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From the constructions of the quantum spacetime, a four dimensional quantizedspacetime can be embedded in a five dimensional continuous spacetime. Thus toobserve from the five dimensional continuous spacetime where the fourdimensional quantized spacetime is embedded, there exist the energy-momentumflows between the five dimensional continuous spacetime and the fourdimensional quantized spacetime. This makes the energy-momentum not locallyconserved generally on the four dimensional quantized spacetime. We proposethat energy-momentum tensors of noncommutative field theories constructed fromthe Noether approach are just the correct forms for the energy-momentum tensorsof noncommutative field theories. The non-vanishing of the total divergences ofthe energy-momentum tensors of noncommutative field theories just reflect thatenergy-momentum are not locally conserved on noncommutative spacetime. At thesame time, from the constructions of the quantum spacetime, we propose that thetotal spacetime dimension of the quantum spacetime is infinite.

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