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  This week is all about special relativity.   Newtonian physics breaks down at relativistic speeds which are  those approaching the speed of light.  The laws that govern physical events in this realm can conceptually be grasped, especially with the aid of visual media.  This weeks web assignment will deal with this visualization.

    The first concept in understanding relativity is that moving clocks run slower.  The is because the speed of light is the same in all inertial reference frames.   To see this phenomenon for yourself view the  flashlet below.  After you have gone through it once go back and answer these questions. 

        1.  Is it a problem that there is no time units specified?  Why?

        2.  Why is the sounds total speed greater in the moving reference frame?

        3.  Why can't the light in the moving frame have a greater total speed then that of the stationary frame. 

        4.  Explain in your own words why moving clocks run slower.

    Here is an applet that lets your view both the stationary and moving events simultaneously.   There are no questions associated with this applet.

    Use this applet to derive the time dilation equation on the last page. 

Length Contraction

    The simple statement that the speed of light is the same in all inertial reference frames produces some profound results.  You have just seen how a moving reference frame creates a time dilation.  What you will now see is this same statement requires a simultaneous length contraction.   Moving reference frames appear length contracted in the direction of travel.   Use these applets to explore this phenomenon and answer the questions.    

       1. In a few sentences explain what experimental evidence muons pose for the validity of relativity.

    Length contraction is a consequence of special relativities time dilation.  This applet shows that if moving clocks run slower then moving objects must also have to contract in length.   View this applet and derive the equation for length contraction from that of time dilation.

    To understand some of the mysteries of length contraction view this applet.  This applet is for your own curiosity, there are no questions associated with it.  

Simultaneity

    One of the most counter-intuitive problems to resolve in relativity is that of simultaneity.  Events that classically appear to happen at the same time can't in the realm of relativistic speeds.  From this difficult question of simultaneity comes a number of fun and interesting paradoxes.  This first applet simply looks a simple problem and goes through each event.  Answer each of the 5 questions at the end of the applet. 

    This next applet is very similar and a run through it will help grasp the basic concept of simultaneity.   Answer the questions associated with this applet.

        1.  When the detector is on the train why is it that the light traveling in the direction of the train appears to move at the same speed as the light moving opposite the direction of the train?  Is there a problem with the applet not performing a velocity addition?  

Pole in a Barn Paradox   

    To explore the counter-intuitive problems with simultaneity I will pose a paradox for you to resolve.  This is a famous one involving a moving pole and stationary barn.   Use of the simultaneity applets should aid in resolving this paradox.  

    A runner is carrying a pole of proper length 20m.  Holding the pole parallel to the ground the runner moves at a speed v=0.97*c  (ya pretty fast).   As he approaches the barn of proper length 10m a farmer opens the barn door to let him in.  As soon as the runner and the pole are completely inside the barn the farmer closes the door.  There is also a back door to the barn with another farmer standing by it.   As soon as the runner approaches, this farmer opens the door and closes it again as soon as the pole is completely out of the barn.

    After some discussion the farmers agree that the pole was only 5m long and that for a brief interval of time, both barn doors were closed with the runner and his pole inside the barn.  The runner, however, sees the barn contracted to 2.5m and his 20 m pole simply can't fit inside.  How can this paradox be resolved?  Who is right?