GPS & GR: Exploring Ashby's Langevin Metric

In summary, the conversation is about the use of the Langevin metric in the study of GPS and GR. The participants are frustrated with the lack of information on this metric and they are seeking help from others. One participant suggests checking out the version of "Born coordinates" on Wikipedia and warns about the reliability of information on relativistic physics on the site. Another participant shares a simplified analysis of GPS based on a book by Taylor and Wheeler.
  • #1
psychedelic
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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
 
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  • #2
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.)
 
  • #3
The Langevin metric

psychedelic said:
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
 
  • #4
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1. What is GPS and how does it work?

GPS, or Global Positioning System, is a satellite-based navigation system that provides location and time information to receivers on Earth. It works by using a network of 24 satellites orbiting the Earth, which transmit signals to GPS receivers. The receivers then use the signals to determine their location, speed, and direction.

2. What is GR and how is it related to GPS?

GR, or General Relativity, is a theory developed by Albert Einstein that explains the force of gravity as a result of the curvature of space and time. It is related to GPS because the satellites in the GPS system are affected by the Earth's gravitational field, causing a time dilation effect that must be taken into account for accurate GPS measurements.

3. What is Ashby's Langevin Metric and how does it improve GPS accuracy?

Ashby's Langevin Metric is a mathematical model that incorporates both GR and the effects of Earth's atmosphere on GPS signals. It improves GPS accuracy by accounting for the time dilation effect predicted by GR as well as the delay and distortion of signals caused by the atmosphere. This allows for more precise location and timing measurements.

4. How does the use of Ashby's Langevin Metric impact everyday use of GPS technology?

The use of Ashby's Langevin Metric has greatly improved the accuracy and reliability of GPS technology in everyday use. It allows for more precise navigation and timing information, which is crucial for various industries such as transportation, emergency services, and telecommunications.

5. Are there any limitations or challenges to using Ashby's Langevin Metric in GPS?

One potential limitation of using Ashby's Langevin Metric in GPS is that it requires a high level of technical expertise and complex algorithms to implement. This may make it more challenging for non-experts to understand and use in their own research. Additionally, the model may need to be updated as new data and technology become available in order to maintain its accuracy.

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