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.