A relativistic Zeno effect

Johnson

2009

Found Phys

Self Cite

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 counterintuitive results, including one in which all the balls move with the same velocity after every collision has taken place.

Section: Infinite Number Of Colliding Ballssupporting

confidence: 85%

“…[10,11]. Energy-momentum is lost even when m n decreases as a negative exponential of n, in contradistinction to the nonrelativistic situation.…”

Section: Forward Zeno Processmentioning

confidence: 98%

Nonconservation of Energy and Loss of Determinism I. Infinitely Many Colliding Balls

Johnson

2009

Found Phys

Self Cite

“…It will be proved in this paper that in classical mechanics the total momentum is necessarily conserved, but energy can be lost (depending on the specific model for the masses). However, in relativistic mechanics neither momentum nor energy is conserved whenever there is an infinite number of balls with monotonically decreasing masses, the total mass of all the balls being finite (Atkinson, 2006). So the answer to (1 ) is still 'no' !…”

Section: Introductionmentioning

confidence: 99%

Losing energy in classical, relativistic and quantum mechanics

Studies in History and Philosophy of Science Part B: Studies in

2007

Self Cite

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. Relativistic mechanics, on the other hand, implies that energy and momentum conservation are always violated. Quantum mechanics, however, seems to rule out the Zeno configuration as an inconsistent system.

“…In a previous paper [3] (which we shall call I), where we built upon ideas that had been introduced by one of us [4,5], we analyzed a generalized version of Laraudogoitia's system of an actually infinite system of balls, in which however the masses of the balls were not all equal. Our conclusion was that, also for this generalized system, the laws of mechanics (whether classical or relativistic) do not in general lead to conservation of energy-momentum, nor to determinism.…”

Section: Introductionmentioning

confidence: 99%

Nonconservation of Energy and Loss of Determinism II. Colliding with an Open Set

Johnson

2009

Found Phys

Self Cite

An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite number of elements. With this restriction indeterminism, energy nonconservation and creatio ex nihilo no longer occur. A numerical analysis of finite systems of colliding balls is given, and the asymptotic behaviour that corresponds to the potentially infinite system is inferred.