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

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Peter P. Yim" <peter.yim@xxxxxxxx>
Date: Thu, 23 Feb 2006 10:37:37 -0800
Message-id: <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)

--    (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 
> 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/
> ******************************* 
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