Anders Sandberg (
07 May 1998 21:02:13 +0200

Hal <> writes:

> It seems clear to me that the Novikov table could not exist and be
> consistent with free will. (BTW do you have a reference to Novikov's
> paper?)


Time machines and the Principle of Self-Consistency as a consequence
of the Principle of Stationary Action (II): the Cauchy problem for a
self-interacting relativistic particle

We consider the action principle to derive the classical,
relativistic motion of a self-interacting particle in a 4-D
Lorentzian spacetime containing a wormhole and which allows
the existence of closed time-like curves. In particular, we
study the case of a pointlike particle subject to a
`hard-sphere' self-interaction potential and which can
traverse the wormhole an arbitrary number of times, and show
that the only possible trajectories for which the classical
action is stationary are those which are globally
self-consistent. Generically, the multiplicity of these
trajectories (defined as the number of self-consistent
solutions to the equations of motion beginning with given
Cauchy data) is finite, and it becomes infinite if certain
constraints on the same initial data are satisfied. This
confirms the previous conclusions (for a non-relativistic
model) by Echeverria, Klinkhammer and Thorne that the Cauchy
initial value problem in the presence of a wormhole `time
machine' is classically `ill-posed' (far too many
solutions). Our results further extend the recent claim by
Novikov et al. that the `Principle of self-consistency' is a
natural consequence of the `Principle of minimal action.'

> It's the classic paradox. You watch the hole, and when
> nothing comes out, you throw a ball in. Oops, it was supposed to have
> come out one second ago. What happened?

A fast ball comes out of the exit when you don't expect it and kicks
your ball in much faster than you intended? :-)

Anders Sandberg                                      Towards Ascension!                  
GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y