From: hinson@bohr.physics.purdue.edu (Jason W. Hinson)
Newsgroups: rec.arts.startrek.tech
Subject: Re: Not the Technical Manual
Date: 18 Nov 92 02:28:42 GMT
Organization: Purdue University Physics Department

chris@keris.demon.co.uk (Chris Croughton) writes:
>
>In article <8738@dirac.physics.purdue.edu>
>           hinson@bohr.physics.purdue.edu writes:
>
>>First,  I do have a problem with many time travel stories in Star Trek.
>
>Not just in Star Trek, I assume, but most other time travel stories as
>well...
>
>>No one seems to realize the impact that changing one single thing in
>>time can have on future events.  Star Trek always comes out with some
>>way of handling it, such as Samual leaving his watch where he knew it
>>would be found.  But he HAD to do that, so he didn't have free will.
>>But time travel is another discussion all together.
>
>It depends on your model of time.  One theory says that small changes
>will only have local effects, so in a few hundred years time it won't
>matter. 

This idea has never seemed realistic in the least to me.  Someone once
pointed out that all you have to do is run around a town on any given
night and knock on doors and run.  By doing this, you are going to
"interrupt" some people, and since time of conception can change the
type of child born, you probably have changed who will be around to
effect furure events.  Just think of when you personally tell someone
something that has a small effect on their lives.  That effect may be
small, but it is there, and it effects other things. ANYWAY


>
>>As far as violating causality through FTL travel, I beleive I have a good
>>argument as to why it is not done in ST technology.  If it were, we would
>>see its effects all the time!  You get a distress call from a planet. You
>>are running out of time to get there.  All you have to do is get in the
>>right frame of reference out of warp, then enter warp, and you can get there
>>any amount of time after the destress signal was sent or even before it
>>was sent.  We do NOT see this at all.  This is why I don't think the idea
>>you mentioned about keeping the same F.O.R. you have before you enter warp
>>is correct.
>
>This I don't see.  Planet (A) sends a call to the Enterprise (E).  This
>is not at infinite speed, so it takes a time Tsig = Dae / Vsig.  E
>receives the signal, and travels to the planet.  This takes a time
>Te = Dae / Ve.  This time is still positive.  Because of relativistic
>effects E and A may disagree on exactly how *large* this time is in
>subjective time, but both will agree that it is positive.
>
>The only time that Te could be negative is if you try to force the time
>dilation equations of Special Relativity to handle velocities greater
>than c.  That gives complex values, rather than negative, anyway, which
>I don't think means reversing time, but (if it has any meaning at all)
>moving somehow 'sideways' in time...
>
>Surely special relativity wouldn't apply anyway, because E is
>accelerating wrt A?
>

Funny you should ask.  I just gave this explantion to a net-friend.  It
is important that you understand a Lorentz transforms. NOTE: two different
frames of reference CAN dissagree as to whether an event is in the future
or the past.  

SO, here is an example of how a causality problem can occure:

You are traveling at the same speed as another ship that is 2 light years
away from you.  You receive their message at x = t = 0.  NOW, lets say
they sent the message at x = -2 lyrs and t = -1.31893E-3 yrs.  That's how
long it would take the signal to get to you at warp 9 (I used it just
because it is easy to calculate).  By setting the ship at a negative
x, I have just defined the direction of the one space coordinate that
I will use.

NOW, using Lorentz transforms, I came up with the following fact: If you
travel away from the ship at a velocity of 
v = 1.45220878778E-3 c then (keeping all numbers in light years and
years and expressing c as 1 lyr/year) you get:

ct' = gamma(ct - beta x)
    = (1.00000105446) [-1.31893E-3 yrs (1 lyr/year) - beta*(-2 lyrs)]
    = 1.68649E-3 years = 13.8 hrs IN THE FUTURE

This assumes that you can get to that speed (about 435663m/s) very
quickly so that you are still close to x = 0 when you get to that 
velocity. If not, then you have to add on a little correction.

So, in that FOR, the event has not happened yet.  It is 13.8 hrs in 
the future.  Now, if you can then inter warp while KEEPING this frame
of reference, you can go to warp 9 and get there in 11.6 hrs.  This
gives you over 2 hours to help them BEFORE they send you the signal.

A space time diagram helps you see this:


 
               ct axis
                   ^     ct' axis
                   |    /
                   |
                   |
                   |  /
                   |               , x' axis
                   |        ,
                   |/ ,
-------------------+----------------->x axis
                ' /|
  *        '       |
      '            |
 '              /  |
                   |
                   |
              /    |
 
You can see that in the K' system, the event "*" is in the future, while
in the K system, it is in the past.  Normally, this wouldn't help you,
after all, you are going away from the ship that you wish to get to.  BUt
with your idea, you can enter warp with that FOR and go to the ship before
the event *.  

Let me mention that this is only ONE situation where this idea of keeping
the same FOR when you enter warp will give a causality violation.


Finally, if any of this is not clear, feel free to ask questions.  Also,
keep an eye out for my post that will give a better explanation of all
of this.

-Jay