The String Uncertainty Relations Follow from the New Relativity Principle

The String Uncertainty Relations have been known for some time as the stringy corrections to the original Heisenberg's Uncertainty principle. In this letter the Stringy Uncertainty relations, and corrections thereof, are explicitly derived 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. The Regge behaviour of the string's spectrum is also a natural consequence of this New Relativity Principle. Recently we have proposed that a New Relativity principle may be operating in Nature which could reveal important clues to find the origins of M theory [1]. We were forced to introduce this new Relativity principle, where all dimensions and signatures of spacetime are on the same footing, to find a fully covariant formulation of the p-brane Quantum Mechanical Loop Wave equations. This New Relativity Principle, or the principle of Polydimensional Covariance as has been called by Pezzaglia, has also been crucial in the derivation of Papapetrou's equations of motion of a spinning particle in curved spaces that was a long standing problem which lasted almost 50 years [2]. A Clifford calculus was used where all the equations were written in terms of Clifford-valued multivector quantities; i.e one had to abandon the use of vectors and tensors and replace them by Clifford-algebra valued quantities, matrices, for example. In this letter we will explicitly derive the String Uncertainty Relations, and corrections thereof, directly from the Quantum Mechanical Wave equations on Noncommutative Clifford manifolds or C-spaces [1]. There was a one-to-one correspondence between the nested hierarchy of point, loop, 2-loop, 3-loop,......p-loop histories encoded in terms of hypermatrices and wave equations written in terms of Clifford-algebra valued multivector quantities. This permits us to recast the QM wave equations associated with the hierarchy of nested p-loop histories, embedded in a target spacetime of D dimensions , where the values of p range from : p = 3D0, 1, 2, 3......D − 1, as a single QM line functional wave equation whose lines live in a Noncommutative Clifford manifold of 2 D dimensions. p = 3DD−1 is the the maximum value of p that saturates the embedding spacetime dimension. The line functional wave equation in the Clifford manifold, C-space is : dΣ …