Einstein’s Special Relativity

Postulates 1. The speed of light is a universal constant 2. All laws are the same in any inertial reference frame

Speed of Light James Clerk Maxwell determined the speed of electromagnetic transmission to be a constant value of C = 3.0x10 8 m/s James Clerk Maxwell determined the speed of electromagnetic transmission to be a constant value of C = 3.0x10 8 m/s Einstein recognized that this is the speed of light – the speed of a photon. He believed it to be an upper limit – nothing can go faster Einstein recognized that this is the speed of light – the speed of a photon. He believed it to be an upper limit – nothing can go faster Unlike sound, C does not depend on anything (pressure, temperature). It is the same value everywhere. Unlike sound, C does not depend on anything (pressure, temperature). It is the same value everywhere.

Inertial Reference Frames The laws of physics only work for inertial reference frames. The laws of physics only work for inertial reference frames. Galileo (1650) knew this, so we sometimes call these Galilean frames of reference. Galileo (1650) knew this, so we sometimes call these Galilean frames of reference. A Galilean frame of reference is one that is moving at a constant speed (not accelerating) with respect to something A Galilean frame of reference is one that is moving at a constant speed (not accelerating) with respect to something

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

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

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

Repercussions of the Postulates of Special Relativity S.R. says that light goes at one speed, regardless of how fast the observer is going. S.R. says that light goes at one speed, regardless of how fast the observer is going. S.R. also says that all basic laws (Newton’s 3 laws, Conservation of Energy, Conservation of Momentum) should be consistent as long as you are measuring from a inertial reference frame. S.R. also says that all basic laws (Newton’s 3 laws, Conservation of Energy, Conservation of Momentum) should be consistent as long as you are measuring from a inertial reference frame.

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

Simultaneity Imagine a person looking at four clocks on a wall. Each clock is set at exactly the same time. Imagine a person looking at four clocks on a wall. Each clock is set at exactly the same time. We say that each tick of the clocks is simultaneous We say that each tick of the clocks is simultaneous

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

To the stationary observer watching the stationary clocks, they seem to be in sync. To the stationary observer watching the stationary clocks, they seem to be in sync. To the observer running past the clocks, they seem to be out of sync. To the observer running past the clocks, they seem to be out of sync. What you observe is relative to how you are moving. Even things we take for granted as being universal such as time and distance are not constant. What is 1m or 1 second to you might be different than 1m and 1 second to me! What you observe is relative to how you are moving. Even things we take for granted as being universal such as time and distance are not constant. What is 1m or 1 second to you might be different than 1m and 1 second to me!