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    On Alexandrov's theorem

    I came across Alexandrov's theorem which says that if X is a Polish space then so is any Gδ subset of X. The set of irrationals appears to be a ground for suspicion : irrationals form a G-delta set of the reals & yet are not a complete metric space ( all under the usual metric). There...
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    Mach's Principle in Particle Physics

    Is there a version of Mach's Principle in Particle Physics? If yes, does it hold true? A version could possibly look as follows: certain properties of a particle can be attributed entirely to the existence of other particles ( for instance, can the charge of a particle be attributed to...
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    Chaotic Orbits

    Consider a dynamic system with a periodic trajectory. Given an arbitrary duration T of time, does there exist a chaotic trajectory of a similar system which approximates the closed orbit for the duration T with a given accuracy? Chaotic orbits which I've seen so far...
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    Observer as a quantum object?

    What happens if we treat the observer as a quantum object in an experimental set-up? I don't have a specific model of an 'observer' - all suggestions are welcome. I'm curious whether the consequences are compatible with the principle of relativity (that observers shouldn't be...
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    On G.H. Hardy's Comment

    Who maintains a more objective view of reality - a mathematician or a physicist? I might have laughed this off , but I'm bewildered by G.H. Hardy's views (who was a mathematician). I'll present an excerpt from his book , 'A Mathematician's Apology' (The most relevant...
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    Heisenberg's & Schrodinger's Picture

    Is the Heisenberg's picture really equivalent to Schrodinger's ? It may seem so at a first glance & both produce the same results.But space & time are treated equally in Heisenberg's formulation : the operators are time dependent.In Schrodinger's formulation, states are...
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    Is periodicity relativistic?

    Is a phenomenon which is periodic in a frame A of reference also periodic in another frame B moving at a constant speed v with respect to A ? I think general relativity will answer this in the negative. How about special relativity? Consider a world line in A with...
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    Earnshaw's Theorem Generalised

    Consider a system of N (>1) point charges inside a box with a totally reflective inner wall.Assume that there are no interactions other than electromagnetic interactions. Earnshaw's theorem implies that the system can't stay in equilibrium. Can the system have a periodic solution for...
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