Volume 18: Pages 565-570, 2005
On the Structure of Space-time
E. Y. Hsu
1442A Walnut Street No. 294, Berkeley, California 94709 U.S.A.
A specific model of the space‐time structure is proposed. Local time is represented by three operator‐valued coordinates that satisfy the commutation relations [T1, T2] = iτT3 and cyclic permutations, where τ is the elementary quantity of time expected to be of the order of (Ghħ/c5)1/2. Using a method in analogy with the representation of an arbitrary angular momentum in terms of an assembly of spin 1/2s, correspondence is established to classical time. The space part of a reference frame, constructed as a swarm of local clocks coordinated by electromagnetic signals, has three c‐number stochastic coordinates. The linear vector space of local time is naturally identified as the seat of the internal symmetries of the standard model.
Keywords: noncommutative coordinates, Planck time, quantum
Received: June 13, 2005; Published online: December 15, 2008