9.3 "Folding" Space (Without Special Provisions)
Description
This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
9.3 "Folding" Space (Without Special Provisions)
Another concept which pops into the minds of science fiction lovers
when considering FTL travel is that of "folding" space. Basically, the idea
is to bring two points in space closer together in some way so that you can
travel between them quickly without having to "actually" travel faster than
light. Of course, by our definition of FTL travel in Section 6.1 (where the
light you are "racing" against goes through normal space between the
starting and ending points) this would still be considered FTL travel.
A frequently used approach for picturing this idea is to think of two
dimensions of space represented by a flat sheet of paper. Then consider
yourself at some point on the paper (call this point "o"). If you want to
travel to some distant point ("D"), you simply fold/bend/crumple/etc the
paper and place "o" and "D" close to one another. Then its just a matter of
traveling the now short distance between the points.
Again, we see an FTL concept which is built in order to get around the
problem of the light speed barrier. However, we will see, once again, that
the second problem of FTL travel is not so easily fixed.
We begin to understand this when we consider again the sheet of paper
discussed above. Every object in that two dimensional space has a place on
the paper. However, because objects may be moving, their position depends on
the time at which you are considering them. Basically, if you are sitting at
"o", you imagine every point on that sheet of paper as representing space as
it is "right now" according to your frame of reference. However, as we have
discussed, what is going on "right now" at a distant location TRULY depends
on your frame of reference. Two observers at "o" in two different frames of
reference will have two different ideas of what events should be represented
on the paper as going on "right now". This difference in simultaneity
between different frames of reference is what allowed for the "unsolvable
paradox" problem to exist in the first place. Thus, even though you "fold"
the paper so that you don't "actually" travel faster than light, you don't
change the fact that you are connecting two events at distant points (your
departure and your arrival) which in another frame of reference occur in the
opposite order. (In the other frame of reference, you aren't just bending
space, you're bending space-time such that you travel backwards in time.) It
is that fact which allowed the unsolvable paradoxes to be produced.
In the end, unless special provisions are present, one can use this
form of FTL travel in our FTL bullet example (I refer you back to the
listing of events in Section 8.3). Op will fold space in his frame of
reference to connect the passing event with the event "*", while the third
observer will fold space from his frame of reference to connect the event
"he sees the victim die" with an event "O learns of the victims death before
the FTL bullet is sent". Thus, you can used this method to produce an
unsolvable paradox as we discussed earlier.
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