Einstein’s Special RelativityEinstein’s Special Relativity

PostulatesPostulates

1.1. The speed of light is a universal constantThe speed of light is a universal constant

2.2. All laws are the same in any inertial All laws are the same in any inertial reference framereference frame

Speed of LightSpeed of Light

James Clerk Maxwell determined the speed of James Clerk Maxwell determined the speed of electromagnetic transmission to be a constant electromagnetic transmission to be a constant value of C = 3.0x10value of C = 3.0x108 8 m/sm/s

Einstein recognized that this is the speed of light Einstein recognized that this is the speed of light – the speed of a photon. He believed it to be an – the speed of a photon. He believed it to be an upper limit – nothing can go fasterupper limit – nothing can go faster

Unlike sound, C does not depend on anything Unlike sound, C does not depend on anything (pressure, temperature). It is the same value (pressure, temperature). It is the same value everywhere.everywhere.

Inertial Reference FramesInertial Reference Frames

The laws of physics only work for The laws of physics only work for inertial inertial reference frames.reference frames.

Galileo (1650) knew this, so we Galileo (1650) knew this, so we sometimes call these sometimes call these GalileanGalilean frames of frames of reference.reference.

A Galilean frame of reference is one that is A Galilean frame of reference is one that is moving at a moving at a constant speedconstant speed (not (not accelerating) with respect to somethingaccelerating) with respect to something

Inertial Reference FramesInertial Reference Frames

Standing still, you are in a Galilean Standing still, you are in a Galilean reference frame. You could use a law of reference frame. You could use a law of physics, say Fnet = ma on an object (a physics, say Fnet = ma on an object (a book on a desk) to find its weight.book on a desk) to find its weight.

Galilean Reference FramesGalilean Reference Frames

If you are on a train If you are on a train moving at a constant moving at a constant speed, you could speed, you could weigh the book and weigh the book and the result would be the result would be identical. The train identical. The train and the classroom and the classroom are both Galilean are both Galilean reference frames.reference frames.

Non-Inertial Reference FrameNon-Inertial Reference Frame

An accelerating frame of An accelerating frame of reference is not a reference is not a Galilean reference Galilean reference frame. The laws of frame. The laws of physics will not be physics will not be consistent. For consistent. For example, if you are in example, if you are in free-fall (an elevator or free-fall (an elevator or the space shuttle), the the space shuttle), the book will have zero book will have zero weight!weight!

Repercussions of the Postulates of Repercussions of the Postulates of Special RelativitySpecial Relativity

S.R. says that light goes at one speed, S.R. says that light goes at one speed, regardless of how fast the observer is regardless of how fast the observer is going.going.

S.R. also says that all basic laws S.R. also says that all basic laws (Newton’s 3 laws, Conservation of Energy, (Newton’s 3 laws, Conservation of Energy, Conservation of Momentum) should be Conservation of Momentum) should be consistent as long as you are measuring consistent as long as you are measuring from a inertial reference frame. from a inertial reference frame.

Repercussions (cont’d)Repercussions (cont’d)

Suppose I am on a plane, traveling at a Suppose I am on a plane, traveling at a constant speed of ½ the speed of light. constant speed of ½ the speed of light. The plane has a head light, shining The plane has a head light, shining forward. From the point of view of forward. From the point of view of someone on the ground, the light from the someone on the ground, the light from the plane will appear to be going 1½ times plane will appear to be going 1½ times the speed of light. This breaks Einstein’s the speed of light. This breaks Einstein’s first postulate. So something must be first postulate. So something must be wrong.wrong.

SimultaneitySimultaneity Imagine a person looking at four clocks on a Imagine a person looking at four clocks on a

wall. Each clock is set at exactly the same wall. Each clock is set at exactly the same time. time.

We say that each tick of the clocks is We say that each tick of the clocks is simultaneoussimultaneous

SimultaneitySimultaneity Now have a friend drive by the clocks at a Now have a friend drive by the clocks at a

high speed. As he goes by, the closest clock high speed. As he goes by, the closest clock will appear fast compared to the further will appear fast compared to the further clocks. This is because it takes time for the clocks. This is because it takes time for the light to arrive from the clocks at different light to arrive from the clocks at different distances.distances.

To the stationary observer watching the To the stationary observer watching the stationary clocks, they seem to be in sync.stationary clocks, they seem to be in sync.

To the observer running past the clocks, they To the observer running past the clocks, they

seem to be out of sync.seem to be out of sync.

What you observe is relative to how you are What you observe is relative to how you are moving. Even things we take for granted as moving. Even things we take for granted as being universal such as time and distance are being universal such as time and distance are not constant. What is 1m or 1 second to you not constant. What is 1m or 1 second to you might be different than 1m and 1 second to me!might be different than 1m and 1 second to me!