What time dilation in relativity explain muon decay with the concept of time dilation?

Muons travel at relativistic speeds and are unstable particles with a mean lifetime at rest T0 ~ 2.2 µs. At the relativistic speeds the muons experience time dilation. This dilation allows them to reach the Earth’s surface before they decay.

Why does time move slower as you approach the speed of light?

As light is spread out by the observer moving away from the source of the light time is decreased. The faster the observer moves the more light is spread out and time slows down. Time slows down as you travel faster because momentum bends the fabric of spacetime causing time to pass slower.

What is the proper time experienced by the muon before it reaches the ground the time experienced by the muon )?

Some collisions of these particles with nuclei in the upper atmosphere result in short-lived particles called muons. The half-life (amount of time for half of a material to decay) of a muon is 1.52 μs when it is at rest relative to the observer who measures the half-life. This is the proper time interval.

How did the muon experiment confirmed the theory of relativity?

Evidence for time dilation as predicted by the special theory of relativity came in experiments that dealt with elementary particles such as muons. Indeed such experiments confirmed the fact that when an elementary particle travels with a very high velocity, its lifetime increases.

How do muons reach the Earth?

radiation. Muons are by-products of cosmic rays colliding with molecules in the upper atmosphere. Muons reach earth with an average velocity of about 0.994c. On earth’s surface, about 1 muon passes through a 1 cm2 area per minute (~10,000 muons per square meter in one minute).

Why does time slow down around a heavy object?

Gravitational time dilation occurs because objects with a lot of mass create a strong gravitational field. The gravitational field is really a curving of space and time. The stronger the gravity, the more spacetime curves, and the slower time itself proceeds.

Why can muons reach the Earth?

Muons are unstable particles created when cosmic rays interact with the upper atmosphere. They move at very high velocities (β ~ 0.9999) and have very short lifetimes, τ = 2 × 10-6 s, as measured in the lab. ∴ distance = 0.9999c × 1.4 × 10-4 s ≅ 42 km Since 42 km > 10 km, the muons will reach the ground.

What does time dilation and length contraction in relativity mean?

length contraction: Shortening of distance. time dilation: Clocks moving relative to an observer run more slowly compared to the clocks that are at rest relative to the observer. twin paradox: Illustrates questions of the relativity of time.

Why are muons detected on Earth?

Primary cosmic radiation is a high-energy particle radiation (predominantly protons) that interacts with the Earth’s atmosphere upon impact. This produces a secondary radiation that can be detected on the Earth’s surface (predominantly muons).