Assess Your STR Knowledge
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.
- What does E = mc2 mean? Is it the most important equation in STR? Why or why not?
- What is a "reference frame"? Why does it matter that a reference frame be "inertial"?
- What is the difference between the terms "invariant" and "constant"? How can the speed of light be invariant?
- What is spacetime?
- Can two events be truly "simultaneous"? Why or why not?
- 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?
- 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?
- 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?
- Find the rest energy of (A) an electron and (B) a proton in joules. Convert to eV, MeV, and GeV.
- 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.
- In the LHC, 7 TeV protons collide with 7 TeV protons. What is the relative speed between colliding protons in this case?
- 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.)