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Lost in Langevin's language


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Dear VandD & Tim, your answers do not coincide.


If I have to follow VandD then it goes like this:

* Dground is the measurement of the ground taken in the FOR of the ground.car


* Dcar is the measurement of the moving ground car taken in the FOR of the car.


* Dground is longer than Dcar.


* Dcar is shorter than Dground




Dear Michel, the key to the confusion is what I warned you about several times: VandD is -mostly- not discussing the ("simultaneous") distance measurement of the ground by the car. Instead, after the first two lines he is discussing a completely different measurement: the simultaneous measurement (for example with laser pulses) of the length of the car by the ground! In fact he also warned you about that, as follows (emphasis mine:

"For the length contraction of the car the scenario is different (see my previous sketches)."



Always considering that a measurement must include simultaneity, otherwise it gives a false result.


IOW the car observer measures that 1 meter in its own frame corresponds to 1,50m on the ground. It means that his measurement of a 1,50m placed on the ground is 1 meter (the measurement is 1 meter). He is observing an object of 1,50m contracted to 1 meter.


And then Langevin's statement gets comprehensible to me with the following addition (sorry for that)


The spatial distance of two events [that happen on the ground]* that are simultaneous for the car observers, is shorter for them than for ground observers in motion relative to them.


* [that happen on the ground] added by me


Please confirm.


As for that part: Yes indeed! :)

Edited by Tim88
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Yes, both Tim88 and VandD said it right.


Again ... the car observer makes a simultaneous measurement of the separation between the dropped balls (that are dropped simultaneously), which is a proper-length (LP). The measurement is made by a ruler at rest with the car, of proper-length LP, and fits precisely between the balls.


The ground observer, makes a simultaneous measurement of the length of the moving length-contracted car-ruler, and measures it at L = LP/γ.


The balls impact the ground simultaneously, per the car. The LTs require they cannot impact the ground simultaneously per ground, if they were simultaneous per the car, as differing POVs must disagree as to what are simultaneous events. The ground observer therefore records those impact-events as asynchronous.


Per ground observers ... the length-contracted car-ruler MOVES between those 2 asynchronous impact-events, and so the separation between those impact-events includes BOTH the moving car-ruler's contracted-length (LP/γ) PLUS its traversal distance (vt) between the events. By the LTs, the spatial separation between those asynchronous events as measured by the ground is dilated ... and to the precise tune of ... γ*LP. So, the moving car-ruler is length-contracted by 1/γ, while yet the spatial separation between the impacts events upon the ground is dilated by γ (per ground). No paradox.


Best regards,


Edited by Celeritas
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