Energy-momentum non-conservation on noncommutative spacetime and the existence of infinite spacetime dimension

Abstract

From the constructions of the quantum spacetime, a four dimensional quantized spacetime can be embedded in a five dimensional continuous spacetime. Thus to observe from the five dimensional continuous spacetime where the four dimensional quantized spacetime is embedded, there exist the energy-momentum flows between the five dimensional continuous spacetime and the four dimensional quantized spacetime. This makes the energy-momentum not locally conserved generally on the four dimensional quantized spacetime. We propose that energy-momentum tensors of noncommutative field theories constructed from the Noether approach are just the correct forms for the energy-momentum tensors of noncommutative field theories. The non-vanishing of the total divergences of the energy-momentum tensors of noncommutative field theories just reflect that energy-momentum are not locally conserved on noncommutative spacetime. At the same time, from the constructions of the quantum spacetime, we propose that the total spacetime dimension of the quantum spacetime is infinite.