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Nov 7, 2022, 3:15:04 AM11/7/22

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In my animation

https://www.geogebra.org/m/ytws9kbr

there are two trolleys that start from stationary on the rail and

accelerate to speed v=0.866c (range=2).

In one case, the two carriages remain at the same distance (and the belt

does not break), in the other the trolley B moves twice as far away from

the trolley A (and the belt breaks): which of the two conditions is

correct?

https://www.geogebra.org/m/ytws9kbr

there are two trolleys that start from stationary on the rail and

accelerate to speed v=0.866c (range=2).

In one case, the two carriages remain at the same distance (and the belt

does not break), in the other the trolley B moves twice as far away from

the trolley A (and the belt breaks): which of the two conditions is

correct?

Nov 8, 2022, 11:37:37 AM11/8/22

to

carriage A, and I think you intend that both start at the same time, in the

initial rest frame. In that case the top animation with the carriages pulling

apart is mostly correct.

I say mostly correct because the animation does not take into account how

the observers in carriage A will see only a delayed image of B, and thus

when starting up will initially see B stationary for a moment before the

light from B gets to A. In fact A will always see a delayed image of B,

yet the string will stretch and break. Likewise, initially the string will

not be pulled by B, as seen at A, until the acceleration of B can

propagate down the string at the speed of sound.

Also you do not show the Lorentz contraction of the railroad ties as the

carriages speed increases. That is happening also.

Rich L.

Nov 9, 2022, 1:33:05 AM11/9/22

to

turns out that the accelerations cannot both remain the same as

experienced by the trolleys, and the same as determined by an observer

who remains at rest relative to the initial state.

So you have to choose which it will be, and your choice will affect the

outcome.

Sylvia.

Nov 10, 2022, 10:36:37 AM11/10/22

to

Luigi Fortunati <fortuna...@gmail.com> wrote:

> In my animation

> https://www.geogebra.org/m/ytws9kbr

> there are two trolleys that start from stationary on the rail and

> accelerate to speed v=0.866c (range=2).

There's a very nice discussion of this in the physics FAQ:
> In my animation

> https://www.geogebra.org/m/ytws9kbr

> there are two trolleys that start from stationary on the rail and

> accelerate to speed v=0.866c (range=2).

https://math.ucr.edu/home/baez/physics/Relativity/SR/BellSpaceships/spaceship_puzzle.html

There's also a nice discussion of this paradox (including a link to

the above physics FAQ article) in

https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox

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Nov 10, 2022, 11:44:26 AM11/10/22

to

In the first case, which of the two conditions is correct?

And in the second case?

Luigi.

Nov 11, 2022, 11:33:57 AM11/11/22

to

Jonathan Thornburg [remove -color to reply] giovedě 10/11/2022 alle ore

16:36:34 ha scritto:

space.

The two trolleys have the same acceleration in the reference of the

tracks where they maintain the same distance.

But is the initial distance of only one rail and, therefore, neither of

my two animations are correct?

16:36:34 ha scritto:

> Luigi Fortunati <fortuna...@gmail.com> wrote:

>> In my animation

>> https://www.geogebra.org/m/ytws9kbr

>> there are two trolleys that start from stationary on the rail and

>> accelerate to speed v=0.866c (range=2).

>

> There's a very nice discussion of this in the physics FAQ:

>

> https://math.ucr.edu/home/baez/physics/Relativity/SR/BellSpaceships/spaceship_puzzle.html

>

> There's also a nice discussion of this paradox (including a link to

> the above physics FAQ article) in

> https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox

Yes, my animation reproduces Bell's paradox, set on Earth instead of in
>> In my animation

>> https://www.geogebra.org/m/ytws9kbr

>> there are two trolleys that start from stationary on the rail and

>> accelerate to speed v=0.866c (range=2).

>

> There's a very nice discussion of this in the physics FAQ:

>

> https://math.ucr.edu/home/baez/physics/Relativity/SR/BellSpaceships/spaceship_puzzle.html

>

> There's also a nice discussion of this paradox (including a link to

> the above physics FAQ article) in

> https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox

space.

The two trolleys have the same acceleration in the reference of the

tracks where they maintain the same distance.

But is the initial distance of only one rail and, therefore, neither of

my two animations are correct?

Nov 12, 2022, 12:57:33 AM11/12/22

to

On 11/11/2022 3:44 am, Luigi Fortunati wrote:

> Sylvia Else marted=EC 08/11/2022 alle ore 15:33:00 ha scritto:

> Sylvia Else marted=EC 08/11/2022 alle ore 15:33:00 ha scritto:

> Consider both cases individually.

>

> In the first case, which of the two conditions is correct?

>

> And in the second case?

>

> Luigi.

I think it would be more helpful for you to explain what you think will
>

> In the first case, which of the two conditions is correct?

>

> And in the second case?

>

> Luigi.

happen in the two cases, and why. Then we could look at your analysis.

Sylvia.

Nov 12, 2022, 4:30:10 PM11/12/22

to

moving away from me by twice the initial distance (as Bell says in his

explanation).

At the same time, I see the distances between the track sleepers (the

rail) shrinking.

The effect of both causes increases the number of rails between me and

trolley B from 1 to 4, as is the case at the top of my animation.

But 4 rails between me and B contrast with my speed over the ground

(v=0.866c range=2), for which there should only be 2 rails (twice as

much) between me and B (as is the case at the Bottom of my animation)

and not 4 rails.

