

An Ecosystem of δPotentials  IVB Blip: Fermionic or Bosonic?
3^{rd} September 2022

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"Simply put, quantum geometry is the appropriate modification of standard classical geometry to make it suitable for describing the physics of string theory."  Brian Greene, String Theory On CalabiYau Manifolds, arXiv:hepth/9702155. "Finsler geometry is much broader than Riemannian geometry and can be treated in an elegant way. It will be the subject of the basic course on differential geometry within the next ten years in many universities."  Shiing Shen Chern, Notices of the AMS, V0l.45(7), pp. 860868, 1998. "Two unequal numbers being set out, and the less being continually subtracted in turn from the greater, if the number which is left never measures the one before it until an unit is left, the original numbers will be prime to one another." Euclid's Elements, Book Seven, Proposition 1. "The principle of gaining knowledge of the external world from the behaviour of its infinitesimal parts is the mainspring of the theory of knowledge in infinitesimal physics as in Riemann’s geometry, and, indeed, the mainspring of all the eminent work of Riemann, in particular, that dealing with the theory of complex functions."  Hermann Weyl, SpaceTimeMatter, Dover Publications, 1952. "The elevation of gauge fields to the level of the gravitational fields is a substantial achievement, but is by no means the end of the story. "  Lochlainn O'Raifeartaigh, The Dawning of Gauge Theory, Princeton Series in Physics, 1997. ***

....continuing
The idea here, is that in a qualitative description we can express our rods and clocks system, in terms of the observers' relative efficiencies rather than their relative velocities. We keep in mind that in the topological space (also the dBspace), the clock disappears. And that in dBspace (deBroglieSpace), the rods' length and mass are correlated by jML.^{1} Let us define the relative efficiency for an observer in the reference frame S', as η'. In the case of an observer with relativistic K.E., η' = v^{2}/c^{2}. The efficiency for Obs_{c} defining dBspace is, η_{c} = 1. We can rewrite the relativistic relationships for length, time, and mass as shown below: We
note that by describing these
relationships in terms of the
efficiency of the observer, we can
also account for the case with very
high structural potential
energy. Thus if an observer or a
δfunction
has a very rich information content,
which translates into an equally high
resource requirement (KE, PE, or KE +
PE both), we can express the variation
in arclength ds with respect to an
entropy dependent parameter t,
represented as dx^{4}, by the
relationships just described
above.
We do not connect the mass m in the above relationship to either inertial mass or gravitational mass unless we know for sure that the nature of δfunctions in S and S' are similar, i.e. Lorentz and Möbius invariance, are followed between S and S' frames. This is a rather important issue and we will discuss it a little later. Let us now examine the observer's efficiency η in jspace. We have to decide on a criterion based on which the accuracy of the observer's measurements can be determined. The upper limit for the Obs_{c} efficiency η_{c} in q_{3}information space, is defined as 1_{j}.
We further note
the following:
However we can also have a measurement
space in which the origin's definition is
that based on the measurements
corresponding to η_{c}.
In this case the probability of finding a
particle at the origin is finite and we
can have symmetric and antisymmetric
wavefunctions both. Hence in this
case Fermions and Bosons are both exist in
various energy states including the ground
state GS_{j}. (String Theory)
Let us wind down for now, by
summarizing our discussions so far:
Equivalently a macroscopic observer Obs_{M} measures a QuarticPotential as a QuadraticPotential due to lack of resources, as shown below.
We will be discussing
some of the following ideas in
forthcoming blogs:
So
how do we think of δpotential(s)
in the measurementsystem we are
discussing? We already know
that any
structure from a higher
information space, q = 1 or 2, will
show up as a δpotential and hence a
coherent
state in the measurements made
by Obs_{M}
in our universe, represented
by q = 3 information
state.
And, our immediate objective is to
understand the structures in the
universe as we know it. 1. The Lorentz factor $$, cancels out for the product between m and l relationships in Sframe i.e. m x l = mo x l'. 2. The origin in jspace corresponding to q = 3 can never be precisely determined, which we already know, since we do not have an observer who can measure SLC in q = 3 information space. Therefore the "Well" here, can have the dimension of the universe and it will still be a quantum problem of measurement. 3. Although we are using the analogy with an Harmonic Oscillator to simplify our arguments, the Harmonic Oscillator and Ladder Operators are not valid description tools for the curved spacetime. They are useful only in the flat spacetime. 4. We also have ZeroEntropy mass m_{ZE} in jspace. *** 
Previous Blogs: An Ecosystem of δPotentials  IVA
An Ecosystem of δPotentials  III An Ecosystem of δPotentials  II An Ecosystem of δPotentials  I Nutshell2019 Stitching the Measurement Space  III Stitching the Measurement Space  II Stitching the Measurement Space  I Mass Length & Topology 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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