Lights in Relativity

In 1905, Einstein theory was based on 2 postulates.  First, there is no way to tell if one is moving or standing still.  Imagine two rocket moving towards each other.  If there is no background object to showed their position relatively, any observer on one of these rockets will not be able to tell if he is moving, or the other, or both.

Second, light behaves like wave but it does not require a medium to transmit, contrary to sound wave.  Light reaching an observer from a source, moving or not, will travel at the same speed.  This is same as other wave like sound.  The Doppler effect affect the frequency and not the speed.

When an observer shine a light from one of the rocket, he would see the light leaving the rocket at the usual speed as if he is stationary.  The light reaches to the other rocket and the observer on board there will see the light travelling at the usual speed as well.  In other words, both measure the speed of light and nd it to be the same.

The only way light can travel at the same speed for all observers regardless of how fast they are moving with respect to each other is if they measure distances and times differently.

Muon are particles travelling at above 99% of light speed.  They are created by colliding cosmic ray with air molecules.  The lifetime of muon is about 2 microsecond.  Therefore, muon created at high altitude should not have made it to the surface of the Earth.  This is not as such.  Therefore, the muon's time is dilated.  Another observation is to the muon, as the speed is fixed and known and the time reaching the surface of the earth is fixed, the distance must be shortened.  This is called length contraction.

Relativity theory indicated that the closer one speed is to light speed, the larger the length contraction is.  For a distance of 100 light-years, if one travelling at 99% of light speed, he could make the journey in 14 years.  For one travelling at 99.99% of light speed, it only takes 1 year to reach.  If the ship is travelling at 99.9999999% of light speed, the journey only takes less than 2 days.  However, to an observer on Earth, you will take 100 years to reach.