Muon Decay
By Bye Bye Miss American Pions
newbooksinbrief.com
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www.alternativephysics.org
Our Experiment
The Scintillator
Scintillator
Scintillation
detector
Theory of Poisson Decay
dp =λdt given
Dp =
Probability that the muon will decay
λdt
P(0,dt) = (1-λdt) Probability that the muon won’t decay
What is the probability that the muon has not decayed by the time t + dt ?
What is the probability that the muon has not decayed by the time t +
dt ?
At time dt decay won’t happen
P(0,dt)
At time t decay won’t happen
P(0,t)
1-p
1-p
At time dt decay won’t happen
P(0,dt) = t + dt
P(0,dt)
At time t decay won’t happen
P(0,t)
P(0,t) X p(0,dt)
P(0,t+dt) = p(0,t)x p(0,dt)
1-p
= p(0,t)(1-λdt)
1-p
Won’t
happen
Now we know the probability that muon decay
won’t happen which is p(0,t)(1-λdt)
P(0,t+dt) = P(0,t)- λdtp(0,t)
P(0,t+dt) - P(0,t) = - λdtp(0,t)
P(0,t+dt)− P(0,t)
= - λ 𝑃 0, 𝑡
𝑑𝑡
Rearrangement making - λ 𝑃 0, 𝑡 subject
P(0,t+dt)− P(0,t) 𝑑𝑝(0,𝑡)
= 𝑑𝑡
𝑑𝑡
𝑑𝑝
= −λ𝑝
𝑑𝑡
Integration
1
Dp(0,t) 𝑝(0,𝑡) =
−λ𝑑𝑡
𝑑𝑡 =
1𝑋𝑑𝑡
𝑡 0 𝑑𝑡
P(0,t) = -λt + c
P(0,t) = 𝑒 −λt + c
P(0,t) = 𝑒 −λt + c = 1
0 = -λt + c
c= λt
t+c
P(0,t) = 1
Substitute c= λt into P(0,t) = 𝑒 −λt + c
P(0,t) = e^-λ(t + t1)
So why do we care?
6 km
0.994c
= 2.01x10-5s
20.1µs >
http://www.deepscience.org/contents/summary.shtml
2.2µs
Time Dilation
2d
t=
c
http://www.astronomyforum.net/astrophysics-forum/133179-cause-gravitational-time-dilation.html
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html
2b
t=
c
Thank you for listening