# Day 15

```Announcements
•Exam 3 is scheduled for Wednesday April 8.
Will be pushed back to Monday April 13
Tentatively will cover the rest of Chapter 4, all of
Chapters 5, 6, 7 &amp; 8. New Sample Questions
that include Chapter 8 are posted.
The Cosmological Principle
Our universe is obviously not
homogeneous or isotropic close by
On a scale of a billion lightyears
it starts to look isotropic and
homogeneous
On the largest scales it is
homogeneous and isotropic, mostly
Colored Card Question
ClassAction website Cosmology module
Cosmological Principle
Another coloredcard Question
If you could be instantaneously transported to the
edge of the visible universe 14 billion lightyears
away from Earth, you would see
A. the region around you filled with glowing hot
gas from the Big Bang
B. nothing, if you looked in the direction
opposite the Earth
C. pretty much the same thing you see here,
just different star patterns.
D. planets, stars and galaxies unlike anything
we see near Earth
One final requirement to
understanding the universe
The laws of physics are the same
everywhere and everywhen
Coordinates
The coordinate system determines
how you find the shortest distance
between two points
s
s=
s  x 2  y 2  z 2
Inertial Reference Frames
Accelerated
Reference
Frame
A consequence
of our reference
frame being
non-inertial is
the Coriolis
effect
An inertial reference frame near
a gravitational object is free fall
Since the inertial mass of
an object is equal to the
gravitational mass, an
object in freefall is in an
inertial reference frame
Relativity According to Galileo
According to Galileo light should
Speed observed by S` is c (299792458 m/s)
Speed observed by S is c + v
If the train is moving at 100 m/s then
c = 299792558 m/s
Moving Reference Frames
x  x  vt
y  y  y0
z   z  z0
t  t
An example of moving reference
Maxwell’s Equations aren’t
invariant under Galilean
transformation
The equations governing the electromagnetic force change
when a Galilean transformation is done on them
What is the reference frame of light?
The Michelson-Morley
Experiment
They were trying to
detect the luminiferous
aether. They didn’t find it.
Watch the King’s Special
Relativity apps Michaelson-Morley
Experiment
Watch Mechanical Universe and
Beyond: The Michelson-Morley
Experiment
In 1889 George FitzGerald
proposed another type of
transformation
Hendrik Lorentz added in a transformation of time as well
as space so we now call it a Lorentz transformation
In 1905 Einstein explained why
the Lorentz transformations are
the correct transformations
for Special Relativity
•The laws of physics are the same in all
inertial reference frames.
•The speed of light in a vacuum is the
same in all inertial reference frames
The “special” of special relativity is that it only applies if
the relatives velocities are constants. There must be
no acceleration.
The problem of simultaneity
Different observers do
not see the two events
as simultaneous
Simultaneous
events video
Time Dilation: Time is not absolute
The light travel
time is shorter
for the observer
that is stationary
with the light
than the outside
observer that
sees the light
moving
Watch Time Dilation video
The amount of time dilation
depends on the relative speed
Note that it is always the other clock that runs slow. Your
clock, the one stationary with respect to you, always runs
at the right speed. It doesn’t matter who is moving. In fact,
you can’t tell who is moving, only relative motions.
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