I added one variable to a similar posting I did to see how this scenario is explained.

Scenario:
There are four inertial reference frames, F0, F1, F2 and F3 with relative velocities along the x-axis. F1 has a velocity of V = 0.6c in the positive x direction relative to F0. F2 has a velocity of V = c*sqrt(3)/2 in the positive x direction relative to F0. F3 has a relative velocity of V = c*sqrt(3)/2 in the positive x direction relative to F2.
At rest in frame F0 is a 10 meter rod and three small point objects, A, B1 and B2. The 10 meter rod is aligned along the x-axis. Object A is at the left end of the 10 meter rod, the right end of the rod I'll call B, and objects B1 and B2 are 10 meters away from object A at the right end of the rod (at slightly different y coordinates so their motion doesn't affect each other when they start moving). Per Einstein, F1 measures the rod to be 8 meters in length and points B1 and B2 to be 8 meters away from A. F2 measures the rod to be 5 meters in length and points B1 and B2 to be 5 meters away from A. When small point objects A, B1 or B2 accelerate, each small point object accelerates with the exact same acceleration rate, although the start time of each acceleration may vary.

At time t0 in F0, object A and the 10 meter rod traveling along with object A start accelerating in the positive x direction along the x-axis. The acceleration rate is very slow, say 0.01g. The acceleration of object A and the acceleration of the left end of the 10 meter rod are identical. As the rod accelerates, each inertial reference frame that the rod has zero relative velocity with respect to as it passes through that inertial reference frame measures the length of the rod to be essentially 10 meters. So, observers in rest in frame F1 say the rod is 10 meters in length when it has essentially zero velocity with respect to F1. Observers in frame F2 says the rod is 10 meters in length when it has essentially zero velocity to F2 and observers in frame F3 says the rod is 10 meters in length when it has essentially zero velocity with respect to F3.

Now if you agree with that, then here's the situation I haven't been able to get an explanation for. At time t0 in F0 when point A and the rod start accelerating in the positive x direction toward F3, observers in F1 simultaneously start the acceleration of the small point object B1 in the positive x direction. And at time t0 in F0 when point A and the rod start accelerating, observers in F2 simultaneously start the acceleration of the small point object B2 in the positive x direction. Per Einstein, the start of the accelerations of A, B1 and B2 as observed in F0 are not simultaneous. And the start of the accelerations of B1 and B2 are not simultaneous as observed in F1 and F2. Since the acceleration rates of A, B1 and B2 are identical, observers in F1 measure that the separation between A and B1 is always 8 meters in length throughout the acceleration from F0 to F3. Observers in F2 measure that the separation between A and B2 is always 5 meters as they travel from F0 to F3.
Now an observer always accelerating at A along with the 10 meter rod sees that the separation between A and B1 is getting smaller and smaller relative to the length of the 10 meter rod. When A and the 10 meter rod have zero velocity with respect to F1, the point objects A and B1 are separated by 8 meters along the 10 meter rod. However, as the acceleration continues instead of objects A and B1 moving closer and closer to each other along the length of the rod, those two objects start moving farther and farther apart. When those objects have a relative velocity of 0.6c relative to F1 objects A and B1 are separated by the length of the rod as they were at the start of the scenario.
Likewise, when object B2 accelerates to F3 along with object A and the 10 meter rod, the observer accelerating with the 10 meter rod sees that the separation between objects A and B2 is getting smaller and smaller relative to the length of the 10 meter rod. This continues as the acceleration continues past F1 until A, B2 and the rod have zero velocity with respect to F2. At that point, the rod is 10 meters in length but the separation between A and B2 is 5 meters. As the acceleration continues, instead of the separation between A and B2 getting smaller and smaller, the separation between A and B2 gets larger and larger compared to the length of the rod. When they have zero velocity with respect to F3, the separation between A, B2 are the same length as the rod as they were at the start of the scenario.
So what is the physics explanation for the motion of B1 and the motion of B2 relative to the 10 meter rod during the accelerations from F0 to F3? Both B1 and B2 move toward the midpoint of the 10 meter rod just after the accelerations begin. Then B1 starts moving back toward the B end of the rod while B2 continues moving toward the midpoint of the rod. Then B2 starts moving away from the midpoint of the rod toward its starting location at B on the rod.

