Transcript March 3 - Astronomy

Discussion
What are the two assumptions in Einstein’s
Special Theory of Relativity?
Discussion
What are the predictions of Einstein's
Special Theory of Relativity?
Spacetime
The constancy of the speed of light, connects
the three dimensions of space with time. The
speed of light (measured in m/s) can be
considered a conversion factor between space
and time.
Spacetime is not relative
All observers will agree on distances
measured in the 4-dimensions of spacetime.
4-dimensions
We live in a 4-dimensional universe and all
the objects we see have 4-dimensions.
Imagining the fourth dimension
Discussion
What would a 3-dimensional sphere look like
to a 2-deminsional being as it passed
through a 2-dimensional plane?
Discussion
What would a 4-dimensional sphere look like
as it passed through our 3-dimensional
space?
Discussion
What does a person look like in 4dimensional spacetime?
But, time is different, or is it?
Consider what a universe with 4 equal space
dimensions and no time dimension would be
like if you and me and everything else were
moving very close to the speed of light in
some direction.
Moving the speed of light
Lengths in the direction of motion would
shrink to 0.
We wouldn’t be able to move in this fourth
dimension.
We would be forever stuck at a single point.
Spacetime diagrams
We can try to visualize spacetime by
collapsing the 3 dimensions of space onto
one or two axes and plotting time on the
remaining axis.
Spacetime diagrams
time
future
present
y
x
past
Discussion
Draw a spacetime diagram of your path
through spacetime during this class.
Spacetime diagrams
time
future
You sitting
in class
present
y
x
past
Me on the way to work
time
Traveling the speed limit
hours
Getting speeding ticket
Speeding
miles
x
y
Stopping at a red light
Discussion
What does the Earth’s orbit look like on a
three dimensional spacetime diagram?
Principle of relativity
Accelerated motion
Discussion
Jackie claims that she is at rest and you are
moving. But you claim that you are at rest
and she is accelerating away from you.
Assuming Jackie cannot tell your engines
are running, how can she prove that you
are accelerating?
Inertial forces
Fictitious forces felt by an object trying to move in
a straight line at a constant velocity but unable to
do so because its reference frame is being
accelerated.
Einstein’s happiest thought of his
life
If you fall in a gravitational field, you will not
feel gravity. You will feel weightless.
Discussion
If the space shuttle orbits at a distance of 20
miles from the Earth’s surface, according to
Newton’s universal law of gravity, Earth’s
gravitational force is a little less (because the
distance from Earth’s center is 20 miles
larger) than on the Earth’s surface. Yet,
astronauts are weightless. How can this be?
Accelerated motion in a gravitational field
(freefall) can cancel gravity.
Accelerated motion far from any
gravitational field, feels just like gravity.
The equivalence principle
The effects of gravity are exactly equivalent to
the effects of acceleration.
Discussion
You are driving in a car with a bunch of helium
balloons in the back seat. When you accelerate
at a stop light, which way to the balloons
move? Use the equivalence principle to
explain.
Discussion
If you planted some seeds in a pot that you
rotated on a turntable with the light source
directly above the rotating pot, in which
direction would the plants grow?
Discussion
How does the equivalence of accelerated
motion and gravity make even accerated
motion relative?
Discussion
What is the shortest distance between two
points?
Discussion
If you were to fly a plane from Philadelphia to
Beijing, approximately at the same latitude, you
would just follow a straight path due west? Why or
why not?
General Relativity
Gravity is not a mysterious “force” of nature
between two masses as viewed by Newton.
Instead, mass warps or curves spacetime.
Objects falling in a gravitational field are
following geodesics, the shortest path
between two points in a curved spacetime.
Discussion
Imagine a time (before 500 BCE) when people
thought the Earth was flat. Two explorers set
out in exactly opposite directions, one east, one
west. What do they discover?
Discussion
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!
Where can we do this experiment and get this
result in out lifetime?
Gravity slows time
Clocks tick more slowly in a gravitational field.
Not the Same as SR time dilation
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.
Discussion
If you shine a laser into the window of a
rocket that is accelerating past you, draw
the path of the laser as it would appear to
those inside the rocket.
Discussion
Because this is the same as being in a
gravitational field, what can you say about the
path of light near the surface of the Earth?
Gravity bends light rays
Light always takes the shortest path
between two points. In a gravitational
field, where spacetime is curved, light
follows a geodesic, a curved path.
Gravitational lens
Discussion
Explain physically why light bends in a
gravitational field. What is happening to the
light to make it curve?
Hint: How does a lens made of glass bend
light?
Discussion
You’re on the top floor of the Empire State
building. On the ground floor there is a
clock that you can see that flashes very
second. However, if you time the flashes,
you find that they arrive a intervals greater
than a second. Explain why.
Discussion
If time moves more slowly on a star that has a
higher surface gravity, how will this effect this
the light we see emitted from the surface of
the more massive star compared to that of
the less massive star?
Hint: Think about how the light we see is
actually created.
Gravitational redshift
General Theory of Relativity
Gravity is the same as the effects of acceleration,
caused by a warping of spacetime
Slows the passage of time
Bends the path of light
Causes light to be redshifted