ABSTRACT
The nonlocal exchange of the conserved, gauge invariant quantity e (i/variant Planck's) (p(k)-(e/cA(k))L(k)), L(k)=const, k=1,2 between the charged particle and the magnetic flux line (in the k=3 direction) is responsible for the Aharonov-Bohm effect. This exchange occurs at a definite time, before the wave packets are brought together to interfere, and can be verified experimentally.
ABSTRACT
A gedanken experiment is proposed for "weighing" the total mass of a closed system from within the system. We prove that for an internal observer the time tau, required to measure the total energy with accuracy DeltaE, is bounded according to tauDeltaE>Planck's over 2pi. This time-energy uncertainty principle for a closed system follows from the measurement backreaction on the system. We generally examine what other conserved observables are in principle measurable within a closed system and what are the corresponding uncertainty relations.
ABSTRACT
In certain topological effects the accumulation of a quantum phase shift is accompanied by a local observable effect. We show that such effects manifest a complementarity between nonlocal and local attributes of the topology, which is reminiscent but different from the usual wave-particle complementarity. This complementarity is not a consequence of noncommutativity, rather it is due to the noncanonical nature of the observables. We suggest that a local/nonlocal complementarity is a general feature of topological effects that are "dual" to the Aharonov-Bohm effect.
