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The Rossi-Hall Experiment 1941

The Rossi-Hall Experiment 1941. The Muon and Relativity. Cosmic Rays. Wilhelm Roentgen discovers X-Rays using Crookes tubes(1895) Marie Curie discovers radiation in elements such as Uranium and Plutonium. Discovers new elements Polonium and Radium (1898)

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The Rossi-Hall Experiment 1941

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  1. The Rossi-Hall Experiment1941 The Muon and Relativity

  2. Cosmic Rays Wilhelm Roentgen discovers X-Rays using Crookes tubes(1895) Marie Curie discovers radiation in elements such as Uranium and Plutonium. Discovers new elements Polonium and Radium (1898) Victor Hess discovers radiation coming from outer space while in a hot-air balloon. Hess coins the term “cosmic rays”. (1909)

  3. Cosmic Rays High energy particles (mostly protons) hitting Earth from outer space. Hess detects particles in a balloon during an eclipse – particles are not coming from the sun. Origin of particles was a mystery – now believed to come from the supernova of stars.

  4. Muons When high energy protons collide with oxygen or nitrogen molecules high in our atmosphere, they explode into muons and other particles. A muon is a charged particle, more massive than an electron and less massive than a proton. It only lasts a few microseconds before decaying into an electron and two neutrinos.

  5. The Rossi-Hall Expt Rossi and Hall built a detectorto study the muons raining down on us. They measured: The muons’ half-life to be 1.56μs. The speed of the muons to be 0.995c.

  6. Rossi-Hall (cont’d) They placed their detector on top of mount Washington (altitude 2000m). They detected muons at a rate of 560 per hour. Given a half-life of 1.56μs how many muons should they expect to make it to the bottom of mount Washington (alt. 650m)?

  7. Non-Relativistic Calculation Calculate the time it takes to get down from 2000m to 650mgoing at 0.995c: t = d/v = 1350/(0.995x3x108 ) = 4.52x10-6s It takes 4.52μs to get to the bottom of the mountain. How many muons will make it to the bottom?

  8. How many muons make it to the ground? N = No (½)t/λ N = 560 ( ½ ) 4.52/1.56 N = 75 muons You can expect around 75 muons to make it to the bottom of the mountain each hour.

  9. Rossi and Hall brought their detector to the bottom of the mountain, and counted: 420 muons per hour! That’s 350 too many  Let’s try recalculating the speed they fall at: 420 = 560 ( ½ ) t/1.56 t = 0.647 μs V = d/t = 1350/0.647x10-6 V = 20.9 x 108 m/s (!!) This is more than the speed of light. Obviously something is not right.

  10. Time Dilation The muon’s half-life is 1.56μs. This is a value found in the lab, while the muon is at rest. When the muon is falling to Earth at 0.995c, it appears to live longer from our perspective. At this speed, γ = 10.0 t’ = γto t’ = 10(1.56) = 15.6 μs

  11. How many will make it to the bottom now? N = No (½)t/λ N = 560 (½)4.52/15.6 N = 458 This is much closer to the experimental value of 420 muons per hour found by Rossi and Hall.

  12. Length Contraction According to the scientists on Earth, the muon appears to live slower, lasting longer. This gives the muon more time to get to the ground before it decays. We can also approach this from the muon’s perspective. Time for the muon is not altered, but the muon’s perception of Earth is.

  13. Length Contraction To the muon, the Earth is rushing up to it at 0.995c. At that speed, the Earth looks contracted. Mountains look shorter, for example. L’ = Lo /γ L = 1350/10.0 = 135.0m According to the muon, Mount Washington is only 135m tall!

  14. Length Contraction The muon will fall this distance in a time of: T = d/v T = 135.0/(0.995x3x108) T = 0.452μs So in this time there will be: N = No (½)t/λ N = 560 (½)0.452/1.56 N = 458 muons left at the bottom This is the same result as before.

  15. Conclusion • The Rossi-Hall experiment supported Einstein’s Relativity Theory. • In classical theory, very few muons should make it to the Earth’s surface. • Relativity extends their lifetime (from my point of view), or shortens the distance they travel (from their point of view). • Either way, more of them make it to the ground before they decay.

  16. Conclusion Since 1941, the Rossi-Hall experiment has been improved upon multiple times. A modern variation of the experiment is done with circular accelerators. Exotic particles that only last for nanoseconds are difficult to study ordinarily. By speeding them up to nearly the speed of light, the particles can be made to last much longer, making them easier to study.

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