Le leggi della Natura
 

I gemelli e la stazione spaziale

LuigiFortunati 2 Ago 2017 18:06
La stazione spaziale S è posizionata a diversi anni-luce di distanza
ed è in quiete con la Terra T:
T----------------------------------------S-->x

Poiché T ed S sono in quiete tra loro, il tempo terrestre è identico
a quello della stazione spaziale.

Il gemello viaggiatore parte al tempo zero di tutti gli orologi,
viaggia a gamma=8 e arriva in S quando il suo orologio segna il tempo
di 5 anni.

Quale tempo segna l'orologio della stazione spaziale S?

(Twins and space station
Space station S is positioned at several light years away and is
quiet with Earth T:
T ---------------------------------------- S -> x
Since T and S are in quiet, Earth time is identical to that of the
space station. The traveling twin starts at zero time of all the
clocks, travels to gamma=8 and arrives in S when his watch marks the
time of 5 years. What time does the space station clock mark?)

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
LuigiFortunati 4 Ago 2017 19:21
Mike Fontenot alle ore 08:47:53 del 04/08/2017 ha scritto:
> Assuming that the traveler instantaneously accelerates to gamma = 8, the
> clock at S will read 40 years when T reaches there at age 5 years. But
> T says that the ******* twin is only 5/8 years old then. (As soon as T
> accelerates to gamma = 8, he will no longer regard the clock at S to be
> synchronized with the ******* twin's age. He says that the clock at S
> reads (40 - 5/8) once he has reached gamma = 8. I.e., he says that the
> clock at S suddenly changes from reading zero to reading (40 - 5/8)
> years when he accelerates (instantaneously) from gamma = 0 to gamma = 8.)
>
> Likewise, if T instantaneously reverses course, and goes back to the
> stay-at ******* twin at gamma = 8, he will conclude that she only ages 5/8
> year during the constant-speed portion of his trip back.
>
> The important question is this: if the ******* twin only ages 5/8 year
> during each of the two constant speed portions of T's trip (a total of
> 10/8 years), how can she be much older (80 years older than T's 10
> years) when he returns (as we know she must be)?
>
> The answer is that, during the instantaneous turnaround of T, he
> concludes that her age instantaneously increases by (80 - 10/8) years.
> THAT is the important resolution of the twin "paradox".

Sì, questa brillante soluzione al paradosso ci dice che in 10 anni di
viaggio (del gemello viaggiatore) il fratello terrestre invecchia
soltanto un anno e poco più (1,25) mentre bastano le due accelerazioni
per farlo invecchiare istantaneamente di quasi 79 anni!

Le accelerazioni sono proprio micidiali!

(Yes, this brilliant solution to the paradox tells us that in 10 years
of travel (of the traveling twin) the earthly brother ages only one
year and little more (1.25) while the two accelerations are enough to
make it instantaneously almost 79 years old! Accelerations are just
lethal!).

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
LuigiFortunati 4 Ago 2017 19:36
Sylvia Else alle ore 09:29:47 del 04/08/2017 ha scritto:
>> Space station S is positioned at several light years away and is quiet
>> with Earth T:
>>
>> T ---------------------------------------- S -> x
>>
>> Since T and S are in quiet, Earth time is identical to that of the space
>> station.
>
> Presumably the intent is that S is at rest relative to Earth. They have
> to be rather more than "several" light years apart to make this work,
> since a gamma of 8 implies a velocity in excess of 99% of the speed of
> light, so the separation between S and the Earth has to be a little less
> than 40 light years.
>
>>
>> The traveling twin starts at zero time of all the clocks, travels to
>> gamma=8 and arrives in S when his watch marks the time of 5 years.
>
> This is a problematic statement, since it implies that the twin is not
> moving relative to Earth, otherwise the space station clock will not
> show zero in the frame of the twin. However, if we take it that this
> describes the situation just before the twin rapidly accelerates to the
> required velocity, then it makes sense.
>
>>
>> What time does the space station clock mark?
>>
>
> When the twin arrives at S, the space station clock will show 40.
>
> Sylvia.

