Abstract
\nThis thought experiment addresses loss of volume that occurs when a three-dimensional object is
\ncontracted due to relativistic processes. Specifically we investigate the dependence of contraction
\ndue to orientation relative to direction of motion. Length contraction states that relative constant
\nvelocity will lead to a shortened distance in the direction of motion, when viewed from a
\nseparate inertial reference frame. When applied to two dimensional shapes, this results in a
\nreduced area. The problem initially focuses on a square pyramid with the height perpendicular to
\nthe direction of motion. Using geometry, it is found that the area of the base is invariant under
\nrotation. The problem is then expanded to general shapes. Any shape can be approximated by
\ninscribing circles within the perimeter, coming arbitrarily close to the shape\u2019s actual area. Since
\ncircles are fundamentally invariant under rotation, the change in area of a circle is independent of
\norientation. This argument is used to postulate that any two dimensional shape, when contracted
\nin one direction, will have a reduced area that is invariant under rotation. Therefore the
\ncontracted area and subsequent reduced volume depend only on the Lorentz factor \u03b3, and not on
\nrelative orientation of the object. A key next step is to determine if this can be extrapolated to
\nthree dimensions, using spheres instead of circles.<\/p>\n
Morgan Andrew Davis
\nHanjoon Kim
\nJohn Patrick McCulloch
\nMason Duran Waaler<\/p>\n