Special Relativity

Topics

• Motion is Relative • Michelson-Morley Experiment • Postulates of the Special Theory of Relativity • Simultaneity • Spacetime • Time Dilation • The Twin Trip • Addition of Velocities • Space Travel • Length Contraction • Relativistic Momentum • Mass, Energy, and E = mc2 • The Correspondence Principle

Mechanical Universe

• 41. The Michelson-Morley Experiment– In 1887, an exquisitely designed

measurement of the earth's motion through the ether results in the most brilliant failure in scientific history.

• http://www.learner.org/resources/series42.html

Motion is Relative

• Frame of Reference: place from which motion is observed and measured

• An object may have different velocities from different frames of reference

Relative Velocity

Michelson-Morley Experiment

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• Designed to prove the existence of the ether – the still reference frame

• Speed of light was the same no matter the direction relative to the earth’s motion

Null Result

Lorentz-Fitzgerald Contraction

• Length is contracted in the direction of motion

• Accounts for the null result• Amount of shrinkage:

2 21 v c

Special Theory of RelativityPostulates

• All laws of nature are the same in all uniformly moving frames of reference.

• The speed of light in free space has the same measured value for all observers, regardless of the motion of the source or the motion of the observer; that is, the speed of light is a constant.

The speed of a light flash emitted by the space station is measured to be c by observers on both the space station and the rocket ship.

Simultaneity• two events are simultaneous if they

occur at the same time.

From the point of view of the observer who travels with the compartment, light from the source travels equal distances to both ends of the compartment and therefore strikes both ends simultaneously.

Simultaneity• Two events that are simultaneous in one

frame of reference need not be simultaneous in a frame moving relative to the first frame.

Because of the ship's motion, light that strikes the back of the compartment doesn't have as far to go and strikes sooner than light strikes the front of the compartment.

Check Yourself

• Suppose that the observer standing on a planet sees a pair of lightning bolts simultaneously strike the front and rear ends of the high-speed rocket ship compartment. Will the lightning strikes be simultaneous to an observer in the middle of the rocket ship compartment?

Check Yourself• No; an observer in the

middle of the compartment will see the lightning that hits the front end of the compartment before seeing the lightning that hits the rear end.

• (a), we see both lightning bolts striking the ends of the compartment simultaneously according to the outside observer.

• (b), light from the front lighting bolt reaches the observer within the rocket ship.

• (c) Slightly later, light from the rear lightning bolt reaches this observer.

Time Dilation

• A light clock. A flash of light will bounce up and down between parallel mirrors and “tick off” equal intervals of time.

Time can be stretched.

Time Dilation

• Light Clock Movie – open from browser• Time Dilation Movie – open from

browser

Mechanical Universe• 42. The Lorentz Transformation

If the speed of light is to be the same for all observers, then the length of a meter stick, or the rate of a ticking clock, depends on who measures it.

• 43. Velocity and Time Einstein is motivated to perfect the central ideas of physics, resulting in a new understanding of the meaning of space and time.

• 44. Mass, Momentum, Energy The new meaning of space and time make it necessary to formulate a new mechanics.