**Problem : **
Someone on a moving train on the earth measures the speed of a meteor in
space to be 5×10^{6} m/s. Someone in outer space measures the
speed to be 4×10^{6} m/s. Who is right?

The first postulate says that neither observer is 'right' and that they
are both right. Motion is relative, so any measurement made from an
inertial reference frame is as good (or bad) as any other; both views
have validity from their own points of view. Of course this assumes that
one is considering the earth to be an inertial frame; this is roughly true
but technically the rotation of the earth and the motion around the sun
means than the earth is not an inertial frame (it is accelerating).

**Problem : **
Two spaceships are hurtling towards one another at a constant speed of
0.8*c*. When they are still 10 000 kilometers apart, one spaceship radios
the other to warn them of the impending collision. How much time does it
take for the radio wave to reach the other ship, as observed by someone on
the receiving ship (assume that the spaceships move little in the time
taken for the signal to travel between them)?

Despite the relative speed of the spaceship light still travels between
them at speed

*c*, according to our second postulate. Thus the time taken
is just

*t* = *d* /*v* = 10000/3×10^{8} = 3.33×10^{-5} m/s.

**Problem : **
Consider the situation described in Section 1. If the flashes
from the sources are observed to occur simultaneously by an observer
standing on the ground (at rest relative to the sources), what is the time
difference between the events according to an observer on a train speeding
past at 0.15*c*, if that observer measures the distance between the
sources to be 1 kilometer?

The distance between the sources is 1000 meters so here we have

*l* = 500m. Then

*t*_{r} = = = 1.96×10^{-6} seconds, and

*t*_{l} = = = 1.45×10^{-6} seconds. Thus the time difference is

*t*_{r} - *t*_{l} = 5.12×10^{-7} seconds. Even at the immense speed of 45000 kilometers
per second, the time difference is hardly noticeable.

**Problem : **
What if the scenario described in Section 1 is performed with
baseballs (which travel at a constant speed *b* < *c*) instead of light
pulses. Will the observers still disagree?

*O*_{A} would still see the baseballs arrive simultaneously and conclude
that they were thrown simultaneously.

*O*_{B} sees the baseball on the
source on the right thrown with speed

*b* - *v* and the baseball from the
source on the left thrown with speed

*b* + *v*.

*O*_{B} then calculates the
speeds relative to the throwers as

(*b* - *v*) + *v* = *v* on the left and

(*b* + *v*) - *v* = *v* on the right. Thus

*O*_{B} too concludes that the baseballs arrive
simultaneously. There is no disagreement; this comes about as a
consequence of the weird properties of

*c*.

**Problem : **
Consider again the scenario described in Section 1. Now
consider changing the setup by placing only a single emitter at the center
position (where *O*_{A} was), and having two receivers placed where the
sources formerly were. The source emits two signals, one in each
direction (that is, one towards each receiver). An observer at rest with
respect to the source and receivers concludes that the source emitted its
two signals simultaneously. What does an observer traveling to the right
at velocity *v* observe?

This situation is exactly analogous to the one described in

Section
1. The only difference is that the light on the left of the
center point is now traveling to the left, and the light to the right of
the center point is moving to the right. Thus the moving observer
concludes that the left- moving light takes a time

*t*_{l} =
to reach the left receiver, and the right-moving light takes a time

*t*_{r} = to reach the right receiver. Thus the 'left' and 'right'
times are swapped.