, when the shutter is open, electrostatic field will be emanated from the box, as indicated by a black arrow, propagating from the box into the spatial direction of the x-axis. At the very beginning (t1 and t2), there is not yet any field being emanated, but at the moment t3, when the shutter is being opened, the field begins to propagate into the x-direction. This situation is kept through t4 until to the moment Copyright © 2013 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2013, 2(3): 153-183 155 of t5 , when the shutter is being closed again. During the time-interval from t3 to t5 , the box provides field to the space, which propagates from the position of the box xa, up to the position xc, where xca x c tt53 . After t5 , we see the field-pulse running into the space, i.e. into the x-direction, independently from the question, whether there will be any field being emanated later not. The field- pulse propagates with the vacuum speed of light, as it is its nature. And this will be done, even if the metallic box and the electrostatic charge is being removed completely, as done at t8 . Fig. 1: Illustration of the propagation of an electrostatic field during space and time There is a discussion, whether only field alterations can be followed along their propagation through space and time, or whether the field itself (and with it, its alterations) can be following along its way. Actually, the latter perception is reality, i.e. the field same as field alterations can be traced during their propagation, as can be understood from the following consideration. Let us regard an electrical charge from the moment of its genesis on, the time t = 0, no matter whether this was the moment at very beginning of the universe, or whether it was the moment, when a charged particle was created by some reaction in the laboratory. At the moment now, the time tnow describes the age of the electrostatic charge, and the electrostatic field being produced by the charge, fills a sphere with the radius of rnow = c tnow . If we wait for another day, the field propagates for Copyright © 2013 by Modern Scientific Press Company, Florida, USA Int. J. Modern Theo. Physics, 2013, 2(3): 153-183 156 another day, i.e. for the time Δtday , so that after this day, the radius of the sphere being filled with field will be rnow+day = c (tnow + Δtday) . From this point of view, we come to the crucial question. 2 Q 0 Ee The energy density of the field is known as u E , with the Coulomb field of 2 r . Thus, the 2 4π0r total energy of the complete field has grown during the additional day, by the amount of rr 2π πnow day22 2π π now day QQ2 1 Eday urdV r sin drdd drdd sin 32π2rr 4 32π 2 2 00 spherical0 0 r rnow 0 0 r r now shell 2 2ππ 2 (1) Q rnow day Q 11 r1 sin dd 4π 2 2 32π rnow 32π rrnow now day 0 00 0 2 4π The fact is that this amount of energy is definitely not zero. This means, that the electrostatic charge must have produced energy or it must have got this energy from somewhere. (We will identify this “somewhere” in the further course of the article.) But how could this field’s energy come from the electrostatic charge as the field source, into the outer shell from rnow to rnow+day ? This rhetorical question has a rather obvious answer: The field flux is propagating into the space. It starts at the position of the field-source, this is the electrical charge, and it propagates with the speed of light, so that the field is running from the inner shells into the outer shells, and the field source supports the innermost shell with field and field-energy, namely the shell of which the inner diameter is the diameter directly surrounding the charge. This is only possible way of explanation, because our electrostatic charge is the only entity of physics in our thought-experiment, which can produce an electrostatic field. The law of energy conservation forces us to identify the source of energy, which supports the electrostatic charge, to enable it, to produce the mentioned electrostatic field. For our electrostatic charge is in contact only with the mere space, and there are no visible objects in contact with our electrostatic charge, the only entity of physics, where the charge can get energy from, are the invisible objects of the mere void, which is normally given the name of “dark energy of quantum vacuum”. This means in the very last consequence, that every electrostatic charge, producing electrostatic field, must be supported from the energy of the quantum vacuum. What we see is a conversion from the invisible energy of the quantum vacuum, into the energy of an electrostatic field. But the energy conversion has a second aspect, which we can understand as soon as we follow the field during its propagation into space and time.
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