

Stitching the Measurement Space Together  III
2^{nd} November 2019

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 Dirac "Until now, the only planets whose formation was compatible with disc instabilities were a handful of young, hot and very massive planets far away from their host stars. With GJ 3512b, we now have an extraordinary candidate for a planet that could have emerged from the instability of a disc around a star with very little mass. This find prompts us to review our models."  Hubert Klahr, Max Planck Institute for Astronomy. https://www.bbc.com/news/scienceenvironment49855058
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Let us consider a simple interaction, between an electron and a photon, resulting in a change in momentum of the electron due to absorption of the photon, and hence a change in the field as shown below: The picture shown above represents the "coupling" between an electron and a photon. Other possibility is the emission of a photon by an electron as its momentum is changed, as shown below: However
the actual process of an interaction is not as barebones as shown
here, where a single electron (e) and a single photon (γ), are assumed to
exist. In Quantum Electrodynamics (QED), to accurately
estimate the effect of a simplest eγ interaction, we
must include the effects of the vacuum polarization and the
electronpositron pair formation. Subsequently
there are infinite possible paths for the simplest eγ interaction. We already know that in a discrete measurement space or jspace,
a perfect point particle can not be measured. We are showing below a representative diagram based on QED concepts, with the conventional time axis along the horizontal line, for the fieldchange with respect to time, for an arbitrary point in space in the discrete measurement space. Please note that to simplify the discussion, so far we are not accounting for the change in physical location (x, y, z) as the momentum of the electron changes, due to its interaction with the photon. However the uncertainty principle requires change in position corresponding to the change in momentum of the interacting electron. Thus the picture based on the basic electronphoton interaction in jspace looks as follows: We can easily extrapolate this statement to all the jpixels possible in space and time for a given epoch, by stating that in Aku's measurement space, they are "seamlessly" connected to each other by Lorentz and Möbius transformations in time and space^{1}. Furthermore there are likely to be manybody interactions between various elementary particles, aka HartreeFock picture, which must be accounted for before we can describe field φ at a point (x, y, z) at time instants t and t+δt, as measured by AMS for Aku (Obs_{M}). Please note that the progression of an individual jpixel with respect to time is irreversible, as entropy in jspace is continuously increasing. Before proceeding further, we must mention that the discussion above, corresponds to the exterior region1 of KruskalSzekeres Coordinates. We also note that since the picture we are developing is based on measurements by AMS using electronphoton interaction, we are essentially in Fermi space. Discussion so far has been strictly limited to the structure of the measurement space based on a simple eγ interaction. We assume this jspace structure as the basic fabric of spacetime, and try to describe the various physical structures embedded into it. Again the question maybe asked that in the information space what do we mean by "various physical structures embedded into the discrete measurement space". The situation is as follows: The information structures and subsequent physical structures are represented by δfunctions, where each delta function has its own definition for zeros and infinities. In a simplified picture unified by Lorentz Invariance, we can assume zeros and infinities to be identical for various physical structures (Newtonian Mechanics). However for more complex information structures, renormalization procedure has to be used to account for the redefinition of the integration limits. The picture shown above translates into different scenarios in the physical world as follows^{2}: The advantage of the description developed in a discrete measurement space, is quite evident. The cosmic and elementary structures, both correspond to the measurements made in jspace. Therefore the physical laws developed for discrete measurement space, will be universally true, independent of the physical picture, they are applied to. This procedure is far more simpler than trying to unify the physical laws corresponding to different information spaces, i.e. Cosmic (Gravitation) and Elementary (Nuclear, Quantum etc.). The nature of force in each of these pictures, would depend upon the interaction used to make measurements in jspace. Another advantage, is the presence of the curvature in the information space due to δfunctions. The quantity "mass", is a measured quantity in space time. The nature of mass is different for each quadrant in KruskalSzekeres Coordinates. While some of the complex δfunctions are likely to have corresponding higher mass and hence the curvature in spacetime (regionI), it is also possible that more complex δfunctions, can not be measured at all due to the relativistic nature of corresponding higher order information spaces. Such structures may have very small measured mass, but they will have extraordinarily strong pull similar to gravitation. (We are moving away from the idea that the inertialmass measured in region1, alone is responsible for the curvature in spacetime. Aku's physical universe correspond to the measurements, only in region1.) Finally, we will briefly discuss how to develop the mathematical structures based on the measurements performed in jspace. We use Hamilton's principle for a given path in the measurement space as follows: The metric tensor g_{μν} contains
the information about the jspace and thus the nature of the
interaction. In jspace we refrain from assigning known
coordinate frames to dx and dy variables^{3}. The geodesic is used to rewrite Hamilton's principle, in presence of the physical structures or equivalently information space δfunctions as:
The quantity {μν, σ} is known as Christoffel threeindex symbols and it represents the effect of the information δfunctions on jspace fabric, as its curvature near information sources. In the absence of the information structures, {μν, σ} = 0 and jspace is flat. Furthermore per Obs_{c} measurements ds = 0_{j}. We can visualize the Hamilton's principle for the familiar spacetime description, as follows: We note that for light rays, ds = 0. In jspace the equivalent condition is that for Obs_{c}, ds = 0_{j}, i.e. ds is zero for ^{133}Cs, and HeNe, but per Obs_{i} criterion ds is finite^{4}. Finally we also note that multiple measurement fabrics corresponding to different interaction mechanisms within jspace, will exist as shown below: In each of these jspace fabrics, Christoffel threeindex symbols, {μν, σ}, would have different values. We will discuss the Special Theory of Relativity in the information space and its implications for the discrete measurement space or jspace next. ___________________ 1. In jspace what is seamless for Obs_{M} and Obs_{c}, is granular for Obs_{i}. 2. The jspace can not be either irrotational or sourcefree. We have discussed this aspect of the discrete measurement space before. 3.
We will discuss the requirements for the coordinate frames, based on
jspace measurements later on. The description based on
conventional coordinate systems such as spherical or cylindrical, has
limited effectiveness. 4. Obs_{i}
criterion in jspace is equivalent to Maxwell's demon in
thermodynamics. We should also think how does the entropy of the
measurements in jspace, affect the value of 0_{j}?
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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 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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