You are wrong.
> But "backward-in-time" doesn't make
> sense.
Right! Which is why your claims also make no sense.
> Certainly, A can send a signal to B, and some moving
> observers C and D can observe that something happened
> at B before something else happened at A, but they can't
> observe tachyons going backward in time (they have no
> energy at u = c²/v, which is the demarcation point).
You are wedded to your fantasy and are not THINKING. My scenario NEVER
has any receiver or observer trying to observe any tachyon that was not
emitted by a transmitter at rest in the same frame as the
receiver/observer. So your objection here simply does not apply.
If A can send a tachyon signal to B, with both at rest in inertial frame
S, then if SR is valid, D can send a similar tachyon signal to C, with
both of them at rest in inertial frame S'. In my previous post I
computed the coordinates of all transmission and reception events in
both S and S'. It is INESCAPABLE that in frame S the final reception
event at A happens BEFORE the initial transmission event at A (this
final reception is NOT a tachyon signal, it is an ordinary signal over
zero distance with zero delay from C to A, which are co-located at that
event).
It does not matter what the dynamics of tachyon signaling are, or
whether you think they have no energy -- if the speed of a tachyon
is >c relative to the frame in which its transmitter is at rest, and a
receiver at rest in the same frame can receive it, then my conclusion
follows. NOBODY ever has to "observe a tachyon going backwards in time",
but yet the (ordinary) signal from C to A closing the loop comes to A
BEFORE the first tachyon was launched by A.
********
* Here are diagrams drawn from the standpoint of frame S [@],
* with w=∞, v=0.5 and L=16 characters. Note that S' is "Lorentz
* contracted" here, so in these diagrams 0-to-D in S' is the
* same number of characters as A-to-B in S; 0-to-C in S' is 1/4
* of those characters (= v^2). As before, ignore the vertical
* separation on the page.
*
* [@] I.e. the positions of everything are drawn at the
* value of t given for the diagram, as measured in S.
*
* Here is the situation at t=-vL, when A receives the signal from C:
* S': 0---C-----------D (Moving to the right at v (= 0.5)
* S: ----A---------------B (note A is at x=0)
*
* Here is the situation at t=0, when A launches the first tachyon,
* B receives the first tachyon, B sends a zero-length signal with
* zero delay to D, and D launches the second tachyon:
* S': 0---C-----------D
* S: ----A---------------B
********
> How is it possible to dispute what the physicist
> actually OBSERVES in his laboratory? He OBSERVES C at
> xC = 0, tC' = γ(L/w - vL/c²)) when the tachyon is launched by
> D, right?
Your "when" is AMBIGUOUS, as is the location of your physicist.
Moreover, no possible physicist can observe both C and D. So this
paragraph is impossible and I ignore it.
Note that we are analyzing this from a global perspective not limited to
either frame or to any location. As this is a gedanken, we can COMPUTE
when and where each event occurs, relative to either frame, and I did
just that in my previous post.
The first tachyon propagates instantaneously relative to S, but the
second tachyon propagates instantaneously relative to S' -- that is NOT
simultaneous in S as you seem to claim here. Indeed, as I calculated in
the previous post, that second tachyon induces C to send a zero-distance
zero-delay signal that arrives at A at x=0,t=-vL, so it comes to A
BEFORE the first tachyon was launched by A at t=0.
> How can a signal traveling between D and C (in S') have any
> effect whatsoever on a clock in S? It can't, of course.
GO BACK AND READ MY SCENARIO -- that does not happen. When C receives
the second tachyon, C is adjacent to A and can send an ordinary signal
to A over zero distance with zero delay. THAT signal closes the loop,
and comes to A before A launched the first tachyon.
>> Note that A and B are locations at rest in S, and C and D are locations
>> at rest in S'. In S, C is adjacent to A BEFORE D is adjacent to B.
>
> In which case, D couldn't have received the message from B, so it would
> be impossible to complete the loop.
NONSENSE! Go back and read my description of the scenario. D is adjacent
to B when B receives the first tachyon, and C is adjacent to A when C
receives the second tachyon [#]. Note that C and D are at rest in S',
and C is located between x'=0 and D (x'=gL), so it is QUITE CLEAR that C
is adjacent to A before t=0 -- see the above diagrams. Yes, the scenario
must start before t=0 (and also before t'=0).
[#] As I said before, we must PRE-COMPUTE locations
for C and D and place them there, so they are indeed
where the scenario needs them to be. Since this is a
gedanken, that is easy to do (in the real world it
would be a challenge). My previous post gives the
values and the above diagrams use them.
When observers in frame S observe the coordinates of the second tachyon,
via direct observation at B and via a zero-delay signal from C at A,
they conclude it propagated backwards in time, but they never actually
had to observe the second tachyon. I did that because detecting such
tachyons is problematical -- in this scenario tachyons are received by
receivers at rest in the same frame as the transmitter.
> (1) D didn't have the message to transmit the signal to C,
Sure D did. By construction, D is adjacent to B when B receives the
first tachyon signal, and B passed an ordinary signal to D over zero
distance with zero delay. THAT'S WHAT THE SCENARIO IS.
> (2) When D gets the message (being adjacent to B), C wasn't at x = 0, so
> so the message loop fails and causality isn't violated.
YOU ARE CONFUSED. When D receives the signal from B (D being adjacent to
B at that event), it simply does not matter where C is located. C's
location only matters when C receives the second tachyon signal from D,
and at that event C is adjacent to A (i.e. x=0). THAT'S WHAT THE
SCENARIO IS.
You seem to have confused simultaneity between the
two frames -- they are DIFFERENT.
The second tachyon propagates with infinite speed RELATIVE TO S', not S.
In S the second tachyon is effectively going BACKWARDS IN TIME, which
cannot be expressed by any speed -- this tachyon is observed only in S'
at C; in S the ordinary zero-delay signal C->A permits S to INFER when
the second tachyon arrived at C, and thus at A since they are co-located
at this event. See the above diagrams.
Bottom line:
The scenario and calculations I presented demonstrate the impossibility
of preserving all of these:
A) the validity of SR
B) tachyon signaling at speed > c relative to an inertial frame
C) ordinary concepts of causal order (transmission of a signal
must occur before its reception, both referred to the same
inertial frame) [for w=∞, before => simultaneous]
You keep making mistakes, such as using "when" without specifying a
frame, and so remain confused. But you have presented NOTHING that
disputes the scenario I presented, in which causal ordering is violated.
Tom Roberts