In a linear four-dimensional Finsler space with a Chernoff metric function, it is necessary to construct transformations that could have a physical interpretation of transitions from one timelike worldline in the form of a straight line to another similar one.
The metric of Chernoff space in an isotropic basis has the form of a symmetric polynomial in four variables of the third degree:
S³=x₁x₂x₃+x₁x₂x₄+x₁x₃x₄+x₂x₃x₄.
In a basis similar to the orthonormal one, obtained by the following linear transformation of the isotropic basis:
x₁=ct+x+y+z,     x₂=ct+x-y-z,     x₃=ct-x+y-z,     x₄=ct-x-y+z
The Chernoff space metric takes the form:
S³=4ct(c²t²-x²-y²-z²)+8xyz.

To be awarded the prize, the solution must be presented on the forum pages: http://www.scientific.ru/dforum/altern and found satisfactory by the jury, represented by V.M. Chernov.
The prize amount is 25,000 (twenty-five thousand) rubles.
The competition period is until December 31, 2008.
If desired, the author will be given the opportunity to publish the solution in the journal "Hypercomplex Numbers in Geometry and Physics."