Hence my doubt that I was hoping someone could clarify, because if one

solution is right, the other is wrong (and vice versa).

Luigi

Nov 12, 2022, 10:08:54 PM11/12/22

to

On 13/11/2022 8:30 am, Luigi Fortunati wrote:

> Sylvia Else venerd=EC 11/11/2022 alle ore 14:57:28 ha scritto:

> Sylvia Else venerd=EC 11/11/2022 alle ore 14:57:28 ha scritto:

>>> Consider both cases individually.

>>>

>>> In the first case, which of the two conditions is correct?

>>>

>>> And in the second case?

>>>

>>> Luigi.

>>

>> I think it would be more helpful for you to explain what you think will

>> happen in the two cases, and why. Then we could look at your analysis.

>>

>> Sylvia.

>

> I am on board of trolley A and, during acceleration, I see trolley B

> moving away from me by twice the initial distance (as Bell says in his

> explanation).

>

> At the same time, I see the distances between the track sleepers (the

> rail) shrinking.

>

> The effect of both causes increases the number of rails between me and

> trolley B from 1 to 4, as is the case at the top of my animation.

>

> But 4 rails between me and B contrast with my speed over the ground

> (v=0.866c range=2), for which there should only be 2 rails (twice as

> much) between me and B (as is the case at the Bottom of my animation)

> and not 4 rails.

>

> Hence my doubt that I was hoping someone could clarify, because if one

> solution is right, the other is wrong (and vice versa).

>

> Luigi

In this scenario, the choice you've made is that the two trolleys
>>>

>>> In the first case, which of the two conditions is correct?

>>>

>>> And in the second case?

>>>

>>> Luigi.

>>

>> I think it would be more helpful for you to explain what you think will

>> happen in the two cases, and why. Then we could look at your analysis.

>>

>> Sylvia.

>

> I am on board of trolley A and, during acceleration, I see trolley B

> moving away from me by twice the initial distance (as Bell says in his

> explanation).

>

> At the same time, I see the distances between the track sleepers (the

> rail) shrinking.

>

> The effect of both causes increases the number of rails between me and

> trolley B from 1 to 4, as is the case at the top of my animation.

>

> But 4 rails between me and B contrast with my speed over the ground

> (v=0.866c range=2), for which there should only be 2 rails (twice as

> much) between me and B (as is the case at the Bottom of my animation)

> and not 4 rails.

>

> Hence my doubt that I was hoping someone could clarify, because if one

> solution is right, the other is wrong (and vice versa).

>

> Luigi

accelerate at the same rate as determined by the observer at rest

relative to the initial state.

They accelerate at different rates in their respective frames (which
implies that differing, and indeed changing, forces are being applied to

them). If the trolleys were connected by an inextensible tether, then it

would break.

Sylvia

Nov 13, 2022, 5:10:38 AM11/13/22

to

Sylvia Else sabato 12/11/2022 alle ore 12:08:50 ha scritto:

>> I am on board of trolley A and, during acceleration, I see trolley B

>> moving away from me by twice the initial distance (as Bell says in his

>> explanation).

>>

>> At the same time, I see the distances between the track sleepers (the

>> rail) shrinking.

>>

>> The effect of both causes increases the number of rails between me and

>> trolley B from 1 to 4, as is the case at the top of my animation.

>>

>> But 4 rails between me and B contrast with my speed over the ground

>> (v=0.866c range=2), for which there should only be 2 rails (twice as

>> much) between me and B (as is the case at the Bottom of my animation)

>> and not 4 rails.

>>

>> Hence my doubt that I was hoping someone could clarify, because if one

>> solution is right, the other is wrong (and vice versa).

>>

>> Luigi

>

> In this scenario, the choice you've made is that the two trolleys

> accelerate at the same rate as determined by the observer at rest

> relative to the initial state.

>

> They accelerate at different rates in their respective frames (which

> implies that differing, and indeed changing, forces are being applied to

> them). If the trolleys were connected by an inextensible tether, then it

> would break.

>

> Sylvia

So the scenario of the top of my animation
>> I am on board of trolley A and, during acceleration, I see trolley B

>> moving away from me by twice the initial distance (as Bell says in his

>> explanation).

>>

>> At the same time, I see the distances between the track sleepers (the

>> rail) shrinking.

>>

>> The effect of both causes increases the number of rails between me and

>> trolley B from 1 to 4, as is the case at the top of my animation.

>>

>> But 4 rails between me and B contrast with my speed over the ground

>> (v=0.866c range=2), for which there should only be 2 rails (twice as

>> much) between me and B (as is the case at the Bottom of my animation)

>> and not 4 rails.

>>

>> Hence my doubt that I was hoping someone could clarify, because if one

>> solution is right, the other is wrong (and vice versa).

>>

>> Luigi

>

> In this scenario, the choice you've made is that the two trolleys

> accelerate at the same rate as determined by the observer at rest

> relative to the initial state.

>

> They accelerate at different rates in their respective frames (which

> implies that differing, and indeed changing, forces are being applied to

> them). If the trolleys were connected by an inextensible tether, then it

> would break.

>

> Sylvia

https://www.geogebra.org/m/ytws9kbr

where the ribbon breaks is correct.

But how do you justify the fact that reaching the speed v=0.866c

(gamma=2) the distance between A and B (in the reference of the trolley=

A) is 4 sleepers (quadruple) and not 2 (double)?

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