A relativistic Zeno effect
A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be flawed.
Nonconservation of Energy and Loss of Determinism I. Infinitely Many Colliding Balls
An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution that corresponds to the injection of an arbitrary amount of energy (classically), or energy-momentum (relativistically), into the system at the point of accumulation of the locations of the balls. Specific examples are given that illustrate these counter-intuitive results, including one in which all the balls move with the same velocity after every collision has taken place.
A new genus and species of Thyasiridae (Mollusca, Bivalvia) from deep-water, Beaufort Sea, northern Alaska
Abstract Bivalve mollusk shells were collected in 2350 m depth in the Beaufort Sea, Arctic Ocean off northern Alaska. Initial identification suggested the specimens were a member of the bivalve family Thyasiridae, but no known eastern Pacific or Arctic living or fossil thyasirid resembled these deep-water specimens. Comparisons were made with the type of the genera Maorithyas Fleming, 1950, Spinaxinus Oliver & Holmes, 2006, Axinus Sowerby, 1821, and Parathyasira Iredale, 1930. We determined the Beaufort Sea species represents a new genus, herein described as Wallerconcha. These specimens also represent a new species, herein named Wallerconcha sarae. These new taxa are compared with known modern and fossil genera and species of thyasirds.