128 reputation
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bio website math.jussieu.fr/~leila/…
location Lhasa, Tibet
age 18
visits member for 1 year, 8 months
seen Feb 7 '13 at 8:37

We choose to do mathematics, not because it is easy, but because it is hard.

$$ \text{Einstein's Field Equations:} \quad \mathbf{G} = \frac{8 \pi G}{c^{4}} \mathbf{T}. $$


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comment Setting up a local-coordinate system in space-time using only a single clock and light beams
Thank you, Retarded Potential! The link that you’ve provided contains another link to just the paper that I’m looking for.
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awarded  Scholar
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accepted Setting up a local-coordinate system in space-time using only a single clock and light beams
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comment Setting up a local-coordinate system in space-time using only a single clock and light beams
For example, can a concentrated collection of nano-clocks allow us to compute the metric tensor of curved space-time? Also, it seems that clocks are doing most of the work, and the role of light beams is simply to relay information between clocks. This sounds absolutely fine to me, as long as it gives us a meaningful way to make measurements, even in regions of space-time with high curvature, such as near a black hole.
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comment Setting up a local-coordinate system in space-time using only a single clock and light beams
Terry, thank you for a really informative explanation. I still have some questions left. Your description of clock synchronization fits neatly into the operational view of space-time, as it can be carried out physically (I like the idea of a time-stamp). However, this makes sense only in flat space-time. In curved space-time, however, how does one carry out measurements in a valid manner? Any region of curved space-time, no matter how small, is ultimately still curved. Can a huge collection of clocks in a volume of curved space-time yield direct information about the curvature itself?
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awarded  Supporter
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awarded  Student
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comment Setting up a local-coordinate system in space-time using only a single clock and light beams
Answers to both questions would be greatly appreciated, but I am more interested in the first question. Also, as I am interested in curved space-time, I suppose that we can only talk about local-coordinate systems. I know that many philosophical questions can be answered using light beams, such as what it means for a curve to be ‘straight’, but I would like to see how one can use light beams and a single clock to set up, in a logically consistent way, a local coordinate system in order to perform measurements, all in a manner that conforms to the operationalist view of space-time.
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asked Setting up a local-coordinate system in space-time using only a single clock and light beams
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awarded  Autobiographer