75.167.87.115: /* History */

2013-12-11T19:31:08Z

History

← Older revision		Revision as of 21:31, 11 December 2013
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	~~Nice to satisfy you~~, ~~I am Marvella Shryock. Managing people has been his working day occupation for~~ a ~~whilst~~. ~~To gather coins~~ is ~~what her family~~ and ~~her enjoy. For a while I've~~ been in ~~South Dakota and my mothers and fathers reside close by~~.<br><br>~~Here is my website: std home test - [https:~~/~~/mostlymusiccom~~.~~zendesk~~.~~com~~/~~entries~~/~~53427870~~-~~Prevent~~-~~Candida~~-~~Albicans~~-~~Before-Hand-With-These-Tips visit the following website]~~ -		{{ShouldBeSVG\|diagram}}
			== Summary ==
			This figure depicts, in the [[Born coordinates\|Born chart]], the desynchronization of clocks carried by observers riding on a rigidly rotating disk. The z coordinate is inessential and has been suppressed in the figure.

			Consider integral curves of the third spacelike Langevin [[frame fields in general relativity\|frame vector]]
			:<math>\vec{p}_3 = \sqrt{1-\omega^2 \, r^2} \, \frac{1}{r} \, \partial_\phi + \frac{\omega \, r}{ \sqrt{1-\omega^2 \, r^2}} \, \partial_t</math>
			which pass through <math>\phi=0, \, t=0</math>. As the figure shows, we can use these to form a ''spatial hyperslice''. But two things go wrong.

			First, the spatial hyperslice we obtain only contains the second spacelike Langevin frame vector
			:<math>\vec{p}_2 = \partial_r </math>
			along one radius. By the [[Frobenius integrability theorem]], it is in fact impossible to find a spatial hyperslice to which the unit vector fields <math>\vec{p}_2, \; \vec{p}_3 </math> are ''tangent''. The Frobenius integrability theorem can be viewed in terms of the failure of our two vector fields to form a two-dimensional [[Lie algebra]] of vector fields, so this is Lie theoretic obstruction to defining spatial hyperslices for the Langevin observers.

			Second, as the figure shows, our spatial hyperslice is not only non-orthogonal to most of our Langevin observers, it also leads to a discontinuity (the coral colored vertical "jump"). If we tried to define a slicing of [[Minkowski spacetime]] into a family of spatial hyperslices isometric to this one, we would be forced to allow multiple valued time. This obstruction is global and arises from our inability to synchronize the clocks of Langevin observers riding even a ring, much less a disk (which we can think of as formed from concentric rings).

			This figure was created by [[User:Hillman]] using [[Maple computer algebra system\|Maple]] to export a jpg image and [[Eye of GNOME\|eog]] to convert this to a png image.

			== Licensing ==
			{{GFDL-self-with-disclaimers\|migration=relicense}}

			{{Copy to Wikimedia Commons\|bot=Fbot\|priority=true}}

en>Hmainsbot1: /* History */AWB general fixes and, delink dates per :WP:DATELINK, :WP:YEARLINK and :MOS:UNLINKYEARS using AWB (8097)

2012-07-21T16:49:44Z

History: AWB general fixes and, delink dates per WP:DATELINK, WP:YEARLINK and MOS:UNLINKYEARS using AWB (8097)

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Nice to satisfy you, I am Marvella Shryock. Managing people has been his working day occupation for a whilst. To gather coins is what her family and her enjoy. For a while I've been in South Dakota and my mothers and fathers reside close by.<br><br>Here is my website: std home test - [https://mostlymusiccom.zendesk.com/entries/53427870-Prevent-Candida-Albicans-Before-Hand-With-These-Tips visit the following website] -

Polar modulation - Revision history

75.167.87.115: /* History */

en>Hmainsbot1: /* History */AWB general fixes and, delink dates per :WP:DATELINK, :WP:YEARLINK and :MOS:UNLINKYEARS using AWB (8097)