@Darby, there are times when a parallel line can be 'knocked' to the side and cross the line it is parallel to. This momentary connection is what I am referring to. Even in the beginning of an event can be the cross parallel (such as the moment of birth in a alternative dimension), they were one line then split into multiple lines that run along side one another parallel, but there was a moment when they were interconnected whether 'bumping' into one another or
being one and the same line at one moment in time.
Aside from the problem with the definition of parallel we now have the problem of simultaneity. Part and parcel to Special Relativity is the fall of the idea of absolute simultaneity of events. Different observers traveling at differing velocities with respect to the observed event will not agree on when the event occurred.
We have another ill defined situation regarding these parallel "time lines". I believe that we mean world lines, not time lines. The terms are from Minkowski.
We haven't defined what we mean here. These world lines do represent separate universes. In one instance we have two (or more) universes that are created entirely indepentant from one another. They have zero commonality and have no chance of ever communicating with each other. They may not even share common laws of physics. In the other instance we might be talking about the Many Worlds Interpretation view of the collapse of the probability wave. In that interpretation of quantum mechanics an event occurs, the probability wave collapses and reality divides into as many outcomes as are covered by the probability. But those universes aren't "parallel". A graph of their world lines would show them to be on diverging hyperbolic curves. They start out with a different outcome for the event. Each of those universes then evolves on its own based on the outcome. In a very short time those universes look much like the first instance above - they no longer have any real commonalities. They share the same laws of physics but they do not communicate and the difference between worlds is not "blue eyes instead of green".
I'll give you an example to ponder that isn't parallel worlds but it does exemplify the effects of divergence.
In talking about time travel the question is asked "what would you change?" Invariably the answer tends to be "Kill Hitler" and avoid WWII. The war was a bit more complex than that but let's go along with the answer. We kill Hitler and actually avoid WWII. But during the war about 80 million people in all theaters of the war died from all causes, That's both military and civilian deaths.
So what do we do with the 80 million? Do you think that they would have a small or a rather significant effect on the evolution of the world? Given that they currently represent zero new marriages and births what would their effect be on the current population if we prevent WWII? WWII began sometime between 1931 (Japanese invasion of Manchuria) and 1936 (Spanish Revolution with German and Italian intervention) so it's been about 80 years and three plus generations. Would you even be here? Eighty million new folks means 80 million alternate choices for spouses by 1945. Add two more generations and that's another 160 to 200 million people... It's possible that none of us would exist.
You see my point? Divergence. By today in this time travel altered world we get that "seven degrees of separation" feeling and are unlikely to have much in the way of commonality with history as we know it. The two world lines are not parallel, they are hyperbolic and the angle is increasing with the passage of time.
(Yes - I'm aware that Karinthy's theory was six degrees of separation. I like seven because just one more step and *poof*. No more old world.
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