In my animation
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that
moves like a transmission belt, so that each revolution of Earth 1 corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of
the 2 Terre are always synchronized with each other.
Question: do the clocks of the two Earths remain synchronized with each
other in the reference K' of the spaceship?
In my animation
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that
moves like a transmission belt, so that each revolution of Earth 1 corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of
the 2 Terre are always synchronized with each other.
Question: do the clocks of the two Earths remain synchronized with each
other in the reference K' of the spaceship?
In my animation
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that moves like a transmission belt, so that each revolution of Earth 1 corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of
the 2 Terre are always synchronized with each other.
Question: do the clocks of the two Earths remain synchronized with each other in the reference K' of the spaceship?No, not as viewed in telescopes (i.e. via light from each earth) nor as calculated by K' as the time "now".
On 12-Aug-23 5:58 pm, Luigi Fortunati wrote:
In my animation
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that moves like a transmission belt, so that each revolution of Earth 1 corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point QTo be clear, for this to mean anything, it has to be a statement in the
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
frame of reference of the two Earths.
It will not be the case that when
the travelling twin reaches Q, they will determine that both Earth
clocks show 24 hours, since, in answer to your later question, the Earth clocks are not synchronized in the travelling twin's frame.
...In my animation=20
https://www.geogebra.org/m/ez4jk4qm=20
Il giorno domenica 13 agosto 2023 alle 09:56:56 UTC+2 Richard Livingston ha scritto:
In my animation
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that moves like a transmission belt, so that each revolution of Earth 1 corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q when the time of the two Earths is exactly equal to 24 hours (one complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of the 2 Terre are always synchronized with each other.
My animation really serves to make the time of distant objects current.Question: do the clocks of the two Earths remain synchronized with each other in the reference K' of the spaceship?No, not as viewed in telescopes (i.e. via light from each earth) nor as calculated by K' as the time "now".
Indeed, the traveling twin of my animation does not need to watch from afar how Earth 1 and Earth 2 move.
He just needs to look at the belt that runs in front of his eyes to know how much the two Earths have rotated.
The advancement of the belt measures the time of the rotation of *both* Earths and not only one: how could the belt move regularly (as indeed it does) if the two Earths rotated at different times?
Luigi.
Il giorno domenica 13 agosto 2023 alle 09:56:56 UTC+2 Richard Livingston ha scritto:
In my animationNo, not as viewed in telescopes (i.e. via light from each earth) nor as
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that
moves like a transmission belt, so that each revolution of Earth 1
corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of
the 2 Terre are always synchronized with each other.
Question: do the clocks of the two Earths remain synchronized with each
other in the reference K' of the spaceship?
calculated by K' as the time "now".
My animation really serves to make the time of distant objects current.
Indeed, the traveling twin of my animation does not need to watch from afar how Earth 1 and Earth 2 move.
He just needs to look at the belt that runs in front of his eyes to know how much the two Earths have rotated.
The advancement of the belt measures the time of the rotation of *both* Earths and not only one: how could the belt move regularly (as indeed it does) if the two Earths rotated at different times?
Luigi.
In my animation
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that
moves like a transmission belt, so that each revolution of Earth 1 corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of
the 2 Terre are always synchronized with each other.
Question: do the clocks of the two Earths remain synchronized with each
other in the reference K' of the spaceship?
https://www.geogebra.org/m/ez4jk4qm...
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The travelling twin looks at the belt and infers a remote time on Earth from it. But that remote time has no physical meaning, and cannot be measured directly.
Instead, the travelling twin can look at the remote Earth's clock
through a telescope...
Il giorno mercoledì 16 agosto 2023 alle 01:54:10 UTC+2 Sylvia Else ha scritto:
In my animation...
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The travelling twin looks at the belt and infers a remote time on Earth from >> it. But that remote time has no physical meaning, and cannot be measured
directly.
Instead it is a direct measurement because the length of the belt that
passes in front of the traveling twin's eyes is *directly* connected to
the rotation of the clock hand highlighted in red in my animation.
Each section of the belt corresponds to a precise rotation of the red hand, no more and no less.
Instead, the travelling twin can look at the remote Earth's clock
through a telescope...
