Equivalence principle

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Equivalence principle
The effects of acceleration are exactly the same
as the effects of gravity.
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Curve path for light
Light will follow a curved path through an
accelerating reference frame.
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Discussion
What does this tell you about the path of light
in a gravitational field?
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Discussion
If you throw a ball straight up from the surface
of the Earth what will happen to its kinetic
energy as the ball rises? Does it increase
decrease or remain the same?
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Discussion
Does light have kinetic energy? Why or why not?
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Discussion
If I shine a laser straight up, what happens to
its kinetic energy?
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Discussion
If light loses energy, what happens to its
frequency and wavelength?
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Gravitational Redshift
As light travels up from the surface of a planet
or a star against gravity it loses energy (shifts
to a lower frequency) and becomes redshifted.
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Atomic clocks
The most accurate clocks ever made use the
frequency of electromagnetic radiation emitted by
a particular transition of the cesium 133 atom.
The interval of a second is defined as
9,192,631,770 periods of this oscillation.
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Discussion
Suppose you observe an atomic clock sitting on
the Earths surface from high above the ground.
What will you notice about the frequency of the
transition being used to measure time?
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Gravitational time dilation
Gravity slows the passage of time. The stronger
the gravitational field, the greater the time
dilation.
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Gravitational redshift
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Discussion
Can there be such a thing as a gravitational
blueshift? Explain.
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How can gravity bend light?
Light has energy, therefore it has mass and thus
should fall in a gravitational field just like
any other mass. Gravity slows the passage of
time.
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Discussion
Suppose you and a friend are in a long space ship
traveling at a constant velocity near the speed
of light. You are at the front of the ship and
your friend is in the back. Both of you have
clocks that emit a flash of light every second.
Will you observe any difference in the rate of
the clocks? Why or why not?
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Discussion
Now assume the space ship turns on its rocket
engine and starts to accelerate. Do the light
flashes from the clocks take the same amount of
time to reach either side of the ship. Why or
why not?
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Notice that this is different than time dilation
in Special Relativity. Both clocks remain at
rest relative to each other regardless of the
acceleration. Both observers agree that the
clock in front is ticking faster than the clock
in back.
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Discussion
How does a glass lens bend light?
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Gravitational lens
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Discussion
If the speed of light slows in a gravitational
field, doesnt this violate the second postulate
of the Special Theory of Relativity?
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Photons and masses
Einstein wondered, if gravity can bend the path
of light by slowing the passage of time, couldnt
we explain the curving of a mass in a
gravitational field by the warping of time as
well?
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Discussion
Einstein spent several years trying to explain
gravity by warping time and leaving space flat
but failed. Why doesnt this work?
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Curved spacetime
Gravity is not a mysterious force of nature
between two masses as viewed by Newton. Instead,
mass warps spacetime. This warping of
spacetime causes the effects of gravity which is
not a real force, but a fictitious inertial
force.
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Newton on Gravity
That one body may act upon another at a distance
through a vacuum, and force may be conveyed
from one to another, is to me so great an
absurdity, that I believe no man who has a
competent faculty in thinking, can ever fall into
it. Isaac Newton 1692
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Straight world lines
A free float frame is a reference frame that
follows the shortest path through spacetime.
In a free float frame you feel weightless and
the passage of time is maximized. Photons,
traveling at the constant speed of light, travel
straight lines through spacetime.
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Discussion
What does the world line of the Earth following
its orbit about the Sun look like on a
three-dimensional spacetime diagram?
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Discussion
Is the Earths motion accelerated or not? How
can you tell?
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Discussion
Draw a spacetime diagram of a skydiver, assuming
air resistance can be neglected. Is the path
through spacetime a straight line?
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Accelerated motion, where the velocity is
changing, is curved on a spacetime diagram. An
object in freefall in a gravitational field is
accelerating and therefore follows a curved path
through spacetime.
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Discussion
Draw yourself sitting in this classroom on your
spacetime diagram. Which path through spacetime
is the shortest?
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Discussion
Is freely falling in a gravitational field
actually a free-float frame? Why or why not?
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Discussion
What about the passage of time? For whom does
time pass the quickest, the skydiver or you
sitting in class?
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The shortest path
The shortest path between two points is a
straight line connecting the two points.
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Discussion
When is the shortest path between two points not
a straight line?
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Discussion
If you were to fly a plane from Philadelphia to
Beijing, approximately at the same latitude,
would you just fly due west? Why or why not?
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On a curved surface the shortest path between two
points is a geodesic. On the Earth, the
shortest distance between two points is arc of a
great circle, passing through the two points and
centered on the center of the Earth.
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Geodesics in spacetime
Objects moving in a gravitational field are not
accelerating due to a force acting on them. They
are simply following the shortest path between
two points in a spacetime that is not flat but
curved.
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How do we imagine a four-dimensional curved
spacetime?
Imagine a time (before 500 BCE) when people
thought the Earth was flat. Two explorers set
out in exactly opposite directions. Eventually,
they meet.
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Consider being in outer space. Because you did
not study your astronomy, you firmly believe that
spacetime is flat. You decide to explore the
Universe by sending out two probes in exactly
opposite directions. To your great surprise, the
probes send back pictures of one another!
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Discussion
Can you think of a situation where you can
actually perform this experiment and get this
same result?
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