From: hinson@bohr.physics.purdue.edu (Jason W. Hinson)
Newsgroups: rec.arts.startrek.tech
Subject: Re: Einstein and Warp Speed
Date: 16 Dec 92 09:08:03 GMT
Organization: Purdue University Physics Department

chris@keris.demon.co.uk (Chris Croughton) writes:
<hinson@bohr.physics.purdue.edu writes:
<
<>An event (event A) occurs right here next to you.  Event B occurs many
<>light years away from here at the same time in your frame of reference
<>as event A. (Note here that the light from such an event won't get to
<>you for many years; however, the event does occure at the same time
<>in your frame of reference.)  Using Lorentz _Transformations_, one will
<>find that a frame of reference can exist right next to yours such that
<>in that frame, event B occured years ago.
<
<Call that FOR frame C.
<
<Here's where I get lost.  How long in C's past can it have occurred?
<The same (at most) as the time it would take light to travel from the
<event to C?  And won't it seem to C that it occured in A's past as well?
<
<Is it actually sensible to talk about observers in different FORs having
<anything in their past, present or future with respect to each other
<anyway?

First, event B can have occured millions of years ago or just a few seconds
ago depending on how fast the observer in the C system is moving with 
respect to you.

Second, I am not comparing the two observers directly.  To one observer,
who could care less about the other observer, the event is happening 
right now.  He (actually I said this observer was you above)--> You know
that the event is happening at the same time as event A because in a few
years when the light from event B gets to you, you can calculate how long
it took it to get to you, count bacwards in time, and see that the event
actually occured (in your FOR) when A was occuring.


<
<>Normally, this is OK, because in either frame of reference, light cannot
<>have gotten to this point yet.  So even though it is in one frame's past
<>and one frame's present, neither of the two observers can know about or
<>effect the event.
<
<So normally you can't talk about it being in C's past until the light
<gets there.

Not exactly. Normally it IS occuring in C's past, but he has NO way of
know about it or acting on the fact that it has occured until light
reaches him.

<
<>Now let's say that you allow for instantaneous travel.  Then in my frame
<>of reference, it is possible to send a signal to event B.  But in the other
<>frame of reference, since event B is in his past, I WILL be sending a
<>signal into his past.  If the other observer could get to me a couple of
<>seconds before event A occured, he could tell me that event B is going to
<>occure, and I could send a signal to effect an event that has already
<>occured in his frame of reference.  That is a violation of causality.
<
<Hold on - how did A know about the event anyway?  If it's at lightspead,
<then it will arrive at C at essentially the same time, so that *defines*
<their common 'present'.  If the communication A to B is instantaneous
<(which it has to be, otherwise B wouldn't send the signal to C).  In
<which case, when C receives the signal from B, he *can't* know about A,
<so it can't be in his past (he may *reason* that it should have happened
<a long time ago, if he doesn't know about FTL travel, but that's his
<problem).

Let's try a specific example to help clear things up:

First, you must realize that instantaneous is defined in the frame of
reference of the guy sending the signal.  So let's look at C's point of
view.  He is zipping along in his ship towards us on earth.  Now, let's
say that at some point he sends an instantaneous message out to some 
distant point x.  Also, let's define the occurance of his message reaching
point x as our event B.  It is possible for him to be traveling at a 
fast enough speed, and for x to be far enough away from him so that at the
time he reaches us, event B has not yet occured in our frame of reference.
SO, even though he has send a message which to him reached point x a 
good while ago, we do not think the message has reached it yet.  Obviously,
if we can send an instantaneous message from our frame of reference, then
we can send a signal out to point x that will get there BEFORE his message
gets there.  In our point of view, we have simply sent a message 
instantaneously.  In his point of view, we have send a singnal back in time. 

<
<Or am I misunderstanding the phrase "in his past"?  From my point of
<view, if something is in C's past that means he already knows about it.
<But how can he know about something happening a long time ago when it
<has only just happened?
<
<Chris

An event can be in your past without you knowing about it.  If a star 
dies 10 light years from here while you are reading this message, you won't
know about it for 10 years.  However, that does not negate the fact that
in your frame of reference, the star was dying while you read this message.

Again, this is what normally saves causality.  Let's say that an event
had occured in our past.  We are zipping past another observer in who's 
frame the event has not occured yet.  If this is the case, then it will 
be true that the event is so far away that (though it is in our past) we
cannot know that it has happened.  Therefore we cannot tell the other 
observer, "Hay, here is an event that will happen in your future."  Also,
even if we could, he could not effect the event, because it would be so far
away that he couldn't get to the point where the event takes place before
the event had occured.  Therefore, without FTL travel/communication, 
causality is safe.

-Jay

PS.  If you can find some simple information on space time diagrams and
the way they work, this can help you understand these things.  I give a
brief explanation in my upcoming post (only one more section to write).
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