results of frisch-smith experiment. curves computed
m
n
e
w
t
o
n
{\displaystyle m_{\mathrm {newton} }}
,
m
s
r
{\displaystyle m_{\mathrm {sr} }}
.
if no time dilation exists, muons should decay in upper regions of atmosphere, however, consequence of time dilation present in considerable amount @ lower heights. comparison of amounts allows determination of mean lifetime half-life of muons.
n
{\displaystyle n}
number of muons measured in upper atmosphere,
m
{\displaystyle m}
@ sea level,
z
{\displaystyle z}
travel time in rest frame of earth muons traverse distance between regions, ,
t
0
{\displaystyle t_{0}}
mean proper lifetime of muons:
m
n
e
w
t
o
n
=
n
exp
[
−
z
/
t
0
]
m
s
r
=
n
exp
[
−
z
/
(
γ
t
0
)
]
{\displaystyle {\begin{aligned}m_{\mathrm {newton} }&=n\exp \left[-z/t_{0}\right]\\m_{\mathrm {sr} }&=n\exp \left[-z/\left(\gamma t_{0}\right)\right]\end{aligned}}}
rossi–hall experiment
in 1940 @ echo lake (3240 m) , denver in colorado (1616 m), bruno rossi , d. b. hall measured relativistic decay of muons (which thought mesons). measured muons in atmosphere traveling above 0.99 c (c being speed of light). rossi , hall confirmed formulas relativistic momentum , time dilation in qualitative manner. knowing momentum , lifetime of moving muons enabled them compute mean proper lifetime – obtained ≈ 2.4 µs (modern experiments improved result ≈ 2.2 µs).
frisch-smith experiment
a more precise experiment of kind conducted david h. frisch , smith (1963), measured approximately 563 muons per hour in 6 runs on mount washington. measuring kinetic energy, mean muon velocities between 0.995 c , 0.9954 c determined. target located in cambridge, massachusetts difference in height of 1907 m, should traversed muons in 6994640000000000000♠6.4 µs. assuming mean lifetime of 2.2 µs, 27 muons reach location if there no time dilation. however, approximately 412 muons per hour arrived in cambridge, resulting in time dilation factor of 7000880000000000000♠8.8±0.8.
frisch , smith showed in agreement predictions of special relativity: time dilation factor muons on mount washington traveling @ 0.995 c 0.9954 c approximately 10.2. kinetic energy , velocity diminished until reached cambridge 0.9881 c , 0.9897 c due interaction atmosphere, reducing dilation factor 6.8. between start (≈ 10.2) , target (≈ 6.8) average time dilation factor of 7000840000000000000♠8.4±2 determined them, in agreement measured result within margin of errors (see above formulas , image computing decay curves).
other experiments
since then, many measurements of mean lifetime of muons in atmosphere , time dilation have been conducted in undergraduate experiments.
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