|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 metric has to follow 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 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:
In the sections describing the formation of knots, we will describe the formation of Trefoil knot in j-space. Later we will add sections on Figure-8 knot and Unknot. We will also discuss the formation of composite knots because of the measurements made by a macroscopic observer and how they lead to higher order polynomials.
String Theory vs. Knot theory? It is reasonable to expect that the laws of nature will be metric independent, therefore may be we should sort out things in topological space first.
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Cauchy and Gaussian Distributions
Discrete Space, b-field and lower mass bound
The cat in box
The initial state and symmetries
Discrete measurement space
The frog in well