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PART IV: Faster Than Light Travel--Concepts and Their "Problems"
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This is PART IV of the "Relativity and FTL Travel" FAQ. It
discusses the various problems involved with FTL travel and how they
apply to particular FTL concepts. This section is written under the
assumption that the reader understands the concepts discussed in PART
I of this FAQ which should be distributed with this document.
For more information about this FAQ (including copyright
information and a table of contents for all parts of the FAQ), see the
"Relativity and FTL Travel--Introduction to the FAQ" portion which
should be distributed with this document.
Contents of PART IV:
6. Introduction to the FTL Discussion
6.1 A Few Notes On The Meaning of FTL Travel
7. The First Problem: The Light Speed Barrier
7.1 Effects as One Approaches the Speed of Light
8. The Second Problem: FTL, Causality, and Unsolvable Paradoxes
8.1 What is Meant Here by Causality and Unsolvable Paradoxes
8.2 How FTL Travel Implies Violation of Causality
8.3 How We Get Unsolvable paradoxes.
9. FTL Concepts with these Problems in Mind
9.1 Tachyons (Without Special Provisions)
9.2 Using a Special Field/Space/etc. (W/o Special Provisions)
9.3 "Folding" Space (Without Special Provisions)
9.4 Space-Time Manipulation (Without Special Provisions)
9.5 Special Provisions
9.5.1 Consistency Protection
9.5.2 "Producing" Restricted Space-Time Areas
9.5.3 A Special Frame of Reference for the purpose of FTL Travel
10. Some Comments on FTL Travel in Star Trek
10.1 Which Provision is Best for Explaining Warp Travel
10.2 Subspace as a Special Frame of Reference
10.3 The "Picture" this Gives Us of Warp Travel
10.4 Some Notes on Non-Warp FTL Travel and Time Travel in Trek
10.5 To sum up...
11. Conclusion.
6. Introduction to the FTL Discussion
The following discussion completes the purpose of this FAQ by
considering faster than light travel with relativity in mind. After
this brief introduction, I will discuss the general problems
associated with FTL travel. These problems will apply differently to
different FTL concepts, but I need to go over the general idea behind
the problems first, while we will consider their applications to
specific FTL concepts in the section which follows. Finally, because
this FAQ is written for the rec.arts.startrek.tech newsgroup, I will
go over some notes and arguments for why "warp" drive should be
explained in a particular way in order to get around the FTL problems
and give us what is seen on the show.
6.1 A Few Notes On The Meaning of FTL Travel
Before we begin the discussion, I wanted to go over the basic
idea of what we mean by FTL travel. To do so, we should start by
noting that most of space-time through which we would want to travel
is fairly flat. For those who have not read part III of this FAQ,
that means that special relativity describes the space-time fairly
well without having resorting to general relativity (which applies
when a gravitational field is present). Sources of gravity are few
and far between, and even if you travel "close" to one, it would have
to be a significant source of gravity in order to destroy our flat
space-time approximation. Now, some FTL travel concepts we consider
will involve using certain areas of space-time which are not flat (and
I will go over them when we get there); however, the important thing
for us is that all around these non-flat areas, the space-time can be
approximated fairly well as being flat.
Thus, for our purposes, we can use the following to describe FTL
travel. Consider some observer traveling from point A to point B. At
the same time this observer leaves A, a light beam is sent out towards
the destination, B. This light travels in the area of fairly flat
space-time outside of any effects that might be caused by the method
our observer uses to travel from A to B. If the observer ends up at B
in time to see the light beam arrive, then the observer is said to
have traveled "faster than light".
Notice that with this definition we don't care where the observer
is when he or she does the traveling. Also, if some space-time
distortion is used to drive the ship, then even if the ship itself
doesn't move faster than light _within_ that distortion, the ship
still travels faster than the light which is going through the normal,
flat space-time that is not effected by the ships FTL drive. Thus,
this ship still fits our definition of FTL travel.
So, with this basic definition in mind, let's take a look at the
problems involved with FTL Travel.
7. The First Problem: The Light Speed Barrier
In this section we discuss the first thing (and in some cases the
only thing) that comes to mind for most people who consider the
problem of faster than light travel. I call it the light speed
barrier. As we will see by considering ideas discussed in Section 1
(PART I of the FAQ), light speed seems to be a giant, unreachable wall
standing in our way. I note that various concepts for FTL travel may
deal with this problem, but here we simply want to talk about the
problem in general.
7.1 Effects as One Approaches the Speed of Light
To begin, consider two observers, A and B. Let A be here on
Earth and be considered at rest for now. B will be speeding past A at
a highly relativistic speed as he (B) heads towards some distant star.
If B's speed is 80% that of light with respect to A, then gamma for
him (as defined in Section 1) is 1.6666666... = 1/0.6. So from A's
point of view, B's clock is running slow and B's lengths in the
direction of motion are shorter by a factor of 0.6. If B were
traveling at 0.9 c, then this factor becomes about 0.436; and at 0.99
c, it is about 0.14. As the speed gets closer and closer to the speed
of light, A will see B's clock slow down infinitesimally slow, and A
will see B's lengths in the direction of motion becoming
infinitesimally small.
