Losing energy in classical, relativistic and quantum mechanics

A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. In relativistic mechanics, however, neither energy nor momentum are conserved unless the convergence of the mass series is extremely rapid. Finally, quantum mechanics seems to rule out the Zeno configuration on the grounds of incoherence.