Home | Mass, Length, & Topology |

19^{th} May 2019 |
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"There are at present fundamental problems in theoretical physics awaiting solution, e.g., the relativistic formulation of quantum mechanics and the nature of atomic nuclei (to be followed by more difficult ones such as the problem of life), the solution of which problems will presumably require a more drastic revision of our fundamental concepts than any that have gone before."
- P.A.M. Dirac; Proc. Roy. Soc. A 133, 60 1931. " In any case, models must, of course, be constructed in accordance with acceptable physical theory since the values which distinguish the cosmological speculations of the scientist from those of the crank arise from the attempt of the former to make his work logical and coherent with the rest of physics."
- Richard Chance Tolman; Relativity, Thermodynamics, and Cosmology. "Neither space nor time has any existence outside the system of evolving relationships that comprises the universe. Physicists refer to this feature of general relativity as background independence."
- Lee Smolin; Three Roads to Quantum Gravity. "Show that the theory defined on this book is fully consistent; if it is not, correct it. Find observable and testable consequences. Using these, test theory. If the theory is confirmed, we will feel good, and feeling good is good enough..." - Carlo Rovelli and Francesca Vidotto, Exercise 13.1 in Covariant Loop Quantum Gravity: An elementary introduction to quantum gravity and spinfoam theory. |
Previously we introduced a constant j One would expect a dimensionless constant for a true topological space. However we are developing a description for the discrete measurement space or j-space, in which the topology is defined as the entropy-free space. The entropy-free space implies that time will not be a factor. Thus the constant j where m _{o} is the rest mass for elementary particles, the value of j_{ML} should come out to be the same for every elementary particle. The following table shows the calculated value of j_{ML} for some of the elementary particles^{1}:
No surprises here, as λ _{Compton}'s are calculated values to begin with. It is just a sanity check confirming that in the relativistic region, which represents the underlying topological structure for a discrete measurement space, the value of the time-independent constant j_{ML}, does not change. Here we will like to point out that, it is a standard practice in relativistic physics to assume h = 1 and c = 1. However in a discrete measurement space we place the ratio h/c equal to one, instead of h = 1 and c = 1 individually ^{2}. (h÷c = 1 leads to Mass × Length = 1 or M = Length^{-1}, the length in this case would represent λ_{Compton}.)Now the fun part! Let us consider next a relativistic structure observed at the cosmic scale, a black hole. The Schwarszchild metric in General Theory of Relativity, is given as: We move into the topological space by making the metric g R Subsequently using the criterion that the constant j
_{ML}, representing the inherent topology of a given measurement space, does not change for all structures in j-space, we can write,Substituting for λ . The estimated mass of a black-hole is of the order of solar mass, approximately 2 × 10
If we recall, R The entropy of black hole measurement is very high, due to limitations of the electron-photon interaction ( . In order to move to the topology in the exterior region-I, we can replace M _{ZE}_{ }_{ }corresponds to the condition for the space-time interval equal to zero (0_{j}). The relationship becomes,
___________________ 1. Based on the values for Compton wavelengths from National Institute of Standards and Technology (NIST). The units are in MKS. 2. The condition of h/c = 1 rather than h = 1 and c = 1 raises an interesting scenario. In the measurement space of a macroscopic observer, entropy and hence corresponding time-axis are bound to exist. However it is also plausible that values of the fundamental constants would also change. Since these constants relate to Planck space, a macroscopic observer need to perform experiments at the edge of the universe, to detect variations in their values. If such measurements were possible, the constants h and c, are likely to show similar variations, variations which are not independent of each other. 3. In discrete measurement space, we are not interested in the removal of the geometrical singularity at the origin. It is understood that a certain region smaller than the Least Energy Surface, will remain inaccessible to Aku and hence could not be measured by Aku. We note that the least energy surface provides with the definition of origin 0 |
Previous Blogs:
A Timeless Constant Space Time and Entropy Nutshell-2018 Curve of Least Disorder Möbius & Lorentz Transformation - II Möbius & Lorentz Transformation - I Knots, DNA & Enzymes Quantum Comp - III Nutshell-2017 Quantum Comp - II Quantum Comp - I Insincere Symm - II Insincere Symm - I Existence in 3-D Infinite Source Nutshell-2016 Quanta-II Quanta-I EPR Paradox-II 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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