# relativity and accelerating BBs

#### dseppala

Woody,
During the journey from F1 to F0 let the co-accelerating observer have a 10 meter rod that he generally keeps aligned perpendicular to the direction of the acceleration. Every now and then he rotates the rod so that it is aligned in the direction of acceleration so he can compare the separation between the two BBs to the length of the rod. He then returns it so that it is perpendicular to the direction of the acceleration until he makes some future measurement.

Whenever he makes a measurement with the rod the measurement is essentially the same as the measurement someone does in an inertial reference frame that has zero relative velocity wrt to the co-accelerating observer at the time of the measurement. I made the acceleration rate extremely low so the bending of the rod has negligible effect.

At the start of the accelerations, the rod and the two BBs are each 10 meters apart. But when the speed of the BBs and co-accelerating observer is zero with respect to F0, everyone in F0 measures the separation of the BBs to be 5 meters apart. So when the co-accelerating observer rotates the 10 meter rod so that it is aligned with the BBs he finds that the separation between the BBs is only half the length of the rod at this point in time. He then returns the rod so that it is perpendicular to the direction of the acceleration.

David Seppala
Bastrop TX

#### Woody

No No No and No again

You seem to insist that the observer in F0 always sees the separation as 5m
Which you then say implies that the observer in FA must see the length change.

But exactly the opposite is true!
The observer in FA sees the length as constant.
The observer in F0 sees the length changing.

#### dseppala

Woody,
At the start of the scenario, the BBs are 10 meters apart in their rest frame of F1. F0 measures them to be 5 meters apart because of its velocity V relative to F1. F0 starts the acceleration of both BBs simultaneously. They accelerate in the identical way therefore F0 always measures the separation between the BBs as a constant 5 meters (center to center).
David Seppala
Bastrop TX

#### Woody

Still No.

Having F0 start the acceleration is totally immaterial.
The relative velocities are unaffected by who starts the acceleration or from which frame of reference.

F0 will see the separation change from 5m to 10m to 5m as the relative velocity between FA and F0 changes.

You seem to be wanting to place the BBs in the F0 reference frame
But only objects travelling at the same velocity as F0 can be in the F0 reference frame,
That is the whole point of an inertial reference frame.

Anything travelling at a different velocity is in a different reference frame.
For everyday life, the difference is too small to be noticed, but it is there.

#### dseppala

Woody,
Frame F0 observes the BBs to be 5 meters apart before the acceleration starts due to length contraction. When he starts them simultaneously, they remain 5 meters apart in their journey to F0 as observed by F0 observers. The co-accelerating observer measures the BBs to be 10 meters apart before the acceleration starts. When he arrives in frame F0, the co-accelerating observer like everyone else who now has zero velocity with respect to F0 measures the BBs to be 5 meters apart. The co-accelerating observer says the BBs went from 10 meters apart to 5 meters apart when they reached F0.

David Seppala
Bastrop TX

#### Woody

What makes you insist that F0 observers will always see them as 5m apart?
What is special about the relationship of F0 observers to the BBs?

#### dseppala

Woody,
The two BBs are originally at rest in frame F1 and are separated by a distance of 10 meters. Frame F0 has a relative velocity of V = sqrt(3)/2*c with respect to frame F1. Per Einstein, that gives a length contraction of a factor of 2. So doesn't frame F0 measure that the BBs while at rest in F1 are only 5 meters apart?
David Seppala
Bastrop TX

#### Woody

Yes But.

The two BBs are originally at rest in frame F1 and are separated by a distance of 10 meters. Frame F0 has a relative velocity of V = sqrt(3)/2*c with respect to frame F1. Per Einstein, that gives a length contraction of a factor of 2. So doesn't frame F0 measure that the BBs while at rest in F1 are only 5 meters apart?
The key part of the above is; "while at rest in F1"

But they don't stay at rest in F1,
they are gradually accelerating so their relative velocity with respect to F0 is changing.
The length contraction is a function of the relative velocity of the objects and the observer.
So their length contraction (as observed from F0) is changing in accordance with this change in relative velocity.

#### dseppala

Woody,
Both BBs are initially at rest in F1. Observers in the F0 frame start the acceleration of each BB simultaneously. Both BBs accelerate in the identical way. Ergo, since the accelerations were identical and the two BBs started accelerating simultaneously as measured in F0, F0 observers measure that the BBs always keep the same separation they had when they were at rest before the acceleration started.
David Seppala
Bastrop TX

#### Woody

One last time.

F0 observers measure that the BBs always keep the same separation they had when they were at rest before the acceleration started
The whole point of the theory is that they don't.
Measurements, in the direction of relative velocity, depend on the relative velocity of the objects and the measurer.

In their own frame (FA) the BBs are 10m apart, at all times.
As viewed from any other frame, the distance between them depends on the relative velocity of FA to the observers frame (F0).

If the velocity of FA relative to F0 is changing then the observed distance will change.

I have said as much in different words many times in this thread.
If you still insist on sticking to your own (wrong) interpretation
then I don't think there is much point in me continuing to respond.