Per il gemello viaggiatore è la Terra T che s'allontana e la stazione
spaziale S che s'avvicina mentre lui è immobile.

Quindi nel suo riferimento il tempo dilatato è quello di T e di S,
non il suo.

Inoltre non c'è alcuna inversione di marcia.

Luigi.

(For the traveling twin is the Earth T that is far behind and the space
station S approaching while he is motionless. So in its reference the
dilated time is that of T and S, not its own. There is also no
reversal).

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
LuigiFortunati 4 Ago 2017 20:04
Tom Roberts alle ore 08:47:53 del 04/08/2017 ha scritto:
> Your "quiet" is a HIGHLY unusual phasing. I assume that when you say "quiet"
> you mean that S is at rest in the same inertial frame as earth. Compared to
> the traveling twin, the earth and S are accurately at rest in an inertial
> frame. When you say "zero time" for both earth and S, I assume that the
> earth and S clocks are synchronized in their inertial frame (i.e. they both
> display that frame's time coordinate, for which t=0 at the traveling twin's
> departure).
>
> The general formula for elapsed proper time of an object moving relative to
> an inertial frame is:
> T_obj = \integral dt / gamma(v)
> where the integral is taken over the path of the moving object, v is its
> speed relative to the frame (as a function of t), t is the time coordinate
> of the frame, and gamma(v)=1/sqrt(1-v^2/c^2).
>
> So in the above formula, T=5 years, and gamma(v)=8. Since gamma(v) is
> constant the integral is trivial, with result
> t_elapsed = 5 years * 8 = 40 years.
>
> t_elapsed is the elapsed time in the inertial frame, which is also the value
> of the clock at S.
>
> Tom Roberts

But even the ship's reference is inertial because after the initial
acceleration it travels for 5 years with out-of-engine engines.

(Però anche il riferimento dell'astronave è inerziale perché dopo
l'iniziale accelerazione viaggia per 5 anni a motori spenti).

Luigi.

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
LuigiFortunati 5 Ago 2017 10:55
Mike Fontenot alle ore 08:47:53 del 04/08/2017 ha scritto:
>> Space station S is positioned at several light years away and is quiet
>> with Earth T:
>>
>> T ---------------------------------------- S -> x
>>
>> Since T and S are in quiet, Earth time is identical to that of the space
>> station.
>>
>> The traveling twin starts at zero time of all the clocks, travels to
>> gamma=8 and arrives in S when his watch marks the time of 5 years.
>>
>> What time does the space station clock mark?
>>
>
> Assuming that the traveler instantaneously accelerates to gamma = 8, the
> clock at S will read 40 years when T reaches there at age 5 years. But
> T says that the ******* twin is only 5/8 years old then. (As soon as T
> accelerates to gamma = 8, he will no longer regard the clock at S to be
> synchronized with the ******* twin's age. He says that the clock at S
> reads (40 - 5/8) once he has reached gamma = 8. I.e., he says that the
> clock at S suddenly changes from reading zero to reading (40 - 5/8)
> years when he accelerates (instantaneously) from gamma = 0 to gamma = 8.)

Hai perfettamente ragione, quando l'astronave del gemello viaggiatore
accelera istantaneamente da gamma=1 (non gamma=0) a gamma=8, avvengono
cose strane.

La stazione spaziale S (che prima era distante quasi 40 anni-luce)
improvvisamente s'avvicina a quasi 5 anni-luce (altrimenti non potrebbe
raggiungerla in soli 5 anni).

Quindi improvvisamente lo spazio si contrae di 8 volte (da 40 a 5) e
altrettanto improvvisamente il tempo si dilata di 8 volte.

I corpi vanno verso dietro (s'avvicinano) e il tempo va in avanti (il
gemello terrestre invecchia istantaneamente e altrettanto
istantaneamente la Terra gira 40 volte intorno al Sole).

Il gemello terrestre, la Terra, il Sole e l'intero sistema solare
"vivono" 40 anni della loro vita mentre il gemello viaggiatore ha
soltanto il tempo di fumarsi una sigaretta!

