[SR and synchronization] Cognitive Dissonances and Mental Blockage

**An Interesting Case of Mental Blockage and Cognitive Dissonance:**
*Einstein-Poincaré Synchronization Procedure and Dr. Lengrand*
What’s fascinating about certain cranks is that just when you think you’ve seen all the absurdities they can come up with, they manage to produce something even worse. Their cognitive dissonance and ability to pull out bizarre notions from who knows where, on top of a perfectly well-defined technical procedure, is astonishing. We’ve seen this before with GPS, where Hachel invents all sorts of fantasies, like atomic clocks in the receivers or synchronization with a clock infinitely far away in a fourth spatial dimension...
This is a report of exchanges on the synchronization procedure described by Einstein in his 1905 paper, discussions that took place 17 years ago and more recently on sci.physics.relativity and fr.sci.physique.
https://groups.google.com/g/fr.sci.physique/c/KgqI9gqTkR8/m/oMc9X0XjCWMJ
*Reminders on the Procedure:*
Two identical clocks, A and B, are stationary relative to each other at a certain distance. Their identical functioning (within measurement accuracy) allows us to assume that they "tick at the same rate." NOTHING more is assumed, especially regarding the time they display; the purpose is PRECISELY to adjust one of these clocks by applying a correction after a calculation involving the values indicated on these clocks during specific events, events that occur AT THE LOCATION OF EACH CLOCK.
Einstein’s procedure is not strictly a synchronization procedure but a method to VERIFY their synchronization. This is the main difference from Poincaré’s approach. However, it can be proven that Poincaré’s method leads to clocks synchronized in Einstein’s sense. You can also transform Einstein’s verification method into a synchronization procedure because it allows calculating the correction to apply to clock A.
*Steps of Einstein's Method:*
When clock A shows t_A, a light signal is emitted from A towards B.
When this signal is received at B, clock B shows t_B, and a light signal is sent from B back towards A.
When the signal is received at A, clock A shows t'_A.
The values t_A, t_B, and t'_A relate to events that all occur exactly at the location of the clock displaying these measurements. They are perfectly objective and independent of any observer. Anywhere in the universe, whether at A, B, or on Andromeda, observers can obtain these values (via astronaut carrier pigeons, for example).
Hachel/Lengrand manages to deny this simple FACT. This is the first level of severe cognitive dissonance.
Einstein points out that the experiment (measuring time during round trips, thus involving only one clock) justifies the formula: 2(AB)/(t'_A - t_A) = c (*).
He then introduces a *convention*: t_B - t_A = t'_A - t_B (**).
Here, Hachel/Lengrand believes this is only possible if the clocks have been specially pre-set, but there is nothing like that in Einstein’s procedure. The point is *precisely* to check whether this formula holds or not. And if it doesn’t, to find a way to make it true.
This shows Hachel/Lengrand’s ability to introduce additional conditions out of nowhere (to put it politely) and then go completely off track with objective values that don’t have the same value for everyone, comparing it to an entirely irrelevant "Langevin-style" scenario...
*Epilogue: What to Do if (**) Is False??*
Starting from:
2(AB)/(t'_A - t_A) = c
t_B - t_A = t'_A - t_B
Elementary algebra allows us to express t_A in terms of the other quantities involved:
t'_A = t_A + 2(AB)/c
t'_A = 2*t_B - t_A
=> t_A + 2(AB)/c = 2*t_B - t_A
=> 2*t_A = 2( t_B - (AB)/c )
=> t_A = t_B - (AB)/c
The value t_A should have been t_B - (AB)/c.
If the value was different, say t_Aerr, then adjust clock A by t_Aerr + t_B - (AB)/c.
An operator at A knows all the involved values; either they’ve been observed, known in advance (distance AB), or received via some transport method (t_B).
The procedure works regardless of the initial settings of the two clocks. We can then call the relationship (**) verified by the two clocks as "A is synchronized with B" or "A synch B."
To validate this, we still need to verify that "synch" (under the hypothesis 2(AB)/(t'_A - t_A) = c, which Hachel/Lengrand considers true!):
A synch A (reflexivity)
A synch B => B synch A (symmetry)
A synch B AND B synch C => A synch C (transitivity)
Einstein deemed it unnecessary to do this in his paper, considering it obvious to his readership (he wasn’t there to preemptively manage cranks).
The procedure is also experimentally falsifiable, despite its conventional aspect: by retesting synchronization after a minute, an hour, a year, or a century for the same clocks left to run their course, one would notice a desynchronization due to some phenomenon (except for a technical defect in the clocks), which gives meaning to the often-read phrase in popular science books: "time flows more or less quickly here and there." Countless experiments validate this aspect of Einstein’s procedure.
This procedure gives meaning to the coordinate "t" of an event for any inertial reference frame (thus t', t'', etc.).
In General Relativity, we find this procedure with a limitation: it is purely local; it holds in the spatiotemporal vicinity of an event. And it must be taken into account that, by the definition of Gravitation, two freely moving bodies (no acting forces) can see their trajectories diverge or converge.
This subtlety sheds light on a circular aspect of physics (which is entirely normal and quite a good sign): clocks are set to make Newton’s
first law true, and Newton’s first law allows clocks to be set
consistently (locally). Thanks to J. J. Lodder for pointing out this.
It’s no coincidence that the "real-time" event labeling proposed by Hachel/Lengrand is incoherent in this sense: with such coordinates, Newton’s first law is systematically violated; at worst, we even get a speed ("apparent") that is not only variable but *discontinuous* (if the body's trajectory crosses the observer).
I’ve written a small Python program that graphically demonstrates this phenomenon:
https://gitlab.com/python_431/cranks-and-physics/-/tree/main/Hachel/code