A question of history concerning Rindler Coordinates

  • Thread starter Ammah
  • Start date
  • #1
6
0
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
 

Answers and Replies

  • #2
PeterDonis
Mentor
Insights Author
2020 Award
32,862
11,360
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?
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
jtbell
Mentor
15,727
3,878
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:
  • #4
PAllen
Science Advisor
8,265
1,518
Does MTW list any references? I don't have a copy handy to check.
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:
  • #5
PeterDonis
Mentor
Insights Author
2020 Award
32,862
11,360
Does MTW list any references?
AFAICT MTW only lists Rindler's book as a reference, no journal articles.
 
  • #6
George Jones
Staff Emeritus
Science Advisor
Gold Member
7,413
1,054
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:
  • #7
6
0
Thank you so much!!!
 
  • #8
6
0
Thank you all so much, your answeres have been so helpful! Thank you for the time and kindness (on top of knowledge)
Bless you
 

Related Threads on A question of history concerning Rindler Coordinates

  • Last Post
Replies
10
Views
6K
  • Last Post
Replies
2
Views
1K
  • Last Post
2
Replies
33
Views
5K
  • Last Post
Replies
6
Views
6K
Replies
2
Views
4K
Replies
6
Views
589
Replies
29
Views
1K
Replies
4
Views
2K
Replies
4
Views
505
Top