In addition, If B's speed is 0.8 c with respect to A, then A will
see B's energy as a factor of gamma larger than his rest-mass energy:
E(of B in A's frame) = gamma*m(B)*c^2 = 1.666*m(B)*c^2
where m(B) is the mass of observer B. At 0.9 c and 0.99 c this factor
is about 2.3 and 7.1 respectively. As the speed gets closer and
closer to the speed of light, A will see B's Energy become infinitely
large.
Obviously, from A's point of view, B will not be able to reach
the speed of light without stopping his own time, shrinking to
nothingness in the direction of motion, and taking on an infinite
amount of energy.
Now let's look at the situation from B's point of view, so we
will consider him to be at rest. First, notice that the sun, the
other planets, the nearby stars, etc. are not moving very
relativistically with respect to the Earth; so we will consider all of
these to be in the same frame of reference. Remember that to A, B is
traveling past the earth and toward some nearby star. However, in B's
point of view, the earth, the sun, the other star, etc. are the ones
traveling at highly relativistic velocities with respect to him. So
to him the clocks on Earth are running slow, the energy of all those
objects becomes greater, and the distances between the objects in the
direction of motion become smaller.
Let's consider the distance between the Earth and the star to
which B is traveling. From B's point of view, as the speed gets
closer and closer to that of light, this distance becomes
infinitesimally small. So from his point of view, he can get to the
star in practically no time. (This explains how A seems to think that
B's clock is practically stopped during the whole trip when the
velocity is almost c.) If (in B's frame) that distance shrinks to
zero as his speed with respect to A goes to the speed of light, and he
is thus able to get there instantaneously, then from B's point of
view, c is the fastest possible speed.
From either point of view, it seems that the speed of light
cannot be reached, much less exceeded. This, then, is the "light
speed barrier", but most concepts people have in mind for producing
FTL travel explicitly deal with this problem (as we will see).
However, the next problem isn't generally as easy to get away with,
and it probably isn't as well known among the average science fiction
fan.
8. The Second Problem: FTL, Causality, and Unsolvable Paradoxes
In this section we will explore a problem with FTL travel that
doesn't always seem to get consideration. The problem involves ones
ability to violate causality in certain frames of reference with the
use of FTL travel. While this in itself doesn't necessarily make FTL
travel impossible, the ability to go further and produce an unsolvable
paradox would make the FTL travel prospect logically self
contradictory. So, I will start by discussing the meaning of
causality and the problems of an unsolvable paradox. I will then try
to show how any form of FTL travel will produce violation of the
causality principle. Finally, I will explain how, without special
provisions being in place, FTL travel can go further to produce an
unsolvable paradox.
8.1 What is Meant Here by Causality and Unsolvable Paradoxes
The principle of causality is fairly straight forward. According
to causality, if there is some effect which is produced by some cause,
then the cause must precede the effect. So, if for some observer (in
some frame of reference) the effect of a cause truly happens before
its cause occurs, then causality is violated for that observer. Now,
recall one of the first things I mentioned in section 1 of this FAQ.
I took a moment to explain that when I talk about the order of events
in some frame of reference, I mean there actual order, and not
necessarily the order in which they are seen. One can imagine a
situation whereby I could first receive light from the effect and
later receive light from the cause. However, after I take into
account the time it took the light to travel, I will find the order in
which the events truly occurred, and this will determine whether or
not there is a true violation of causality in my frame. This true
violation of causality is what I will be talking about, NOT some trick
concerning when observers _see_ events, but a concept concerning the
actual order of the events in some frame of reference.
Now, one can argue that the idea of causality violation doesn't
necessarily destroy logic. The idea seems odd--to have an effect come
first, and then have the cause occur--but it doesn't have to produce a
self-contradictory situation. An unsolvable paradox, however, is a
self-contradictory situation. It is a situation which logically
forbids itself from being. Thus, when one shows that a particular set
of circumstances allows for an unsolvable paradox, then one can argue
that those circumstances must logically be impossible.
8.2 How FTL Travel Implies Violation of Causality
I refer you back to a diagram in the second section so that I can
demonstrate the causality problem involved with FTL travel. In
Diagram 2-8 (reproduced below) two observers are passing by one
another.
Diagram 2-8 (reproduced from Section 2)
t t'
| /
+ /
| / __--x'
+ / __C'-
|/__--
-+---+---+-__o---+---+---+- x
* __-- /|
__-- / +
-- / |
/ +
/ |
The origin marks the place and time where the two observers are right
next to one another. The x' and t' axes are said to represent the
frame of reference of O' (I'll use Op--for O-prime--so that I can
easily indicate the possessive form of O as O's and the possessive
form of O' as Op's). The x and t axes are then the reference frame of
the O observer. We consider the O system to be our rest system, while
the Op observer passes by O at a relativistic speed. As you can see
from the two coordinate systems, the two observers measure space and
time in different ways. Now, consider again the event marked "*".
Cover up the x and t axis and look only at the Op system. In this
system, the event is above the x' axis. If the Op observer at the
origin could look left and right and see all the way down his space
axis instantaneously, then he would have to wait a while for the event
"*" to occur. Now cover up the Op system and look only at the O
system. In this system, the event is below the x axis. So to O, the
event has already occurred by the time the two observers are passing
one another.
