On the Complementarity of Spectral and the Renormalization Dimension of Quantum Spacetime

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Research areas:
Year:
2020
Type of Publication:
Article
Keywords:
Spectral Dimension, Dimensional Regularization, E-Infinity Theory, Hardys Quantum Entanglement, Cantorian Spacetime
Authors:
Mohamed S. El Naschie
Journal:
IJAIM
Volume:
9
Number:
3
Pages:
64-66
Month:
November
ISSN:
2320-5121
Abstract:
The paper takes a deep look at the relevance and connections between R. Loll et al spectral dimension of spacetime, namely converging to and ‘tHooft-Weltman-Wilson renormalization fractal dimension of the same spacetime where and is Hardy’s quantum probability of entanglement of two quantum particles and is the golden mean. Proceeding in this way we see that in the limit of we have and consequently one finds that . That means the result is exactly equal to 21 and not any non-integer value one may have wrongly expected. In other words we have a ratio equal where is remarkably the approximate value of the exact one, namely and is also the approximate value to the exact one namely . It is now time to recall the two critical dimensions of open and closed strings namely and . Consequently we have and . The limiting value gives us the well known E-infinity exact value of the dark energy density of the cosmos in agreement with the exact measurements and observations of COBE and WMAP, namely that . This proves that D(spectral) and D(renormalisation) are indeed complementarity.
Full text: IJAIM_630_FINAL.pdf

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