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Aug 12, 2023, 3:58:08 AM8/12/23

to

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 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?

Aug 13, 2023, 3:56:55 AM8/13/23

to

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 Q

> when the time of the two Earths is exactly equal to 24 hours (one

> complete rotation around its own axis).

To be clear, for this to mean anything, it has to be a statement in the
> 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).

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.

>

> 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?

Aug 13, 2023, 3:56:56 AM8/13/23

to

calculated by K' as the time "now".

Rich L.

Aug 13, 2023, 11:43:13 AM8/13/23

to

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.

Aug 14, 2023, 2:56:01 AM8/14/23

to

Il giorno domenica 13 agosto 2023 alle 09:56:55 UTC+2 Sylvia Else ha scritto:

> 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 Q

> > when the time of the two Earths is exactly equal to 24 hours (one

> > complete rotation around its own axis).

> To be clear, for this to mean anything, it has to be a statement in the

> frame of reference of the two Earths.

Certain! My animation is (exactly!) in the K frame of reference of the two Earths.
> 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 Q

> > when the time of the two Earths is exactly equal to 24 hours (one

> > complete rotation around its own axis).

> To be clear, for this to mean anything, it has to be a statement in the

> 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.

Luigi.

Aug 15, 2023, 3:14:34 AM8/15/23

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Il giorno luned=C3=AC 14 agosto 2023 alle 08:56:01 UTC+2 Luigi Fortunati ha=

scritto:

> > > In my animation=20

> > > https://www.geogebra.org/m/ez4jk4qm=20

> ...

In terrestrial reference frame, the belt moves at the speed of rotation of =

the two Earths: if the Earths rotate fast, the belt moves fast, if they rot=

ate slowly, the belt also moves slowly.

In the spaceship reference frame, if Earth-1 rotates at a different angular=

velocity than Earth-2, does the belt adjusts its speed at Earth-1's rotati=

on or Earth-2's rotation?

Luigi.

scritto:

> > > In my animation=20

> > > https://www.geogebra.org/m/ez4jk4qm=20

> ...

In terrestrial reference frame, the belt moves at the speed of rotation of =

the two Earths: if the Earths rotate fast, the belt moves fast, if they rot=

ate slowly, the belt also moves slowly.

In the spaceship reference frame, if Earth-1 rotates at a different angular=

velocity than Earth-2, does the belt adjusts its speed at Earth-1's rotati=

on or Earth-2's rotation?

Luigi.

Aug 15, 2023, 7:54:10 PM8/15/23

to

On 14-Aug-23 1:43 am, Luigi Fortunati wrote:

> Il giorno domenica 13 agosto 2023 alle 09:56:56 UTC+2 Richard Livingston ha scritto:

> Il giorno domenica 13 agosto 2023 alle 09:56:56 UTC+2 Richard Livingston ha scritto:

>> No, not as viewed in telescopes (i.e. via light from each earth) nor as

>> 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.

People often think of special relativity as being a complete description
>> 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.

of events. Popular science descriptions do nothing to dispel this

illusion. But it is not. It is part of a model that includes other

aspects of physics, such as the propagation of light. The complete model

describes the results of measurements, including things that are seen by

way of light that has been emitted by objects at a distance and later

received by a person's eye.

Attempting to construe special relativity alone as describing events

leads to the kind of confusion illustrated by your example. 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. If the twin observes the belt and infers a time

"now" for Earth, and then waits a time for light to travel the distance

from Earth, the twin would expect to see the previously identified "now"

time through the telescope. But that's not what they would see, because

they've used the wrong model to make their prediction.

Sylvia.

Aug 15, 2023, 7:55:20 PM8/15/23

to

On Sunday, August 13, 2023 at 10:43:13=E2=80=AFAM UTC-5, Luigi Fortunati wrote:

> Il giorno domenica 13 agosto 2023 alle 09:56:56 UTC+2 Richard Livingston ha scritto:

> Il giorno domenica 13 agosto 2023 alle 09:56:56 UTC+2 Richard Livingston ha scritto:

> > No, not as viewed in telescopes (i.e. via light from each earth) nor as

> > 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 light of special relativity, starting up that belt is problematic.
> > 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.

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.

Rich L.

Aug 15, 2023, 7:55:39 PM8/15/23

to

Op 12/08/2023 om 9:58 schreef Luigi Fortunati:

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.

--

guido wugi

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.

--

guido wugi

Aug 18, 2023, 3:44:36 AM8/18/23

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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.