Normally, this fact gives us no trouble. If you draw a light
cone (as discussed in the Section 2) through the origin, then the
event will be outside of the light cone. As long as no signal can
travel faster than the speed of light, then it will be impossible for
either observer to know about or influence the event. So even though
it is in one observer's past, he cannot know about it, and even though
it is in the other observer's future, he cannot have an effect on it.
This is how relativity saves its own self from violating causality.
However, consider the prospect of FTL travel with this diagram in
mind. As O and Op pass by one another, the event "*" has not happened
yet in Op's frame of reference. Thus, if he can send an FTL signal
fast enough, then he should be able to send a signal (at the origin)
which could effect "*". However, in O's frame, "*" has already
occurred by the time O and Op pass by one another. This means that
the event "Op sends out the signal which effects *" occurs after the
event which it effects, "*", in O's frame. For O, The effect precedes
the cause. Thus, the signal which travels FTL in Op's frame violates
causality for O's frame. Similarly, since "*" has not occurred in O's
frame when O and Op pass one another, then in his frame a FTL signal
could be sent out from "*" which could tell O about the event as the
two observer's past. However, for Op, the event "O learns about * as
O and Op pass one another" comes before * itself. Thus, the signal
which is FTL in O's frame violates causality in Op's frame.
In short, for any signal sent FTL in one frame of reference,
another frame of reference can be found in which that signal actually
traveled backwards in time, thus violating causality in that frame.
Notice that in this example I never mentioned anything about how
the signal gets between the origin and *. I didn't even require that
the signal be "in our universe" when it was "traveling" (remember our
definition of FTL travel). The only things I required were that (1)
the signal's "sending" and "receiving" were events in our universe
and
(2) the space between the origin and "*" is flat (i.e. it is correctly
described by special relativity diagrams). Some FTL ideas may
invalidate the second assumption, but we will consider them a bit
later. We will find, however, that violation of causality still
follows from all the FTL travel concepts.
8.3 How We Get Unsolvable paradoxes.
As I mentioned before, violations of causality (as strange as
they may be) do not have to truly, logically contradict themselves.
However, it isn't too difficult to show (starting with the above
arguments) that FTL travel can be used to produce an unsolvable
paradox (a situation which contradicts its own existence). As a note,
in the past I have called such situations "gross" violations of
causality.
I'll illustrate the point with an example: Remember we said that
as O and Op pass, Op can send an FTL message out (from his frame of
reference) which effects "*". However, rather than having him send a
message out, let's say that Op sends out a bullet that travels faster
than the speed of light. This bullet can go out and kill someone
light-years away in only a few hours (for example) in Op's frame of
reference. So, say he fires this bullet just as he passes by O. Then
the death of the victim can be the event (*). Now, in O's frame of
reference, the victim is already dead ("*" has occurred) when Op
passes by. This means that another observer (stationare victim's death, and
that signal
could reach O before Op pass to
prevent the victim's death, and that is a self contradicting
situation. Thus, if there are no special provisions (which we will
discuss later) FTL travel will not only allow violation of causality,
but it can also produce unsolvable paradoxes.
At this point, I want to clearly list the various events which
must happen to produce an unsolvable paradox in our "FTL bullet"
example. This will be helpful as a reference listing through the rest
of our FTL discussion.
Event Listing and Comments:
(1) As observers O and Op pass by one another (as shown in Diagram 2-
8) Op uses some method to send out an FTL bullet from his
reference frame. The event "O and Op pass one another" will be
called the "passing event" from here on.
(2) The bullet strikes and kills a victim who's death is the event
marked "*" in Diagram 2-8. This event occurs after the passing
event in Op's frame of reference, but it occurs before the passing
event in O's frame.
(3) A third observer is at the victim's side as he dies and thus he
witnesses the death. This third observer is stationary in O's
frame of reference (i.e. his frame is the same as O's), so the
passing event (when the bullet was fired) occurs after the victims
death in this third observer's frame. Thus, the third observer
has witnessed a result which comes from an event in his future--he
has information about a future event in his frame of reference.
(4) The third observer sends this information about the future to O
using an FTL signal, and in the third observer's frame of
reference, O can receive this information before the passing event
occurs (and thus before the bullet is fired).
(5) O receives the message and learns of the victims death before the
bullet is fired. He thus knows about the bullet being fired--an
event in his own future which will occur at his very location.
(6) O uses this information to prevent Op from firing the bullet, thus
causing an self-inconsistent she
tachyon losses energy, it gains speed. One result of this is that if
a charged tachyon were to exist, then because it would travel faster
than light, it would give off a radiation known as Cherenkov
radiation. This would take energy away from the tachyon and cause it
to go faster and faster, continually giving off more and more energy.
Neutral tachyons, however, wouldn't do this.
In any case, we can consider the possibility that tachyons exist
and always travel faster than light. They then never have to cross
the light speed barrier, and they do not have infinite energy (but
there energy is negative). However, they still cause trouble because
of the second problem--if you can use them for FTL communication, they
can be used to create unsolvable paradoxes using the same arguments as
we did in our "FTL bullet" example.
To explore the question of using tachyons for FTL communication,
one can apply quantum mechanics to the energy equation of the tachyon.
