# Relativity time dilation and length contraction

1. Nov 28, 2015

### Drizzy

1. The problem statement, all variables and given/known data

can somebody help my figure out what t0 l0 l and t is?

For instance: A girl an her dad are in an airplane, the girl starts running 20m in 8 seconds. There is also a boy standing beneath the plane (lets pretend that the airplanes floor is seethrough.

2. Relevant equations

3. The attempt at a solution
What is the thumb rule here? I thought that the boy is t0 because he is standing still. The boy is also l0 because he is not moving. The girl is l cuz she is in motion and the dad is t cuz he is taking the time and he is not moving. I got a key from my teacher and this is totally wrong... Help me sort this out?

2. Nov 28, 2015

### MarcusAgrippa

Relativity is about how space and time is measured in different inertial frames of reference. Zero subscripted quantities generally refer to the value of that quantity measured in an inertial frame in which the object is at rest. Unsubscripted quantities refer to the value measure in an inertial frame relative to which the object is in motion.

In your problem, the distance and time measurements are measurements made by a person at rest in the plane using a tape measure that is at rest in the plane and a clock that is at rest in the plane. These are $l_0$ and $t_0$. Assuming the plane moves with uniform motion in a straight line, a system of coordinates constructed inside the plane is an inertial frame.

The boy on the ground measures the distance run by the girl to be $l$, and the time she takes to run that distance he measures to be $t$. These values differ from those measured by a person at rest in the plane.

The "rule of thumb" is 1. identify the two inertial frames in which the measurements are made. 2. Convert the measurements made in one frame to those made in another frame.