Eric, if time was the dimension being traveled and the player was being surrounded by enemies, he would move backward in time to BEFORE the enemies were there, not to a different PLACE where there are no enemies.
That is an idea to use a forth spacial dimension to travel through 'options' or variations in the current 3D reality, and a good one. Basically, alternate realities.
I love how this game would work.
Now, there will be people who come on here and say things along the lines of, "it wouldn't work because we couldn't see the other options all at once. We only see 3D etc.'
I would like to remind them right now that we don't have to. A normal 3D view of the world with the ability to move through the 4th is enough.
Now how exactly would we create the 'random variation' in a way that could be used in actual gameplay?
It must have limits and be very predictable variation so that level design does not boil down to random 'sandbox' style generation.
I agree with you, rwilson, and the word for what you're describing in the last sentence is "continuity". We're only adding one additional linear dimension, and we're requiring change along this dimension to be continuous, which is precisely how the concept of "time as the fourth dimension" operates.
I guess the person who originally suggested this probably had in mind that "regular time" would be operating as normal, and this other extra dimension would be in addition. That would be kind of like two-dimensional time, with the player free to move back and forth in one of the two time dimensions. It is certainly an interesting idea.