What one finds is that eight. In either of these cases, the tachyon cannot
be used to
produce an FTL signal.
A third idea would also allow the tachyon to exit without the
possibility of using the tachyon to send FTL signals. The basic idea
is that there would be no way to distinguish between the situation
through which you could receive a tachyon and the situation though
which you could transmit a tachyon. To show what I mean, consider
Diagram 2-8 from section 2 yet again. From the O frame of reference,
a tachyon could be sent "from" * and "to" the origin. However, as
long as you cannot distinguish between the transmitter and the
receiver, then the Op observer could reinterpret this as a tachyon
being sent "from" the origin "to" *. Neither, then, will believe
that
the tachyon went backwards in time. Obviously, there is no way for a
message to be sent (because then you could identify the sender and
decide which way the tachyon "really" went), and it wouldn't be quite
right to call this FTL travel. However, it would allow tachyons to
exist (though uselessly) without causing any problems.
And so, we find that with tachyons, one of the following must be
true:
(1) Tachyons do not exist,
(2) Tachyons exist but cannot be used to send FTL signals, or
(3) Tachyons exist and can be used to send FTL signals, but some
special provision will keep anyone from using them to produce an
unsolvable paradox.
9.2 Using a Special Field/Space/etc. (W/o Special Provisions)
This next concept is often found in FTL travel methods of science
fiction. The basic idea is that a ship (for example) can use a
special field or travel in another space/dimension in order to "leave"
the physics of our universe and thus not be limited by the speed of
light.
Again, we see that this concept is basically designed to get
around the light speed barrier problem; however, it doesn't deal very
well with the problem of producing unsolvable paradoxes.
Though the FTL observer or signal which travels using this
concept would leave the realm of our physics, the relationship between
two observers who stayed behind (within the realm of our physics)
would not be effected. This means (if you recall the points made
earlier about the "second problem") that the arguments for producing
an unsolvable paradox must still hold (unless there are special
provisions), because those arguments were based on the relationship
between the two observers who themselves never traveled FTL (and thus
never left the realm of our physics).
Thus, we very quickly see that with any such methods (as long as
no special provisions apply) one can produce an unsolvable paradox.
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 (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 watch. However, as we have discussed, what is going on "right
now" at a distant location 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 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. 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.
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
presented in a paper by Miguel Alcubierre of the University of Wales
(the paper is available via the world wide web at URL http://www.
astro.cf.ac.uk/local/groups/relativity/papers/abstracts/miguel94a.html).
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 inter one "mouth" of the
wormhole and exit from the other very distant "mouth" so as to travel
FTL (by our definition).
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. Let's call the starting point of the trip "A". B
will
then be the destination point of the 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 (x and y are spatial dimensions)
y
|
| A B
|
| D C
|
+--------------x
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 (event "*" in Diagram 2-8).
(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:
(e) The third observer sends a signal over to C using ordinary
(slower-than-light) means.
(f) 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.
(g) An observer at D receives the signal before event (a) (and thus
before the bullet effected any space-time).
(h) 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", 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.
9.5 Special Provisions
Thus far, we have seen that the second problem is not easily
gotten around using any FTL concept. However, we have also insisted
during our arguments that none of these FTL concepts include "special
provisions". The specific provisions we were referring to will be
discussed here. Basically, these are ideas which allow one to bypass
the second problem in some way, and the ideas are generally not
specific to any one form of FTL travel. They don't require that you
bend space-time in some way or that you travel in some other universe
or that you be made of some specific form of matter when you do your
FTL traveling. What they do require is for the universe itself to
have some particular property(ies) which, in conjunction with whatever
form of FTL travel you use, will prevent unsolvable paradoxes.
There are three basic types of provisions, but we can express the
general idea behind them all before we look at each one specifically.
Recall that in producing the unsolvable paradox in our "FTL bullet"
example, there was a series of events listed, each of which had to
occur to produced the paradox. The provisions simply require that at
least one of these events be prevented from occur. With the first
provision we will discuss, no restrictions necessarily have to be
placed on the actual FTL travel, and any of the events (even those not
directly dealing with the FTL travel) can be the "disallowed" event.
The other two provisions place restrictions on the actual FTL travel
in certain cases in order to prevent the unsolvable paradox.
9.5.1 Consistency Protection
The first provision is what I am calling "consistency
protection". The idea is that the universe contains some sort of
built-in mechanism whereby some event in the series of events which
would produce an unsolvable paradox would not be allowed to occur.
An example of such a mechanism can be found when we look at the
situation through quantum mechanics. (A theory of Steven Hawking
called the "chronology protection conjecture" (CPC) attempts to do
just that--the jury is still out on this theory, by the way, and will
probably be out for a long time.) In quantum mechanics (QM), we do
not think in certain terms of whether or not an event will occur in
the future given everything we can possibly know about the present.
Instead we consider the probability of an event (or string of events)
occurring. One form of consistency protection would insist that QM
prevents the unsolvable paradoxes because the probability of all the
events occurring so as to produce an unsolvable paradox is identically
zero.
