L 1 can be referred to as
the proper length, which
is the length measured
in the frame at rest with
respect to the object. In
this case, the ship is the
object, so the proper
length is measured by a
ruler at rest with respect
to the ship. The length L 2 ,
measured in a different
inertial reference frame,
can be referred to as the
contracted length.To see how these lengths would be related, imagine the following. In my reference
frame, let me call the length of my spaceship L 1. If my velocity past you is v, then
the length that you’d measure for my ship will be
where γ is the relativistic factor. Because γ is greater than 1, the length you’d
measure would be shorter than what I’d measure. This is known as length
contraction; lengths that are parallel to the velocity v are shortened by a factor of
γ.
Questions 16-18A type of radioactive, subatomic particle, a μ lepton (also known as
a muon, for short) is created by cosmic rays from space entering the
earth’s atmosphere. Suppose that a muon is traveling downward
toward the earth at a speed of 0.99c, relative to the earth.- At rest, a muon typically lives for about 0.2 microsecond before
it decays. How long will the moving muon survive, as measured by
observers here on Earth? - How far does the muon travel, as measured by Earth observers?
- How far does the muon travel, as measured by the muon itself?