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Quiz QuestionWhat 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 MPHB: 45 MPHC: 70 MPHD: 74 MPHE: 95 MPH
Galilean Relativity• Laws of physics should be the same
in any inertial reference frame
• What’s an inertial reference frame?
Galilean Relativity
x
y
z S
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 FrameBoth lightning bolts strike at the same time
The observers on the ground conclude that theobserver 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 26:23For behold, my beloved brethren, I say unto you that the Lord God worketh not in darkness.
Time Dilation
Time Dilation
Time Dilation
Time Dilation
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 tothe proper frame, the light must travel further than L.
The inertial frame in which two events occur at the same placeis known as the “proper” frame for the two events.
Not all pairs of events have a proper frame!
So there is a larger time between the two events in the movingframe than the proper frame!
Thought QuestionTwo 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 labB : The one moving slowest with respect to the
labC : The one in which the events occur furthest
apartD : The one in which the events occur closest
togetherE : It depends on other information.
Time Dilation∆ 𝑡=𝛾 ∆ 𝑡𝑝𝛾=
1
√1− 𝑣2𝑐2
Discussion question: The value of γ is
2
2
1
1
cv
A. Less than 1B. Greater than 1C. Can be either depending on
the velocity
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 spaceB : The little twin who stayed homeC : The little twin who had roast beefD : The little twin who had noneE : They will be the same age
Who measures the “proper time” for the round trip?
A : GosloB : SpeedoC : Neither of themD : 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 : GosloB : SpeedoC : Neither of themD : Both of themE : Miss Manners
Length Contraction
Length Contraction
Proper frame is the one in which the object isn’t moving
𝐿=𝐿𝑝
𝛾
The Barn Door Paradox