Under this explanation using QM, our bullet example would be
resolved through arguments similar to this: It may be that the Op
observer is unable to produce the FTL bullet (perhaps his FTL gun
fails), thus averting the paradox. If he is able to get the FTL
bullet on its way, then perhaps the bullet will end up missing its
mark. If it does hit the victim, then perhaps the victim's friend
will be unable to send an FTL signal back to the O observer (perhaps
his FTL message sender fails). If the signal to O gets sent, it still
might not be received by O. If O receives it, he may be unable to
stop Op from firing the bullet. In any case, this particular QM
explanation would insist that one of these events must not occur,
because the quantum mechanics involved forces the probability of all
of the events occurring to be zero.
To sum up, this provision requires that some mechanism exists in
the universe that would prevent at least one of the events from
occurring so that the unsolvable paradox does not come about. This
mechanism does not have to specifically target any of the FTL
trips/messages which one might want to make/send, but it could
disallow any of the events which must be present for the unsolvable
paradox to occur. Also, we should note that this provision could be
applied to any of the FTL concepts we have discussed in order to allow
them to exist without being self-inconsistent.
9.5.2 "Producing" Restricted Space-Time Areas
This provision is sort of an extension on the previous one, but
its mechanism specifically targets the FTL travel so as to restrict
one of the FTL trips or messages one must use to produce an unsolvable
paradox. Remember that in the list of events for our FTL bullet
example, there were two different FTL portions (the FTL bullet and the
FTL message from the third observer to O). This provision would cause
the sending or receiving of one of these "messages" to strictly
prohibit the sending or receiving of the other. I will try to
illustrate the basic way in which such restrictions could work to
always prevent unsolvable paradoxes. I will then give an example
where this provision is implemented with a particular FTL concept.
For the illustration, we need to consider each of two
possibilities within our FTL bullet example. In the first
possibility, the Op observer is allowed to send his FTL bullet which
strikes the victim, but that FTL trip must then restrict the third
observer's ability to send the FTL message to O. In the second
example, the third observer happens to decide to send some FTL signals
to O at some point before the event "*" (which is the event in our
example that usually marked the victim's death). Now, we let the
third observer continue to send those FTL signals until some point
after "*". Then, if the victim dies at "*" because of the FTL bullet,
then since the third observer is sending FTL signals to O at that
point, he would be able to tell O about the victim's death, and the
paradox would still be possible. Thus, in this second case, the FTL
bullet must not be allowed to strike the victim (the FTL travel of the
bullet is restricted because the third observer sends FTL signals to
O).
So, how would these restrictions work in these two possible
cases? Well, as it turns out, if all unsolvable paradoxes are going
to be averted while only placing restrictions on particular FTL trips,
then there must be a very specific provision in place. To explain
this, we will look at both possible situation, and consider diagrams
which explain each one. (Note that these diagrams are drawn a little
differently from Diagram 2-8 so as to better show the point I am
trying to make here.)
Diagram 9-2 (Case 1--The FTL bullet is allowed to strike at the
event "*")
t t'
. | /
. + /
. | / __--x'
. . + / __C'-
. . |/__--
+---+.--+---+---+.--+---+---+-__o---+---+---+- x
. . __--./| .
. . __-- . / + .
* __-- . / | .
__-- . / + .
__-- . / | .
In this diagram we mean to illustrate case one in which the FTL bullet
leaves the "passing event" (i.e. the origin, "o") and is
"received" by
the victim who immediately dies at event "*". Now, I have also drawn
parts of two light cones (marked with dots). One part is the "upper
half light cone of the event '*'," and the other is the "lower half
light cone of the passing event, 'o'". The upper half light cone of
"*" contains all events which an observer at "*" (like the third
observer in our bullet example) can influence without having to travel
FTL. All observers agree that all events in this area occur some time
after "*" (as discussed in Section 2). Also, the lower half light
cone of "o" contains all the events which could effect "o" (which,
remember, is the event at which the FTL bullet is sent) through non-
FTL means. Thus, as long as no FTL signal/traveler can leave as an
event in the upper half light cone of "*" and be received as an event
in the lower half light cone of "o", then ALL unsolvable paradoxes
will be averted. There would be no way for the third observer to
witness the death of the victim and afterwards get a signal to O
before the bullet is fired.
Now, that seems to be straight forward. We just need to make
this provision: When an FTL signal is transmitted as event T, and it
is received as event R, then it must be impossible for any information
to be sent as an event in R's upper ("future") light cone and end up
being received as an event in T's lower ("past") light cone. If the
universe restricted FTL travel in this way, it would be impossible to
produce unsolvable paradoxes.
However, we can see that the matter can get a little complicated
when we consider things from O's frame of reference (which is also the
frame of the third observer). In this frame, after the third observer
witnesses the victim's death at "*", the event "the bullet leaves"
hasn't occurred yet. He might then argue that no FTL signal has yet
been sent which would keep him from sending a FTL message to O. The
problem with his argument is that he has already witnessed the result
of the FTL bullet being sent (even if it hasn't occurred in his frame
yet). Thus, any FTL signal he tries to send to O (in the lower half
light cone of the origin/passing event/bullet-being-fired event) must
be prevented from being received by O.
Ah, but what if he (the third observer) just happened to decide
to start sending FTL signals to O (just to chat) before the bullet
strikes the victim? That leads to our second case. Here, then, is a
diagram we will use to describe this second case.