Why should the traveling twin prefer the complications relating to the observation of a distant watch (with all the related problems) when he
can know the terrestrial time by directly observing the belt passing in
front of his eyes?
Luigi
Op 12/08/2023 om 9:58 schreef Luigi Fortunati:
In my animation
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that moves like a transmission belt, so that each revolution of Earth 1 corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of
the 2 Terre are always synchronized with each other.
Question: do the clocks of the two Earths remain synchronized with each other in the reference K' of the spaceship?No of course. To both "earths" the traveler will be at the same location
X at a given, common (synchro), moment T.
But at that event X,T, traveler's space axis will point toward a past
event of Earth1, and toward a future event of Earth2. So no, they're not synchronised in a moving system like traveler's.
Their time is running at the same pace though in traveler's system, as co-members of the same inertial system, obviously.
Op 12/08/2023 om 9:58 schreef Luigi Fortunati:
In my animationNo of course. To both "earths" the traveler will be at the same location
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that
moves like a transmission belt, so that each revolution of Earth 1
corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of
the 2 Terre are always synchronized with each other.
Question: do the clocks of the two Earths remain synchronized with each
other in the reference K' of the spaceship?
X at a given, common (synchro), moment T.
But at that event X,T, traveler's space axis will point toward a past
event of Earth1, and toward a future event of Earth2. So no, they're not synchronised in a moving system like traveler's.
Their time is running at the same pace though in traveler's system, as co-members of the same inertial system, obviously.
...In my animation
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
In light of special relativity, starting up that belt is problematic.
First of all,
simultaneous is not a well defined condition for starting because different observers can have different ideas about when is the same time on both earths. Second, starting such a long belt will take a long time due to
finite stiffness of the belt. When one earth starts rotating (or engages
with the belt) the motion of the belt will propagate at the speed of sound
in the belt towards the other earth.
Now, in principle, you could start up the belt in such a way that eventually the entire belt is moving and at constant tension and the two sides of the belt are synchronized as you are assuming.
But that does not establish
a unique synchronization between the two earths. Moving observers,
including the distant observer looking at the belts, will still see different synchronizations between the two earths depending on the state of motion
of the observer. You can't get around special relativity this way.
Il giorno mercoled=C3=AC 16 agosto 2023 alle 01:55:39 UTC+2 wugi ha scritto:
Op 12/08/2023 om 9:58 schreef Luigi Fortunati:
In my animationNo of course. To both "earths" the traveler will be at the same location
https://www.geogebra.org/m/ez4jk4qm
there is Earth 1 (ours) and there is Earth 2 at some fixed distance.
The 2 Earths (which rotate at the same speed) are joined by a belt that
moves like a transmission belt, so that each revolution of Earth 1
corresponds to a revolution of Earth 2 and an advancement of points P
and Q equal to a circumference of the earth .
The traveling twin V starts with a certain speed v and reaches point Q
when the time of the two Earths is exactly equal to 24 hours (one
complete rotation around its own axis).
These are the times in the terrestrial reference K, where the clocks of
the 2 Terre are always synchronized with each other.
Question: do the clocks of the two Earths remain synchronized with each
other in the reference K' of the spaceship?
X at a given, common (synchro), moment T.
But at that event X,T, traveler's space axis will point toward a past
event of Earth1, and toward a future event of Earth2. So no, they're not
synchronised in a moving system like traveler's.
Their time is running at the same pace though in traveler's system, as
co-members of the same inertial system, obviously.
Velocity v=0.866c, gamma=2.
Spaceship reference frame: t=Spaceship time, t1=Earth-1 time,
t2=Earth-2 time.
Start: t=0, t1=0, t2=0.
After a spaceship time 2 is t=2: what are the values of t1 and t2
in the spaceship reference frame?
...
Here you can toy with parameters: https://www.desmos.com/calculator/kxi1hft38c?lang=nl
T = the two terras, Earths
V = voyager position at terra events T
T' = terra events at voyager's V event
b = velocity, g = gamma value, L = scale param;
s = Voyager position
Redundant data:
B = synchro belt control events (belt linking two rotating terras)
a = Earth diameter (has to be small to correspond with time unit 1)...
d = belt velocity (following the terra rotations)
wugi il 21/08/2023 09:11:23 ha scritto:
...
