# Muon Lifetime and time dilation effect

```MUON LIFETIME AND TIME
DILATION EFFECT
Measuring the stopping rate of muons, as a function of depth in the
atmosphere to demonstrate the time dilation effect of special
relativity.
Melinda Jolley
THE MUON WAS SO UNEXPECTED THAT, REGARDING
ITS DISCOVERY, NOBEL LAUREATE ISIDOR ISAAC RABI
FAMOUSLY QUIPPED, “WHO ORDERED THAT?”
Where do muons come
from?
•
Not completely sure
•
Somewhere in deep space?
•
Very recent NASA research
Muons were originally
thought to be meson
It’s name is a combination of mu
and meson
•
•
Femi Coupling Constant (πΊπ )
The Muon
•
•
Nope, it is a Lepton
Nicknamed ‘The Heavy Electron’
•
π&plusmn; →e&plusmn; +2 ν
THE GOALS OF MY EXPERIMENT
Determine the
the Muon
Muon Physics
•
•
•
•
Moun.exe
π π‘ = π0 π
•
Use the measured τ
•
π‘
π
−
Accepted τ = 2.20 &micro;s
Is there no Time
Dilation?
The Fermi Coupling
Constant
πΊπ =
•
β 192π3
ππ π5
•
•
Rates of Muon decays at one
elevation
Approximation for rate at second
elevation
Correction factors for Energy Loss
over distance and Variations in the
shape of the muon energy
spectrum
CORRECTING FOR
ENERGY LOSS
•
•
βπΈ = πΆπ ∗ βπ» ∗ ππππ
ππππ
•
ππ£π
=
1 β2
π
βπ» β1 0
ππ£π
&times;π
π0 = 1.28 &times; 10−3
−β
8400 π
π
.
ππ3
THE MUON
ENERGY
SPECTRUM
•
ππππ€ =
ππ‘ππππππ πππ‘π ππ‘ β1
ππ‘ππππππ πππ‘π ππ‘ β2
•
π(ππππππ π βπππ) = π
•
π‘′ =
ππ
ππππ(ππ£π) πΆπ
•
•
ππ =
−π‘′
π
πΎ2
πΎ1
πΎ2 −1
πΎ1 =
πΈ1
ππ 2
ππππ€
π(ππππππ π βπππ)
ππΎ
THE PREDICTIONS
• πππππ· = ππ ∗
π(πππππππ‘ππ)π πππ ππ‘βππ β (ππ π‘πππ πππππ‘πππ)
• =π0 &times; π
−π‘
π
• ππππ· = ππ ∗
π(πππππππ‘ππ)π πππ ππ‘βππ β (π‘πππ πππππ‘πππ)
• =π0 &times; π
(
−π‘′
)
π
THE EQUIPMENT
USED
•
Scintillator is placed at the bottom of
a black anodized aluminum alloy
tube
•
Transparent Material
HOW THE DATA LOOKS
MY DATA
• High Voltage set to -1154 Volts
• Threshold Voltage set to 206 MeV
• First location:
Pueblo, CO, Elevation 1420 m
• Second location:
Monarch Mountain Base Summit, CO, Elevation 3290 m
• ΔH= 1870 m
• Much more Pueblo Data than Monarch Data
FERMI COUPLING
CONSTANT
•
•
Mass of the Muon = 106
πππ
π2
Reduced Planck’s Constant = 6.58 &times;
10−25 πΊππ ∗ π
• Accepted value: 1.17 &times; 10−5 πΊππ −2
• Pueblo value : 1.18 &times; 10−5 πΊππ −2
• Monarch value : 1.19 &times; 10−5 πΊππ −2
STOPPING RATES
•
Pueblo’s Stopping Rate =
0.0284
•
ππ’πππ
π ππ
Monarch’s Stopping Rate =
0.0644
ππ’πππ
π ππ
• t=6.28 &micro;sec or π‘ = 2.85 π
RATES
ACCOUNTING FOR
ENERGY LOSS
•
•
Remember t is the transit time
assuming no Time Dilation
t’ assumes Time Dilation Effects
• ππππ = 972
π
.
π3
• βπΈ = 364 πππ, πΈ1 = 508 πππ, πΎ1 = 4.9
• π‘ ′ = 2.38 π sec ππ π‘ = 1.08 π
• π(πππππππ‘ππ)ππ’ππππ(ππ π‘πππ ππππππππππ) = π0 &times; 0.0578
• π(πππππππ‘ππ)ππ’ππππ(π‘πππ πππππ‘πππ) = π0 &times; 0.339
MUON ENERGY
SPECTRUM
CORRECTION
AND PREDICTIONS
•
π(ππππππ π βπππ) = 0.339
•
ππππ€ =
•
ππ =
0.0284
0.0644
0.441
0.339
= 0.441
= 1.30
• π(πππππππ‘ππ)ππ’ππππ(ππ π‘πππ πππππ‘πππ) = 1.30 &times; 0.056 = 0.0749
• π(πππππππ‘ππ)ππ’ππππ(π‘πππ πππππ‘πππ) = 1.30 &times; 0.339 = 0.441
GREAT INCONSISTENCY OF THE
HYPOTHESIS THAT THERE IS NO
RELATIVISTIC TIME DILATION
EFFECTS ON THE MUON
The data was consistent with the Relativistic Time Dilation
Hypothesis.
“
IF WE KNEW WHAT IT WAS WE WERE
DOING, IT WOULD NOT BE CALLED
RESEARCH, WOULD IT
Einstein
Thanks to:
Dr. Brown
Dr. Wallin
My family
Special thanks to Annika, Thomas, and Olivia
”
```