Thought experiment: Time happens, part I

Physics of the Mundane

Adam Johnston

 

In previous labs, you have observed and learned the following concepts, along with many others:

bullet Electric charges naturally repel or attract.  “Same” charges repel, while “opposite” charges attract.  This feature is what keeps atoms and molecules together, so this is a very important force to have around!
bullet Moving electric charges (i.e., “electricity”) produce magnetic forces.  Magnetic forces can repel or attract one another.
bullet Waves are a means of transferring energy from one place to another.  Sound is one example of a wave, as is light.  With any wave, diffraction and interference are standard features that may be more observable than the wave itself.  Also, even though no material travels with a wave, the wave itself travels with a particular speed from one place to another. 

 

Having learned all of the above, you and a buddy should be able to think about the following problems.  Work on these in order, one at a time.  After each problem we will debrief as a class.

 

  1. You are standing in a glass box with two electrons (each with a negative charge).  You pinch each electron between your thumb and forefinger (you have really really really really small hands), one in your left and one in your right hand, one above the other.  What would the electrons do when you let go of them, assuming that the only influences they each experience are the result of one another?
  2. Imagine the same situation as above, except that your glass box is moving at a constant velocity.  What would the electrons do according to your perspective when you let go of them.  Again, ignore any influences other than those caused by the electrons themselves.
  3. Now imagine that your physics professor is standing outside the glass box.  He is standing on the ground while you are traveling past him in your glass box.  So, the physics professor observes two moving electrons.  What forces does the physics professor observe for these electrons?  How does this affect what the electrons will do?

 

At this point, you should make sure that you understand everything above.  Then, you can go on to the final question of this thought experiment:

 

  1. You, inside the box, and your physics professor, outside the box, both witness the electrons separating from one another.  In other words, you both witness the same event occur.  What is different about this event from each of your perspectives?


 

Thought experiment: Time happens, part II

Physics of the Mundane

Adam Johnston

 

In the previous thought experiment, you showed that for some situations, two different observers could actually measure two different amounts of time for the same event.  This phenomenon is known as time dilation, and is admittedly very very strange according to our everyday perspectives.  But, it is a strangeness that physics must rectify.  Albert Einstein showed that everything could be rectified with the theory of special relativity. 

 

Special relativity basically states that since time is a measurement that is relative to one’s frame of reference, something else must hold constant.  (Our common sense experience holds that time should be the same for all observers, but thought experiment #1 showed that this isn’t always the case.)  What Einstein found to be truly constant is the speed of light.

 

For this thought experiment, consider the following two scenarios.  In picture A, you are sitting inside a box and observing a beam of light as it travels from the bottom of your box to the top.  In picture B, you are observing the same box and the same beam of light from the outside.  Think about the following:

  1. Compare the amount of distance that the beam of light is observed to travel from each perspective.  Which observed distance is longer?  Why?
  2. Compare the time each beam of light is observed to travel.  Which is longer?  Why?
  3. How do your answers support the idea of time dilation in special relativity?

 

 

 

If you get bored with the thought experiment above, you could also do this one:

In the spaceship diagramed below, you shoot two laser pulses (at the speed of light) from the center of your craft to the ends.  Your spaceship is moving from left to right.

A.        From your perspective (inside the spaceship), compare the time it takes for each beam of light to hit a wall.  Remember that the speed of light is the same in all directions and from all perspectives.

B.        From an outsider’s perspective, compare the time it takes for each beam to hit a wall.  Consider how much distance each pulse of light must travel to reach a wall (as seen from this perspective).

C.        How do your answers support the idea of time dilation in special relativity?