

Stitching the Measurement Space Together  I
29^{th} June 2019

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Earlier we were discussing the topological space underlying the measurement space for Aku the amoeba, a macroscopic observer. The measurement space description, is dependent upon the observer's (Aku's) measurement capability. The upper limit for the measurement capability, is defined by the fine structure constant α. What α tells us is, that if we shake an electron on average 137 times, the electron spits out one photon. In fact the value of α represents the efficiency of the manifold wrapped around the topological space. It is the efficiency of this manifold, we are trying to improve. If we could improve the efficiency even to ~1/134, it will be a huge accomplishment. The topological space itself corresponds to the relationship: δi ≡ ∞j .
And it is characterized by the timeindependent jspace constant j_{ML} defined as:
where m_{o} is the rest mass for elementary particles, and λ_{Compton }is Compton wavelength. However Aku lives in a dynamic world, dynamism which is the consequence of the entropy inherent in the nature of the discrete measurement space. Then how do we visualize the jspace and the resulting universe for Aku? What we would like to do in next few blogs, is to develop a multifaceted fabric in discrete measurement space, a fabric in which physical structures can be introduced. The physical structures here, could be elemental or cosmic. Usually the measurements are defined for a point in spacetime. When we speak of stitching together a discrete measurement space, we are discussing how the measurements corresponding to different points in spacetime, are to be combined together.
1. Resources are needed even for the Simplest measurement: The timeindependence of action is assumed only when we write waveequations in Aku's measurement space using t, for a conservative system. However any conservative system is a very small subset of information contained in a discrete measurement space. The concept of a conservative system is extremely useful for developing a mathematical structure for an observed physical phenomenon, but it also has fairly limited prediction capability.
We can not simply reverse the process described above, by lumping all the details together and then start sorting out the different types of objects from a big gigantic blob of information^{1}. We will be stuck in a quagmire of sheer madness. No decision making will be possible, which is actually all nature wants to do with minimum or no hassles, with the process inherent in nature we can call "continuation". The "continuation" is defined as the progression through successive zeroentropy measurements. Going around in circles, does not count as continuation. Nature does not repeat itself, an observer does. We will discuss "continuation" in jspace in further details later on. Notice that the direction of the tangential component t , remains the same, however the direction of the normal component n, changes across locations in the spacetime grid in jspace. The unit vectors n and t , are similar to the fundamental dyad of a metric tensor g_{μν} . We will discuss the geometrical significance of having a normal vector in jspace, and why we need tensors in jspace when we go surfing in (t, x, y, z) phasespace a little later.
Let us sum up:
To be continued..
___________________ 1. Actually we sort of can, by assuming various Symmetries and forming Groups etc. (aka matrix formulation), then describe measurements in corresponding fields by Differential Equations and Boundary Conditions (aka wave formulation). But then nobody understands what is really happening inside Melephant. Clearly in this case, the circuits can not be completed in jspace and hence the precision in the description will be missing. For example, one may end up with a wooden basket with 6.2 red colored oranges and 3.8 orange colored apples with one leg each, sitting on a wicker table with no legs. That will still be okay perhaps, if the number of dimensions turns out to be 26. 2. Imagine a phase space with a single cell at t = 0_{j}. This single cell will contain all the information about δ_{i}. And the phase space consisting of only this single cell, is called the initial state represented as <t = 0_{j}>. As the entropy of the system increases, we can think of this single phase space cell, dividing and multiplying as time t progresses, according to observer's or system's capability (v << c), while combined phase space still has the same information content, i.e. δ_{i}. The combined phase space has its own clock τ, which stays frozen for Aku's reference frame S, hence the assertion that the universe is equivalent to a single zeroentropy measurement. ***

Previous Blogs: Chiral Symmetry
Sigmaz and I Spin Matrices Rationale behind Irrational Numbers The Ubiquitous zAxis Majorana ZFC Axioms Set Theory Nutshell2014 Knots in jSpace Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions Discrete Space, bField & 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 Visual Complex Analysis The Einstein Theory of Relativity *** 

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