Chapter 15 Assignment Answers

Ch 15 Review Answers:

  1. Space-time is a concept that unifies space and time, so that space and time are no longer separate and different concepts, they are two aspects of the same thing.  
  2. Yes. When you remain at rest you are still traveling in time.
  3. (a) Yes, light travels through space, at c = 300,000 km/s.
    (b) No, light does not travel through time - time does not pass for a light wave.  
    (c) Well, I would say yes - light travels through space-time since it travels through space. (The text's answer is "No." - without explanation.)
  4. Time dilation is the "stretching" or slowing of time due to an object's motion through space.  
  5. To say "motion is relative" means that the number that you calculate for an object's velocity depends on the frame of reference from which you measure it.  
  6. No. The speed of light will be the same no matter what the relative speeds of the source and the observer.
  7.  To say "the speed of light is constant" means not only that its speed never changes in a particular reference frame, but also that its speed is not relative - everyone will measure the same speed no matter the frame of reference they use to measure it.
  8. The first postulate of special relativity says that the laws of physics are the same in all inertial reference frames.
  9. The second postulate of special relativity says that all observers will measure the same speed of light in a vacuum.
  10. Since d = ct for light, d/t = c, the speed of light.  
  11. The light does not appear to be moving faster because, according to the postulates of Special Relativity, the speed of light is constant for all observers.
  12. If we see someone else's "clock running slowly," they will see our clocks running slowly by the same factor.  
  13. When a flashing light source approaches, the frequency (number of flashes/time interval) of the light flashes will increase, but the velocity of the light flashes will remain the same.  
  14. (a) The stay-at-home twin in the Twin Paradox experiences one frame of reference.
    (b) The traveling twin in the Twin Paradox experiences (at least) two frames of reference during her trip.  
  15. Yes, it is possible for a person with a 70-year life span to travel farther than light travels in 70 years (70 light-years). Since time for the moving person slows down, a person traveling at speeds near the speed of light to travel several times farther than 70 light-years during their lifetime. To them, the trip still seems like 70 years, but relative to us (at rest), it might be several hundred years! 

Ch 15 Think & Explain Answers:

  1. If you were on a smooth-riding train with no windows, you:
    (a) could not sense the difference between uniform motion and rest. Velocities are relative.
    (b) could sense the difference between accelerated motion and rest. Accelerated motion could be detected by the sloshing of water in a bowl, for instance.
  2. If you are playing catch with a friend in a moving train and you toss a ball in the direction that the train is moving, the speed of the ball is increased (by the speed of the train) for an observer standing at rest outside the train. For instance, if you are riding in a train moving at 40 m/s (relative to Earth) and you toss the ball at a speed of 5 m/s (relative to the train) in the direction that the train is moving, the outside observer (measuring relative to Earth) would measure the speed of the ball as 45 m/s. When your friend throws the ball back to you, opposite the direction the train is moving, the outside observer would measure its speed as 35 m/s.  
  3. If you are shining a light in the direction that the train is moving, an outside observer would measure the speed of the light wave to be "c," the same as you. If you shine the light in the direction opposite to the trains velocity, the outside observer would still measure the speed of the light wave to be "c," the same as you.  This is a postulate of Special Relativity.
  4. Yes, an astronaut traveling with a speed less than the speed of light can travel farther than 10 000 light years in 10 years - as measured by her. Due to relativistic time dilation, 10 years on the astronaut's clock could correspond to much more than 10 years on our (at rest) clock.  
  5. No. No matter how fast you go, time still moves forward for you. In fact, time always seems to move "normally" for you - it's the other guy whose clocks are running slowly! 
  6. When you look out into the Universe on a starry night, the light that reaches your eyes from distant stars may have been traveling for tens of millions of years. Therefore, you see that star as it was tens of millions of years ago - as it was at the time that the light left it. So when you look out into space, you are really looking back into time.
    Light travels about a foot in a picosecond, so when you look at a person across the room, you really don't see them as they are now, you see them as they were several picoseconds ago! Everywhere you look, you are looking back in time!

Ch 15 Think & Solve Answers:

  1. Josie travels in a spaceship to a start 4 light-years distant at a speed of 0.8c.
    (a) How much older is Jose (her twin) when Josie returns?
    The distance that Josie travels is 2(4 light years) = 8 light years for the round trip. Since d = vt, t = d/v = (8 light-years)/(0.8c) = 10 years. Jose is 10 years older.

    (b) How much older is Josie when she returns?


    (c) The twin situation is not symmetrical, since Josie, the traveling twin, experienced an acceleration and traveled in two different frames of reference, while Jose, the stay-at-home twin, experienced just one frame of reference.
  2. Since Joe measures his trip as taking 5 years, Joe's age upon return will be 30 years + 5 years = 35 years. Due to time dilation, Joe's daughter will measure the time for Joe's trip as:
    t =35.4 years
    Therefore, on Joe's return, his daughter's age will be 6 years + 35.4 years = 41.4 years. Hmmm....

last update April 28, 2009 by JL Stanbrough