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)
 Victor Hess discovers radiation coming from outer
space while in a hot-air balloon. Hess coins the term
“cosmic rays”. (1909)
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.
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.
The Rossi-Hall Expt
 Rossi and Hall built a detector to 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.
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)?
Non-Relativistic Calculation
 Calculate the time it takes to get down from 2000m
to 650m going 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?
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.
 Rossi and Hall brought their detector to the bottom of
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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.
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
 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.
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.
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!
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.
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.
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.