Jos Bergervoet alle ore 09:00:51 del 30/07/2017 ha scritto:
>> The traveling twin starts and goes back to Earth where he finds his
>> 80-year-old brother aged as he is only 10 years old.
>>
>> The wristwatch on the twin traveler's wrist marks (of course) the
>> 10-year time.
>>
>> The earth twin during the years of the trip has been flashing every 10
>> years (his).
>>
>> The last lightning is emitted at the time of the return of the ship,
>> when the Earth clock marks the 80-year time and the wrist watch on
>> the twin traveler marks 10 years.
>>
>> Calculation (perhaps) impossible is this: at the ejection of the
>> penultimate lightning (when the Earth clock marked 70 years) what time
>> was the watch on the wrist of the traveling twin?
>
> You assume constant speed except for the instantaneous
> change at turn-around and at departure and arrival, I
> assume?
>
> And you want the answer for the simultaneous events
> in the Earth's reference frame coordinates, I assume?
> Then it is 8.75 years (if the watch shows, years..)
>
> The answer is different if you ask for simultaneous
> events in the traveling twin's reference frame. In
> that case it is 5 years, it is in the moment when
> the twin changes direction (very suddenly) and in
> his frame of reference the Earth-bound clock moves
> from 0.625 years to 79.375 years, and the Earth sends
> 7 flashes of light in one single moment. Actually the
> twin changes his reference frame infinitely fast at
> that point, which is rather unphysical.
>
> You should better take a scenario with a smooth
> reversal of direction at the turn-around. But that
> wouldn't change the basic fact: the answer depends
> on the reference frame if you ask "what was the
> situation *on the ship* when a certain event happened
> *on Earth*".
>
> This is best analyzed by imagining two very long
> trains, one moving with high velocity past the other.
> Then there is a point of the first train adjacent to
> a point of the other train for all the questions of
> the kind you are asking here. As long as you *do not*
> try to change direction of the moving train it is
> relatively simple in that case.
Naturalmente avevo fatto i miei calcoli già prima d'avviare la
discussione e mi ritrovo perfettamente con tutti i tuoi numeri.
Nel riferimento del gemello viaggiatore, alla fine del viaggio
d'andata (quando il suo orologio segna il tempo di 5 anni) il tempo
simultaneo terrestre è di 0.625 anni e quindi non c'è stata ancora
alcuna simultaneità con l'emissione dei lampi del gemello terrestre.
Ma anche nel viaggio di ritorno non c'è alcuna simultaneità con gli
eventi terrestri da 1 a 7 perché appena dopo la virata il tempo sulla
Terra è schizzato da 0.625 a 79.375 saltando tutti gli eventi, compreso
l'evento "emissione del lampo 7" che è già avvenuto più di 9 anni
prima.
La simultaneità degli eventi terrestri E1..E7 (emissioni dei lampi
terrestri 1...7) non avvengono all'andata e neanche al ritorno,
avvengono tutti durante l'inversione di marcia.
E' lì, in quel breve tempo che il gemello terrestre invecchia di
quasi 79 anni mentre l'orologio e l'invecchiamento del gemello
viaggiatore restano pressoché fermi.
A una sequenza d'eventi terrestri che durano 60 anni sulla Terra,
sono simultanei eventi dell'astronave che avvengono nel breve tempo
della virata ma senza poter ricavare i tempi esatti di ogni
simultaneità sull'orologio del gemello viaggiatore.
(Of course I had done my calculations before I started the discussion
and I find myself perfectly with all your numbers. In the travel twin
reference, at the end of the forward trip (when his watch marks the
5-year time), the simultaneous earth time is 0.625 years and therefore
there is still no simultaneous emission with the Earth twin flash. But
even on the return trip there is no simultaneousness with earth events
from 1 to 7 because just after the turn the time on Earth has shrunk
from 0.625 to 79.375 by skipping all events, including the "flash 7
emission" Which has already happened more than 9 years earlier. The
simultaneity of Earth events E1..E7 (land light emitted 1...7) does not
occur at the start and even when the return occurs, all occur during
the reversal. It is there, in that short time, that the Earth's twin
ages almost 79 years, while the watch and aging of the traveling twin
are almost firm. A landmark sequence of earth events lasting 60 years
on Earth are simultaneous events that take place in the short
turnaround but without the exact times of any simultaneity on the twin
traveler clock).
--
Luigi Fortunati
Credere e' piu' facile che pensare
Believing is easier than thinking
Received on Sun Jul 30 2017 - 13:10:44 CEST