Diagram 9-3 (Case 2--The FTL bullet may not be allowed to strike at
the event "*")
t t'
. | /
. + / .
. | / . __--x'
. + / ._C'-
. |/__.-
+---+---+---+---+---+---+---+-._o-.-+---+---+- x
__-- /R
T __-- / |
. * . __-- / |
. s _.-- / +
. __-- . / |
Now, there are a few extra events here. The point "s" marks the point
where the third observer starts sending FTL signals to O while "T"
marks the point where he finishes sending those FTL signals. The
point "R" marks the point where O receives the last message which was
sent at "T". Now, here we have drawn the upper and lower half light
cones of interest, and according to our discussion above, it would be
impossible for Op to send his bullet at the origin, "o" (which is in
the upper half light cone of R) and have it "received" by the victim
at "*" (which is in the lower half light cone of T). So, according to
that argument, the bullet doesn't strike while the third observer is
sending FTL signals to O, and so the third observer never tells O
about the victim's death.
However, this doesn't HAVE to be what happens, and we might just
end up back at the first case. You see, either (1) the signals sent
by the third observer are all successful, and the FTL bullet is
restricted from striking the victim at "*" (that's the second case);
or (2) the FTL bullet does strike the victim at "*" and any FTL
signals that the third observer sends after "*" are restricted from
reaching the O observer before the bullet is fired (this is the first
case, even though the third observer _was_ sending signals to O just
BEFORE the bullet hit). The obvious question, then, is "which one of
these two cases actually occurs?" The answer happens to be, "it
really doesn't matter." You see, as long as one or the other does
occur, the situation remains self consistent and no self inconsistent
paradoxes are produced. Roll some dice and pick one, if you like, or
let some unknown force decide which happens. It really doesn't matter
for our argument. Is that a bit odd? Yes. Is it self-inconsistent
so as to produce unsolvable paradoxes? No.
Finally, as example to show this provision in action with a
particular FTL concept, let's consider a case where space-time
manipulation is used via a wormhole. Recall that in our discussion of
this FTL concept, we showed that one can still produce unsolvable
paradoxes. Notice, that there still must be two FTL parts (we
discussed one FTL "trip"--the bullet--from A to B and another--an FTL
message--from C to D). Now, to prevent the paradox, the existence of
the wormhole that allows the bullet to travel from A to B could forbid
the existence of the wormhole that allows the FTL message to go from C
to D. This is a situation where case 1 applies, and here the way the
provision is satisfied comes from the conceptual ability of one
wormhole's existence to forbid the existence of another wormhole.
And so, we have a provision which simply restricts (in a very
particular way) certain FTL trips because of other FTL trips. We have
found that there doesn't have to be a discernible answer to the
question of whether trip A disallows trip B or trip B disallows trip
A, but as long as it is one case or the other, this provision will
keep all situations self consistent and thus avoid unsolvable
paradoxes.
9.5.3 A Special Frame of Reference for the purpose of FTL Travel
The third 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 apply with this
situation, 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 is 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 (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. As the FTL method is activated, our new provision
requires that it use the special property of the field. This
means that the bullet's frame of reference must 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 bullet strikes and kills a victim, and again this event
occurs after the "passing event" in Op's frame of reference and
before the "passing event" in O's frame.
(3) Again, a third observer (who is in O's frame of reference)
witnesses the victim's death, and again this third observer will
then have information about an event which will happen in his
future (according to his frame of reference).
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 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. 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 the diagram 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
victom at the event "*" since that event has already occured 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 get rid of time dilation (for example) and 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 three 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.
10. Some Comments on FTL Travel in Star Trek
Since this post is meant for the rec.arts.startrek.tech
newsgroup, it seems appropriate to take all we have discussed and
apply it to what we see in Star Trek. Of course, it would be foolish
to assume (unfortunately) that the writers for the show take the time
to learn as much about these concepts as we now know, and I am
certainly not implying that a conscious effort was made to incorporate
what we know to be true in a consistent way on the show (after all,
this _is_ Star Trek :'). However, interestingly enough, if we apply
the concepts correctly, we can explain most of what Star Trek has
shown us. That is what I will try to do here.
10.1 Which Provision is Best for Explaining Warp Travel
First, we might want to consider the three provisions and try to
decide which one would best fit Trek so that everyday warp travel
couldn't be used to produce unsolvable paradoxes.
Let's consider the first provision. There, neither of the two
FTL trips in our FTL bullet example will necessarily be forbidden.
So, if we consider that example yet again, we can make the following
argument: Let Op be the Enterprise. Then, rather than sending a
bullet, the Enterprise could itself travel from the origin to "*". It
could then (through ordinary acceleration) change it's frame of
reference to match O's. Then it could travel from "*" (or just after
"*"--we have to give them a little time to do their acceleration) back
to the O observer, and it could get to O before it ever left for its
first FTL trip (i.e. we put the Enterprise in place of the FTL signal
sent by the third observer). Thus, since this first provision doesn't
have to forbid any of these actions, the Enterprise could use everyday
warp travel via this method to easily travel back in time without
having to do something as dangerous as zipping around the sun (as they
have had to do on the show). In addition, if this provision governed
normal warp travel, it would require Star Trek ships to be careful as
to which frames of reference they were in when they decided to enter
warp. After all, they may not want to accidentally meet themselves
from a previous trip (in which case the universe may destroy them to
protect self consistency). So, there seems to be some daunting
arguments against using the first provision to keep ordinary warp
travel from producing unsolvable paradoxes in Trek.
