9.4 Space-Time Manipulation (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.
9.4 Space-Time Manipulation (Without Special Provisions)
The final concept we will discuss before looking at special provisions
is what I call space-time manipulation. The idea is to change the
relationship between space and time in a particular region so that the
limitation of light speed no longer applies. This is basically confined to
the realm of general relativity (though the more simplified concept of
"changing the speed of light" can also be handled by the arguments in this
section). We won't worry too much about the particulars of how GR can be
used to produce the necessary space-time, because the arguments that will be
made will apply regardless of how you manipulate space-time in the region of
interest.
There are two general types of space-time manipulation to consider. The
first I will call "localized", because the space-time that is effected is
that surrounding your ship (or whatever it is that is traveling FTL). A
basic example of this is the idea for FTL travel is presented in a paper by
Miguel Alcubierre of the University of Wales (the paper is available via the
world wide web (URL=http://arXiv.org/abs/gr-qc/0009013)). In the paper,
Alcubierre describes a way of using "exotic matter" (matter with certain
properties which may or may not exist) to change the space time around a
ship via general relativity. This altered space-time around the ship not
only keeps the ship's clock ticking just as it would have if the ship
remained "stationary" (in its original frame of reference), but it also
"drives" the ship to an arbitrarily fast speed (with respect to the original
frame of reference of the ship before it activated the FTL drive).
The second type is thus "non-localized", and it involves the
manipulation of space-time which at least effects the departure and arrival
points in space-time (and perhaps effects all the space-time between). A
basic example of this is the idea of a wormhole. A wormhole is another
general relativity concept. Again, exotic matter is used, but here
space-time is effected so that two distant locations in space are causally
connected. You can enter one "mouth" of the wormhole and exit from the other
very distant "mouth" so as to travel FTL (by our definition in Section 6.1).
Both of these concepts get around the light speed barrier problem, but
again we will argue the case for the problems with unsolvable paradoxes. To
do this, we will first carefully describe the situation in which a couple of
FTL trips will occur. Let's call the starting point of the first trip "A". B
will then be the destination point of that trip. Also, consider a point (C)
which is some distance to the "right" of B ("right" being defined by an
observer traveling from A to B), and finally consider a corresponding point
(D) which is to the right of A. Diagram 9-1 uses two dimensions of space (no
time is shown in this diagram) to depict the situation (at least from some
particular frame of reference).
Diagram 9-1
y
|
| A B
|
| D C
|
+--------------x
(x and y are spatial dimensions)
Now, let's go back to the FTL bullet example through which we first
explained the unsolvable paradox problem. In this case, the FTL bullet
travels from A to B through space-time manipulation. (The event "the bullet
leaves A" is event (1) in our list from Section 8.3). This means that all
the space-time along the bullet's path between A and B might be affected by
the space-time manipulation. Thus, we can no longer assume (after the
bullet's trip) that a space-time diagram such as those we have drawn (which
only apply to special relativity, not GR) will still apply. However, the
space between D and C does not have to be effected by the FTL drive. Because
of that we can make our argument by considering the following events:
* (a) Op sends an FTL bullet from A to B (using space-time manipulation)
as the "passing event" occurs
* (b) The bullet strikes and kills a victim at B (event "*" in Diagram
8-1).
* (c) The third observer witnesses the death. However, now (because the
FTL travel of the bullet may have changed the space-time between A and
B, we can no longer assume that our space-time diagram of the situation
is correct. It may be that with the changed space-time, this third
observer's frame of reference no longer has the victim's death
occurring before the passing event. However, we can continue as
follows:
* (d) The third observer sends a signal over to C using ordinary
(slower-than-light) means.
* (e) An observer at C sends an FTL signal to D. Since the space-time
between C and D need not be effected by the bullet's FTL travel, our
space-time diagrams can be applied.
* (f) An observer at D receives the signal before event (a) (and thus
before the bullet effected any space-time).
* (g) The observer at D can now send a signal over to O, and O can
receive it before (a) occurs.
The above events show that even though the space-time may be changed
between A and B during the bullet's trip, the O observer can still know
about and use the fact that the victim was killed in order to prevent the
victims death. We use the same arguments we did in the section concerning
the "second problem" (Section 9.1 ), except that the two FTL portions (the
bullet and the signal from the third observer) are sent from two different
locations so that neither is affected by the other's effects on space-time.
Thus, as long as there are no special provisions, this form of FTL travel
will still allow for unsolvable paradoxes.
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