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Natural Science Forum / Physics / General Physics / July 2008Cosmic Inflation, Dark Mass and Dark Energy:
Sorry Sam, I don't mean to be so exuberant, going on about Emmy, sometimes late at night, after a few glasses of wine... Noether's theorem seems foundational for determining the validity of a system, which would include my system (diadien). Noether's theorem derives conserved quantities from symmetries, the principal of least action. I need help in showing fitness to this system (diadein) which revolves around particle/wave dualities; where previously these dualities have been considered an anomaly of experimentation, they could become central to our understanding of mater and energy dynamics. My question is, can we reverse Noether's theorem, finding the types of Lagrangians functions that conserve x because of continuous symmetries; and like summing the area under the curve is the reverse of a derivative, determine if a quantity is conserved finding the Lagrangians that describe the physical system? P.C.Stelzner > Sorry Sam, > [quoted text clipped - 15 lines] > > P.C.Stelzner I'm glad you are excited, Paul! http://www.springerlink.com/content/138732615q5t7753/ http://adsabs.harvard.edu/abs/1980JPhA...13..803R http://www.jstor.org/pss/2029651 http://www.iop.org/EJ/abstract/0305-4470/13/3/014/ Sam, I'm at a severe disadvantage with my web-tv system, I go to your links and see very little of what you would present, I must wait till I'm at my work place and can scan with a regular PC to see the whole message. Sam, I'm not complaining, I just hope for understanding and empathy, will you help me or are my ideas with-out total merit? P.C.Stelzner > Sam, > [quoted text clipped - 5 lines] > > P.C.Stelzner Paul-- You would have a lot better chance of satisfying your goals if you got some basic physics under your belt... such as 2nd or 3rd year classical mechanics course (Calculus and differential equations are a must). -Sam > Sorry Sam, > [quoted text clipped - 15 lines] > > P.C.Stelzner All symmetries are associated 1:1 with conserved observables. All conserved observables are 1:1 associated with symmetries - both through Noether's theorems. However, the symmetry must be continuous or approximated by a Taylor series (convergent limit of summed infinitesimals). Noether's theorem depends upon smooth Lie groups. The Lagrangian or the action is invariant under continuous transformation. Parity, for instance, is not a Noetherian symmetry. A symmetry can be broken explicitly - a term in the action or equations of motion may not be invariant. A symmetry can be broken anomalously - not all classical theory symmetries exist in the corresponding quantum theory. Quantum field theory anomaly spoils renormalizability. Anomaly absence in the Standard Model is crucial. A symmetry can be broken spontaneously if it is an exact symmetry of the equations of motion but not of a particular solution therein. Noether's theorem holds if the symmetry is not broken explicitly. Conservations can be relaxed in subsystems displaying reduced symmetry (Born scattering approximation, Fermi's golden rule, Snell's law). A classical field theory conserved quantity does not demand a quantum field theory conserved quantity in kind.  SignatureUncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/lajos.htm#a2 > Sorry Sam, > [quoted text clipped - 15 lines] > > P.C.Stelzner Dark matter had a comon origin with normal matter at the Big Bang. To this day they are completely comingled. The Earth Sun and stars are made primarily of Dark Matter. > Sorry Sam, > [quoted text clipped - 15 lines] > > P.C.Stelzner Generally speaking, if a Lagrangian is a function of only the generalized velocity of a coordinate, there is a symmetry and thus conserved quantity associated with that coordinate. That severely constrains the form of the Lagrangian. Additional symmetries introduce additional constraints, though I can't give a generalization of form regarding those. Does that help? |
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