In: Physics
Suppose a 2-dimensional space is spanned by the coordinates (v,
x) and that the line
element is defined by:
ds2 = -xdv2 + 2dvdx
i) Assuming that the nature and properties of the spacetime line
element still hold,
show that a particle in the negative x-axis can never venture into
the positive
x-axis. That is, show that a particle becomes trapped if it travels
into the
negative x-axis.
ii) Draw a representative light cone that illustrates how a
particle is trapped.