## Time waits for no man

Time is an odd thing. We say it passes, but it sometimes feels more like we are travelling through. As the old joke goes, we all travel through time – at a rate of one second per second.

While that might bring a smile, it does raise a question about time travel, because if one travels through time, one presumably travels through it at some rate or other, say ten years per minute. The problem with that it is that we are measuring a rate, which is a change of some variable with respect to another, but in this case we are measuring the rate of change of time with respect to time as well.

The time intervals over which the traveller is passing are measured in the usual way by a clock, but how does the traveller measure his time by? He could carry a clock with him, which he could then use to estimate his progress along the standard time scale. In other words the time traveller would somehow have to carry his own time scale with him which is different to the usual time scale.

Of course, Einstein’s Special Relativity shows that, in a way, we do carry our own time frames around with us, and if we are in motion relative to some other frame then time passes differently the two frames.  Of course, to simply travel in time, we would not want to travel in space, so we can’t use Special Relativity to allow us to use a different time frame, so far as I can see.

Also, we can only travel forward in time by using this loophole. No matter how fast we move relative to someone else, we both move forward in time, so we can’t use Special Relativity to go back in time and kill dear old Grandad.

Einstein’s General Relativity considers that space-time (the conjunction of space and time) possesses curvature, and some theories use this to allow backwards time travel. However these solutions produce “closed time-like curves” which is not so much time travel as a time loop, perhaps like the loop in “Groundhog Day” where Bill Murray’s character repeatedly awakes to the same day.

It appears that we need to look further for some way to travel in time. If we can’t use current physics, we will need to consider something more “science fiction” than modern physics. Of course science fiction time travellers don’t seem to explain their travels in more than a cursory way, because, after all, the mechanism is only secondary to the story line.

Two different possible mechanisms spring to mind.

Firstly, one way is to assume a sort of parallel world. A time traveller can enter this parallel world from any point in time and re-enter the standard universe at a different point, earlier or later in time. The traveller travels in time by analogously travelling in space in a world which has its own space-time with one of its space dimensions parallel to the conventional world’s time dimension.

Secondly, the author can conjecture a viciously curved space-time so that the characters can, at certain locations, move from one part of space-time to another part of time which is either earlier or later in the time dimension. Typically the character will “step sideways” or something to jump between times, either with the help of a machine or maybe not.

One such tale of the second sort is “By His Bootstraps” by Robert A Heinlein, is which the main character passes through a portal to a distant future, only to entangle himself with later (and, relatively, earlier) versions of himself. He encounters a mysterious character who identifies himself as “Diktor”.   I’ll leave it there, as I don’t want to spoil the story for those who haven’t read it yet.

An example of the first sort is “The Corridors of Time” by Poul Anderson, where the main character is recruited into a war raging up and down the “corridors of time”.

Most stories, however, don’t specify in more than a cursory way the physics that is supposedly employed by the time traveller.

The effects of time travel are what is explored by these stories. If the traveller goes back in time he or she must interact with the world at the earlier time from when he started. There are time stories in which the traveller changes things so the state of the future time from which he can is changed.

This is the premise behind the Terminator series of films, where the Cyborg assassin (played by Arnold Schwarzenegger) is sent back in time to kill the mother of John  Connor, the leader of the rebellion against the killer machines. Obviously, in the future from which the Terminator comes, John Connor is born so the Terminator is trying to change the future from which he comes.

The obvious paradox here is that the Terminator risks changing the future into one in which he was never created. In which case he would not be able to come back in time to kill Sarah Connor.

The other sort of time travel story treats time as if it were immutable. Any events that happen are eventually shown to have logically been the consequence of the time travel in the first place. For instance, the mysterious stranger on the street turns out to be the time traveller, keeping an eye on the earlier version of himself. All is explained so that the stream of events is logical both from the time sequential point of view and also from the point of view of the traveller. The aforementioned “By His Bootstraps” is a story of this sort.

Is it possible that events in the past could have changed? We would not know it! As far as we would be concerned the past event would have have always happened, since there would be a temporal progression from the past event to our current time. Of course the language is tricky here, as it does not handle such matters as changes to the past.

To use the physicists’ favourite analogy of a rubber sheet, if time is considered to be along one dimension of the sheet, and space along the other, then an event which changes the past is like someone pulling a point on the sheet to one side, which affects all the points from both the future and the past of the point which has been moved. But the sheet itself remains intact.

However, I think that this scenario is unlikely. There doesn’t seem (at the present time) any physical mechanism by which time travel could be achieved, and even though it appears that time travel is logically possible (under the sort of scenario as in “By His Bootstraps”) in a deterministic universe, the simplest conclusion is that time travel is most likely unachievable in this universe.