Eliahu Cohen — Page 8

arXiv2013

Broadening the scope of weak quantum measurements I: A single particle accurately measured yet left superposed

Weak measurement is unique in enabling measurements of non-commuting operators as well as otherwise-undetectable peculiar phenomena predicted by the Two-State-Vector-Formalism (TSVF). This article, the first in two parts, explores novel applications of weak measurement. We first revisit the basic principles of quantum measurement with the aid of the Michelson interferometer. Weak measurement is then introduced in a simple visualized manner by a specific choice of the reflecting mirror's position and momentum uncertainties. Having introduced the method, we proceed to its refinement for a single particle. We consider a photon going back and forth inside the interferometer, oscillating between a superposed and a localized state, while subjected to alternating strong and weak measurements. This cyclic process enables directly measuring both the photon's position ("which-path") and momentum (interference), without disturbing either. An alternative explanation of this result, not invoking weak values, is thoroughly considered and shown to be at odds with the experimental data. Finally a practical application of this experiment is demonstrated, where a single photon measures the various transmission coefficients of a multiport beam-splitter yet remains superposed. This method is then generalized to measurement of the wave-function itself, performed again on a single particle.

quant-ph↗

arXiv2012

Charge Acceleration and Field-Lines Curvature: A Fundamental Symmetry and Consequent Asymmetries

When a charge accelerates, its field-lines curve in a typical pattern. This pattern resembles the curvature induced on the field-lines by a neighboring charge. Not only does the latter case involve a similar curvature, it moreover results in attraction/repulsion. This suggests a hitherto unnoticed causal symmetry: charge acceleration-field curvature. We prove quantitatively that these two phenomena are essentially one and the same. The field stores some of the charge's mass, yet it is extended in space, hence when the charge accelerates, inertia makes the field lag behind. The resulting stress in the field stores some of the charge's kinetic energy in the form of potential energy. The electrostatic interaction is the approximate mirror image of this process: The potential energy stored within the field turns into the charge's kinetic energy. This partial symmetry offers novel insights into two debated issues in electromagnetism. The question whether a charge radiates in a gravitational field receives a new twist: If all the charge's field-lines end with opposite charges that also resist gravity, no radiation is expected. Similarly for the famous absence of a physical manifestation of the Maxwell equations' advanced solution: Just as Einstein argued, the reason for this absence is probabilistic rather than reflecting some inherent time-asymmetry. Despite the apparent equivalence between the "ontological" and "instrumentalist" viewpoints concerning the physical reality of field-lines, there may be cases in which their experimental predictions differ.

physics.gen-ph↗