Hilbert Book Model Project/Slide F6

Hilbert Book Model Project

F6

The solutions of ${\color {white}\boxdot \ \psi =(\nabla _{r}\nabla _{r}+\langle {\vec {\nabla }},{\vec {\nabla }}\rangle )\psi =0}$
offer one-dimensional shock fronts as part of its solutions

These solutions occur equidistant in strings

These strings feature a frequency, but they are NO waves

We focus on warp shock fronts of the form ${\color {white}{\vec {\psi }}=f_{r}(c\tau -{\vec {r}})\,{\vec {i}}}$

The real scalar ${\color {white}c}$ equals the speed at which the shock front travels

The vector ${\color {white}{\vec {r}}}$ is the distance from the trigger location to the shock front

Vector ${\color {white}{\vec {i}}}$ represents the amplitude of the front, which directs perpendicular to ${\color {white}{\vec {r}}}$

The function ${\color {white}f_{r}(q)}$ is a real function that describes the shape

of the front in the direction of ${\color {white}{\vec {r}}}$

In the string the direction of vector ${\color {white}{\vec {i}}}$ may rotate as a function

of the sequence number of the warp.

This gives the string a circular polarization

Circular polarization of warp string. The arrows represent the amplitudes of the warps that constitute the string. The red line is a help line. No wave is involved!