Is Quantum Spacetime Infinite Dimensional ?

Abstract

The Stringy Uncertainty relations, and corrections thereof, were explicitly derived recently from the New Relativity Principle that treats all dimensions and signatures on the same footing and which is based on the postulate that the Planck scale is the minimal length in Nature in the same vein that the speed of light was taken as the maximum velocity in Einstein's theory of Special Relativity. A simple numerical argument is presented which suggests that Quantum Spacetime may very well be $infinite$ dimensional. A discussion of the repercusions of this new paradigm in Physics is given. A truly remarkably simple and plausible solution of the cosmological constant problem results from the New Relativity Principle : The cosmological constant is $not$ constant, in the same vein that Energy in Einstein's Special Relativity is observer dependent. Finally, following El Naschie, we argue why the observed D=4 world might just be an $average$ dimension over the infinite possible values of the Quantum Spacetime and why the compactification mechanisms from higher to four dimensions in String theory may not be actually the right way to look at the world at Planck scales.

Revised Tex file, 8 pages. A remarkably simple resolution of the cosmological constant is proposed

References in corpus (5)

• RG-Flow, Gravity and the Cosmological Constant
• The String Uncertainty Relations follow from the New Relativity Principle
• Hints of a New Relativity Principle from $p$-brane Quantum Mechanics
• Dimensionally Democratic Calculus and Principles of Polydimensional Physics
• Lessons from Quantum Field Theory - Hopf Algebras and Spacetime Geometries

Cited by in corpus (16)

• Algebraic and Dirac-Hestenes Spinors and Spinor Fields
• Spin Gauge Theory of Gravity in Clifford Space: A Realization of Kaluza-Klein Theory in 4-Dimensional Spacetime
• The String Uncertainty Relations follow from the New Relativity Principle
• Higher Derivative Gravity and Torsion from the Geometry of C-spaces
• Kaluza-Klein Theory without Extra Dimensions: Curved Clifford Space
• Fuzzy dimensions and Planck's Uncertainty Principle for p-branes
• The status and programs of the New Relativity Theory
• Clifford Space as a Generalization of Spacetime: Prospects for QFT of Point Particles and Strings
• On the quantum potential
• On Negative Energies, Strings, Branes, and Braneworlds: A Review of Novel Approaches
• An Elementary Derivation of the Black-Hole Area-Entropy Relation in Any Dimension
• Issues and Ramifications in Quantized Fractal Space Time: An Interface with Quantum Superstrings
• Issues in Quantized Fractal Space Time
• Branes and Quantized Fields
• P-Loop Oscillator on Clifford Manifolds and Black Hole Entropy
• Extended Relativity: Beyond