## Nonparadoxical Time Travel

Most science
fiction fans are aware of the problems with time travel (or at least
with travelling backwards through time). One of the most commonly
quoted paradoxes is the *grandfather paradox*, in which a person
travels backwards in time and murders an ancestor, causing themselves
to not be born and therefore not be able to commit the murder.

There are possible
several solutions to this. It could be that backwards travelling is
completely excluded by the laws of physics – although at present we
have numerous examples in which it could happen and no strong reasons
to expect it forbidden. It also could be that when such a time
machine is turned on it immediately explodes. One argument to this
effect is that the cosmic microwave radiation that fills the Universe
would fall into the time machine, then travel back to the future and
fall in again, and continue to repeat until so much energy is exiting
the machine that it melts down. This is certainly a possibility that
must be considered.

It is possible that
the Universe branches off into different futures, as this has been
seriously discussed as an interpretation of quantum mechanics. Then
the murder would occur in a different branch of the Universe, and not
affect the future of the time traveller.

There is yet
another option that may be the most interesting – at least for
discussions of free will. It is possible that the laws of quantum
mechanics cause the paradox to be avoided through bad luck or random
chance. In the case of the grandfather paradox, this could mean that
a small chance of the gun misfiring becomes a certainty, or that even
a marksman finds his aim is off, or that the grandfather has a high
probability of tripping and avoiding the shot.

This explanation
can be thought of in terms of the Feynman path integrals. For those
who are not familiar with these, the path integrals are one methods
of doing calculations in quantum mechanics. The basic idea is that
the probability of a particle to get from point A to point B is
calculated by first calculating the effects on a wave (which contains
information on the original particle) which travels along one
specific path. Then the effects of all waves following all possible
paths are added together. The waves interfere with each other, and
the resulting sum (or more accurately the square of the sum) gives
the probability that the particle has arrived at point B.

Extending this
method to time travel means considering closed paths in which a
particle travels forward in time and then backwards in time to
interfere with itself. But anytime a wave propagates along a closed
curve, it must only contain certain frequencies which correspond to
the length of the path. The resonant frequencies are strengthened by
interference, while non-resonant frequencies decay away quickly.

And so for a time
travelling particle, the decay of non-resonant frequencies mean that
the probabilities are different from those of a particle which only
travels forward in time. The resonant frequencies will have a higher
probability of occurring.

Of course quantum mechanics on the macroscopic scale of human time travels is far too complex to calculate, but it is possible that a similar sort of quantum resonance can occur which excludes paradoxes. The time traveller killing his grandfather means his future wavefunction changes, which in turn means the wavefunction when travelling backwards in time changes, which means the wavefunction for the murder changes, and so on. This process is analogous to the particle whose non-resonant frequencies cancel themselves out, and lead to a boost of those frequencies that can travel around the closed path without destructive interference.

In practical terms,
this would mean an event which is non-paradoxical – no matter how
improbable – gets a boost in probability while paradoxical events
get suppressed. And in the case of the grandfather paradox, it means
that something will always happen to prevent the murder.