Newsgroups: sci.physics
Subject: Re: FTL communication in SR does not violate causality
From: mcirvin@husc8.harvard.edu (Matt McIrvin)
Date: 18 Dec 92 23:10:20 GMT
Keywords: FTL SR causality Special Relativity

metares@well.sf.ca.us (Tom Van Flandern) writes:

>and mcirvin@husc8.harvard.edu (Matt McIrvin) writes:

>> Suppose that there is apparatus at rest in O2's frame that is just like
>> O1's, and vice versa.  O2 can set up events F1 and F2 which are both at
>> the origin of O2's spatial coordinates; F1 follows E and F2 follows F1,
>> according to O2's time coordinate.  F1 causes event F which is at the
>> origin of O1's spatial coordinates, which in turn causes F2, all of this
>> reckoned using O2's time coordinate.  This must be possible if SR
>> applies and the apparatus works everywhere.
>>
>> Now if O2's frame is moving at a sufficiently high speed relative to O1,
>> it's easy to see that F can *precede* E1 according to O1's time coordinate.

>     A good counter-argument, but I think there is a subtle fallacy in it. By
>hypothesis, F1 follows E in O2's frame.  Therefore F1 follows E as seen by
>all observers, including observer O1.  Using Mark's assumptions, if F1 ---
>causes---> F ---causes---> F2, and F1 follows E, then F must also follow E
>and E1.

It seems to me that if those are Mark's assumptions, then Mark's
model violates SR.  A notion of causation that obeys such rules is not
Lorentz invariant, and a communication method that only allows messages
to be transmitted in such a manner is not Lorentz invariant either.
On the other hand, it could be made consistent with all current
evidence in favor of SR: see below...

>     Since this point is subject to much confusion because of the lack of
>distant simultaneity in SR, let me modify the example a bit for clarity.
>Infinite velocity is still a defined concept in SR, even if only hypothetical
>"tachyons" can achieve it.  Assume O1 sends an infinite-velocity tachyon beam
>to O2, who then sends it back.  E1 (sending beam) causes E (beam received on
>Mars) causes E2 (beam returns to Earth).  The world line for this sequence is
>horizontal in a space-time diagram.

>     Now assume that, after event E on Mars, observer O2 initiates his own
>tachyon beam (F1), which reaches Earth (F) and is returned to Mars (F2). This
>world line is also horizontal, but always above the first such line.  The two
>world lines cannot cross.  Regardless of the velocity of O2 relative to O1,
>and regardless of what their clocks read when these events occur, nothing can
>make F happen before E1 as seen by any observer.

That's quite consistent, and, I might add, quite possible physics.  But
it *doesn't* obey special relativity.  One of the postulates of SR states 
that the laws of physics are the same in all inertial frames.  If these
tachyon world lines are not allowed to cross, that means that they are
restricted to follow certain planes, which we've defined as horizontal,
in spacetime.  The laws of physics therefore look locally quite different
for physicists traveling at different speeds; one will be able to send
tachyon beams in all directions at exactly infinite velocity, whereas
another (whose spatial directions are tilted with respect to the
preferred planes) will have to send tachyons forward in time at finite
velocity in some directions, backwards in time in other directions, and
at exactly infinite velocity in still others. 

The nice thing about such a theory is that although it violates SR,
it doesn't require violation of SR by anything other than these
mysterious superluminal beams.  Therefore it can be made consistent
with all the current *evidence in favor* of SR without violating
causality.  But that's not the same thing as consistency with SR
itself; such a thing would require a modification of SR, an escape
clause of sorts.

To echo an issue raised by Mark Corscadden and others (there was a
nice reprinted lecture of J.S. Bell's about it in Physics World a
few months ago), you are allowed to define a preferred frame and
do all physics with that preferred frame without violating SR, 
*as long as the dynamics of the theory are Lorentz invariant to begin
with*.  (For example, an explanation of Lorentz contraction in terms
of the effects of velocity on the fields that bind matter is
still a correct explanation, even though you never explicitly
invoke Lorentz transformations, because the fields are constructed
to be Lorentz invariant no matter what you do!) 

If you don't know what the dynamics are, however, as when postulating
various ways signals could be sent using currently unknown physics,
you have to use the Lorentz symmetry explicitly in order to avoid
violating SR because you have nothing else to go on. 
-- 
Matt McIrvin
Newsgroups: sci.physics