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Lecture9 General Relativity

# Lecture9 General Relativity - General Relativity Hawley...

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1 General Relativity Hawley & Holcomb, Chapter 8

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2 Equivalence Principle Let’s imagine that you are in an elevator. What happens when the elevator begins to go up? What happens when the elevator begins to go down? What happens when the elevator moves at constant speed? What would happen when the wire on which the elevator is suspended is cut? Let’s imagine that you are an astronaut on board a space station. Why do you think you are a weightless? What would you do to make “gravity” in flight?
3 Acceleration = Gravity Newton’s 2 nd law of motion relates force to acceleration F = m a Newton’s force of gravity relates gravitational force to the spatial distribution of other bodies F = m g Therefore, a = g , for a freely falling body But why were we justified in using the same mass? Mass can be measured in two completely different ways: Mass could be measured by applying a force and measuring acceleration Mass could be measured by measuring the gravitational force (weight) of an object In principle, these two masses may not have been the same.

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4 Inertial Mass = Gravitational Mass Inertial mass, m inertial , may be defined by Inertial force = m inertial a Gravitational mass, m gravity , may be defined by Gravitational force = m gravity g Then, Newton’s equation becomes m inertial a = m gravity g Simultaneously drop two objects with different masses from some height in the absence of air drag (inside vacuum tube on the Earth, or anywhere on the Moon), and they will reach the bottom simultaneously. Therefore, m inertial = m gravity
5 Equivalence Principle Gravity can be canceled or mimicked by acceleration: A small object in free fall does not experience gravity (the reason that only small objects in free fall are oblivious to gravity is explained on a following page). An object accelerating at a constant rate experiences the same conditions as a stationary object in a gravitational field. When gravity is canceled by acceleration, all the laws of physics, including the laws of special relativity, are still perfectly valid; the free-falling frame and the inertial frame are completely equivalent. Terminology: Freely falling frame is a reference frame, that is, the point of view of an observer, that experiences no force other than the force of gravity (examples: planets in the solar system, satellites and the international space station, space shuttle with its engines powered off are all in the state of free fall).

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Lecture9 General Relativity - General Relativity Hawley...

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