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1. Given that two particles separated by distance L'=L initially at rest in inertial frame O' accelerate along the line through both.
2. Given that the distance L' as measured in O' between the two particles is always equal to L.
3. Assume the acceleration is such that a(tau) is the same for both particles.
4. Item 3 implies that the two particles have zero velocity in a comoving inertial reference frame O.
5. Item 4 implies the separation between the two particles in O is L.
6. Item 1 and the definition of acceleration implies that at any time later than the time at which the acceleration started, frame O' has an non-zero velocity along the line through both particles relative to frame O.
7. Special Relativity implies that the on O' projected separation of the particles L' is less than L.
8. Item 7 contradicts the given item 2.
9. The assumption in item 3 leads to a contradiction.
10. The assumption in item 3 is false.