Evidence for Time Dilation: Muons, Atomic Clocks and Accelerators

Can we test this?

Time dilation is a bold prediction. If it were wrong, special relativity would collapse. Physics does not accept a theory because it is clever; it accepts it because measurements agree with it. In this lesson you will look at three kinds of evidence: particles from space, atomic clocks on airplanes, and particles in accelerators. You will also analyse decay data yourself, the way an experimenter would.

Muons from the sky

When cosmic-ray protons hit the upper atmosphere (typically 10 to 15 km up), they create showers of particles. Some of these become muons. A muon at rest decays with a mean lifetime of about 2.2 µs, which means a half-life of about 1.52 µs (2.2 µs × 0.693).

Even at nearly the speed of light, a muon living 2.2 µs would travel only about 3.00 × 10⁸ m/s × 2.2 × 10⁻⁶ s ≈ 660 m. Without time dilation, almost none would survive the 10 km or more to the ground. Yet more than a hundred muons pass through every square metre at sea level every second. (Some are passing through you as you read this.)

Remember from Grade 11: in Thermal and Nuclear Energy you used half-life: after n half-lives, the fraction left is (1/2)ⁿ. We use that here.

The mountain experiment

In 1963, David Frisch and James Smith measured the number of fast muons (speeds of about 0.995c) arriving per hour at the top of Mount Washington in New Hampshire, then at a site near sea level about 1907 m lower. Their counts were about 560 per hour at the top and about 410 per hour at the bottom.

• Newtonian prediction: the trip takes 1907 m ÷ (0.995 × 3.00 × 10⁸ m/s) = 6.39 µs. That is 6.39 ÷ 1.52 = 4.20 half-lives. Fraction left: (1/2)^4.20 = 0.0543. Expected: 560 × 0.0543 ≈ 30 per hour.
• Relativistic prediction: γ = 1/√(1 − 0.995²) = 10.0. The muons' own clocks record only 6.39 ÷ 10.0 = 0.639 µs, which is 0.420 half-lives. Fraction left: (1/2)^0.420 = 0.747. Expected: 560 × 0.747 ≈ 420 per hour.

The measured value, about 410, agrees with relativity and is more than ten times the Newtonian prediction.

Atomic clocks on airliners

In October 1971, Joseph Hafele and Richard Keating flew four caesium-beam atomic clocks around the world on regular passenger flights, first eastward, then westward, and compared them with clocks at the U.S. Naval Observatory.

Two effects were predicted:

1. Special relativity (speed): think from a frame that does not rotate with Earth (centred on Earth's axis). Earth's surface moves eastward. An eastbound plane adds its speed to Earth's, so it moves faster than the ground clocks and should lose time. A westbound plane moves slower than the ground (it partly cancels Earth's rotation) and should gain time relative to the ground clocks.
2. General relativity (gravity): clocks higher up, where gravity is slightly weaker, run slightly faster. Both flights gain from this.

Results (ns = nanoseconds):

• Eastbound: predicted −40 ± 23 ns, measured −59 ± 10 ns.
• Westbound: predicted +275 ± 21 ns, measured +273 ± 7 ns.

The measured values agree with the predictions within the experimental uncertainties. Later experiments with better clocks have confirmed the same physics far more precisely. In 2010, physicists at the U.S. National Institute of Standards and Technology even detected time dilation with optical clocks moving at speeds of less than 10 m/s.

Particle accelerators: daily confirmation

Physicists at accelerators work with fast unstable particles every day, and the lifetimes always follow Δt = γΔt₀. In the 1970s, an experiment at CERN stored muons moving in a ring with γ ≈ 29.3. Their measured lifetime was about 64 µs, about 29 times the at-rest value, in close agreement with time dilation. If time dilation did not happen, beams of pions, kaons and muons would decay long before reaching detectors, and accelerator experiments could not be designed the way they are.