Rereading Poul Anderson's Time Patrol series reopens the issues of the two "Logic of Time Travel" articles at the beginning of this blog.
In the standard science fiction causality violation scenario, a time traveler originates in timeline 1 and travels to the past of that timeline but then "changes the past," thus generating timeline 2. One way to picture this is to represent timeline 1 by a horizontal line and timeline 2 by a second line emerging at an angle from the point representing the moment of the causality violation but this entails that, at that moment, the time traveler disappears from timeline 1 and creates around himself an entire new universe for timeline 2! I do not think that either the functioning of a time machine or the actions of a time traveler would be able to create all that organized matter and energy.
I think that it makes more sense to model temporal change on experienced change. Thus, in experienced change, a single temporal dimension connects states changed from to states changed to. Each of these states is a configuration of the entire three dimensional universe. Similarly, in temporal change, a second temporal dimension connects changing states. Each of these states is an entire four dimensional continuum with its own internal temporal dimension. It is these temporal dimensions that we call timelines 1, 2 etc.
A time traveler originates in timeline 1 but either transforms timeline 1 into timeline 2 or causes timeline 2 to succeed timeline 1 along the second temporal dimension - these are alternative descriptions of a single process. In The Shield Of Time, Poul Anderson presents another scenario: a quantum change in space-time-energy transforms timeline 1 into timeline 2.
If a story were set in the timeline 2 of the quantum change scenario but without time travelers, then readers would recognize an alternative history or parallel universe story. However, "parallel" implies simultaneity or co-existence whereas I argue that timeline 1 does not coexist with timeline 2 but preexists and causes it along the second temporal dimension. In that dimension, timeline 1 is not contemporary with but earlier than timeline 2 and therefore is inaccessible to a time traveler who can either remain in timeline 2 or advance to timeline 3 but not return to timeline 1. That is how Anderson describes the relationship between the current and deleted timelines in the Time Patrol series.
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