What is Relativity? Relating measurements in one reference frame to those in a different reference frame moving relative to the first 1905 - Einstein s first paper on relativity, dealt with inertial reference frames (Special Relativity) 1915 - Einstein published theory that considered accelerated motion and its connection to gravity (General Relativity)
Special Relativity GR describes black holes, curved spacetime, and the evolution of the universe; very mathematical SR deals with a special case case of motion - motion at a constant velocity (acceleration is zero) SR is restricted to inertial reference frames - relative velocity is constant
Reference Frames Inertial Reference Frame:
Reference Frames Inertial Reference Frame: A reference frame in which Newton s first law is valid
Reference Frames Which of these is an inertial reference frame (or a very good approximation)? a. Your bedroom b. A car rolling down a steep hill c. A train coasting along a level track d. A rocket being launched e. A roller coaster going over the top of a hill f. A skydiver falling at terminal speed
Standard Reference Frames S and S
Galilean Transformations of Position If you know a position measured in one inertial reference frame, you can calculate the position that would be measured in any other inertial reference frame... Suppose a firecracker explodes at time t. The experimenters in reference frame S determine that the explosion happened at position x. Similarly, the experimenters in S (which moves at a velocity v) find that the firecracker exploded at x in their reference frame. What is the relationship between x and x?
Galilean Transformations of Velocity If you know the velocity of a particle in one inertial reference frame, you can find the velocity that would be measured in any other inertial reference frame... Suppose the experimenters in both reference frames now track the motion of an object by measuring its position at many instants of time. The experimenters in S find that the object s velocity is u. During the same time interval Δt, the experimenters in S measure the velocity to be u.
Galilean Transformations of Velocity Use u and u to represent the velocities of objects with respect to reference frames S and S. Find the relationship between u and u by taking the time derivatives of the position equations. (Recall: u x = dx/dt)
Example An airplane is flying at speed 200 m/s with respect to the ground. Sound wave 1 is approaching the plane from the front, sound wave 2 is catching up from behind. Both waves travel at 340 m/s relative to the ground. What is the speed of each wave relative to the plane?
A simpler example... Ocean waves are approaching the beach at 10 m/s. A boat heading out to sea travels at 6 m/s. How fast are the waves moving in the boat s reference frame?
Einstein s Principle of Relativity All the laws of physics are the same in all inertial reference frames.
Maxwell s Contribution Maxwell s equations are true in all inertial reference frames Maxwell s equations predict that electromagnetic waves, including light, travel at speed c = 3 x 10 8 m/s Therefore, light travels at speed c in all inertial reference frames.
Implications
Implications Recent experiments use unstable elementary particles, π mesons, that decay into high energy photons of light. Every experiment designed to compare the speed of light in different reference frames has found that light travels at speed c in every inertial reference frame, regardless of how the reference frames are moving with respect to each other.
Example Use a Galilean transformation to determine the bicycle s velocity.
Example Repeat your measurements but measure the velocity of the light wave as it travels from the tree to the lamppost.
Example Repeat your measurements but measure the velocity of the light wave as it travels from the tree to the lamppost. Δx differs from Δx u differs from u BUT experimentally, u = u What does this tell us about our assumptions regarding the nature of time?
Events and Measurements Event: a physical activity that takes place at a definite point in space and a definite instant in time. Spacetime coordinates (x, y, z, t)
Measurements The (x, y, z) coordinates of an event are determined by the intersection of the meter sticks closest to the event. The event s time, t, is the time displayed on the clock nearest the event.
Stop and Think A carpenter is working on a house two blocks away. You notice a slight delay between seeing the carpenter s hammer hit the nail and and hearing the blow. At what time does the event hammer hits nail occur? a. at the instant you hear the blow b. at the instant you see the hammer hit c. very slightly before you see the hammer hit d. very slightly after you see the hammer hit
Synchronization of Clocks Detection of light wave sent out from origin. How long does it take for light to travel 300 m?
Finding the time of an event Experimenter A in a reference frame S stands at the origin looking in the positive x-direction. Experimenter B stands at x = 900 m looking in the negative x-direction. A firecracker explodes somewhere between them. Experimenter B sees the light flash at t = 3.0 µs. Experimenter A sees the light flash at t = 4.0 µs. What are the spacetime coordinates of the explosion?
Finding the time of an event
Simultaneity When two events occurring at different positions take place at the same time. An experimenter in reference frame S stands at the origin looking in the positive x-direction. At t = 3.0 µs she sees firecracker 1 explode at x = 600 m. A short time later, at t = 5.0 µs, she sees firecracker 2 explode at x = 1200 m. Are the two explosions simultaneous? If not, which firecracker exploded first?
Stop and Think A tree and pole are 3000 m apart. Each is suddenly hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant in time. Nancy is at rest under the tree. Define event 1 to be lightning strikes tree and event 2 to be lightning strikes pole. For Nancy, does event 1 occur before, after, or at the same time as event 2?
A Thought Experiment... A long railroad car is traveling to the right with a velocity v. A firecracker is attached to each end of the car, just about the ground. Each firecracker will make a burn mark on the ground when where they explode. Ryan is standing on the ground; Peggy is standing in the exact center of the car with a light detector.
The Event in Ryan s Frame
The Event in Peggy s Frame
The real sequence of events in Peggy s reference frame
Relativity of Simultaneity Two events occurring simultaneously in reference frame S are not simultaneous in any reference frame S moving relative to S.
Stop and Think A tree and a pole are 3000 m apart. Each is hit by a bolt of lightning. Mark, who is standing at rest midway between the two, sees the two lightning bolts at the same instant of time. Nancy is flying her rocket at v = 0.5c in the direction from the tree toward the pole. The lightning hits the tree just as she passes by it. Define event 1 to be lightning strikes tree and event 2 to be lightning strikes pole. For Nancy, does event 1 occur before, after, or at the same time as event 2?
Time Dilation Time is no longer an absolute quantity: it is not the same for two reference frames moving relative to each other. Time interval between two events Whether two events are simultaneous Depends on the observer s reference frame.