Time Reversal in Classical Mechanics: A Paradox

Macomber, Hilliard K.

doi:10.1119/1.1986829

Cited by 1 publication

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“…The only exception is Ref. [7], where this problem is raised, but its solution is left to the reader. 2 ) If the integral in (3) diverges, then the question of the subsequent evolution of this particle does not arise because the ascent takes infinite time.…”

Section: At the Top Of A Hillmentioning

confidence: 97%

“…7 Our main concern here is with the classical path integral for indeterministic systems. As the simplest example we refer to a non-relativistic particle that moves to the top of the hill U(q) = −κ 2 |q| having the total energy E = 0, equilibrates at q = 0 for a period T , and then descends down the hill:…”

Section: Refinement Of the Path-integral Concept In Classical Mechanicsmentioning

confidence: 99%

“…Let a particle be capable of spontaneous decaying into two interacting particles, with the total energy of this system being equal to zero. Then one extends analytically this history back in time according to (7). Of course, this trick only helps in rendering the "real" history of forming the aggregate of two particles a virtual history (which is to drop out of sight).…”

Section: At the Top Of A Hillmentioning

confidence: 99%

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Is Classical Reality Completely Deterministic?

Kosyakov¹

2007

Found Phys

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We interpret the concept of determinism for a classical system as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally believed to hold for all autonomous classical systems. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension provides counterexamples of this belief. Given the initial conditions of a particular type, the Cauchy problem may have an infinite set of solutions. Therefore, random behavior of closed classical systems is indeed possible. With this finding, we give a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems.

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Section: At the Top Of A Hillmentioning

confidence: 97%

Section: Refinement Of the Path-integral Concept In Classical Mechanicsmentioning

confidence: 99%

Section: At the Top Of A Hillmentioning

confidence: 99%

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