Nib asked
Why is the speed of light constant for all observers?
The constancy is not a quirk of light. Maxwell's equations contain one speed with no reference frame, experiments confirm it, and the only way for every observer to measure the same c is for time and length to bend, as the light clock…
5 steps, drawn by Nib. Read it here, or watch him draw it. Updated .
1the puzzle
Everyday speeds add. A ball thrown forward at 30 metres per second from a train moving at 20 is going 50 relative to the ground. Light breaks this. A beam from a moving train is measured at exactly c, about 299,792,458 metres per second, by the passenger and by someone on the platform, no matter how fast the train goes.
Light's measured speed does not add to the speed of its source or of the observer.
A train moves at half of c and shines a headlight forward. How fast does a platform observer measure the light?
Show the answer
Exactly c, not one and a half times c.
2the evidence
Maxwell's equations predict electromagnetic waves travelling at a speed fixed by two constants of nature, the vacuum permittivity and permeability, with no mention of a medium or an observer's motion. If light needed an ether, the Earth's motion through it should have shown up. The Michelson-Morley experiment of 1887 looked for that and found nothing. Einstein, in 1905, took the constant speed as a principle and asked what must follow.
The equations contain one speed with no reference frame, and the ether search found none.
a common mix-upThe constant speed is not a mysterious property that only light has. It follows from the laws being the same for everyone.
3a light clock
A light clock bounces a pulse between two mirrors a distance L apart. One tick is the round trip, which takes 2L divided by c. For L equal to one metre that is about 6.7 nanoseconds. Someone riding with the clock sees the light go straight up and down.
A light clock ticks once per round trip, 2L over c.
4seen moving
For an observer watching the clock fly by, the pulse travels diagonally, so it covers more distance between ticks. If c is the same for this observer too, each tick must take longer. At 0.6 c the stretch factor is one over the square root of one minus 0.36, which is 1.25. Moving clocks run slow, and that is time dilation. Lengths along the motion contract and distant clocks disagree about simultaneity, so that everyone still measures c.
Same c over a longer path means a longer tick: moving clocks run slow, by 1.25 at 0.6 c.
At 0.6 c, how much slower does a moving clock tick?
Show the answer
By a factor of 1.25, since one over the square root of one minus 0.36 is 1.25.
5the whole idea
Put the pieces together. The laws of physics, Maxwell's equations included, are the same for every observer in uniform motion. They contain one speed, so every observer must measure that speed. Distance divided by time can only stay fixed for everyone if time and length bend, which the light clock shows. That speed is the cap on how fast any cause can reach any effect, and light, being massless, travels at it.
Everyone measures the same c because time and length bend to make it so.
Why is the speed of light the same for all observers?
Show the answer
The laws are the same for everyone and contain one speed, so time and length adjust until every observer measures that same value.
Light's speed does not bend to us; instead our clocks and rulers bend, so that everyone measures the same c.