9.5.4 A Special Frame of Reference for the purpose of FTL Travel
Description
This article is from the Relativity and FTL Travel FAQ, by Jason W. Hinson jason@physicsguy.com with numerous contributions by others.
9.5.4 A Special Frame of Reference for the purpose of FTL Travel
The fourth and final provision is (again) something of an extension to
the previous one. This provision also forbids certain FTL signals, but it
does so in a very specific and interesting way (there will be no question as
to which trips are allowed and which are not). To explain this provision, I
will start by describing a situation through which the provision could be
applied. I will then explain how the provision works, given that particular
situation.
Now, as I describe the situation, I will use the idea of a "special
field" to implement the "special frame of reference". However, it isn't
necessary to have such a special field to imagine having a special frame of
reference. I am simply using this to produce a clear illustration.
So, join me now on a journey of the imagination. Picture, if you will,
a particular area of space (a rather large area--say, a few cubic
light-years if you like) which is permeated with some sort of field. Let
this field have some very particular frame of reference. Now, in our
imaginary future, say we discover this field, and a way is found to
manipulate the very makeup (fabric, if you will) of this field. When this
"warping" is done, it is found that the field has a very special property.
An observer inside the warped area can travel at any speed he wishes with
respect to the field, and his frame of reference will always be the same as
that of the field. This means that the x and t axes in a space-time diagram
for the observer will be the same as the ones for the special field,
regardless of the observer's motion. In our discussion of relativity, we saw
that in normal space, a traveler's frame of reference depends on his speed
with respect to the things he is observing. However, for a traveler in this
warped space, this is no longer the case.
For example, consider two observers, A and B, who both start out
stationary in the frame of reference of the field. Under normal
circumstances, if A (who starts out next to B) began to travel with respect
to B, then later turned around and returned to B, A would have aged less
because of time dilation (this is fully explained in Section 4.1 of Part II
if you are interested). However, if A uses the special property of this
field we have introduced, his frame of reference will be the same as B's
even while he is moving. Thus, there will be no time dilation effects, and
A's clock will read the same as B's.
Now, for the provision we are discussing to work using this special
field, we must require that all FTL travel be done while using this field's
special property. How will that prevent unsolvable paradoxes? Well, to
demonstrate how, let's go back to our FTL bullet example and consider one of
two cases. In case 1, we will let Op's frame of reference be the same as the
frame of reference of our special field. With this in mind, let's go through
the events listed in Section 8.3 once again; only this time, we will require
any FTL travel to use the special property of the field we have discussed.
So, here is the new list of events given that the special frame of
reference of the field is the same as Op's frame. Remember, our new
provision requires that any FTL trip will have to use the property of our
special field, thus the object/person/message traveling FTL will be forced
to take on the frame of reference of our special field (Op's frame in this
example). (It may be good for you to review the original list before reading
this one):
1. Again (just as in our original argument), as observers O and Op pass by
one another, Op uses some method to send out an FTL bullet. This time,
as the FTL method is activated, our new provision requires the bullet's
frame of reference to become the frame of reference of the special
field. However, since Op's frame is the same as that of the special
field in the case we are considering, the bullet will still be sent out
from Op's frame of reference, just as it was in our original argument.
2. Again, the event marked "*" occurs after the "passing event" in Op's
frame, so again the bullet can travel FTL to strike and kill a victim
at "*", and again that event occurs before the "passing event" in Os
frame.
3. Again, a third observer (who is in O's frame of reference) witnesses
the victim's death, and again the death will have occured before the
bullet was sent in his frame of reference. Thus again this third
observer will have information about an event which will happen in his
future.
But that is where the "agains" stop. You see, in the original argument event
(4) was possible in which the third observer sends this information about
the future to O via an FTL signal. In the frame of reference of O (and the
third observer), that FTL signal could be sent after the victim's death and
arrive at O before the passing event (when the bullet was fired). But now,
as the FTL signal is sent, it must take on the frame of reference of the
special field. That frame of reference is the frame of Op, and in that frame
the victim dies after the bullet is fired. So, in the new reference frame of
the message (forced on it by the provision we are making) the bullet has
already been sent, and thus the FTL message cannot be received by O before
the bullet is sent.
From the frame of reference of the third observer, he simply cannot get
the FTL signal to go fast enough (in his frame) to get to O before the
bullet is sent. From Op's frame of reference (that of the special field) any
FTL signal (even an instantaneous one) can theoretically be sent using our
provision. However, from O's frame (and that of the third observer) some FTL
signals simply can't be sent (specifically, signals that would send
information back in time in Op's frame of reference--look again at Diagram
8-1 to make this clear). This prevents the unsolvable paradox.
We can also consider case 2 in which the special frame of reference of
the field is the same as O's frame of reference. In this case, any FTL
traveler/signal/etc must take on O's frame of reference as it begins its FTL
trip. Thus, as Op passes O and tries to send the FTL bullet from his frame
of reference, the bullet will have to take on O's frame as it begins is FTL
trip. But in O's frame of reference, the event "*" has already occurred by
the time O and Op pass one another. Therefore, from the FTL bullet's new
frame of reference (forced on it by the provision we are making), it cannot
kill the victim at the event "*" since that event has already occurred in
this frame. Thus, the paradox is obviously averted in this second case as
well because of our provision.
So, in the end, if all FTL travelers/etc are required to take on a
specific frame of reference when they begin their FTL trip, then there will
be no way an unsolvable paradox can be produced. This is because it takes
two different FTL trips from two _different_ frames of reference to produce
the paradox. Under this provision, if you are sending tachyons, the tachyons
must only travel FTL in the special frame of reference. If you are folding
space, the folding must be done in the special frame of reference. If you
are using the special field itself to allow FTL travel, then you must take
on the field's frame of reference. Etc. If these are the cases, then there
will be no way to produce an unsolvable paradox using any of the FTL
concepts.
As a final note about this provision, we should realize that it does
seem to directly contradict the idea of relativity because one particular
frame of reference is given a special place in the universe. However, we are
talking about FTL travel, and many FTL concepts "get around" relativity just
to allow the FTL travel in the first place. Further, the special frame
doesn't necessarily have to apply to any physics we know about today. All
the physics we have today could still be completely relativistic. In our
example, it is a special field that actually has a special place in the
physics of FTL travel, and that field just happens to have some particular
frame of reference. Thus, the special frame does not have to be "embedded"
in the makeup of the universe, but it can be connected to something else
which just happens to make that frame "special" for the specific purpose of
FTL travel.
And so, we have seen the four provisions which would allow for the
possibility of FTL travel without producing unsolvable paradoxes. For the
case of the real world, there is no knowing which (if any) of the provisions
are truly the case. For the purposes of science fiction, one may favor one
of the provisions over the others, depending on the story one wishes to
tell.
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