> ...
>> 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
> it. But that remote time has no physical meaning, and cannot be measured

> directly.

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

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

Aug 19, 2023, 2:32:59 AM8/19/23

to

an inference. Such an inference unavoidably requires a model of space

time. The model you're trying to use says that the time on Earth is just

the amount of belt that has reached the observer divided by the belt's

velocity. It's a perfectly good model - it just happens not to be the

correct one for our universe.

Sylvia

Aug 20, 2023, 1:50:28 AM8/20/23

to

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?

Luigi.

Aug 20, 2023, 5:59:35 AM8/20/23

to

Aug 20, 2023, 2:37:40 PM8/20/23

to

Il giorno mercoled=C3=AC 16 agosto 2023 alle 01:55:20 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.

> ...
> > > > 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.

That's exactly the idea.
> 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.

in two different ways: either through light (with all the complications

of the case) or through the belt (with all the simplicity of the case).

The second case is clearly more reliable than the first.

Luigi

[[Mod. note --

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]]

Aug 21, 2023, 3:11:29 AM8/21/23

to

Op 20/08/2023 om 7:50 schreef Luigi Fortunati:

Homework?

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)

--

guido wugi

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)

--

guido wugi

Aug 21, 2023, 4:43:16 PM8/21/23

to

wugi il 21/08/2023 09:11:23 ha scritto:

> ...

- 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?

Luigi

> ...

> 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:
> 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)

- 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?

Luigi

Aug 23, 2023, 3:40:22 AM8/23/23

to

Op 21/08/2023 om 22:43 schreef Luigi Fortunati:

Sorry, in my answer I forgot to put the link to the new desmos version:

https://www.desmos.com/calculator/wreelz925x?lang=nl

(I don't understand how and why Desmos saves updated but un-renamed

versions everytime under a new, different link):

--

guido wugi

https://www.desmos.com/calculator/wreelz925x?lang=nl

(I don't understand how and why Desmos saves updated but un-renamed

versions everytime under a new, different link):

--

guido wugi

Aug 25, 2023, 1:41:27 AM8/25/23

to

Luigi Fortunati il 20/08/2023 06:37:35 ha scritto:

>> In my animation

>> https://www.geogebra.org/m/ez4jk4qm

>> ...
>> In my animation

>> https://www.geogebra.org/m/ez4jk4qm

> [[Mod. note --

> 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]]

The graduated belt of my animation is directly *bound* to the Earth and
> 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]]

its rotation.

This makes its measurement (direct and immediate) more reliable than

the measurement at distance with light.

Aug 25, 2023, 1:41:48 AM8/25/23

to

Op 21/08/2023 om 22:43 schreef Luigi Fortunati:

> 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?

Yes.
> 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?

do 'carry' a different number of rotations. That's precisely why Voyager

has a 'relativistic' POV!

The time unit cT=1 is defined as a 'day', corresponding to one Terra

rotation. So you can count the time for the various points/events.

I've made a few corrections for some point constraints, and clarified

the graph a bit more.

The animation omits the belt time during a half Earth turn, so the belt

is supposed running around a small axis, but at equator rotation speed.

The Earths size is shown though at y=-2.

Another caveat: the belt is also running at 'relativistic' velocities,

so changing its velocity d would impact the relativistic length of the

belt, yet this one is for convenience always equalled to twice the

Earths' proper distance.

--

guido wugi

Aug 26, 2023, 2:39:17 PM8/26/23

to

On Friday, August 25, 2023 at 12:41:27=E2=80=AFAM UTC-5, Luigi Fortunati wrote:

...

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]]

...

> 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
> its rotation.

>

> This makes its measurement (direct and immediate) more reliable than

> the measurement at distance with light.

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]]

Aug 27, 2023, 4:18:42 PM8/27/23

to

Op 26/08/2023 om 20:39 schreef Richard Livingston:

It sounds nice, but it is yet wrong. There is no 'rotation' of the two

Earths relative to a traveller along their axis of symmetry.

What *is* true and correct, is that the belts are observed (Lorentz-wise

as well as 'looking'-wise) to advance at different speeds 'back' and

'fro', by the traveller.

Take a look at the graph I proposed before:

https://www.desmos.com/calculator/wreelz925x?lang=nl

For an example, choose b=0.43 (traveller velocity) and d=0.75 (belt

velocity). Choose "Show voyager's POV" (and unchoose "Show Earths'

POV"). Now let the traveller go from Earth1 (left) to Earth2 (right)

with parameter s. Look at the following events:

O. s=0 :

traveller leaves Earth1. Belt check points B (in Earths' POV) leave

their respective Earth, say, B1 and B2. But in traveller's POV, B'1

coincides with B1, but B'2 is already underway, as traveller's x-axis

points to Earths' future.