Thanks for any physics reply,
David Seppala
Bastrop TX

On 20-Dec-23 10:57 am, sep...@yahoo.com wrote:
> I added one variable to a similar posting I did to see how this
> scenario is explained.
>
> Scenario: There are four inertial reference frames, F0, F1, F2 and F3
> with relative velocities along the x-axis. F1 has a velocity of V =
> 0.6c in the positive x direction relative to F0. F2 has a velocity of
> V = c*sqrt(3)/2 in the positive x direction relative to F0. F3 has a
> relative velocity of V = c*sqrt(3)/2 in the positive x direction
> relative to F2. At rest in frame F0 is a 10 meter rod and three small
> point objects, A, B1 and B2. The 10 meter rod is aligned along the
> x-axis. Object A is at the left end of the 10 meter rod, the right
> end of the rod I'll call B, and objects B1 and B2 are 10 meters away
> from object A at the right end of the rod (at slightly different y
> coordinates so their motion doesn't affect each other when they start
> moving). Per Einstein, F1 measures the rod to be 8 meters in
> length and points B1 and B2 to be 8 meters away from A. F2 measures
> the rod to be 5 meters in length and points B1 and B2 to be 5 meters
> away from A. When small point objects A, B1 or B2 accelerate, each
> small point object accelerates with the exact same acceleration rate,
> although the start time of each acceleration may vary.
>
> At time t0 in F0, object A and the 10 meter rod traveling along with
> object A start accelerating in the positive x direction along the
> x-axis. The acceleration rate is very slow, say 0.01g. The
> acceleration of object A and the acceleration of the left end of the
> 10 meter rod are identical. As the rod accelerates, each inertial
> reference frame that the rod has zero relative velocity with respect
> to as it passes through that inertial reference frame measures the
> length of the rod to be essentially 10 meters. So, observers in rest
> in frame F1 say the rod is 10 meters in length when it has
> essentially zero velocity with respect to F1. Observers in frame F2
> says the rod is 10 meters in length when it has essentially zero
> velocity to F2 and observers in frame F3 says the rod is 10 meters in
> length when it has essentially zero velocity with respect to F3.
>
> Now if you agree with that, then here's the situation I haven't been
> able to get an explanation for. At time t0 in F0 when point A and the
> rod start accelerating in the positive x direction toward F3,
> observers in F1 simultaneously start the acceleration of the small
> point object B1 in the positive x direction. And at time t0 in F0
> when point A and the rod start accelerating, observers in F2
> simultaneously start the acceleration of the small point object B2 in
> the positive x direction. Per Einstein, the start of the
> accelerations of A, B1 and B2 as observed in F0 are not simultaneous.
> And the start of the accelerations of B1 and B2 are not simultaneous
> as observed in F1 and F2. Since the acceleration rates of A, B1 and
> B2 are identical, observers in F1 measure that the separation between
> A and B1 is always 8 meters in length throughout the acceleration
> from F0 to F3. Observers in F2 measure that the separation between A
> and B2 is always 5 meters as they travel from F0 to F3. Now an
> observer always accelerating at A along with the 10 meter rod sees
> that the separation between A and B1 is getting smaller and smaller
> relative to the length of the 10 meter rod. When A and the 10 meter
> rod have zero velocity with respect to F1, the point objects A and B1
> are separated by 8 meters along the 10 meter rod. However, as the
> acceleration continues instead of objects A and B1 moving closer and
> closer to each other along the length of the rod, those two objects
> start moving farther and farther apart. When those objects have a
> relative velocity of 0.6c relative to F1 objects A and B1 are
> separated by the length of the rod as they were at the start of the
> scenario. Likewise, when object B2 accelerates to F3 along with
> object A and the 10 meter rod, the observer accelerating with the 10
> meter rod sees that the separation between objects A and B2 is
> getting smaller and smaller relative to the length of the 10 meter
> rod. This continues as the acceleration continues past F1 until A, B2
> and the rod have zero velocity with respect to F2. At that point,
> the rod is 10 meters in length but the separation between A and B2 is
> 5 meters. As the acceleration continues, instead of the separation
> between A and B2 getting smaller and smaller, the separation between
> A and B2 gets larger and larger compared to the length of the rod.
> When they have zero velocity with respect to F3, the separation
> between A, B2 are the same length as the rod as they were at the
> start of the scenario. So what is the physics explanation for the
> motion of B1 and the motion of B2 relative to the 10 meter rod during
> the accelerations from F0 to F3? Both B1 and B2 move toward the
> midpoint of the 10 meter rod just after the accelerations begin. Then
> B1 starts moving back toward the B end of the rod while B2 continues
> moving toward the midpoint of the rod. Then B2 starts moving away
> from the midpoint of the rod toward its starting location at B on the
> rod.
>
> Thanks for any physics reply, David Seppala Bastrop TX
>

How many times do you expect people to wade through your convoluted
scenarios to find your mistake?

Sylvia.

