What is the significance of Ashby's use of the Langevin metric in GPS and GR?

[psychedelic]

Hello there!
Am actually doing my end of year project on GPS and GR. It's actually a review of Ashby's work. I am kinda stuck with a term. In the choice of metric, Mr Ashby (God bless him! ;-) ) makes use of the Langevin metric. He propounds that it is well know. But lo and behold, on the net, I can scarcely find searches where "Langevin" and "metric" are not disjoint! Geeee! That is sooooo frustrating. So I'd just wonder if any of you guys, enlightened souls, could help me out?
Thanks in advance guys! In return I propose to share songs with you. :p
psychedelic

 

[pervect]

The wikipedia article on the Ehrenfest paradox (i.e. the "paradox" of the spinning disk) mentions this metric:

http://en.wikipedia.org/wiki/Ehrenfest_paradox

1935: Paul Langevin essentially introduces a moving frame (or frame field in modern language) corresponding to the family of disk-riding observers, now called Langevin observers. (See the figure.) He also shows that distances measured by nearby Langevin observers correspond to a certain Riemannian metric, now called the Langevin-Landau-Lifschitz metric. (See Born coordinates for details.)

 

[Chris Hillman]

The Langevin metric

In the choice of metric, Mr Ashby (God bless him! ;-) ) makes use of the Langevin metric. He propounds that it is well know. But lo and behold, on the net, I can scarcely find searches where "Langevin" and "metric" are not disjoint! Geeee! That is sooooo frustrating. So I'd just wonder if any of you guys, enlightened souls, could help me out?

Try the version of "Born coordinates" listed at http://en.wikipedia.org/wiki/User:Hillman/Archive, which describes the Langevin observers in terms of the Born chart (you didn't quote from whatever paper by Neil Ashby you are reading, so I can't be absolutely sure, but the subject of this article is almost certainly what Ashby apparently calls the "Langevin metric"). And don't just take my word for it: check out the papers I cited (many of which are available on-line) and work some computations in order to verify my claims.

Obligatory warning: I cannot vouch for more recent versions, which might be better than the version I wrote, or much much worse. It may be particularly important to be wary of what you read in Wikipedia in articles related to relativistic physics, especially relativistic "paradoxes", because, you know, Wikipedia is the thing which anyone can edit.. ANYONE. Sometimes that results in very good articles. Often it results in very bad ones. Sometimes a very bad article is rapidly and greatly improved. Sometimes just the opposite. If you don't already know a subject well, it can probably be difficult at times to know whether you are reading a hoax article, a well-informed and accurate article, or a highly misleading presentation of a dissident or even woefully incorrect approach as if said approach represents mainstream physics.

Chris Hillman

 

[George Jones]

In https://www.physicsforums.com/showpost.php?p=731738&postcount=5", I give a simple-minded (without proper justification) analysis of GPS that is based on Project A from the book Exploring Black Holes by Taylor and Wheeler.