H7     Problems and Suggestions


  1. Read the Wikipedia entry on what is meant by “Occam's razor” or “Ockham's razor”. Then think about the ether, parallel universes and the extra 6-8 dimensions that modern string theories postulate.
  2. Calculate as in H3 the radius of curvature of a space-time diagram which depicts the situation on the surface of the sun.
  3. Draw flat, unrolled Epstein diagrams for the 4 paths (o, a, b, c) of section H5 as seen by an observer at rest at the origin.
  4. Calculate the net gain of proper time according to GTR and the corresponding loss according to STR as described in H4, for a general parabola 
    v(t) = k – k • t  and  h(t) = k • t – 0.5 • k • t2 describing an object that returns after 2 seconds to its place of departure. Take the first derivative to the total gain and show that for k = g it is a maximum!
  5. Bertrand Russell used for the “principle of maximum proper time” the somewhat rakish expression “principle of cosmic laziness'. To what extent is that justified?
  6. Obtain somehow a sphere attached to two “horns” as described in section H5 (if necessary, simply use two funnels and two tubes). You can then use long, narrow strips of paper attached to this surface to determine the space-time paths of different objects that fall through the earth. What does the total length of the paper represent?
  7. Let a light beam pass through the tunnel of the model of task 6. Do you see clearly that it takes a little longer than an observer in the OFF would expect? This is precisely the Shapiro effect, which we will calculate in I3.
  8. Now shoot a rocket through the earth of the model of task 6. In contrast to the light beam the traversal time for the rocket is reduced thanks to gravity!
  9. A sense of 'straight lines' on curved surfaces (so-called ‘geodesics’) can be obtained by wrapping an ace bandage around your ankle. Which path does the fabric ‘itself’ wish to take? (suggested by Hans Walser)
  10. Read the first three chapters of [34] – “Black Holes & Time Warps - Einstein's Outrageous Legacy“.
  11. The principle of Fermat for the path of a light beam is valid even in GTR! What does this mean for a beam of light, that passes close to the edge of the sun?
  12. Enjoy the two books by Harald Fritzsch in which Newton, Einstein and a Bernese physicist of the present discuss the STR and GTR ([35] for the STR and [36] for the GTR). Newton shows his brilliant and critical mind as he is willing to learn, but first must be presented with good arguments. Einstein is repeatedly impressed how much progress experimental physics has made. But that the STR and GTR have passed all experimental tests does not surprise him one bit ...


Following the confirmation by Eddington of his predicted value of light deflection at the solar limb Einstein was transformed by the press virtually overnight into a celebrity of the first order. Occasionally, he enjoyed this role, but it was mostly just annoying to him. He has demonstrated that himself with different comments:


"To punish me for my contempt of authority, Fate has made me an authority myself."    [17-9]


“In the past it never occurred to me that every casual remark of mine would be snatched up and recorded. Otherwise I would have crept further into my shell.”     [17-15]