(You're perfectly right when the traveling twin spaceship accelerates
instantly from range = 1 (no range = 0) to gamma = 8, strange things
happen. Space Station S (which was nearly 40 years old) suddenly
approaches almost five years light (otherwise it could not reach it in
just 5 years). So suddenly the space is contracted 8 times (40 to 5)
and equally suddenly the time dilates 8 times. The bodies go backward
(they approach) and time goes forward (the Earth's twin grows instantly
and instantly the Earth spins 40 times around the Sun). Earth twin,
Earth, Sun and the entire solar system "live" 40 years of their lives
while the traveling twin has only the time to smoke a cigarette!).

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
amedeoroma99@gmail.com 5 Ago 2017 18:06
Il giorno sabato 5 agosto 2017 12:20:02 UTC+2, LuigiFortunati ha scritto:
> Hai perfettamente ragione, quando l'astronave del gemello viaggiatore
> accelera istantaneamente da gamma=1 (non gamma=0) a gamma=8, avvengono
> cose strane.
>
> La stazione spaziale S (che prima era distante quasi 40 anni-luce)
> improvvisamente s'avvicina a quasi 5 anni-luce (altrimenti non potrebbe
> raggiungerla in soli 5 anni).
>
> Quindi improvvisamente lo spazio si contrae di 8 volte (da 40 a 5) e
> altrettanto improvvisamente il tempo si dilata di 8 volte.
>
> I corpi vanno verso dietro (s'avvicinano) e il tempo va in avanti (il
> gemello terrestre invecchia istantaneamente e altrettanto
> istantaneamente la Terra gira 40 volte intorno al Sole).
>
> Il gemello terrestre, la Terra, il Sole e l'intero sistema solare
> "vivono" 40 anni della loro vita mentre il gemello viaggiatore ha
> soltanto il tempo di fumarsi una sigaretta!
Il ragionamento non fa una grinza, se l'accelerazione da gamma 1 a gamma 8 fa
contrarre bruscamente le distanze di 8 volte, deve far dilatare bruscamente di 8
volte anche il tempo perche' il tempo e lo spazio sono legati indissolubilmente
tra loro.
LuigiFortunati 5 Ago 2017 20:17
John Heath alle ore 18:03:27 del 05/08/2017 ha scritto:
> What if T and S move and the vacationing twin stands still. Now it is
> all backwards with T and S 1 year older and the vacationing twin 79
> years older. Hmmm ?

E' l'accelerazione che fa la differenza.

Indipendentemente da ciò che succede nei 5 anni successivi, già alla
fine dell'accelerazione la distanza di quasi 40 anni-luce s'è ridotta a
soli quasi 5 anni-luce.

Se lo spazio s'è contratto bruscamente anche il tempo si dev'essersi
dilatato bruscamente.

Ma (ripeto) il brusco cambio non è dovuto al moto uniforme bensì
all'accelerazione.

(It's the acceleration that makes the difference. Regardless of what
happens in the next five years, at the end of acceleration, the
distance of nearly 40 years-light has decreased to almost 5
years-light. If the space has contracted abruptly, time must have
expanded abruptly. But (I repeat) the sudden change is not due to
uniform motion but acceleration).

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
LuigiFortunati 6 Ago 2017 10:57
Sylvia Else alle ore 18:03:28 del 05/08/2017 ha scritto:
> The acceleration is performed by the travelling twin. The apparent aging
> occurs to the Earth twin, many light-years away. It would be surprising
> if this were a causal effect.
>
> Instead, the acceleration just changes the travelling twin's frame, so
> as to allow the calculations to be done correctly. It doesn't do
> anything to the Earth twin.
>
> Sylvia.

Il "sorprendente effetto causale" (reale e non apparente) è il brusco
accorciamento della distanza tra la Terra T e la stazione spaziale S
che passa dai quasi 40 anni-luce di prima dell'accelerazione ai quasi 5
anni-luce del dopo accelerazione quando ancora i 5 anni del viaggio
sono ancora tutti da trascorrere.

Se l'accelerazione genera un brusco "salto" spaziale non può che
generare (contemporaneamente) anche un brusco "salto" temporale.

Luigi.

