I recently read Palle Yourgrau's book "A World Without Time" about Gödel's contribution to the nature of time in general relativity.
Gödel published his discovery of closed timelike curves in 1949. Many years later (in 1961), S. Chandrasekhar and James P. Wright pointed out in "The geodesic in Gödel's universe" that these curves are not geodesics, and hence Gödel's philosophical conclusions might be questionable. Again some years later, the philosopher Howard Stein pointed out that Gödel never claimed that these curves are geodesics, which Gödel confirmed immediately. Again much later other physicists have computed that these closed timelike curve must be so strongly accelerated that the energy for a particle with a finite rest mass required to run through such a curve is many times its rest mass. (I admit that I may have misunderstood/misinterpreted this last part.)
- This makes me wonder whether any particle (with finite rest mass) actually traveling on a closed timelike curve wouldn't violate the conservation of energy principle.
- I vaguely remember that light will always travel on a geodesic. Is this correct? Is this a special case of a principle that any particle in the absence of external forces (excluding gravity) will always travel on a geodesic?
- Is it possible for a particle to be susceptible to external forces and still have zero rest mass?
- Is it possible that Chandrasekhar and Wright were actually right in suggesting that Gödel's philosophical conclusions are questionable, and that they hit the nail on the head by focusing on the geodesics in the Gödel's universe?