English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Students encounter harmonic-oscillator models in many aspects of basicphysics, within widely-varying theoretical contexts. Here we highlight theinterconnections and varying points of view. We start with the classicalmechanics of masses coupled by springs and trace how the same essential systemsare reanalyzed in the unretarded van der Waals interactions between dipoleoscillators within classical and quantum theories. We note how classicalmechanical ideas from kinetic theory lead to energy equipartition whichdetermines the high-temperature van der Waals forces of atoms and moleculesmodeled as dipole oscillators. In this case, colliding heat-bath particles canbe regarded as providing local hidden variables for the statistical mechanicalbehavior of the oscillators. Next we note how relativistic classicalelectrodynamical ideas conflict with the assumptions of nonrelativisticclassical statistical mechanics. Classical electrodynamics which includesclassical zero-point radiation leads to van der Waals forces between dipoleoscillators, and these classical forces agree at all temperatures with theforces derived from quantum theory. However, the classical theory providingthis agreement is not a local theory, but rather a non-local hidden-variablestheory. The classical theory can be regarded as involving hidden variables inthe random phases of the plane waves spreading throughout space which providethe source-free random radiation.

Contrasting Interactions Between Dipole Oscillators in Classical and Quantum Theories: Illustrations of Unretarded van der Waals Forces