Einstein’s postulates

1. The laws of nature are the same for everyone.

2. The speed of light in a vacuum is constant for all observers.

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?

Discussion

If you are in a car, which is in an accident, how does everything in the car move that isn’t tied down?

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 outside in the sunshine, in which direction would the plants grow?

Discussion

How does the equivalence of accelerated motion and gravity make even accerated motion relative?

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

past

present

x

y

Discussion

Draw a spacetime diagram of your path through spacetime during this class.

Spacetime diagrams

time

future

past

present

x

y

You sitting in class

Discussion

If an object is moving at a constant velocity, what does it’s world line look like on a spacetime diagram?

Me on the way to work

time

x

y

Getting speeding tickethours

miles

Speeding

Traveling the speed limit

Discussion

If an object is accelerating, what does it’s world line look like on a spacetime diagram?

Stopping at a red light

What does the Earth’s orbit look like on a three dimensional spacetime diagram?

Discussion

What is the shortest distance between two points?

Discussion

Discussion

What is Newton’s first law of motion?

Newton’s 1st law of motion

In the absence of net external forces, an object will travel the shortest possible path through spacetime.

The shortest path is the one for which time ticks the fastest.

Twin Paradox

time

x

y

years

Light years

Cen

Leave Earth

Return toEarth

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?

Discussion

What would the world-line of a skydiver look like on a spacetime diagram?

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.

General Relativity

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?

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?

Discussion

Gravity slows time

Clocks tick more slowly in a gravitational field.

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.

Not the Same as SR time dilation

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?

Light always takes the shortest path between two points. In a gravitational field, where spacetime is curved, light follows a geodesic, a curved path.

Gravity bends light rays

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

Using the fact that gravity slows time, explain why a ball thrown in a gravitational field will follow a curved path?

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

Discussion

If you are in a closed room without windows, according to the equivalence principle is there any way you can tell the difference between falling freely in Earth’s gravitational field and moving at a constant velocity far away from any gravitational field?

Discussion

Suppose you are locked in a closed room where you do not feel your weight. This time I allow you to have two billiard balls. You place the balls side-by-side in front of you. If your closed room is moving at a constant velocity how will the balls move?

Discussion

Suppose you are locked in a closed room where you do not feel your weight. This time I allow you to have two billiard balls. You place the balls side-by-side in front of you. If your closed room is falling freely in a gravitational field how will the balls move?

Discussion

Suppose you place the balls on top of each other in front of you how will they move?

Tidal forces

Free-fall makes the downward pull of gravity disappear, but tidal forces remain.

As you fall toward Earth feet first, your feet feel a slightly stronger gravitational pull and accelerate a little bit faster than your head. Furthermore, your right side will be pulled slightly toward your left side while your left side will be pulled slightly toward your right side.

Discussion

Does the existence of tidal forces invalidate the equivalence principle? How can we make tidal forces go away?

Tidal Forces are the key

Tidal forces show you how space is warped

Space is stretched radially

Space is squeezed tangentially

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