That quantum mechanical measurement processes are indeterministic is widely known. The time evolution governed by the differential Schrödinger equation can also be indeterministic under the extreme conditions of a quantum supertask, the quantum analogue of a classical supertask. Determinism can be restored by requiring normalizability of the supertask state vector, but it must be imposed as an additional constraint on the differential Schrödinger equation.

In two recent papers Perez Laraudogoitia has described a variety of supertasks involving elastic collisions in Newtonian systems containing a denumerably infinite set of particles. He maintains that these various supertasks give examples of systems in which energy is not conserved, particles at rest begin to move spontaneously, particles disappear from a system, and particles are created ex nihilo. An analysis of these supertasks suggests that they involve systems that do not satisfy the mathematical conditions required of Newtonian systems at (...) the time the supertask is due to be completed, or else they rely on the application of the time-reversal transformation to states which are not well-defined. Consequently, it is unjustified to conclude that the paradoxical results are arising from within the framework of Newtonian mechanics. In the last part of this article, we discuss various aspects of the physics of these supertasks. (shrink)

Abraham Pais's Subtle Is the Lord was a publishing phenomenon: a mathematically sophisticated exposition of the science and the life of Albert Einstein that reached a huge audience and won an American Book Award. Reviewers hailed the book as "a monument to sound scholarship and graceful style", "an extraordinary biography of an extraordinary man", and "a fine book". In this groundbreaking new volume, Pais undertakes a history of the physics of matter and of physical forces since the discovery of x-rays. (...) The book attempts to relate not only what has happened over the last hundred years but why it happened the way it did, what it was like for those scientists involved, and how what at the time may have seemed a series of bizarre or unrelated events, now with hindsight emerges as a logical sequence of events. Pais, a noted physicist, was personally involved in many of the developments he describes, and thus Inward Bound, like his earlier book, is filled with unique insights into the world of big and small physics. Between 1895 and 1983, the period he covers, the smallest distances explored have shrunk a hundred millionfold, Pais notes. Along this incompletely traveled "road inward," scientists have established markers that later generations will rank among the principal monuments of the twentieth century. In alternating technical and nontechnical sections, this magisterial survey richly conveys what has been discovered about the constituents of matter, the laws to which they are subject, and the forces that act on them. But the advances have certainly not come smoothly. The book shows that these have been times of progress and stagnation, of order and chaos, of clarity and confusion, of belief and incredulity, of the conventional and the bizarre; also of revolutionaries and conservatives, of science by individuals and by consortia, of little gadgets and big machines, and of modest funds and big money. About the Author: Abraham Pais is Detlev W. Bronk Professor of Physics at the Rockefeller University. The author of the prizewinning biography of Einstein now undertakes a history of modern physics. (shrink)