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Symmetries | Kanitscheider | I 277 Symmetries/Kanitscheider: electromagnetic interaction: quantum electrodynamics, symmetry U(1), Strong Interaction: Quantum Chromodynamics, Symmetry of Color SU(3) Weak WW: Group SU(2) First unification step: Salam/Weinberg: gauge theory with the group structure SU(2)xU(1) Georgi/Glashow: (1974) 'Unification of the electroweak with the strong interaction: GUT/Great Unifying Theory: fundamental symmetry SU(5), which as a subgroup is the product of the three original forces SU(3)cxSU(2)xU(1) with included. I 276 Symmetry breaking/Kanitscheider: the spontaneous symmetry breaking occurs when the symmetric solution is unstable with a symmetric basic law. This transitions the system into an asymmetric state that obscures the original symmetry of the law. A broken symmetry is epistemically a hidden symmetry. I 279 Symmetry/Kanitscheider: a completely isotropic liquid can become anisotropic because of its crystalline character. Permanent magnets lose the common alignment of all elemental north and south poles when heated. In general, a system has higher symmetries at high temperatures than at lower ones. |
Kanitsch I B. Kanitscheider Kosmologie Stuttgart 1991 Kanitsch II B. Kanitscheider Im Innern der Natur Darmstadt 1996 |
Theories | Barrow | I 285ff Gauge Theories/Barrow: modern theories of elementary particles and their interaction. The first gauge theory was Maxwell's theory of electromagnetism. Such theories are entirely based on symmetries. - The descriptions of gravitation, electromagnetism, strong and weak nuclear force are all gauge theories. >Symmetries. The new additional symmetries are called inner symmetries. They correspond to invariants in renaming particle identity. >Invariants. For example, when the identity of all protons in the world is swapped with that of neutrons. The gauge age systematically reduced the laws of the microworld to symmetries. - We are not dependent on observation then. >Proofs, >Provability, >Observation, >Unobservables. Gauge symmetries can also be the key to generating new laws of nature. They describe what kind of particles is allowed, but not how many variants each allowed particle has. It tells us that certain quantities are proportional to others, but it does not determine the values of the proportionality factors. Therefore, gauge theories are not the ultimate descriptions of nature. >Proportions, >Objectivity, cf. >Theory of Everything. I 290 The solutions of symmetric equations do not need to have symmetry! It follows that the true symmetries are hidden, they determine the laws, not their consequences. When a calibration theory is broken in a certain way, the carrier particle necessary to mediate the local calibration invariance assumes a mass. This is probably the origin of the mass. Some calibration theories are not broken (gravitation, electrodynamics) Their carrier particles, graviton and photon, are massless. >Symmetry breaking. |
B I John D. Barrow Warum die Welt mathematisch ist Frankfurt/M. 1996 B II John D. Barrow The World Within the World, Oxford/New York 1988 German Edition: Die Natur der Natur: Wissen an den Grenzen von Raum und Zeit Heidelberg 1993 B III John D. Barrow Impossibility. The Limits of Science and the Science of Limits, Oxford/New York 1998 German Edition: Die Entdeckung des Unmöglichen. Forschung an den Grenzen des Wissens Heidelberg 2001 |
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Substantivalism | Leibniz Vs Substantivalism | Field I 39 Metaphysical Possibility/Essentialism/Modality/Leibniz/Field: the modal argument of Leibniz VsSubstantivalismus: (see above: "empty space is real", not only a logical construction): e.g. question: Does it make sense to accept the possibility of a possible world (poss.w.), which is exactly like our actual one, with the exception of its history which is shifted one mile. (LeibnizVsabsolute space: No!). Every poss.w. which is qualitatively identical with our world would simply be the actual world. LeibnizVsSubstantivalism: He must deny this: Substantivalism needs to take two of those poss.w. as truly separate. And this seems absurd. FieldVsLeibniz: That seems convincing at first glance. But (Horwich, 1978) is it not a strong argument against the existence of electrons as well? e.g. (DS) There is a poss.w. which is distinct from our actual world, but is exactly like our actual one, with the exception of its history which is shifted one mile. (DE) There is a poss.w. which is distinct from our actual world, but is exactly like our actual one. The only difference between the two is that in the poss.w. electron A and B were reversed during all its history. I 40 FieldVsLeibniz: There seems to be a difference. Hennig Genz Gedankenexperimente, Weinheim 1999 VIII 57 Symmetry/Equilibrium/Genz: a balance scale can also be stable in a slanted position! - equilibrium is indifferent ->Sombrero- Leibniz Vs: e.g. >Buridan's donkey. If there is no sufficient reason for a deviation, then there will not be one - Leibniz: there is no indifferent equilibrium > LeibnizVsSubstantivalism: there can be no independent space - because then the universe could be shifted (pointless) - today: VsLeibniz – Solution: spontaneous symmetry breaking. |
Lei II G. W. Leibniz Philosophical Texts (Oxford Philosophical Texts) Oxford 1998 Field I H. Field Realism, Mathematics and Modality Oxford New York 1989 Field II H. Field Truth and the Absence of Fact Oxford New York 2001 Field III H. Field Science without numbers Princeton New Jersey 1980 Field IV Hartry Field "Realism and Relativism", The Journal of Philosophy, 76 (1982), pp. 553-67 In Theories of Truth, Paul Horwich Aldershot 1994 |
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