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Old Feb 23rd 2019, 08:24 PM   #1
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Acceleration contradiction?

Let there be three inertial frames, F0, F1 and F2. F1 is moving in the negative x direction relative to F0 with speed V = sqrt(3)/2 * c. F2 is moving in the positive x direction relative to F0 with speed V = sqrt(3)/2 * c.

In frame F1 there are two BB pellets at rest spaced 10 meters apart as measured in F1. F0, per Einstein, measures the separation between the two BB pellets to be 5 meters. At time t0 in frame F0, frame F0 simultaneously starts both BB pellets accelerating in the positive x direction. The two BB pellets each accelerate in the identical pattern until they have zero velocity relative to frame F2 at which time F0 simultaneously stops the accelerations.

An observer travels with one of the BB pellets accelerating identically as the adjacent BB pellet accelerates. That observer measures that the two BB pellets were initially 10 meters apart. When the BB pellets and the traveling observer have zero velocity with respect to frame F0, the traveling observer measures the BB pellets to be only 5 meters apart, just as every other observer in frame F0 does. When the BB pellets and traveling observer reach frame F2 and stop accelerating, the traveling observer once again measures the separation between the two BB pellets to be 10 meters.

Since the acceleration is always in the positive x direction, and since the pattern is identical for the two BB pellets (we can say make the acceleration constant as measured by the traveling observer), why does the accelerating observer say that the identical acceleration in the positive direction sometime causes the two BB pellets to move toward each other (the first part of the journey) and sometimes causes the two BB pellets to move away from each other (the second part of the journey)?

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Old Feb 25th 2019, 06:47 AM   #2
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You are hopping between reference frames in a carefree manner!
One always has to be very careful when moving between reference frames that all relevant terms are considered.
I haven't had time (yet) to trace your arguments slowly and carefully through each of your jumps,
so I can't comment (yet) on the correctness of your conclusions.
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Old Feb 26th 2019, 04:45 AM   #3
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It was a little confusing because you have a miss-typing in your post:
The pellets start accelerating from Frame F1 (not F0 as your post seems to indicate).

The Pellets are now in their own (accelerating) frame (FP).
At all times the observer in Frame FP will observe the pellets to be 10m apart.

But observers in other frames will observe the distance between the pellets to change as their velocities relative to FP change.
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Old Feb 26th 2019, 05:16 AM   #4
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Woody wrote:
"The Pellets are now in their own (accelerating) frame (FP).
At all times the observer in Frame FP will observe the pellets to be 10m apart."

No, your statement is incorrect. When the accelerating frame FP has zero velocity with respect to frame F0 they measure the same distance between the BB pellets as all other observers in frame F0 do. All F0 observers measure the distance between the BB pellets to be 5 meters from the start to the finish of the acceleration since frame F0 measures the initial distance between the BB pellets to be 5 meters (per Einstein), and the acceleration of each BB pellet started simultaneously from frame F0 point of view.

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Old Feb 26th 2019, 06:04 AM   #5
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When the accelerating frame FP has zero velocity with respect to frame F0 they measure the same distance between the BB pellets as all other observers in frame F0 do.
Agreed.

All F0 observers measure the distance between the BB pellets to be 5 meters from the start to the finish of the acceleration since frame F0 measures the initial distance between the BB pellets to be 5 meters (per Einstein), and the acceleration of each BB pellet started simultaneously from frame F0 point of view.
Wrong.

The whole point of the reference frames is that all objects (and observers) in that frame are moving at the same speed.
Any observations between two (or more) frames (moving a different speeds)
will produce differences to the same observations taken within a single frame.

The pellets (FP) are initially in Frame F1 but are accelerating through Frame F0 (and eventually on to Frame F2).

When they are in Frame F1, observers in F1 will see them 10m apart,
observers in F0 will see them as being 5m apart.

When the pellets accelerate enough to reach Frame F0,
observers in F0 will see them as being 10m apart,
but the observers in F1 will now see them as being 5m apart!

The observers in FP will always see them as 10m apart.
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Last edited by Woody; Feb 26th 2019 at 06:11 AM.
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Old Feb 26th 2019, 07:23 AM   #6
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As stated in the original post, F0 measures the distance between the pellets to be 5 meters when they are in F1. F0 starts the acceleration of each pellet simultaneously, and each pellet accelerates in the identical pattern. Therefore, F0 always measures the distance between the two pellets to be 5 meters through out the entire journey. With identical accelerations and with each acceleration starting simultaneously as measured in frame F0, the distance between pellets as measured in F0 never changes.

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