Quiz Question
What is an “intertial” reference frame?
A. One in which an object is observed to have no
acceleration when no forces act on it.
B. One in which the center of the galaxy is not
moving.
C. On in which the center of the galaxy is not
accelerating.
D. One in which the center of the galaxy is not
accelerating or rotating.
E. One at rest with respect to the surrounding air.
Galilean Relativity
Galilean Relativity
I drive past a baseball field traveling north at 25
MPH. A player throws the ball south at a
speed (relative to the ground) of 70 MPH.
What is the speed of the ball in my inertial
reference frame?
A: 25 MPH
B: 45 MPH
C: 70 MPH
D: 74 MPH
E: 95 MPH
Galilean Relativity
• Laws of physics should be the same in any
inertial reference frame
Galilean Relativity
z
S
y
x
Conventions

The velocity v is the velocity of the S’ frame
origin as viewed by someone in S frame.
– Use u to represent the velocity of an object.

We define our coordinates such that
– the x, y, and z directions are the same for both
coordinate systems,
– v is always in the x direction, and
– the origins of the two coordinate systems overlap at
time t=0.
Galilean Transformations
Problems with Galilean Relativity

Maxwell’s equations describe light . . . But
– Different from other waves
– Speed the same in any reference frame

Ether wind
Michelson & Morley: 1881, 1887
Michelson & Morley: 1881, 1887
Michelson & Morley: 1881, 1887
Michelson & Morley: 1881, 1887
Michelson & Morley: 1881, 1887
Michelson & Morley: 1881, 1887
Michelson & Morley: 1881, 1887
Michelson & Morley: 1881, 1887
Einstein’s Relativity…

Postulates
– 1. The mathematical form of the laws of
physics must be the same in every inertial
reference frame.
– 2. The speed of light in vacuum is a constant,
and is the same constant in every inertial
reference frame.
Consequences…
A Single Observer
A Single Observer
An “Array” of Observers
In “Earth” Reference Frame
In “Earth” Reference Frame
In “Earth” Reference Frame
Both lightning bolts strike at the same time
The observers on the ground conclude that the
observer on the train sees the light from the right bolt
before they see light from the left bolt.
In “Train” Reference Frame
Either the observer on the train sees light from both beams
at the same time…
… or the lightning bolts didn’t strike at the same time!
Simultaneity

Things which happen simultaneously in
one inertial reference frame do not have
to occur simultaneously in a different
inertial reference frame.
2 NEPHI 26:23
For behold, my beloved brethren, I say unto
you that the Lord God worketh not in
darkness.
Time Dilation
Time Dilation
Time Dilation
Time Dilation
The inertial frame in which two events occur at the same place
is known as the “proper” frame for the two events.
Not all pairs of events have a proper frame!
If two events occur in the same place, separated by a time tp …
light can travel a distance L = ctp / 2 and back.
But in the frame of someone moving at a speed v relative to
the proper frame, the light must travel further than L.
So there is a larger time between the two events in the moving
frame than the proper frame!
Thought Question
Two people in different inertial frames measure the time
between two events. In which frame will the time
interval between two events be the shortest?
A : The one moving fastest with respect to the lab
B : The one moving slowest with respect to the lab
C : The one in which the events occur furthest apart
D : The one in which the events occur closest together
E : It depends on other information.
Time Dilation
∆𝑡 = 𝛾∆𝑡𝑝
𝛾=
1
1−
2
𝑣
2
𝑐
Discussion question:
The value of γ is
 
1
v2
 2
Less 1than
c
1
B. Greater than 1
C. Can be either depending on the
velocity
A.
This has been verified . . . many times
• A muon created on earth at rest lives an
average of 2.2 x 10-6 s (2.2 μs)
• A muon traveling at .990c lives an average
of 1.56 x 10-5 s (15.6 μs)
• A muon travels at a speed 0.990c for
2.2 x 10-6 s before it decays. How far does the
muon travel?
The Twin Paradox
After the trip, which twin will be the oldest?
A : The little twin who went into space
B : The little twin who stayed home
C : The little twin who had roast beef
D : The little twin who had none
E : They will be the same age
Who measures the “proper time” for the round
trip?
A : Goslo
B : Speedo
C : Neither of them
D : Both of them
Length Contraction: Goslo’s
Frame
Length Contraction: Speedo’s
Frame
Who measures the “proper time” for the one-way
trip to Planet X?
A : Goslo
B : Speedo
C : Neither of them
D : Both of them
E : Miss Manners
Length Contraction
Length Contraction
𝐿𝑝
𝐿=
𝛾
Proper frame is the one in which the object
isn’t moving
The Barn Door Paradox