Okay, what about the second provision. With that provision it
would be impossible to use ordinary warp travel as a "time machine".
However, this provision does cause certain noticeable restrictions on
some FTL trips. There could be cases where the Enterprise would be
prevented from competing its warp trip on time because of an FTL
signal sent by someone else. We certainly don't see that on the show
(not surprisingly). So, considering this provision, I can't easily
point out any arguments to support using it to keep warp travel from
being self inconsistent.
This leaves us with the third provision, and I think you will see
that it the provision of choice for the purposes of Trek. Of course,
this third provision must involve some special frame of reference;
therefore, we might first ask about where this special frame might
come from. Thus, I will make a proposal for answering such a question
in the next section, and then I will present what I believe are strong
arguments for using the third provision to keep normal warp travel
from being self inconsistent in Trek.
10.2 Subspace as a Special Frame of Reference
When we discussed the "special frame of reference" provision, I
introduced the idea of a field which had a particular frame of
reference. For Star Trek, we can imagine subspace to be this field,
and we can let it pervade all of known space. Then, subspace would
define a particular frame of reference at every point in space. When
you entered warp, you would take on the frame of reference of subspace
and keep it, regardless of your velocity with respect to subspace.
This would ensure that normal, everyday warp travel would not produce
unsolvable paradoxes (as we discussed in section 9.5.3).
So, what does this provision give us that the second provision
didn't? Well, by assuming that subspace defines a special frame of
reference, we can explain some interesting points on the technical
side of Trek. For example, in the "Star Trek the Next Generation
Technical Manual" (and in other sources) we see that the different
warp numbers correspond (in some way) to different FTL speeds. But
when they say that Warp 3 is 39 times the speed of light, we must ask
what frame of reference this speed is measured in. With subspace as a
special frame of reference, it would be understood to mean "39 times
the speed of light in the frame of reference of subspace."
The same idea can be applied to references made to impulse-drive-
only speeds. In the Technical Manual, they mention efficiency ratings
for "velocities limited to 0.5c." They also mention the need for
added power for "velocities above 0.75c." But these velocities are
all relative, and so we must ask why these normal, slower than light
velocity of the Enterprise should matter when considering
efficiencies, etc. After all, the Enterprise is always traveling
above 0.5 c in some frame of reference and above 0.75c in some other
frame of reference. However, since impulse is supposed to use a
subspace field to "lower the mass of the ship" (so that it is easier
to propel), we could argue that the speed of the ship with respect to
subspace (assuming subspace defines a special frame of reference)
would effect efficiencies, etc.
Further, there is a much more documented example which refers to
warp 10. As many of you know, warp 10 is supposed to be infinite
speed in the Next Generation shows. That means that the event "you
leave your departure point" would be simultaneous with the event "you
arrive at your destination". But, as we have discussed, the question
of whether two events are simultaneous or not truly depends on the
frame of reference you are in. So, we ask, in what frame of reference
is warp 10 actually infinite speed. Again, we can use the frame of
reference of subspace to resolve this issue. Warp 10 would be
understood to be infinite speed in the frame of reference of subspace.
Finally, using this provision, there would be a standard,
understood definition for measuring times, lengths, etc. Times would
be measured just as it would tick on a clock in the frame of reference
of subspace, and distances would be measured just as it would be by a
ruler at rest in the subspace frame of reference. Basically, the
feeling we have for the way things work in every day, non-relativistic
life would be applicable to Trek by using the subspace frame of
reference as a standard, understood reference frame.
And so, I believe that the third provision gives us the best
explanation for how normal, everyday warp travel in Trek could be self
consistent.
10.3 The "Picture" this Gives Us of Warp Travel.
Given the previous discussion, we see that the third provision
seems to fits Star Trek like a glove. Thus, it may be best for us to
view warp travel in Star Trek like this: Subspace is a field which
defines a particular frame of reference at all points in known space.
When you enter warp, you are using subspace such that you keep its
frame of reference regardless of your speed. Not only does this mean
that normal warp travel cannot be used to produce unsolvable
paradoxes, but since in warp your frame of reference would no longer
depend on your speed as it does in relativity, relativistic effects in
general do not apply to travelers using warp. Since relativistic
effects don't apply, you also have a general explanation as to why you
can exceed the speed of light in the first place.
(As a note, this is similar to Alcubierre's idea for "warp"
travel (mentioned earlier), but in his idea the traveler did not take
on a "special" frame. Instead, he took on the frame he had before
entering warp, but that allows two trips from two different frames of
reference to produce an unsolvable paradox. If we add subspace as a
special frame of reference to Alcubierre's idea, we could get a self
consistent situation which would be very similar to what we see in
Trek.)
For more information on how this might conceptually work in the
science fiction of world Trek (at least one way I imagine it) you may
want to read my other regular post, "Subspace Physics". Here,
however, we can at least use this "picture" of warp to consider how
the outside universe might appear to someone traveling at warp speed.
