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...
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...
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...
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...
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...
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...
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...
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...