(The "surprising causal effect" (real not apparent) is the abrupt
shortening of the distance between Earth T and Space Station S that
passes from almost 40 light-years before acceleration to almost 5
light-years after acceleration when the 5 years of travel they are
still all to spend. If acceleration generates a sudden "space jumping"
it must only generate (at the same time) a sudden "jump" of time).

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
LuigiFortunati 6 Ago 2017 19:15
Gary Harnagel alle ore 14:19:01 del 06/08/2017 ha scritto:
>> In this discussion there is only the going and not the return.
>>
>> There is an initial acceleration and then for 5 years the traveling twin
>> travels with engines off and arrives in S where reading S time of the
>> clock without reversing the gear.
>>
>> What it does next does not concern the present discussion.
>
> But remember that the times at T and S are no longer synchronized according
> to the traveling twin after acceleration.

Com'è possibile che i tempi di T e di S siano diversi se sono
entrambi in quiete in K?

Facciamo un esempio pratico, l'accelerazione dura un giorno del tempo
dell'astronave così che al temine dell'accelerazione l'orologio
dell'astronave segna il tempo di 24 ore.

Quali potrebbero essere i tempi (diversi) di T e di S?

(How is T and S times different if both are at rest in K? Let's take a
practical example, acceleration lasts one day of the ship's time so
that at the time of the acceleration the clock of the ship marks the 24
hour time. What could be the times (different) of T and S?).

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
LuigiFortunati 6 Ago 2017 19:20
Sylvia Else alle ore 14:37:54 del 06/08/2017 ha scritto:
>> The "surprising causal effect" (real not apparent) is the abrupt
>> shortening of the distance between Earth T and Space Station S that
>> passes from almost 40 light-years before acceleration to almost 5
>> light-years after acceleration when the 5 years of travel they are
>> still all to spend.
>
> This is just a change in coordinates. It's not a real effect in same
> sense as an abruptly aging twin would be if it could be observed, even
> in principle.
>
> Sylvia.

Non è un effetto reale?

Nella stazione spaziale c'è una pillola che può salvare la vita al
gemello a patto che possa averla a disposizione entro 5 anni.

Poiché la stazione spaziale è distante quasi 40 anni-luce, il gemello
sembra essere inesorabilmente spacciato perché neanche alla velocità
della luce (la massima possibile) quella pillola potrebbe arrivare in
tempo (è impossibile percorrere 40 anni-luce in 5 anni!).

E invece il gemello può salvarsi accelerando a gamma=8 perché alla
fine dell'accelerazione gli bastano 5 anni per arrivare alla salvezza.

Infatti alla fine dell'accelerazione la stazione spaziale non è più a
40 anni-luce di distanza ma s'è avvicinata a meno di 5 anni-luce.

Ti sembra un effetto "apparente"?

Luigi.

(Is not it a real effect? At the space station there is a pill that can
save life to the twin, provided it can have it available within 5
years. Since the space station is nearly 40 years old, the twin seems
to be inexorably dispossessed because even at the speed of light (as
much as possible) that pill could arrive in time (it's impossible to
travel 40 years-light in 5 years!). And instead, the twin can save by
accelerating to gamma=8 because at the end of acceleration it takes 5
years to get to salvation. In fact, at the end of acceleration, the
space station is no longer at 40 years-light distance but has
approached less than 5 years-light. Does it seem like an "apparent"
effect?).