On Tuesday, December 19, 2023 at 6:04:17 PM UTC-6, Sylvia Else wrote:
> On 20-Dec-23 10:57 am, sep...@yahoo.com wrote:
> > I added one variable to a similar posting I did to see how this
> > scenario is explained.
> >
> > Scenario: There are four inertial reference frames, F0, F1, F2 and F3
> > with relative velocities along the x-axis. F1 has a velocity of V =
> > 0.6c in the positive x direction relative to F0. F2 has a velocity of
> > V = c*sqrt(3)/2 in the positive x direction relative to F0. F3 has a
> > relative velocity of V = c*sqrt(3)/2 in the positive x direction
> > relative to F2. At rest in frame F0 is a 10 meter rod and three small
> > point objects, A, B1 and B2. The 10 meter rod is aligned along the
> > x-axis. Object A is at the left end of the 10 meter rod, the right
> > end of the rod I'll call B, and objects B1 and B2 are 10 meters away
> > from object A at the right end of the rod (at slightly different y
> > coordinates so their motion doesn't affect each other when they start
> > moving). Per Einstein, F1 measures the rod to be 8 meters in
> > length and points B1 and B2 to be 8 meters away from A. F2 measures
> > the rod to be 5 meters in length and points B1 and B2 to be 5 meters
> > away from A. When small point objects A, B1 or B2 accelerate, each
> > small point object accelerates with the exact same acceleration rate,
> > although the start time of each acceleration may vary.
> >
> > At time t0 in F0, object A and the 10 meter rod traveling along with
> > object A start accelerating in the positive x direction along the
> > x-axis. The acceleration rate is very slow, say 0.01g. The
> > acceleration of object A and the acceleration of the left end of the
> > 10 meter rod are identical. As the rod accelerates, each inertial
> > reference frame that the rod has zero relative velocity with respect
> > to as it passes through that inertial reference frame measures the
> > length of the rod to be essentially 10 meters. So, observers in rest
> > in frame F1 say the rod is 10 meters in length when it has
> > essentially zero velocity with respect to F1. Observers in frame F2
> > says the rod is 10 meters in length when it has essentially zero
> > velocity to F2 and observers in frame F3 says the rod is 10 meters in
> > length when it has essentially zero velocity with respect to F3.
> >
> > Now if you agree with that, then here's the situation I haven't been
> > able to get an explanation for. At time t0 in F0 when point A and the
> > rod start accelerating in the positive x direction toward F3,
> > observers in F1 simultaneously start the acceleration of the small
> > point object B1 in the positive x direction. And at time t0 in F0
> > when point A and the rod start accelerating, observers in F2
> > simultaneously start the acceleration of the small point object B2 in
> > the positive x direction. Per Einstein, the start of the
> > accelerations of A, B1 and B2 as observed in F0 are not simultaneous.
> > And the start of the accelerations of B1 and B2 are not simultaneous
> > as observed in F1 and F2. Since the acceleration rates of A, B1 and
> > B2 are identical, observers in F1 measure that the separation between
> > A and B1 is always 8 meters in length throughout the acceleration
> > from F0 to F3. Observers in F2 measure that the separation between A
> > and B2 is always 5 meters as they travel from F0 to F3. Now an
> > observer always accelerating at A along with the 10 meter rod sees
> > that the separation between A and B1 is getting smaller and smaller
> > relative to the length of the 10 meter rod. When A and the 10 meter
> > rod have zero velocity with respect to F1, the point objects A and B1
> > are separated by 8 meters along the 10 meter rod. However, as the
> > acceleration continues instead of objects A and B1 moving closer and
> > closer to each other along the length of the rod, those two objects
> > start moving farther and farther apart. When those objects have a
> > relative velocity of 0.6c relative to F1 objects A and B1 are
> > separated by the length of the rod as they were at the start of the
> > scenario. Likewise, when object B2 accelerates to F3 along with
> > object A and the 10 meter rod, the observer accelerating with the 10
> > meter rod sees that the separation between objects A and B2 is
> > getting smaller and smaller relative to the length of the 10 meter
> > rod. This continues as the acceleration continues past F1 until A, B2
> > and the rod have zero velocity with respect to F2. At that point,
> > the rod is 10 meters in length but the separation between A and B2 is
> > 5 meters. As the acceleration continues, instead of the separation
> > between A and B2 getting smaller and smaller, the separation between
> > A and B2 gets larger and larger compared to the length of the rod.
> > When they have zero velocity with respect to F3, the separation
> > between A, B2 are the same length as the rod as they were at the
> > start of the scenario. So what is the physics explanation for the
> > motion of B1 and the motion of B2 relative to the 10 meter rod during
> > the accelerations from F0 to F3? Both B1 and B2 move toward the
> > midpoint of the 10 meter rod just after the accelerations begin. Then
> > B1 starts moving back toward the B end of the rod while B2 continues
> > moving toward the midpoint of the rod. Then B2 starts moving away
> > from the midpoint of the rod toward its starting location at B on the
> > rod.
> >
> > Thanks for any physics reply, David Seppala Bastrop TX
> >
> How many times do you expect people to wade through your convoluted
> scenarios to find your mistake?
>
> Sylvia.
How many times? The third time is a charm!
David