Deformation of the Bodies by the Result of Length Contraction: A new Approach to the Lorentz Contraction

It has been more than a century since first Lorentz and later Einstein explored relativistic events and still important consequences of that remains unclear to everybody. The present study extensively focus on Lorentz (Length) contraction phenomenon and takes a different approaches to explain how the shrinking of the body appears if exists. We utilized two postulates of Special Relativity that emphasizes constancy of speed of light and same physical laws in any inertial frame. Finally, we propose Lorentz contraction exists in different form through the shape of the accelerated body. The deformation of its shape depends on the part where it is measured.Comment: 6 pages, 4 figure

The value distribution of incomplete Gauss sums

It is well known that the classical Gauss sum, normalized by the square-root number of terms, takes only finitely many values. If one restricts the range of summation to a subinterval, a much richer structure emerges. We prove a limit law for the value distribution of such incomplete Gauss sums. The limit distribution is given by the distribution of a certain family of periodic functions. Our results complement Oskolkov's pointwise bounds for incomplete Gauss sums as well as the limit theorems for quadratic Weyl sums (theta sums) due to Jurkat and van Horne and the second author