🚀 go-pugleaf

markc@smsc.sony.com (Mark Corscadden) writes:

> Let O1 be an [Earth] observer and let E1 and E2 be two events which take
> place at the origin of O1's reference frame, where E2 happened at a later
> time.  Let O2 be a [Mars] observer.  ...  E1 is the sending of a signal to
> Mars and E2, which takes place only seconds later, is the reception of a
> reply from Mars.  A correct formulation of general FTLC only requires that
> there is some objective event E on Mars which corresponds to the act of
> receiving the signal from Earth and replying to it.  This FTLC capability
> is fully general and applies in all reference frames to all observers:  ...
> E1 ---causes---> E ---causes---> E2  ...  a general FTLC capability does
> not violate SR, contrary to the usual claims.

     Excellent points, Mark.  You have good insights into the fundamentals,
some of which are missed by those who understand only the math of SR.


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 is true that if you use speed-of-light communications, clock readings
can get mixed up.  For example, since O1 and O2 can have their clocks
synchronized at only a single instant, it was already true in the original
example in O1's frame only that event E recorded in O2's frame might occur at
an O2 clock reading earlier than the E1 clock reading in O1's frame.  But
these clock readings are irrelevant.  Mark has defined a causality sequence
which retains the order of events, even when clock readings get mixed up.

     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.

     The infinite tachyon beam performs a sort of "super-synchronization" of
clocks that permits all observers to intercompare events in (as Mark calls
it) "a preferred frame."  In my shortly forthcoming book I present the "Meta
Model," a new cosmology from first principles, which reasons from a different
vantage point to a similar conclusion.  There I call the super-
synchronization a "meta-time," since neither frame is preferred in any
spatial sense.  The principle of relativity is still in full effect, as is
the constancy of the speed of light in all frames.  This is simply a
demonstration of limitations to the meaning of the SR corollary that FTL
communication is impossible.  It isn't necessarily so.  -|Tom|-

-- 
Tom Van Flandern / Washington, DC / metares@well.sf.ca.us
Meta Research was founded to foster research into ideas not otherwise
supported because they conflict with mainstream theories in Astronomy.