• Re: Length contraction - contradiction or explanation?

    From Sylvia Else@21:1/5 to sep...@yahoo.com on Wed Dec 20 11:04:12 2023
    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.

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