Remember, at any point the warp traveler's frame of reference is as if
he is sitting still in subspace's reference frame. We could
illustrate the way such an observer would picture a particular event
by using the following idea: Picture a string of cameras, each a
distance (d) away from the one before it. Let these cameras all be
stationary in the frame of reference of subspace, and let them all be
pointed at the event of interest. Further, let each camera have a
clock on it, and let all the clocks be synchronized in the subspace
frame. Then, we can set each camera to go off with the time between
one camera flash and the next being d/v (where v is the FTL velocity
of the observer we want to illustrate). Then, each picture is taken
in the subspace frame of reference, but the string of pictures (one
from each camera) would form a movie in which each frame was taken
from a different place in space from the previous frame. Thus, we can
use this to produce a film of how an event would look to a warp
traveler.
Of course, in Trek they have subspace sensors which do all their
seeing for them (faster than light, of course). However, the above
does illustrate one's ability to use this view of warp travel to
answer various technical questions.
10.4 Some Notes on Non-Warp FTL Travel and Time Travel in Trek
Now, there are cases in Trek where FTL travel exists without
necessarily using subspace (and thus the subspace frame of reference
would not apply and would not prevent unsolvable paradoxes). For
example, if the wormhole in Deep Space Nine is assumed to be the same
as a wormhole we theorize about today, then it wouldn't need to deal
with subspace to allow FTL travel. (Now, what they call a wormhole
doesn't necessarily have to be what we call a wormhole, but for this
illustration, let's assume it is). So, if the wormholes in Trek
aren't bounded by the subspace frame of reference, we could imagine a
situation whereby they could be used to cause unsolvable paradoxes.
This is true for any form of FTL travel in Trek which might not use
subspace. However, I propose that in cases where subspace isn't used
(so that it's special frame of reference could not prevent unsolvable
paradoxes) then the first provision, consistency protection, would
apply. In that way, we can allow for non-warp/non-subspace-using FTL
travel in Trek while still preventing unsolvable paradoxes.
Further, consider time travel in Trek. Actual time travel
couldn't be accomplished by using subspace alone (the subspace frame
along with the third provision would prevent it). However, I propose
again that such travels in time should not be able to produce
unsolvable paradoxes because the consistency protection provision
would apply (since subspace alone couldn't be in use to produce the
time travel).
For example, consider the Star Trek: The Next Generation episode,
"Time's Arrow" (in which Data's severed head is found on 24 century
Earth, and Data eventually travels back in time to (unintentionally)
leave his head behind to be found). Now, after the head was found,
one of the crew (let's say Riker, just to use an example) could decide
to try to produce an unsolvable paradox. Riker may decide to do
everything in is power so as to keep Data from going back in time. He
may even try to destroy Data and his head to accomplish this task. Of
course, Riker isn't the type of person to do this, but what if he was?
Well, in that case, he would be trying to produce an unsolvable
paradox, and the first provision would prevent it. We could imagine
various ways in which he might fail in his task of trying to keep data
from going back in time. Further, we could consider the case in which
he would succeed in producing an unsolvable paradox and we could
insist that such situations would destroy themselves or prevent
themselves from ever happening.
Such a situation is seen in a particular Voyager episode. In
this episode, members of the crew are caught in a "subspace fissure",
and they travel back in time. By the end of the episode, their trip
back in time has produced a self-inconsistent situation. That series
of events then becomes impossible and ceases to exist by the closing
credits. This could be seen as a result of having the "consistency
protection provision" apply to a case where the subspace frame of
reference is bypassed via "subspace fissures".
So, even though we can be relatively sure that this was not the
intention, the situations shown do seem to comply with the concepts we
have developed.
10.5 To sum up...
To sum up, we have found that by introducing a special frame of
reference which would be "attached" to subspace, and by further
insisting that any type of FTL/time travel done without using subspace
be governed by the "consistency protection" provision, we will not
only have a self consistent universe for our Star Trek stories, but we
can also (coincidentally) explain many of the "but how come...?"
questions which some Star Trek episodes produce.
11. Conclusion
In PART I of this FAQ, I presented some of major concepts of
special relativity, and in PART IV, we have discussed the considerable
havoc they play with the possibility of faster than light travel. I
have argued that the possibility of producing unsolvable paradox is a
very powerful deterrent to all FTL concepts. Further, we have
introduced three basic provisions, at least one of which must be in
place so that FTL trips/signals (sent using any of the FTL concepts)
cannot be used to produce unsolvable paradoxes. Finally, we looked at
the science fiction of Star Trek while considering all that we had
discussed. We concluded that warp travel could be governed by the
third provision (via subspace defining a special frame of reference)
while all other FTL travel (or time travel) could be governed by the
first provision. This, I believe, best explain what we see on Star
Trek.
If you have not read PART II or PART III of this FAQ, and you are
interested in learning more about relativity (special and general),
then you may want to give them a look.
As the end result of this producing this FAQ, I hope that I have
at least informed you to some extent (or perhaps just helped to
clarified your own knowledge) concerning relativity and the problems
it poses for FTL travel.
Jason Hinson
-Jay
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Relativity and FTL Travel
by Jason W. Hinson (