|_||Astrophysical Institute Neunhof|
The three types of entropy
Under the notion entropy, which is of fundamental importance for thermodynamics and statistics, actually three concepts with significant differences are subsumed. Use of the identical name for different types of entropy resulted into appreciable confusion in the literature. In this article the basic conceptual features of the three approaches are reviewed, and their differences are pointed out. We comment on Landauer's suggestion, to unite the various types of entropy to just one "total" entropy.
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Szilard's Theorem and Landauer's Principle
Are information entropy and thermodynamic entropy correlated?
Szilard's theorem, published in 1929, and Landauer's principle, published in 1961, both postulate a relation between information and thermodynamic entropy. In this article, both theorems are described in very detail. Szilard's theorem is disproved. And Landauer's principle, though experimentally neither disproved nor confirmed, is shown to be more damaging than useful.
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Time Dilation of accelerated Clocks
The definitions of proper time and proper length in General Relativity Theory are presented. Time dilation and length contraction are explicitly computed for the example of clocks and rulers which are at rest in a rotating reference frame, and hence accelerated versus inertial reference frames. Experimental proofs of this time dilation, in particular the observation of the decay rates of accelerated muons, are discussed. As an illustration of the equivalence principle, we show that the general relativistic equation of motion of objects, which are at rest in a rotating reference frame, reduces to Newtons equation of motion of the same objects at rest in an inertial reference system and subject to a gravitational field. We close with some remarks on real versus ideal clocks, and the “clock hypothesis”.
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Electrical charges in gravitational fields, and Einstein's equivalence principle
According to Larmor's formula, accelerated electric charges radiate electromagnetic waves. Hence charges should radiate, if they are in free fall in gravitational fields, and they should not radiate if they are supported at rest in gravitational fields. But according to Einstein's equivalence principle, charges in free fall should not radiate, while charges supported at rest in gravitational fields should radiate. In this article we point out indirect experimental evidence, indicating that the equivalence principle is correct, while the traditional interpretation of Larmor's formula must be amended.
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Energy and Momentum of the Metric Field
The Conservation of Energy and Momentum in General Relativity Theory
In General Relativity Theory, the gravitational potential of Newton's theory is replaced by the metric field of four-dimensional spacetime, and the gravitational force is replaced by the Christoffel symbols (which in essence are consisting of the metric field's derivatives with respect to the four spacetime coordinates). Accordingly the metric field can — like the gravitational field in Newton's theory — store energy and momentum, and exchange it with other fields. In particular, the energy-stress-matrix (which is no tensor!) of the metric field, and the “dynamic” energy-stress-tensors of the other fields, which are contained within spacetime, will be evaluated. Concluding, an alleged incompatibility between GRT and the conservation of energy and momentum is discussed.
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Radiation and Radiation-Backreaction
The electromagnetic fields of charged point-particles according to Maxwell's electrodynamics, and the radiation-backreaction according to the theory of Abraham and Lorentz
The four propagators of the classical electromagnetic field are derived. On this basis, the Lienard-Wiechert potentials are computed, and from these again the retarded and advanced fields are derived, which are radiated by point-particle charges. The properties of these fields are investigated, and Larmor's radiation law is computed. Then radiation-backreaction is considered from the point of view of energy conservation. Subsequently the same quantity is derived again, based on the classical model of an extended electron, which has been proposed by Abraham and Lorentz.
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Remarks on Wheeler-Feynman Absorber Theory
The derivation of absorber-theory is outlined in very detail. Absorber theory is based on classical action-at-a-distance electrodynamics, but it deviates from that theory at a crucial point. It is shown that (a) absorber theory cannot achieve any of it's essential results without this deviation, and that (b) this deviation restricts the application range of absorber theory to stationary radiation processes. Furthermore an error which crept into Wheeler's and Feynman's interpretation of their equation (19) is pointed out. These shortcomings can probably be eliminated by a quantum-theoretical formulation of absorber theory.
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Evanescent Electromagnetic Fields
Evanescent fields can be observed, when electromagnetic fields, impinging onto the surface of an optically thinner medium, are totally reflected into the optically thicker medium (total internal reflection). The evanescent fields are penetrating into the thinner medium with exponentially decreasing intensity. It will be demonstrated in this circular that a complete description of the evanescent fields can be achieved within the framework of Maxwell’s theory. No “new physics” are required. Furthermore Snellius' law of refraction, the Fresnel-coefficients, and the phase shifts of all fields for arbitrary under- and overcritical angles of incidence will be derived. Using the Stokes-relations, explicit formulas for the frustrated total internal reflection (FTIR) are computed.
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Some Remarks on Special Relativity Theory
The constitutive physical principles of special relativity are discussed, and the limitations of validity of this theory are described. Einsteins derivation of the Lorentz transformations from the basic physical principles is shown in great detail. Conclusions (time dilatation, length contraction, the tunnel paradox, the twin paradox) are carefully evaluated.
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Space and Vacuum
General relativity theory and quantum theory are using incompatible definitions of these basic notions of physics.
Already in Newton’s physics, there was a subtile inconsistency regarding the definitions of space and vacuum. This matter is delineated in sections 1 and 2.
In the 20. century, the shortcomings of Newton’s physics were overcome by the theory of general relativity, and by quantum theory. Each of these theories – when used for its own – describes nature with unprecedented accuracy. But GRT and QT are using incompatible definitions of space and vacuum. Sections 3 through 6 deal with the gigantic inconsistencies, which resulted from those incompatible definitions. Considering this evolution, some doubt comes up whether consistent physics is possible at all.
This article is written in german.
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Ptolemy’s World Model
With the Almagest, we have a detailed picture of antique Greek astronomy available.
At first, the antique Greek models of the sun’s and the planets’ orbits are developed in several steps. For each step, the model’s respective accuracy is assessed. First Step: Aristarch’s simple circle model, table 1 on page 22. Second step: Hipparch’s model, using circles with shifted center points, see table 2 on page 29. Third step: Ptolemy’s model with equants, table 3 on page 35.
Ptolemy’s world model is reconstructed in section 3. It is demonstrated, that it is a complete, dynamical model, not just a kinematical one. It becomes apparent, that Ptolemy – based on his notions of space and vacuum – had to shape it exactly as he did. Table 6 on page 49 describes the setup of his cosmos.
Beforehand the Almagest’s tradition is sketched in section 1.
This article is written in german.
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