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Light speed is the same for all

Space and time · level 7, lesson 1 of 6

A question to start

You throw a ball forward at 20 m/s from a train moving at 30 m/s. Someone by the track sees the ball move at 50 m/s. Now you shine a torch forward from a spaceship moving at half the speed of light. How fast does the light go for someone watching from outside?

The idea

For balls, speeds add. For light, they do not.

In the 1800s, physicists thought light was a wave in an invisible "ether" filling space. If so, Earth moving through the ether should make light seem faster in some directions than others. In 1887, Albert Michelson and Edward Morley built a very sensitive instrument to find that difference. They found none.

In 1905, Albert Einstein built a theory on two ideas:

  1. The laws of physics are the same for anyone moving at a steady speed.
  2. Light in empty space travels at the same speed, \(c\), for every such observer, however fast the light source moves.

The answer to the question is \(c\), not \(1.5c\). Everything else in this level follows from that.

ship: 0.5 clight: c for everyonenot 1.5 c

Worked examples

1. The train. For a ball, \(30 + 20 = 50\) m/s. At everyday speeds, adding works.

2. The ship. The ship moves at \(0.5c\) and shines light forward. Outside, the light moves at \(c\). Inside, the crew also measure \(c\).

3. Why it is strange. For both to measure the same speed, they must disagree about distances and times. The next lessons show how.

Try it

  1. What did Michelson and Morley look for, and what did they find?
  2. State Einstein's two starting ideas.
  3. A ship moving at \(0.9c\) shines light backwards. How fast does the light move for an outside observer?
  4. Why does adding speeds work for trains and balls?
Answers
  1. A change in light's speed from Earth moving through the ether. They found no change.
  2. Physics is the same for everyone moving steadily; light's speed is the same, \(c\), for all of them.
  3. \(c\).
  4. The speeds are tiny compared with \(c\), so the errors are far too small to notice.

Common mistake

"Light from a moving source goes faster." It does not. The speed of light does not depend on the speed of whatever sends it out.

Where it leads