Gravity: Newton to Einstein

Newton’s Law of Universal Gravitation:

FF

Principle of Equivalence

• Q: How do you feel when you are inside an elevator that accelerates upward?

• A: You feel heavy

• So acceleration feels exactly the same as the force of gravity: Gravity and Acceleration are Equivalent

Principle of Equivalence

• Q: How do you feel when you are inside an elevator that accelerates upward?

• A: You feel heavy

• So acceleration feels exactly the same as the force of gravity: Gravity and Acceleration are Equivalent

Does light always move in straight lines?Gravitational

Lensing

(watch animations)

Gravitational Bending of Light: Gravitational

Lensing• By the Principle of Equivalence: If

acceleration causes light to bend… then gravity must cause light to bend.

Can you feel gravity?• Q: Can you feel the force of gravity acting on

you right now? Close your eyes a moment; what things can you feel pushing or pulling on your body?

• Q: Imagine you were in free fall inside a falling elevator so that gravity was the only force acting on you. What would it feel like? If you let go of an object while you were falling, what would the object do?

• Conclusion: If there is no way to feel the force of gravity, then gravity is not really a force.

Can you feel gravity?• Q: Can you feel the force of gravity acting on

you right now? Close your eyes a moment; what things can you feel pushing or pulling on your body?

• Q: Imagine you were in free fall inside a falling elevator so that gravity was the only force acting on you. What would it feel like? If you let go of an object while you were falling, what would the object do?

• Conclusion: If there is no way to feel the force of gravity, then maybe gravity is not really a force.

Einstein’s Gravity• Gravitational fields do not put forces on

objects. Instead they cause space-time to bend.

• Mass tells space-time how to bend and space-time tells mass how to move.

How can Einstein’s gravity explain this?

• Q: If you drop an object from rest, it’s path is not “bent”. It falls in a straight line.

• A: Path through space-time, not just space.

• Q: If Earth’s gravity has a particular strength, then it should cause all objects in free fall to curve the same amount. But that’s not true.

How can Einstein’s gravity explain this?

• Q: If you drop an object from rest, it’s path is not “bent”. It falls in a straight line.

• A: Path through space-time, not just space.

• Q: If Earth’s gravity has a particular strength, then it should cause all objects in free fall to curve the same amount. But that’s not true.

Tim

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Distance

An alternative to curved space

• Q: Can you see the curvature of space?

• A: No.

• An alternative model that is perhaps easier to visualize is that mass creates extra space in its vicinity. So you can have more space within the same enclosing surface area. For example, if you can’t fit all your clothes inside your suitcase, try putting a VERY massive (but small and dense) object inside. That will create more space inside the suitcase so you can fit more items inside.

An alternative to curved space

• Q: Can you see the curvature of space?

• A: No.

• An alternative model that is perhaps easier to visualize is that mass creates extra space in its vicinity. So you can have more space within the same enclosing surface area. For example, if you can’t fit all your clothes inside your suitcase, try putting a VERY massive (but small and dense) object inside. That will create more space inside the suitcase so you can fit more items inside.

Bending of light again

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