sci.physics.research

On Aug 3, 10:51 pm, Igor Khavkine wrote:
>
> As I understand the text, it's prescribing two curves,
> one x = sqrt(1+t^2) and the second x = sqrt(K^2+t^2). At t=0, the first
> has x = 1, while the second has x = K. These are the initial positions
> of the two rocket ships, so their initial lab frame separation is K-1.
> If you draw these two curves, you'll see that they do not intersect, but
> share a common asymptote, x = t. That is the picture that I believe
> the text is describing.
>
> If you want to shift the two curves, then you do so by shifting both of
> them by the same amount, which won't change their relative asymptotic
> properties. As you've noticed, if you shift them both by different
> amounts, you can make them intersect.
>
> The shape of each curve determines the precise acceleration that the
> corresponding space ship experiences. The two curves, which I explicitly
> gave above, have their accelerations and initial positions precisely
> tuned to get the same asymptote. If change the shape of one of the
> curves, or if you shift one curve with respect to the other, this
> asymptotic property is broken.
>
> Hope this helps. I'm happy to see that the FAQ is getting some new
> illustrations. Good work!
>
> Igor

So, maybe the original author did intend (K-1) here to be the initial
separation of the ships, which he called k before. The problem I have
with that is the physical meaning of an absolute number (1) in terms
of a position. One what? What units?

I also found another inconsistency in the text, which I described in
the original thread in the newsgroup. What is
the acceleration of the curve containing K? Is it greater than the
original curve (containing 1)?