Anders Sandberg (
07 May 1998 11:02:08 +0200

Hal Finney <> writes:

> Anders Sandberg, <>, writes:
> > Actually, the universe doesn't have to be very smart. Novikov makes a
> > careful analysis of the action principle on a billiard table with a
> > time-travel wormhole and a single billiard ball. In quantum mechanics
> > it turns out that the wavefunction for the inconsistent solutions
> > becomes identically zero, while some weird but consistent solutions
> > involving the billiard ball having interactions with
> > itself-from-the-future becomes possible. So the inconsistent stuff
> > doesn't happen, just weird but consistent stuff.
> There is a dramatic use of this in Robert Forward's novel Timemaster.

His use is essentially Novikov's billiard ball trick:

Place the backwards-in-time-wormhole ends like this (anything that
enters the entrance appears one second earlier at the exit). Send a
billiard ball towards the entrance:

Billiard ball #
-----------------------------------------> # Entrance to wormhole
A #
###### Wormhole exit

If you give it the right velocity, a future version of itself will
appear at the exit one second before it enters, and move forward to
block it from entering. PARADOX!!!

But Novikov shows that there is a consistent solution that the
universe might use instead: one second before the ball enters the
wormhole a ball emerges from the exit at a slanted angle, collides
with the ball and sends it into the entrance at an angle. This way the
universe remains consistent, momentum is conserved (OK, there are some
tricky considerations when you use wormholes to turn the momentum
vector about) and we avoid paradoxes.

> I still say that it is black magic. Once you start up one of these
> Novikov collisions, you won't be able to interfere. The whole path is
> pre-ordained. Any universes where you succeed get nulled out.

Actually, I think it is more clever than that. Agents still have their
free will, it is just that they or the world will not behave in such a
way that a paradox results. Suppose you were trying to make a paradox
on the Novikov table by shoving the ball around. When you are planning
to snatch any balls emerging from the exit and throw them into the
wastebasket, none will appear.

> Remember Asimov's short story about the crystals which dissolve *before*
> you add water? The military used them to create a bomb by using a cascade
> of stages to expand the time interval. Once a crystal dissolved there
> *had* to be ("had been") water added in a few hours. Drop the bomb in a
> heavily sealed case in an enemy country, and a bizarre, damaging typhoon
> would arise sufficient to bash open the bomb, along with everything else.
> Not contradictory or inconsistent, but paradoxical in my book.


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