# 10-8 s.

```REMINDER
Muons are unstable particles produced in
the upper atmosphere (around 30 km above
us). They move at about 0.995 c. How long
do they take to travel to the Earth’s surface?
A. ~10-4 s.
B. ~10-5 s.
C. ~10-6 s.
D. ~10-7 s.
E. ~10-8 s.
REMINDER
Muons are unstable particles produced in
the upper atmosphere (around 30 km above
us). They move at about 0.995 c. How long
do they take to travel to the Earth’s surface?
A. ~10-4 s.
B. ~10-5 s.
C. ~10-6 s.
D. ~10-7 s.
E. ~10-8 s.
L 3  10 4
4
t  

10
s
8
c 3  10
REMINDER
Muons are unstable particles produced in
the upper atmosphere (around 30 km above
us). They move at about 0.995 c. Their halflife at rest is t1/2=1.5 10-6 s. What fraction of
N
them arrive to the Earth’s surface N
?
surf Earth
A.  10
20
;
10
B.  10 ;
2
C.  10 ;
D.  1;
E.  10 2.
upper atm
REMINDER
Muons are unstable particles produced in
the upper atmosphere (around 30 km above
us). They move at about 0.995 c. Their halflife at rest is t1/2=1.5 10-6 s. What fraction of
N
them arrive to the Earth’s surface N
?
surf Earth
A.  10
20
;
10
B.  10 ;
2
C.  10 ;
D.  1;
E.  10 2.
upper atm
s, not t!
N surf Earth  1 
 
N upper atm  2 
 s / t1 / 2 
1

s 2  t 2  x 2  x 2  2  1
v

PROBLEM:
However in the frame of the muon its halflife
is 1.5 ms. The muon moves at constant
speed so the “twin paradox resolution” does
not help us here. So, does an observer in
the frame of the muon see the trip taking
NO: in this frame the Earth is moving
toward the muon and the distance appears
shorter by a factor of 10!!
Length contraction
A pole at rest has length 3 (light seconds)
L0  xP  xO  3 light  s
In the other frame (b=0.5) the length is the
distance between O and Q:
L'  x'Q  x'O  x'Q
xQ   ( x'Q   t 'Q )   x'Q
L'  L0 /   3 / 1.15  2.61 light  s
In general:
The other frame moves at b=0.5
L'  L0 / 
A pole at rest has length 3 light s, but moving at
b=0.5 its length is 2.61 light s. It does fit in a barn
with length 2.61 light s.
However, looking at this in the frame at rest w.r.t.
the pole:
the pole length is 3 light s, but the barn has length
2.61/1.15=2.27 light s so it doesn’t fit!
WHICH IS CORRECT??
A pole at rest has length 3 light s, but moving at
b=0.5 its length is 2.61 light s. It does fit in a
barn with length 2.61 light s.
However, looking at this in the frame at rest w.r.t.
the pole:
the pole length is 3 light s, but the barn has
length 2.61/1.15=2.27 light s so it doesn’t fit!
WHICH IS CORRECT??
BOTH!
But the event (Q) in which the front of the pole
goes by the back of the barn is NOT
SIMULTANEOUS with the event O when the
back of the pole aligns with the front of the barn.
A pole at rest has length 3 light s, but moving at
b=0.5 its length is 2.61 light s. It does fit in a barn
with length 2.61 light s.
However, looking at this in the frame at rest w.r.t.
the pole:
the pole length is 3 light s, but the barn has length
2.61/1.15=2.27 light s so it doesn’t fit!
WHICH IS CORRECT??
BOTH!
Ok. But suppose this barn is more like a real barn
with no back door, so the pole can not get through
and the front door is closed once the pole fits. What
happens in the frame of the pole?
The front of the pole hits the back of the barn but it
keeps compressing until the back end goes by the
front of the barn. The compression wave can not
transmit faster than c so there is no contradiction
(even if there is destruction).
The most important reason that an object is
observed to be shorter in a frame where it is
moving than in a frame where it is at rest is
that
A. The force of motion strongly
compresses an object that is moving
at relativistic speeds;
B. “Simultaneity” is not frame-independent;
C. The measuring sticks used by the moving
observer are Lorentz-contracted;
D. The clocks used by the moving observer
run slower.
The most important reason that an object is
observed to be shorter in a frame where it is
moving than in a frame where it is at rest is
that
A. The force of motion strongly
compresses an object that is moving
at relativistic speeds;
B. “Simultaneity” is not frame-independent;
C. The measuring sticks used by the moving
observer are Lorentz-contracted;
D. The clocks used by the moving observer
run slower.
In the pole-and-barn problem, the barn
never actually encloses the pole in the
barn frame, True or False?
A. True;
B. False;
C. Don’t know.
In the pole-and-barn problem, the barn
never actually encloses the pole in the
barn frame, True or False?
A. True;
B. False;
C. Don’t know.
An object is at rest in the Home Frame.
Imagine an Other Frame moving at a speed
of =4/5 with respect to the Home Frame.
The object’s length in the Other Frame is
measured to be 15 ns. What is its length as
observed in the Home Frame?
A. 15 ns
B. 12 ns;
C. 9 ns;
D. 19 ns;
E. 25 ns.
An object is at rest in the Home Frame.
Imagine an Other Frame moving at a speed
of =4/5 with respect to the Home Frame.
The object’s length in the Other Frame is
measured to be 15 ns. What is its length as
observed in the Home Frame?
A. 15 ns
L  L0 /  
B. 12 ns;
C. 9 ns;
D. 19 ns;
E. 25 ns.
L0  L   15  (5 / 3)  25
R7R.1 Space wars paradox. Two spacecraft
of equal rest length, L=100 ns, travel in
opposite directions with =3/5. Laser
cannon shot from ship O when its bow is
lined with the tail of O’.
Anne is on the ground and Brad aboard a
train moving at =0.6. Which best
represents a light wave front from a flash as
seen in Anne’s frame?
Anne is on the ground and Brad aboard a
train moving at =0.6. Which best
represents a light wave front from a flash as
seen in Anne’s frame?
Anne is on the ground and Brad aboard a
train moving at =0.6. Which best
represents a light wave front from a flash as
Anne is on the ground and Brad aboard a
train moving at =0.6. Which best
represents a light wave front from a flash as
representing his view of the light wave front
at a given time (Brad can draw very fast so
he draws all the points simultaneously in his
frame.) Which best represents the drawing
as seen by Anne (Brad never stops)?
representing his view of the light wave front
at a given time (Brad can draw very fast so
he draws all the points simultaneously in his
frame.) Which best represents the drawing
as seen by Anne (Brad never stops)?
```