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
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