special relativity - university of sydneytime dilation – “moving clocks run slow” “proper...

Copyright © 2008 Pearson Education Inc., publishing as Pearson Addison-Wesley

PowerPoint® Lectures for University Physics, Twelfth Edition – Hugh D. Young and Roger A. Freedman

Lectures by James Pazun

Adapted by Anne Green

Special Relativity


Questions to understand for this Topic

•  What are Einstein’s two principles of relativity?

•  What is the relativity of simultaneity?

•  What is time dilation?

•  What is length contraction?

•  What is mass-energy equivalence?


Einstein’s First Principle •  The laws of physics are the

same everywhere. Newton’s Laws work no matter what your point of view (your frame of reference).

•  Inertial Frame of Reference: Newton’s First Law holds. A body acted on by no net force moves at constant velocity (which may be zero).

Example


Einstein’s Second Principle •  The speed of light in a vacuum is a constant.

•  It doesn’t matter how fast you are going or in which direction you travel or if it is the source or observer who is moving.


The Relativity of Simultaneity •  Events which are simultaneous in one reference frame will

not be simultaneous in a second inertial reference frame moving relative to the first frame.


Simultaneity & the lightning flashes Stanley gets both lightning flashes at the same time. He is midway

between A & B. Hence, the flashes must have been emitted at the same time, in his frame of reference.

Mavis is sitting in the middle of the train which has moved forward in the time it takes for the lightning flashes to travel to her. She receives the flash from the front of the train first, then some time later, she receives the flash coming from the back of the train. Flash 1 arrives in less time than the light travel time for a distance of half the train. Flash 2 takes more time. Mavis says the flashes were not emitted at the same time.

Since she knows she is in the middle of the train, she would have received them at the same time if they occurred simultaneously.

Both versions are legitimate. Both observers agree that Mavis does not receive the flashes at the same time.


Time dilation – “moving clocks run slow” “Proper time” is the time interval between two events that occur at the same location in space (i.e. the time interval is measured on one clock by Mavis).

Stanley measures a longer time interval for the same events. He says Mavis’ clock is running slow. They disagree on the time separation of the two events.


Derivation of Time Dilation


Lengths parallel or perpendicular to motion “Proper length” is the length of an object in its rest frame.

Moving objects are contracted in directions parallel to motion. The length of a moving object is measured by 2 observers separated in distance who measure each end at the same agreed time.

Lengths perpendicular to the relative motion are not contracted.


Length contraction parallel to direction of motion


Derivation of Length Contraction


Observers measure lengths differently People in the spaceship measure its proper length as 400m.

Two observers on the ground measure a shorter length.

People in the spaceship measure the distance between the ground observers to be even shorter. All results are valid.


The Lorentz Factor To change the space-time coordinates of an event measured in one frame of reference to those in another frame of reference moving at high speed relative to the first frame, we use a set of equations called the Lorentz transformations. These equations calculate how distance and time change between the two inertial frames.

The Lorentz factor (γ) tells us the strength of any relativistic effects. Remember c = 300,000 km/sec

u = 0.1c gives γ = 1.005

u = 0.5c gives γ = 1.15

u = 0.99c gives γ = 7.1

Note: γ is always ≥1


Relativistic momentum & energy As velocities near the speed of light, the Lorentz (γ) factor means the momentum and kinetic energy of the body becomes larger and larger. The total energy also becomes huge.


Equations for Energy and Momentum Relativistic Momentum:

Relativistic Kinetic Energy:

Total Energy of a particle:


Mass – Energy Equivalence Einstein’s famous equation links rest energy with

mass:

Eo = mc2

special relativity - university of sydneytime dilation – “moving clocks run slow” “proper...

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