Chapter 3 Acceleration and free fall - Light and Matter

150 Chapter 4 Force and motion
could accelerate an object continuously until it was moving faster
than the speed of light (relative to us). But this can’t be so, because
we’ve seen in section 2.6 that relativity forbids objects from moving
relative to one another at speeds faster than the speed of light. We
will see in section 14.7 that an object’s inertia F/a is larger for an
object moving closer to the speed of light (relative to the observer
who measures F and a). It is not equal to a constant m as claimed
by the second law. These variations in inertia have been measured
experimentally, and they can be huge — as much as a factor of
3 × 10 11 for a cosmic ray detected in the sky over Utah in 1994. 4
The second law is nevertheless highly accurate within its domain of
validity, i.e., small relative speeds.
The second law also fails at the microscopic level because particles
are not just particles, they’re also waves. One consequence of
their wavelike nature is that they do not have exactly well defined
positions, so that the acceleration a appearing in a = F/m is not
even well defined.
4 Bird et al., http://arxiv.org/abs/astro-ph/9410067v1