Stochastic Nature of Quanta-I |
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25^{th} September 2016 |
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"The idea of a gravitational tensor belongs to the great construction by Einstein. However its
definition as given by the Author cannot be considered final. First of all, from the mathematical standpoint, it lacks the invariant character that it should instead necessarily enjoy according to the spirit of general relativity. Even worse is the fact, perceived with keen intuition by Einstein himself, that from such a definition it follows a clearly unacceptable consequence about the gravitational waves. For this point he however finds a way out in quantum theory."..... .....“Since this fact” - these are his words - “should not happen in nature, it seems likely that quantum theory should intervene by modifying not only Maxwell’s electrodynamics, but also the new theory of gravitation”. "Actually there is no need of reaching to quanta......" -T. Levi-Civita |
Earlier
we had discussed some of the ideas behind non-locality and how they
relate to EPR-paradox. But we are yet to discuss the underlying problem
which has led to this paradox i.e. whether quantum mechanics provides a
complete description of
the physical world. We will try to define what complete description
really means in a discrete measurement space or j-space. We assume that:
- The measurements are made by an macroscopic observer Obs
_{M}in ʌ_{∞}-plane,
- The VT-symmetry exists, and
- The Locality condition (v/c << 1) applies
to the observer Obs
_{M}.
_{M} is situated in Λ_{∞}-plane. If the capacity of the observer Obs_{M} was increased to v/c =1 then observer will be able to measure all the information represented by the Unit-point Sphere S_{U}. For the capacity v/c<<1, the information represented by the measurements of Obs _{M} is an infinitesimal fraction of the information represented by S_{U}. The situation is shown in the following diagram:And if we really think about it, this how it actually is: The infinite information in the measurement metric of Obs _{M}
is less than the information contained on the infinitesimal region on
the Unit-point sphere. We need to keep in mind that the following hold true
on j-space:- We
are in measurement space not in calculation space. Therefore only the
quantities which we can measure have physical significance. An example
is the equation for the Unit-point sphere l
^{2}+m^{2}+n^{2}= 0_{j}^{1}. The quantity on the right 0_{j}represents the square of radius or r^{2}. The calculated quantity √0_{j}or r, has no physical significance. At best we can consider calculated values such √0_{j}, as an approximation made by the observer in its measurement metric. The measured physical effects corresponding to relativistic limits, will be of the nature corresponding to fn(r^{2}) or e.g. surface of a sphere 4πr^{2}. Examples would be nature of charge or gravity. Since r of S_{U}, can not be measured, the quantity r×r^{2}has no physical significance^{2}.
- The position of all the normals in the measurement metric for Obs
_{M}will always align with respect to the Unit-point Sphere. What it means is that the observer Obs_{M }may think that different locations (t,x,y,z) of the measurement space have different directions for the corresponding normals. But these normals are created with respect to the Obs_{M}'s own definition of the origin using VT-symmetry. For Obs_{M}, all these normals will always be parallel to the normal defined with respect to origin defined in a higher information space. It may seem contradictory in a sense. However Obs_{M}has very limited capacity, hence it can not measure S_{U}. If it can not measure S_{U}, then it can not measure the relationship between its own defined origin and S_{U}. This difference can only be measured by Obs_{i}. - Finally
the directions of tangents, critically important for the structure
formation, are orthogonal to the normals in the measurement metric of
the macroscopic observer Obs
_{M}.
_{j}. For Obs_{M}
the sample space for the measurement of each variable itself, is
infinite. In such scenario, measurements can not be completely
accurate. Therefore the Obs_{M}
can make an estimate at best and that too for a very limited amount of
information. In that case how do we understand the correlation between
j-space and the wavefunction ψ? Also how accurate is the statement ∫ψ*ψ dX = 1, in j-space?
To be continued........... ^{}1. The Unit-point sphere S_{U}
is generated using Pauli's Spin Matrices and therefore represents the
measurements made by the observer in relativistic frame, i.e. Obs_{c}.2.. The volume, fn(r ^{3}),
related physical effects (e.g. dielectrics), correspond to lower information states. These
structures will be measured by the higher capacity observer Obs_{c} (v/c ~ 1) as δ-functions. (Photons would know exactly where to go.) |
Previous
Blogs:
Nutshell-2015 Chiral Symmetry Sigma-z and I Spin Matrices Rationale behind Irrational Numbers The Ubiquitous z-Axis Majorana ZFC Axioms Set Theory Nutshell-2014 Knots in j-Space Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions Discrete Space, b-Field & 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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