We live our lives in space-time as 4-dimensional ‘world-lines’ (actually hypervolumes) which point forwards at an angle less than 45 degrees in a coordinate system where c=1 and time is ‘up’.
To be a time-traveller requires a world-line which can curve back on itself as in the figure. Call the time-traveller Alice. Watching Alice, the red line, this is what you would see as time ‘flows by’. 'You' are not shown. Image a vertical world-line just to the left of the red s-curve - that's you.
Time A. You see Alice next to you and say hello.
Time B. A copy of Alice suddenly appears across the road and splits into two copies.
Time C. There are now three copies of Alice. Alice-1 is next to you and, maintaining conversational continuity, begins to cross the road. Alice-2 begins to walk backwards from the other side of the road towards Alice-1 (Alice 2 seems to be moving backwards in time - she’s talking backwards). Alice-3, meanwhile begins to walk farther away, turns round and waves to you. She is future-Alice.
Time D. Alice-1, walking forwards, and Alice-2, walking backwards, meet in the middle of the road and merge. They then pop out of existence. As they approached, they seemed to be travelling faster and faster towards each other.
Time E. You and Alice-3 get on with your lives. Alice-3 has lived through more time than you have. Between points B and D, Alice-3 could have told you information about your future.
I don’t comment on issues of conservation of mass-energy, information paradoxes or the fact that Alice travelled faster than light at B and D. Just the observer experience, which to happen this way requires no more than world-line continuity. And there was always only one Alice.
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Roy Simpson writes:
Nigel,
I am not sure whether you are aware of the interesting topics surrounding a paper (summarised here) by Greenberger and Svozil on QM Time Travel? They examine quantum paths which traverse from a later t2 to an earlier t1 (rather than take a non-classical path to later times).
The time travel happens in this universe (a bit like your Alice). The quantum aspect brings in probabilities though.
The trick is to use special 50/50 beam splitters at t1 and t2 respectively, one path of which (at t2) has its particle head back in time (to the t1 splitter as one input). There is a risk of getting stuck in this time loop, I would think. There are consistency conditions here though, so that back at t1 one cannot do anything inconsistent with the t2 one has just left, but freedoms remain at t1.
The classic story is of a man left money from a rich aunt whose money was of uncertain origin. Using the money he builds a quantum Time Machine to find out more from the aunt, and back in time he leaves some money for himself and his aunt using his knowledge of the future stock prices. Hence a consistent history!
Shifting from present-past to future-present the authors suggest that maybe the present is influenced by the future in a similar way. Some things happen the way that they do, to make the future happen as it must. Only some aspects of life would be affected this way though, and so we might not ordinarily notice. So where are these beam splitters then???
Roy
PS. Does anyone read these technical blogs?
Nigel Seel replies:
I read the referenced paper and got the drift. As you say, where ARE the beam splitters? Maybe they are components of the time machine no-one has figured out how to build yet.
I was also reminded that my throwaway remarks about Alice having to travel faster than light are void in general relativity, if the light cones can be sufficiently tipped in the local space-time geometry.
No-one reads the technical postings on this blog (apart from you). But who knows who may in the future? Or the past!
Seriously, one can't expect to contribute to the conceptual state of the art in physics unless one is a fully paid-up researcher. There's just too much going on that one doesn't know about. Intelligent speculation is just for fun, I guess.