Here you can toy with parameters:
https://www.desmos.com/calculator/kxi1hft38c?lang=nl
T = the two terras, Earths
V = voyager position at terra events T
T' = terra events at voyager's V event
b = velocity, g = gamma value, L = scale param;
s = Voyager position
Redundant data:
B = synchro belt control events (belt linking two rotating terras)
a = Earth diameter (has to be small to correspond with time unit 1)...
d = belt velocity (following the terra rotations)
In your animation where there is nothing spinning:
- are the two red circles marked by T' the 2 Earths in the reference
frame of the spaceship?
- have these small circles (in the reference frame of the spaceship)
carried out the same number of rotations since the moment of departure
or has one rotated more than the other?
In my animation[[Mod. note --
https://www.geogebra.org/m/ez4jk4qm
...
As Sylvia Else, Richard Livingston (who wrote the passage you quoted
that begins "But that does not establish a unique synchronization"),
and Guido Wugi have pointed out in this thread, using a belt doesn't
provide a simple or unique synchronization. You have *asserted* that
the synchronization is unique, but you haven't *proven* it.
What does it mean for a synchronization convention to be "reliable"?
I truly have no idea what the criteria are for "reliability".
-- jt]]
wugi il 21/08/2023 09:11:23 ha scritto:
...
Here you can toy with parameters:
https://www.desmos.com/calculator/kxi1hft38c?lang=nl
T = the two terras, Earths
V = voyager position at terra events T
T' = terra events at voyager's V event
b = velocity, g = gamma value, L = scale param;
s = Voyager position
Redundant data:
B = synchro belt control events (belt linking two rotating terras)
a = Earth diameter (has to be small to correspond with time unit 1)...
d = belt velocity (following the terra rotations)
In your animation where there is nothing spinning:
- are the two red circles marked by T' the 2 Earths in the reference
frame of the spaceship?
- have these small circles (in the reference frame of the spaceship)
carried out the same number of rotations since the moment of departure
or has one rotated more than the other?
The graduated belt of my animation is directly *bound* to the Earth and
its rotation.
This makes its measurement (direct and immediate) more reliable than
the measurement at distance with light.
On Friday, August 25, 2023 at 12:41:27=E2=80=AFAM UTC-5, Luigi Fortunati wrote:
...
The graduated belt of my animation is directly *bound* to the Earth and
its rotation.
This makes its measurement (direct and immediate) more reliable than
the measurement at distance with light.
I'll try one last time to make this point. The time "now" for events outside the light cone, e.g. events that are spatially separated, are not uniquely defined for different observers.
I must ask what meaning you attach to a time "now" back on earth? It
is not the time you can see, via light, from earth. In fact there is nothing you can do to interact with earth "now" in any way. The only way to
know what is happening "now" is to wait for that event to enter your
past light cone, at which time you can see it. At that later time you can know what happened back when you identified a time as "now".
If you want to define some time as "now" by some mechanism like you
describe, that is OK. But the conventional way to define "now" is to synchronize clocks as described in most any book on special relativity.
That process allows you to define a "now" that conforms with what
we all normally think of as "now". It gives a different result for different inertial observers, but it gives a result that each observer can make
sense of as "now". That is, if they do some experiment such as send
a time message via light, the result is consistent with special relativity.
There is another factor that you are not taking into account: The
Lorentz contraction of each side of the belt will be different for
moving observers. This may seem as it should be negligible for
such a slow moving belt, but note that magnetic fields are the result
of just such a difference in Lorentz contraction even though the
electrons in a wire are moving at less than 1 mm/second. In the
case of your belt model, a rapidly moving observer will see that
one side of the belt has shrunk compared to the other, and thus
the earth is rotated relative to what the "stationary" observer
calculates.
Rich L.
[[Mod. note -- That's a very clear (and completely correct) exposition.
Thank you!
-- jt]]
From this we can conclude:
The belt running in voyager's direction seems shorter and running at
higher velocity (at times, without checkpoint on it).
The belt running in voyager's opposite direction seems longer and
running at lower velocity (at times, with two checkpoints on it).
New simulation:
The Earths and the belt running around and between them, according to Traveller's POV, in this new simulation: https://www.desmos.com/calculator/izfxoxinku?lang=nl
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