A question of history concerning Rindler Coordinates

1. Dec 18, 2014

Ammah

Shalom

1. Does anybody know where it is possible to read the original publication of Wolfganng Ridler (May he live long and be blessed) about Rinder coordinates? (acclerated observer in flat spacetime)

When was it published? when was the decision to name it after him?

2. Is there any difference between the acclerated observer system of coordinates explained in section 6.6 in: "Gravitation" (by Misner, Wheeler & Thorne 1974) and the Rindler coordnate system?

Thanks

2. Dec 18, 2014

Staff: Mentor

Yes; the placement of the spatial origin is different. In standard Rindler coordinates, the spatial origin (which is actually a coordinate singularity in this chart) is placed at the Rindler horizon, so that the proper acceleration of an observer at a distance $x$ from the origin is $1 / x$ . This makes the proper acceleration at the origin itself infinite (which is one manifestation of the fact that the origin is a coordinate singularity). In MTW's coordinates in section 6.6, the spatial origin is placed at the position of some particular accelerated observer, so the proper acceleration at the origin is the proper acceleration of that observer, call it $a$. The Rindler horizon in this chart is then at an $x$ coordinate of $- 1 / a$.

3. Dec 18, 2014

Staff: Mentor

Does MTW list any references? I don't have a copy handy to check.

[added] The earliest reference I can find with some quick Google searching is Rindler's book:

Rindler, W., 1969, Essential Relativity: Special, General, and Cosmological

If there's anything older, e.g. a journal article, you might be able to find it by searching on scholar.google.com for Rindler's articles.

Last edited: Dec 18, 2014
4. Dec 18, 2014

PAllen

All MTW is defining there is standard Fermi-Normal coordinates for a accelerating observer in SR. Note that the trivial coordinate transform:

x' = x-1/a

takes Rindler coordinates to FN coordinates for the world line at x=1/a,t=0 in Rindler coordinates. I don't see any references given in this section of MTW.

Last edited: Dec 18, 2014
5. Dec 18, 2014

Staff: Mentor

AFAICT MTW only lists Rindler's book as a reference, no journal articles.

6. Dec 18, 2014

George Jones

Staff Emeritus
The coordinates appear in the 1966 American Journal of Physics Article "Kruskal Space and the Uniformly Accelerated Frame",

http://scitation.aip.org/content/aapt/journal/ajp/34/12/10.1119/1.1972547

I don't think I see the coordinates explicitly in the Physical Review article "Hyperbolic Motion in Curved Space Time", but I think that he had them in mind,

http://journals.aps.org/pr/abstract/10.1103/PhysRev.119.2082

Also, they might appear (I don't know) in the first (1960) and second (1966) editions of Rindler's book "Special Relativity".

Last edited: Dec 18, 2014
7. Dec 18, 2014

Ammah

Thank you so much!!!

8. Dec 18, 2014

Ammah

Thank you all so much, your answeres have been so helpful! Thank you for the time and kindness (on top of knowledge)
Bless you