Assess Your STR Knowledge

       
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These exercises will help you recall what you already know about the Special Theory of Relativity . . . and make you more aware of gaps in your understanding.

Questions

  1. What does E = mc2 mean? Is it the most important equation in STR? Why or why not?

  2. What is a "reference frame"? Why does it matter that a reference frame be "inertial"?

  3. What is the difference between the terms "invariant" and "constant"? How can the speed of light be invariant?

  4. What is spacetime?

  5. Can two events be truly "simultaneous"? Why or why not?

  6. Is there a difference between the lifetime of a particle at rest in a lab and the lifetime of an identical particle in an accelerator?

Problems

  1. Two twin babies, Tom and Spence, are born together in the year 2045. Tom is whisked off to a spaceship and takes a round trip at 0.95c (that is, 95% of the speed of light) to Alpha Centauri, while Spence lives a quiet life in Geneva, Illinois as the boy mascot of the Kane County Cougars. Tom returns in 2054. How old is Spence? How old is Tom? Does this make sense?

  2. An elementary particle has a lifetime T when isolated in a lab. If the same particle is brought to a speed of 0.99 c in an accelerator, what will its lifetime be from (A) the point of view of the lab scientists and (B) its own point of view?

  3. Find the rest energy of (A) an electron and (B) a proton in joules. Convert to eV, MeV, and GeV.

  4. The equation for the total energy of a particle is E2 = P2c2 + M2c4. It is commonly written by particle physicists as E2 = P2 + M2. Derive or show units for which this is possible.

  5. In the LHC, 7 TeV protons collide with 7 TeV protons. What is the relative speed between colliding protons in this case?

  6. What are the speeds of an 1 GeV electron and a 1 GeV proton? 10 GeV? 1 TeV? (Give answers as decimal fractions of the speed of light, e.g. 0.95 c.)