Talk:Rindler coordinates

To Do list wiped out

Looks my previous todo list somehow got wiped (did someone move the article but forget to move the talk page?), but I will try to reconstruct it. This is an important article needed for many other topics such as Bell's spaceship paradox. Rindler chart is an important example of a coordinate chart, and the Rindler frame is an important example of a frame field.---CH 01:08, 3 May 2006 (UTC)

Hmm... even worse, the allegedly nonsingular version someone added is obviously not free of coordinate singularities! I propose to start with a clean slate. There is a lot to say, but this article confuses some fundamental points early on and both the figures are unfortunately misleading.---CH 01:20, 3 May 2006 (UTC)

Sorry, that was my fault. When I first edited this article, I merely tried to clean it up and didn't really check it for errors--such as the coordinate singularity. Unfortunately I also propogated that error by introducing the term "non-singular" (Minkowski space is non-singular to begin with). Anyway, did a major rewrite, will try to get around to truncated Minkowski space which introduces an artificial singularity at R=0. DonQuixote 21:41, 3 May 2006 (UTC)

New version of Rindler coordinates

In order to address various concerns, I have written a completely new version from scratch with entirely new figures, and have modified the todo list accordingly. The new version currently focuses on elementary considerations. In the future I may elaborate on the analogies between two Killing horizons: the Rindler horizon and the event horizon of a Schwarzschild black hole.

The old version is here. Be careful, since this body of this article and the figures contain some mistakes and is generally misleading in various ways. ---CH 04:05, 5 May 2006 (UTC)

Todo list and student beware

I completely rewrote the May 2005 version, and had been monitoring this article for bad edits, but I am leaving the WP and am now abandoning it to its fate.

As a courtesy, I have removed the "expert" items from the todo list. I doubt anyone else will know how to implement the suggested improvements since this was mostly a note to myself.

See User:Hillman/Archive for the last version I edited. I emphatically do not vouch for anything you might see in more recent versions. Unfortunately, just before departing I became embroiled in a content dispute with Rod Ball (talk · contribs) and Harald88 (talk · contribs). I believe their edits of the related articles Bell's spaceship paradox and Ehrenfest paradox have turned factually accurate articles into gravely misleading and even mathematically incorrect articles.

Good luck to all students in your search for information, regardless!---CH 03:37, 1 July 2006 (UTC)

Units

I don't like the fact that a=1 in this article. Though permissible mathematically, it hides some of the physical content. CHF (talk) 18:34, 13 March 2008 (UTC)

I absolutely agree. In particular, it makes it hard to see why the Unruh effect should depend on a at all.--24.34.222.177 (talk) 22:33, 18 December 2008 (UTC)

rigidity/pardoxial property

I think one should empahsize in the article, that what is meant by "motion in constant acceleration" is not what people are used to as constant 3-accelration. This is clearly seen from the path of the particle which is $X={\sqrt {T^{2}+a}}$ in the globaly flat coordintas. Where what people usually(newtonian) mean by constant accelration is motion of the type $X=a*T^{2}$ .The whole pardox part of the article is somewhat confusing and missleading. If I hold a string, and a car has the other end of it and starts driving at constant 3-acceleration - the string will brake! —Preceding unsigned comment added by 132.77.4.43 (talk) 09:11, 16 May 2008 (UTC)

old version nominated for deletion

Just as a heads up, an old version of this page (not edited since 2006) has been nominated for deletion. If you wish to comment, please do so here. Thanks. --Jordan 1972 (talk) 23:53, 8 October 2008 (UTC)

"motion in constant acceleration" and rapidity

Does "motion in constant acceleration" mean that the rapidity increases linearly with time? Lemmiwinks2 (talk) 19:26, 1 September 2009 (UTC)

Rindler coordinates are appropriate for describing the world (absent gravity) as seen by an observer undergoing constant straight-line proper acceleration. In this case, the rapidity, $c\,\operatorname {arctanh} \left({\frac {v}{c}}\right)\,$, of that observer's motion (relative to a non-accelerating reference frame) increases linearly as a function of his proper time (not the coordinate time in the non-accelerating reference frame). JRSpriggs (talk) 12:30, 3 September 2009 (UTC)

"arctanh" is incorrect but I give up, I can't fight ignorance all alone

I don't know what it is about American educational system but the correct spelling in "artanh" (pronounced "area hyperbolic tangent"), not "arctanh". The inverses of hyperbolic functions are not arcs, they are areas. Any decent high schooler in the world will tell you that. Why do we always have to be so bottom-of-the-barrel, culturally speaking? Jan Bielawski (talk) 22:12, 10 April 2014 (UTC)

Outside America, we use "tanh⁻¹" and avoid the problem. -- Dr Greg  talk  22:34, 10 April 2014 (UTC)

Personally, I (lived in Asia, them Europe) use $\operatorname {atanh}$, and I call it 'arctan-h'.