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking
LuigiFortunati 7 Ago 2017 09:10
Tom Roberts alle ore 05:20:38 del 06/08/2017 ha scritto:
>> The "surprising causal effect" (real not apparent) [...]
>
> This is NOT "real" in the sense that it is part of a valid model
> of the world. Causality is not involved, as at the instant the
> traveling twin measures (or computes) the ******* twin's age they are
> separated by a spacelike interval.
>
> Consider how the traveling twin would measure the ******* twin's age:
> there would have to be an assistant at rest in the traveling twin's
> inertial frame pre- positioned to be co-located with the ******* twin
> at the instant of the measurement, who observes the ******* twin's
> clock; this assistant would then send the measurement data to the
> traveling twin. Do this immediately before and immediately after
> the traveling twin turns around, and the assistants are located and
> moving very differently -- it's no surprise that their measurements
> are very different, as the assistants' clocks are synchronized very
> differently with the traveling twin's clock. It is, of course, that
> change in clock synchronization that is the underlying effect.
>
> The ******* twin, of course, is completely unaffected and notices
> nothing (except the traveling twin's assistants, who pass by in
> opposite directions many years apart).
>
> The whole notion of "what does the traveling twin measure" is highly
> artificial, requiring outrageously impractical assistants; Fontenot's
> "CADO frame" is merely a way to compute the highly artificial value
> that such assistants would measure. As "all physics is local"
> [Einstein and others], this is not part of any valid model of the
> world; it is a measurement over a spacelike interval. The aspect
> of this that proves its artificiality is the fact that it is
> coordinate dependent -- coordinates are arbitrary human constructs
> which Nature does not use, and no natural phenomenon can possibly
> depend on such an arbitrary human choice....
>
> What is real (i.e. unambiguous) is the comparison of the twins'
> ages when they reunite. That is both independent of coordinates and
> very non-local.
>
> Tom Roberts

La distanza TS tra la Terra T e la stazione spaziale S è
perfettamente misurabile senza che ci sia bisogno di assistenti e
quant'altro.

Dalla terra basta inviare segnali elettromagnetici e aspettare il
ritorno.

Il gemello (o chi per lui) l'ha già fatto e quindi sa che la "misura"
della distanza TS è di quasi 40 anni-luce.

Poi il gemello parte e arriva alla stazione spaziale S dove esegue
un'altra misura col suo orologio che segna il tempo di 5 anni.

Quest'altra misura gli garantisce che il viaggio è durato 5 anni e
quindi l'effettiva distanza reale percorsa è stata di quasi 5 anni-luce
(non potrebbe essere altrimenti perché in 5 anni non si possono
percorrere 40 anni-luce!).

Le due "misure" (prima e dopo l'accelerazione) documentano
inequivocabilmente che la distanza Terra-StazioneSpaziale era di quasi
40 anni-luce prima dell'accelerazione e s'è ridotta a quasi 5 anni-luce
dopo l'accelerazione.

Nessuna apparenza, nessun "modello" e nessuna necessità di
assistenti, solo "misure reali" e nient'altro.

Ed è solo l'accelerazione che fa la differenza tra il gemello che
parte e quello che resta, perché uno ce l'ha e l'altro no.

Invece la velocità non discrimina alcunché perché nessuno dei due
gemelli ha una velocità più legittima dall'altro.

E' quindi l'accelerazione (e non la velocità) che contrae lo spazio
e, conseguentemente, dilata il tempo.

Luigi.

(The TS distance between Earth T and Space Station S is perfectly
measurable without the need for assistants and more. From the ground
just send electromagnetic signals and wait for the return. The twin (or
who for him) has already done so and knows that the "measurement" of
the TS distance is almost 40 years-light. Then the twin starts and
arrives at Space Station S where he does another measure with his watch
marking the 5-year time. This other measure guarantees that the journey
lasted 5 years and therefore the actual real distance traveled was
almost 5 years-light (it could not be otherwise because in 5 years you
can not travel 40 light years!). The two "measurements" (before and
after acceleration) unambiguously document that the
Earth-StazioneSpaziale distance was close to 40 years-light before
acceleration and reduced to nearly five years-light after
acceleration. No appearance, no "model" and no need for assistants,
only "real measures" and nothing else. And it is just the acceleration
that makes the difference between the twin part that left and what
remains, because one has it and the other does not. But speed does not
discriminate anything because neither of the two twins has a more
legitimate speed on the other. It is therefore the acceleration (and
not the speed) that contracts the space and consequently expands the
time).

--
Luigi Fortunati

Credere e' piu' facile che pensare
Believing is easier than thinking

Links
Giochi online
Dizionario sinonimi
Leggi e codici
Ricette
Testi
Webmatica
Hosting gratis
   
 

Le leggi della Natura | Tutti i gruppi | it.scienza.fisica | Notizie e discussioni fisica | Fisica Mobile | Servizio di consultazione news.