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.

Gravity is represented this way. Remember, space-time is the Universe. So an object

has to follow the curvature of the universe.

The higher the mass the greater the bending of light.

• 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.

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.

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.

So compare this to trying to throw a ball off of the Earth.

Ball goes up, stops, and comes back down

What about light inside the Event Horizon?

Ball goes up, stops, and comes back down

Light goes up,stops and comes back down.

• 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.

Shining a laser inside a black hole

It is important to see that being in a black hole is not like being trapped in a room.

• There is no wall. There is no boundary. You can chose to go one direction, and as you travel you will eventually return to the same spot. It doesn’t matter if you go left, right, up, down, forward or backward. You always come back to the same spot.

• Inside the black hole, your new universe is closed, in 4 dimensional, space-time.

• There is no “outside”. There is only infinite “inside”.

Cosmology notes for later…

• Our entire universe is similar to being in a black hole. There is no path out of the universe. There is also no edge.

• It is possible for the universe to be finite in extent, and still never have a boundary. A closed universe like this would have no path out. Outside of the universe has no meaning.

• It is also impossible to see an edge to the universe. The edge of the universe is located at YOU! Anything else is in the past.

A Flat Lander (2-D people)

• A flat lander only has two dimensions. They are infinitely thin. Even their eyes.

• We are 3-D people. We can see in three dimensions. Our retina on the back of our eye is two dimensional. But a Flat Lander’s retina has to be a line. It is 1-D.

• The Flat Lander has no concept of up and down. Only forward/backward and side-to-side. They can’t even look up/down.

Effects of being two dimensional

• In some aspects, life would be similar to what we do every day. You could move, east, west, north and south. You would just not know what up/down is.

• What if you encountered a tree. And you took some measurements. What would you conclude?

What would you conclude about the tree?

1 2 3

33% 33%33%1. The tree must grow

out of the surface because trees are tall.

2. The tree is a circle that gets bigger with time

3. The tree is a line the extends through the universe

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• You might conclude that a tree is a circle. When trees grow the circle gets bigger.

• You would know nothing about the trees leaves, or how tall it is. Just that the tree is a circle.

• What about two Flat Landers that are living on the Earth. One says that they are going to go East for the rest of their life. They say good-bye and start heading East. What will happen?

What will happen to the 2-D Flat lander?

1 2 3

33% 33%33%1. Since he lives in a 2-D

world he will never be seen again.

2. He will drowned in the ocean when he tries to cross it.

3. He will eventually return home, even if he continues East.

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How about a Valley? What would the Flat Lander conclude as they travel in the valley?

What would the Flat Lander conclude traveling through a valley

1 2 3

33% 33%33%1. There is a force that

is pulling on them from the center of the valley.

2. There is a force pulling downward from below them.

3. Space is 4 dimensional

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How about a Valley? What would the Flat Lander conclude as they travel in the valley?

Force

• We are 3-D people living in a 4-D universe. For us, time does go by, but we can not move in time. It doesn’t seem like a coordinate, like x, y, and z.

• We conclude (like Newton and the Flat Lander) that the Earth goes around the Sun because the Sun pulls on us with a force. It holds us in orbit.

• A 4-D person would say that the Sun isn’t holding you there. It is the shape of the universe that is holding you there. The Sun’s mass is warping the universe in 4-D.

• The Flat Lander can’t understand how it is possible to travel in a straight line and return to the place of origin.

• A 3-D person says it is possible because the Flat Lander isn’t really moving in a straight line. They are moving on a curved path around the Earth.

• Albert, 2-D, Einstein, would figure it out. He would realize that even though it is nearly impossible to visualize the 3rd dimension, adding another dimension can explain the result.

The same thing works for us.

• In Euclidean space we can write the Space-time metric:

• Δs2 = Δx2 + Δy2 + Δz2 - c2Δt2

• We simply attach time onto the other 3 dimensions. But what does it mean?

• X, Y, and Z are all perpendicular. They are orthogonal to each other. And ct is orthogonal to each of them. How can this be?

Trying to be 4 Dimensional

• Think of the house you grew up in. Now think of every single room in the house.

Trying to be 4 Dimensional

• Think of the house you grew up in. Now think of every single room in the house.

• Now do it again, but this time think of all rooms simultaneously. NO tour through the house. All at the rooms at the same time.

• A four dimensional person would have no difficulty doing this.

• When you think, you think chronologically. Even your thoughts are bound by time. You think of one thing occurring before another.

• A 4-D person has no such constraints. They can think of things all at the same time.

• If you travel through 3-D space, it would appear that you would have no problem traveling in a straight line. What else is there out in outer space?

• But the Flat Lander on the Earth also thought they were traveling in a straight line. Because they couldn’t comprehend 3-D.

• We are aware that near the Earth or Sun, we can’t travel in a straight line. But we usually say that is because the Earth is exerting a Force on us. Making our 3-D path be curved.

• In 4-D we are not moving in a straight line, because the 4-D universe is curved. It is the only path we have to move in.