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Note: "Lineland" here is borrowed from the Flatland novella.

If you were placed as an observer inside a "Lineland" universe, i.e. a Minkowski spacetime that has one space dimension and one time dimension, how would you as an observer determine which dimension is space and which is time if you weren't told beforehand? Would space look different than time in such a geometry?

Edit: As suggested in the answer, I meant that there would be particles available to be observed.

This is somewhat related to my previous question Are we living in a Universe with 3 time dimensions and 1 spatial dimension?. In it I was trying to ask if having 3 dimensions of time and 1 of space is the same as saying 3 dimensions of space and one of time, because I assumed that the real difference between the properties of space and the properties of time is the number of dimensions of each type.

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If you just look at a space-time diagram without any particles (or observers), there is really no physical difference. However, if there are particles, there can't exist both spacelike and timelike particles. Otherwise, paradoxes such as tachyonic antitelephone rise, in which information can be sent into past. So as an observer, it is simple to determine which direction is time: the one where your 2-velocity is directed, just as in our familiar world with 3 spacial dimensions.

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  • $\begingroup$ Thanks. Yes, I meant that there would be particles to be observed. I edited my question to clarify that. $\endgroup$ – sashoalm Feb 16 '15 at 13:55

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