I think the notion of it being an "area" isn't that clear, since the inverse functions are not the antiderivatives of "regular" functions. Yodo9000 (talk) Yodo9000 (talk) 20:46, 13 February 2024 (UTC)

"Notion of distance" paragraph

For some unknown reason, the following comment on this article was left on my talk page:

Please find some comments:

1. 1-"by dividing the round trip travel time, as measured by an ideal clock carried by our observer."

- When you say "dividing", I suppose you mean "divided by two"?

1. 2- a few line below, you give as expression of the null geodesics equations : $t-t_{0}=\log(x/x_{0})$. Then you conclude that the "radar distance" is $x_{0}\,\log \left(1+{\frac {h}{x_{0}}}\right)$. Isn't there some $x_{0}$ factor missing in the expression for $t-t_{0}$ ? My interpretation is that we actually have $t-t_{0}={\frac {1}{g_{0}}}\log(x/x_{0})$, where $g_{0}$ is the acceleration of the first observer in $x=x_{0}$ . Therefore we have indeed ${\frac {1}{g_{0}}}=x_{0}$, which makes it consistent with your second expression.

1. 3- The conclusion would then be that the difference between "radar distance" and "ruler distance" between the two observers will be negligible if $hg_{0}$ << 1, where $g_{0}$ is the acceleration of the first observer.

Do you think this is correct?

Pverlain (talk) 10:17, 9 April 2015 (UTC)

-- Dr Greg  talk  19:55, 27 April 2015 (UTC)

Expansion

I've expanded the article by providing a new introduction, many new references, detailed history (including Kottler and Møller and others), as well as different variants of the coordinates depending on the observer's position. --D.H (talk) 21:32, 18 June 2017 (UTC)

To D.H.: I reverted your edits. My finger slipped as I was starting to write an edit summary, so it did not save a summary. You introduced inconsistent and confusing notation.

You defined X and then immediately changed its meaning (taking out the -1). You added two variables r and η, but did not show how they depended on t and x. You used complex variables unnecessarily which is really asking to confuse the reader. I stopped reading after that. JRSpriggs (talk) 00:27, 19 June 2017 (UTC)

D.H added a lot of good material, but as JRSpriggs noted, it does not all read very well. I've created Draft:Rindler coordinates to hold the last version that D.H created, so that he can work on it in a collaborative environment until his additions are up to standard. Stigmatella aurantiaca (talk) 06:24, 19 June 2017 (UTC)

VQuakr nowiki'ed the categories in Draft:Rindler coordinates (which I didn't know I was supposed to do). When the draft version is ready to copy to main space, be sure to restore the categories. Stigmatella aurantiaca (talk) 07:04, 19 June 2017 (UTC)

Thanks to Stigmatella aurantiaca for creating the draft. I thought the old article was in a terrible shape: There are many variants of "Rindler coordinates", but only one was mentioned. There was a lack of references, no history section was given etc. So I made some changes per WP:Bold. I still think "my" version is much better, but let's work out the problems.

In order to address some concerns of JRSpriggs, I made some modifications: Originally I also used the notation with imaginary numbers of Sommerfeld (r, $\varphi$), which was probably not a good idea. I now replaced it with $x=r$ and directly used $\alpha \tau$, and made some passages shorter.

See Draft:Rindler coordinates

Hopefully it is more readable now, and I'm looking forward to your assessments. --D.H (talk) 07:53, 19 June 2017 (UTC)

I've expanded and rewritten Draft:Rindler coordinates. For further assessments, please see and participate in the discussion at Draft talk:Rindler coordinates. --D.H (talk) 16:51, 25 June 2017 (UTC)

As per Draft talk:Rindler coordinates, I'm planning to copy the new sections later today into this article. --D.H (talk) 14:28, 28 June 2017 (UTC)

Looks much better! Sorry I didn't have time while the article was in draft to do more than a superficial scan, but I've been pretty busy with Spacetime and some projects at home. Stigmatella aurantiaca (talk) 14:15, 3 July 2017 (UTC)

Thanks, the Draft is now deleted because it served its purpose. --D.H (talk) 06:58, 4 July 2017 (UTC)