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Lecture 8

Department

PhysicsCourse Code

PHY100H1Professor

Vatche DeyirmenjianLecture

8This

**preview**shows half of the first page. to view the full**3 pages of the document.**The General Theory of Relativity

Consider the following thought experiments in which air resistance is ignored. Bob is in an

elevator that is stationary at the surface of the Earth. He drops a tennis ball and sees it accelerate

to the floor of the elevator at 10 m/s2. Alice is in an elevator that is far from any stars and is

accelerating upwards at 10 m/s2. She releases a tennis ball. Alice observes it accelerate to the

bottom of the elevator at 10 m/s2 since the floor accelerates upwards at 10 m/s2. This connection

between Alice and Bob’s measurements motivated Einstein to state

The Principle of Equivalence

In a small enough region of space, the results of experiments in a gravitational field are

equivalent to those obtained by an accelerated observer.

The Principle of Equivalence is only valid for a small region of space. How do we describe what

happens in a large region of space? Events such as the collision between a ball and the floor of

an elevator occur at a particular location and time. Space-time is a four-dimensional coordinate

system for identifying events. In Special Relativity, space and time measurements depend on the

motion of observers. Combining three space dimensions (x,y,z) and one time dimension t into a

single system (x,y,z,t) allows for different observers to compare their measurements consistently.

For example, there is an expression involving x, y, z, and t called the space-time distance or

separation that is the same for all observers.

One way of quantifying Bob’s observation is to say that there is a Newtonian gravitational force

or field responsible for the motion of the ball. However, Galileo determined that in the absence

of air resistance all objects, independent of their mass, accelerate at the same rate to the ground.

This is now a well tested fact. Furthermore, there is no gravitational field in Alice’s elevator, but

she sees the ball fall to the floor. This shows that the mass of a falling object and the Newtonian

idea of a gravitational force are not necessary to explain gravity. If the right space-time

coordinate system could be developed, then gravitational effects could be understood in a new

manner. Einstein did this in his General Theory of Relativity, which he finalized in 1915.

In General Relativity (GR), objects and light move along geodesics in space-time. A geodesic is

the path of shortest distance between two events or points in space-time. The geometry or

curvature of space-time is determined by the mass of objects in the universe. The geometry of

space-time may be flat or curved like that of the surface of a table or basketball. Here are some

of the consequences of GR.

Bending of Light in a Gravitational Field

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