2,133 research outputs found
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
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