Newsgroup: it.scienza.fisica
Titolo: Mea culpa: anch'io ho un gemello!!!

NB: prego il moderatore di cestinare se l'articolo
in questione e' stato gia' riportato sul NG
Ciao a tutti.
Questa notte ho fatto un brutto sogno:
avevo un gemello cattivissimo che si divertiva a
fare avanti e indietro da Proxima centauri al
solo scopo far vacillare la mia debole fede scientifica....
Svegliatomi di soprassalto, mi ripetevo, come un rosario, che io e il mio
gemello
non potevamo essere scambiati per via dei diversi sistemi
di riferimento, uno inerziale ed uno no. Iniziai poi a fantasticare di
arditi
esperimenti concettuali.
[Ad esempio,  due gemelli che, esperimentando le stesse accelerazioni,
vanno uno a 10 AL dalla terra e torna indietro, l'altro si ferma a meta'
strada
e torna indietro subito, aspettando il suo gemellino...]
Stamattina ho preso una decisione: prima di alzarmi
in piedi e dire: "IO, ALESSANDRO MURA, SO!"
ho preso il mio umile PC ed ho fatto una ricerca...su internet.
Scherzi a parte:
In italiano non si trovano pagine accurate che parlino del problema,
(almeno le prime 20 su altavista)
mentre invece in inglese, la prima pagina e' veramente esauriente.
In particolare tratta il "paradosso" senza esplicitamente fare uso
della RG, ma solo della RR.
Allego il testo
http://www.suite101.com/article.cfm/advanced_physics/26998
[cut]
... is the standard explanation of the Twin Paradox. However, it is possible
to explain the supposed paradox without mentioning the acceleration which is
not felt by both twins. This is analyzing the problem at a deeper level
using reference frames, which is what I'll do here.
The confusion arises not because there are two equally valid inertial rest
frames, but because there are three. A lot of explanations of the twin
paradox have claimed that it is necessary to include a treatment of
accelerations, or involve general relativity. Actually, this is not true.
The three inertial frames are 1) at-home twin 2) the going-away twin and 3)
the coming-back twin. It doesn't make any difference that the last two are p
hysically the same twin. They still define different inertial frames.
Let's say the two twins are A and B, or Ann and Bob. Ann stays at home and
Bob rockets away at 3/5 light speed. Time dilation is 80%. Bob lets 4 years
pass. Bob returns at 3/5 light speed, again taking 4 years. Ann thinks 10
years have passed, and Ann and Bob agree that Bob is two years younger.
An important question is what is the relative speed of the two Bob frames?
On first glance, it might appear that one is going 3/5c in one direction and
3/5c in the other direction, so that the difference between the two frames
is 6/5c but special relativity does not add speeds this way. The actual
difference is only 15/17c, fast but not faster than light. Now, since
special relativity lets us use either rest frame, we assume Bob is the
at-home twin. Ann speeds away at 3/5c. No problem so far. But after 4 years
of waiting, Bob must change his inertial frame. If we allow Ann to return,
we've only restated the problem with the names switched. In the first
version, Ann stayed in an inertial frame, and she must stay in an inertial
frame in this version. Bob zooms off after Ann at 15/17 light speed and of
course catches up. It takes him 4 years, and he has seen 8 years since Ann
left. Ann has aged 10 years. You get the same result, and there's no
paradox.
This experiment was carried out by Hafele and Keating using atomic clocks.
One clock stayed at the Bureau of Standards, while an identical clock was
taken around the world. When they were brought together again, the traveling
clock had accumulated 273 nanoseconds less time than the other clock.
The Twin Paradox was never considered a paradox by physicists since it's so
easily explained by special relativity. It was only ever considered a
paradox by people who don't fully understand special relativity. It was
essentially invented by physics students. With the Internet, you have an
explosion of people with limited knowledge of physics trying to talk about
it. Therefore, in recent years this trivial entertaining thought experiment
has developed into a huge cottage industry on the Internet with an
irrational devoted following. All sorts of crackpots claim that the Twin
Paradox somehow disproves relativity. Other more knowledgeable people have
hyperanalyzed the problem every which way almost as if they are hoping to
find some contradiction. Each different way they approach it, however, just
leads to a different solution to the paradox. A common solution is the
general relativity solution. Other people thought, well what if there was a
cylindrical universe, where if you travel far enough in a given direction,
you get back to where you were before? This led to the cylindrical universe
solution. To often, those who understand relativity have to spend a long
time explaining to those who don't, the most trivial self- evident details
of relativity, such as the fact that there is not a missing gap in B's life.
It's all very frustrating, and the situation is not helped by the crackpots
who deliberately misrepresent the Twin Paradox.
E' stato solo un brutto sogno....:-)
Ciao , Alessandro.
--

 in questione e' stato gia' riportato sul NG
Regola empirica (non legale!) per tutti:
non è vietato riproporre articoli o interi messaggi già inviati, a due
"condizioni":
1) deve essere passato un po' di tempo dal primo invio (almeno due
settimane come consuetudine);
2) il messaggio (o articolo) non deve la prima volta avere avuto
riscontri (ad esempio se uno chiede "Mi spiegate la legge di Ohm" e non
riceve risposte fa bene a rispedirlo, ma se ha ricevuto risposte e
rispedisce lo stesso io come moderatore gli dico: "Leggiti prima le
risposte che hai già ricevuto"), o almeno riscontri non soddisfacenti.
Cordialmente,
Mauro Venier.
P.S.:
Comunque mi sembra che l'articolo in questione non fosse mai stato
spedito prima.