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## Re: [ontolog-forum] light cone - from wikipedia

 To: "[ontolog-forum]" "Peter P. Yim" Thu, 23 Feb 2006 10:37:37 -0800 <43FE00F1.8010900@xxxxxxxx>
 Duane is referring here to slide 11 of Dr. Matthew West's presentation that we were going through just now. ref: http://ontolog.cim3.net/cgi-bin/wiki.pl?ConferenceCall_2006_02_23#nidK49    (01) =ppy --    (02) Duane Nickull wrote Thu, 23 Feb 2006 09:17:32 -0800: > The light cone calculus is remarkably similar in theorem to Slide 11. > > "Null geodesics lie along a dual-cone defined by the equation > > ds^2 = 0 = dx_1^2 + dx_2^2 - c^2 dt^2 > > or > > dx_1^2 + dx_2^2 = c^2 dt^2 > > Which is the equation of a circle with r=c*dt. If we extend this to three >spatial dimensions, the null geodesics are continuous concentric spheres, with >radius = distance = c×(±time). > > ds^2 = 0 = dx_1^2 + dx_2^2 + dx_3^2 - c^2 dt^2 > > dx_1^2 + dx_2^2 + dx_3^2 = c^2 dt^2 > > This null dual-cone represents the "line of sight" of a point in space. That >is, when we look at the stars and say "The light from that star which I am >receiving is X years old.", we are looking down this line of sight: a null >geodesic. We are looking at an event d = \sqrt{x_1^2+x_2^2+x_3^2} meters away >and d/c seconds in the past. For this reason the null dual cone is also known >as the 'light cone'. (The point in the lower left of the picture below >represents the star, the origin represents the observer, and the line >represents the null geodesic "line of sight".) > > The cone in the −t region is the information that the point is 'receiving', >while the cone in the +t section is the information that the point is >'sending'. > > The geometry of Minkowski space can be depicted using Minkowski diagrams, >which are also useful in understanding many of the thought-experiments in >special relativity." > > Great stuff!!! > > Duane > > ******************************* > Adobe Systems, Inc. - http://www.adobe.com > Vice Chair - UN/CEFACT http://www.uncefact.org/ > Chair - OASIS SOA Reference Model Technical Committee > Personal Blog - http://technoracle.blogspot.com/ > ******************************* > > _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Unsubscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (03) 
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