If the particle were to keep feeling a constant force, its acceleration
with respect to non-accelerating observers who happen to be traveling
along with the particle at the moment would be constant. However, its
acceleration with respect to an observer initially at rest with respect
to it would keep decreasing. Velocities turn out not to add up in the
way we intuitively expect them to. The resulting speed would never
reach c.
Now you might wonder, why not add some oomph to that push and make
the particle keep a constant acceleration with respect to the initial
observer. One problem with that is that it turns out that an INFINITE
amount of work would have to be done on the particle to get it to speed
c.
Mike W.
(published on 10/22/2007)
