Mr Green sees the shorter, straight, green path and Mr. Red sees the longer, curved, red path.

Transcription

1 Mr Green sees the shorter, straight, green path and Mr. Red sees the longer, curved, red path.

2 In an accelerated frame, time runs slow compared to a non-accelerated frame. The Equivalence Principle tells us that there is no difference between the accelerating ship and the gravity on the Earth. Einstein s conclusion: Near massive objects, time runs slow. It is this slower rate of time, that makes things move in a curved path. There is NO FORCE OF GRAVITY. Mass causes Space-Time to bend. (i.e. Clocks to run slow.)

3 What is Space-time? It is the universe. In the vacuum of outer space, we define the universe by the distance between objects. That is 3-D space. So when we talk about outer space, we are usually referring to the space between objects. The space-part IS the universe. That s all there is between objects. So that is what we mean by THE UNIVERSE. Relativity shows us that we must also include time into the equation. So the fabric of the universe, the thing that defines space-time distances, is the universe.

4 The return of look-back time Remember, when we look out in space, we are also looking back in time. The farther away you look, the further back in time you are looking. This is even true, right here in the classroom. Everything you see, is from the past. It isn t noticeable to you because light travels so very fast. But you are always waiting for the light signal to reach you. If someone waves to you on campus, you are actually seeing it in the past. Relativity adds one other complexity. The clock of someone far away, may not be running at the same rate as your clock. The flow of time is relative.

5 The presence of mass, warps space-time around it. There is NO FORCE of Gravity. The sun doesn t pull on the Earth, making it stay in orbit. There is no pulling going on. The mass of the Sun causes time to run slow nearby it. It also distorts meter sticks. So someone far from the Sun will say our clocks are running slow and our meter sticks are either short or long, depending on the direction. We would say there clocks are running fast.

6 A simple example. You and a friend are out in interstellar space where there is no gravity. You throw a ball to your friend. The boxes represent space-time. Time is on the y-axis and distance is on the x-axis. With no mass around you and your friend, your clocks agree and so do your meter sticks. SO the boxes are square. Shortest path is perpendicular to vertical lines.

7 Suppose a massive object is now positioned below you and your friend. The massive object will make clocks run slow near to it, and it will distort distance. The timedistance box isn t square anymore. Clocks slow Massive Object Meter stick shrinks

8 30 What would you have to do to make space-time connected 1. Rotate the trapezoid so that the sides line up again 2. Allow objects to jump in space-time 3. Make the stupid trapezoid, square again % 0% 0%

9 But we have gaps in space-time. This can t happen. We must rearrange the grid. Ball follow curved path through Space-time. It is the only path available threw the universe. It still has to hit the vertical lines perpendicular, unless extra energy is given to it. Massive Object

10 Gravity is represented this way. Remember, space-time is the Universe. So an object has to follow the curvature of the universe.

11 Einstein realized that space-time must be curved near a massive object. He first tested by trying to explain the anomalous precession of Mercury s orbit. The warping of space-time, effects the potential energy of Mercury s orbit just a bit. Causing it to precess.

12 Einstein makes a prediction: Starlight passing close to the Sun should be bent as it follows the curvature of the universe. Not only does he predict light will bend, he calculates the precise angle that it will bend.

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14 To see stars near the Sun you need a total solar eclipse. First available was in Astronomer, Arthur Eddington makes the measurement.

15 Einstein was right. The effect is called Gravitational lensing. Light passing close to a massive object is bent, causing multiple images of the far way object.

16 Here is how it works.

17 Gravitational lensing of distant galaxies as their light passes close to a massive, nearer by galaxy.

18 The higher the mass the greater the bending of light.

19 Today, astronomers use gravitational lensing to measure the mass of objects.

20 Now on to black holes. The closer you get to a massive object the more time slows down. Not for you, but your clock runs slow compared to someone far away from the object. The most extreme case is the black hole. Imagine you and your friend are far from a black hole. Your friend decides to travel into the black hole. As your friend gets closer and closer to the Event Horizon, his clock runs slower and slower compared to yours.

21 When your friend reaches the Event Horizon, his time will finally slow to a stop. You will never see him enter the black hole. He will be frozen for eternity at the Event Horizon. But what about your friend. His clock is running normally. He falls right on in, threw the Event Horizon.

22 Now a little MIND BENDER. Some theories predict that black holes may contain worm holes, which will allow your friend to pop threw the black hole and re-emerge elsewhere in the universe.

23 Now a little MIND BENDER. Some theories predict that black holes may contain worm holes, which will allow your friend to pop threw the black hole and re-emerge elsewhere in the universe. If this is true, then you and your friend can stand together and look at him stuck at the Event Horizon!!!

24 So what s going on here? 1. Space-time has created another version of your friend. 2. What you are seeing is just the light coming from your friend. 3. This wouldn t happen. 33% 33% 33% 1 2 3

25 You are just seeing the image of your friend. At the event horizon time slows to the point that it takes forever for light to climb its way back out. Remember it isn t the pull of gravity do this. It is the slowing of time, near the black hole. So if your friend tries to wave as he is crossing the Event Horizon, it will take forever for the light from his moving hand to reach you. His hand appears frozen.

26 In reality, you would not be able to see your friend. The slowing of the clock causes the light to be red shifted. In other words, the wavelength is stretched out. At the event horizon the wavelength is stretched to infinity. To long to see anymore. This is called gravitational redshift. But note, this is not the same as a Doppler redshift. Here is how it works.

27 Imagine a particle, near a black hole, which is rapidly oscillating up and down. It will produce light, and since it is oscillating rapidly, that light will have a very short wavelength. But if you are far from the black hole, you will see the particle s clock running very slow. To you, the upward and downward motion is very slow. It is in slow motion. This means that the light that is produced will have a very long wavelength. And when the light arrives at your location, this is indeed the case.

28 The redshift is caused by the difference in the rates of the clocks. This effect has also been observed. Even from material falling into black holes. The amount of redshift is precisely what is expected from General Relativity.

29 One little problem left to deal with. Inside the Event Horizon, nothing, not even light can escape. I said earlier that the escape velocity inside the event horizon is greater than the speed of light. Nothing can travel faster than the speed of light, so nothing, not even light can escape.

30 So compare this to trying to throw a ball off of the Earth. Ball goes up, stops, and comes back down

31 What about light inside the Event Horizon? Ball goes up, stops, and comes back down Light goes up, stops and comes back down.

32 The speed of light is invariant. It is always the same for all observers. Inside the Event Horizon the speed of light will still be the same. There is no path out of the black hole. Space-time bends back around on itself and is closed. If you head in one direction you will return to the original spot.

33 Quiz #9 Suppose the Sun were to suddenly become a black hole with all of its mass falling into the black hole. Tell what would happen to the Earth (in terms of its orbit) and explain why.