User talk:Kushik Kaushal Timilsina

Is order topology the second coarsest topology on a simply connected space, next to the indiscreet topology?

Space and Time, topology and geometry
Has any research group tried to treat time as component (maximal connected subset) of space topologically, with the Path or Zeeman topology(which is not locally compact) ? Is there any treating to define a geometry from such topologies on space (or spacetime) which fields exist only on a surface of a manifold, based on a homeomorphism between finite dimensional (in the Lebesgue covering dimension sense) open space and an infinite dimensional closed space, which would then produce corresponding diffeomorphism. Is there any attempts to understand singularities in finite dimensional open systems with homomorphisms to infinite dimensional closed systems?

Kushik Kaushal Timilsina (talk) 18:16, 22 November 2019 (UTC)

Question about strings in String theory
In classical physics we view particles, say an electron as a static point-like stuff. So, if there was a single electron in the universe it would be like there was no charge in the universe because nobody else would feel it's charge and it wouldn't feel any electric field with its charge. That's like saying 1 charge = 0 charge. In Quantum Field Theory, starting from the notion of Dirac Sea one electron would not be a solution to field equations, or given energy in the universe equal electron and positron would be produced and so equal positive and negative charges would be produced. This is kind of an upgrade to the earlier scenario in classical physics; here any charged particle would have at least its oppositely charged anti particle in the whole universe so if it had charge it would interact with at least one other charge, 1 charge is not equal to 0 charges. That works with charge, flavor, and color, but we don't observe anti-mass, or two varieties. In this idea if there was a single photon in the universe, it could decay into electron - anti-electron, but to conserve momentum they would fly off in opposite directions and would never annihilate again if the universe was not closed. So to probe an idea that the universe was open in geometrical or topological perspective, one might do an upgrade. The upgrade is that the electron and positron flying away can each take a positron and an electron respectively from a non-localised photon in the universe and decay annihilate into two photons given they did it together, even if the universe were not closed. In an idea like the dirac sea, if one takes the universe in a 1 dimensional analogy, a photon decays at the origin, electron flies off to inifnity, the anti electron flies off to negative infinity. At some point outside the real line (probably at infinity, in the extended real line) another photon decays into electron and positron and annihilates the pair that initially set out, as long as either one of the resulting photons is absorbed into the field again. I am just guessing this but it might be that the farther away the initial pair goes from each other the probability of this happening increases. But this means that the original photon at origin could have shifted by itself. There are two interesting things here. 1. Even though space (or spacetime) might not be closed, fields are still closed, thereby providing that other photon from outside the real line. 2. Fields are not localised, the shifting of the original photon, and hence can interact with itself. Does 2 map to the vibration of strings giving properties in String theory? Does 1 map to closed strings or degree of freedom associated to open strings in String theory? I would guess that 2 comes in current Quantum Field Theories but 1 doesn't. Does it make any sense?

Kushik Kaushal Timilsina (talk) 18:15, 22 November 2019 (UTC)