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
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.
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