A. s=0.24 :

Checkpoints B'1 and B'2 cross each other midways (same event for both

traveller and Earths)

B. s=0.364 :

Traveller crosses checkpoint B'2 (heading to the left).

C. s=0.47 :

Checkpoint B'1 reaches Earth2 at the right.

! Immediately a "new" checkpoint B'2bis starts heading to the left! [not

shown]

Checkpoint B'2 is still on its way left.

! In the upper part there is no checkpoint at present!

D. s=0.7 :

Checkpoint B'2 reaches Earth1.

! Immediately, but only just now, a new checkpoint B'1bis starts heading

to the right! [not shown]

E. s=1 :

Voyager reaches Earth2.

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).

--

guido wugi

Earths relative to a traveller along their axis of symmetry.

What *is* true and correct, is that the belts are observed (Lorentz-wise

as well as 'looking'-wise) to advance at different speeds 'back' and

'fro', by the traveller.

Take a look at the graph I proposed before:

https://www.desmos.com/calculator/wreelz925x?lang=nl

For an example, choose b=0.43 (traveller velocity) and d=0.75 (belt

velocity). Choose "Show voyager's POV" (and unchoose "Show Earths'

POV"). Now let the traveller go from Earth1 (left) to Earth2 (right)

with parameter s. Look at the following events:

O. s=0 :

traveller leaves Earth1. Belt check points B (in Earths' POV) leave

their respective Earth, say, B1 and B2. But in traveller's POV, B'1

coincides with B1, but B'2 is already underway, as traveller's x-axis

points to Earths' future.

A. s=0.24 :

Checkpoints B'1 and B'2 cross each other midways (same event for both

traveller and Earths)

B. s=0.364 :

Traveller crosses checkpoint B'2 (heading to the left).

C. s=0.47 :

Checkpoint B'1 reaches Earth2 at the right.

! Immediately a "new" checkpoint B'2bis starts heading to the left! [not

shown]

Checkpoint B'2 is still on its way left.

! In the upper part there is no checkpoint at present!

D. s=0.7 :

Checkpoint B'2 reaches Earth1.

! Immediately, but only just now, a new checkpoint B'1bis starts heading

to the right! [not shown]

E. s=1 :

Voyager reaches Earth2.

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).

--

guido wugi

Aug 30, 2023, 3:11:52 AM8/30/23

to

Op 27/08/2023 om 22:18 schreef wugi:

> 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).

(Corrections)

The three distances:

between Eart1 and Earth2,

of belt moving 'along' with traveller, and

of belt moving 'opposite to' traveller,

are of course equal! (And just for a reminder, length-contracted in

traveller's POV WRT Earths' POV.)

But whereas the belt 'at rest' would be *symmetrical* in both halves,

the 'running' belt in traveller's POV will display different velocities

'to and fro', and appear

- "elongated" in his own direction of motion, so that "less than half"

is visible, running at a higher speed; and

- "shrunk" in the opposite direction, so that "more than half" is

visible, running at a lower speed.

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

--

guido wugi

> 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).

The three distances:

between Eart1 and Earth2,

of belt moving 'along' with traveller, and

of belt moving 'opposite to' traveller,

are of course equal! (And just for a reminder, length-contracted in

traveller's POV WRT Earths' POV.)

But whereas the belt 'at rest' would be *symmetrical* in both halves,

the 'running' belt in traveller's POV will display different velocities

'to and fro', and appear

- "elongated" in his own direction of motion, so that "less than half"

is visible, running at a higher speed; and

- "shrunk" in the opposite direction, so that "more than half" is

visible, running at a lower speed.

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

--

guido wugi

Sep 1, 2023, 3:34:51 AM9/1/23

to

Op 30/08/2023 om 9:11 schreef wugi:

> 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

A last (hopefully:) version, showing traveller's POV in both the Earths'

and traveller's rest systems:

https://www.desmos.com/calculator/tddxwyq5mf?lang=nl

And now some homework: do the same for Earths' POV (that is, in both

Earths' and traveller's rest system;)

--

guido wugi

> 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

and traveller's rest systems:

https://www.desmos.com/calculator/tddxwyq5mf?lang=nl

And now some homework: do the same for Earths' POV (that is, in both

Earths' and traveller's rest system;)

--

guido wugi

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