Monday, December 22, 2014

Boundary Between Wave And Particle Interaction

What if,

\(h_o=2\pi a_{ \psi  }mc\)

is not a mistake.  That, this is the case of many particles of different \(a_\psi\), superimposed onto a common center.  And that a particle dropping from a higher \(a_\psi\) to a lower valued \(a_\psi\) does emitted a photon.

At this point we don't have a picture of orbiting particles.

However, from the post "Positively Charged Absurdity", we do have two particles with a common \(a_\psi\) superimposed together producing a outward positive \(F\) (Newtonian) around them.

A particle with \(a_\psi\) has a negative \(F\) between zero and \(a_\psi\), so such a particle is attracted to other particles of the same type within the circle transcribed by \(a_\psi\) but is repulsive to other particles of the same type beyond the same circle.

Two particles on each others' \(a_\psi\) circle is attracted to each other and as a pair repulse other particles of the same type.  They present themselves as a peculiar stable pair.

If particles interact at sufficiently great distances that the solutions to \(F_\rho\) and \(\psi\) for the particles involved does not change, then their interactions can be regarded as the particles with a constant force field around them. For example, a charge with a E field around it or a mass with a gravity field around it.

If however, the particles are at close proximity, then their \(F_\rho\) interacts as shown by the graph below,


Within an interaction distance of \(x=5\), the shape of the \(F_\rho\) curve and so, the \(\psi\) curve changes.  Beyond \(x=5\), individual particles' \(F_\rho\) curves add like integer.

\(\cfrac { G }{ \sqrt { 2{ mc^{ 2 } } }  }x_b=5\)

\(x_b=5\cfrac{\sqrt { 2{ mc^{ 2 } } }}{G}\)

where \(x_b\) is the boundary between wave and particle interaction.  In this context, wave interactions are defined as when such interactions result in changes to \(\psi\) around the particle(s).