Spacetime and the cosmos
1905
Special relativity
Albert Einstein
What would you see if you could ride alongside a beam of light?
Einstein took two rules seriously: physics is the same for everyone moving steadily, and everyone measures the same speed of light. The price is that moving clocks run slow and moving rulers shrink. Time and space depend on who is measuring.
First, make a guess
At 87% of light speed, the moving clock ticks…
- Time stretch γ
- 2.028
- A muon (lives 2.2 µs at rest) lives
- 4.5 µs
- At this speed, 1 year on board is
- 2.03 years for you
Each clock ticks when light bounces between two mirrors. Light moves at the same speed for everyone, so in the moving clock it has a longer, slanted path to cover, and each tick takes longer. Nothing is wrong with the moving clock: to its owner, yours is the slow one.
How they figured it out
At sixteen, Einstein imagined chasing a light beam. If he caught up, he would see a frozen wave, and Maxwell’s equations do not allow such a thing. The puzzle stayed with him for ten years.
In May 1905, working as a “technical expert, third class” at the patent office in Bern, he talked the problem through with his friend Michele Besso and suddenly saw it: two events that are simultaneous for one person need not be for another. Time itself depends on how you move. He wrote the paper in about five weeks. It has no references at all.
The equation
The faster a clock moves past you, the slower you see it tick.
See it in real life
Particles that should not reach the ground
Cosmic rays make muons about 15 km up. A muon lives about 2.2 microseconds: at nearly light speed that is only about 660 m of travel. Yet detectors at sea level catch them all the time. Moving that fast, their clocks run slow.
Where engineers use it
Particle accelerators
Designs at CERN account for particles living longer and getting heavier as they near light speed.
GPS
Satellite clocks run slow by about 7 microseconds a day from their speed alone.
Worked example: A fast muon
- At :
- Its 2.2 µs lifetime becomes about 22 µs, enough to reach the ground.
Where it came from
- Light is electromagnetism 1865
Built on
Einstein’s 1905 paper begins with Maxwell’s theory: light’s speed is the same for everyone.
- The experiment that found nothing 1887
Led to
Relativity made the missing ether drift natural. Historians still debate how much the experiment itself guided Einstein.
What it led to
- E = mc² 1905
Led to
E = mc² followed from relativity within months.
- Spacetime 1908
Led to
Minkowski recast Einstein’s theory as four-dimensional geometry.