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Knots in j-space
28th November 2014 The role of topology in explaining the structure formation in the high-energy physics is becoming more and more prominent. It is required that we first establish a fundamental topological structure before developing the description in (t, x, y, z) physical space. The combination of time axis with Euclidean space to describe an event, is equivalent to developing an associated metric for the topological structure. The space-time metric has to obey the measurement-space topology and therefore if we know the topological properties, we can explain some of the most basic issues such as the definitions of continuity and connectedness. The description in terms of energy and momentum can follow afterwards. For a given structure, an observer of very high capacity, Obsc for example, will measure it as a shallow-well problem or a zero-entropy problem and hence an Unknot is formed. For the same structure and for an observer of infinitesimal capacity or ObsM, the measurement is equivalent to an infinite well or Q-box problem. As a result the entropy is very high for ObsM, and a knot is formed. Therefore the nature of the knot is independent of the nature of the event and depends upon the observer's capacity. It is equivalent to saying that the poor man's black-hole is a rich man's pothole. The basic idea is shown below: ![]() String Theory vs. Knot theory? It is reasonable to expect that the laws of nature will be metric independent, therefore perhaps we should sort out things in topological space first. ![]() ![]() Information on www.ijspace.org is licensed under a Creative Commons Attribution 4.0 International License.
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Previous Blogs: Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions Discrete Space, b-field and lower mass bound Incompleteness II The supersymmetry The cat in box The initial state and symmetries Incompleteness I Discrete measurement space The frog in well |