Here is a redraw of the generic, abstract concept of a light cone. Note that it
is much harder to visualize the concepts in a 3d rendition of 4d. Dr. West
wisely used a 2d rendition on slide 11 and did not include the physical, just
temporal. (01)
Since time has no atom, it is also inherently difficult to express as a
concept. x/y/z all have distinct metrics in our physical world. We use a
clock for a metric of time yes we must realize that at best, this is an
arbitrary imposition of our human perspective. We visualize time as a linear
thing, which it is not. Zero mass things have no concept of time according to
most popularly accepted axioms and time and space are intrinsically related.
For mass, we also often use the earth's gravitational force as a baseline based
on our limited ability to perceive dynamic behaviour of objects, although one
can certainly easily see the effects of small objects at high velocity. (02)
There is another factor to consider - dark energy. Null geodesics are built on
the premise that time is constant which leads to their form being a continuous
concentric sphere. As you can see form the graph on my personal website, there
are theories to the contrary but have not been fully explained:
http://www.nickull.net/darkenergy.html (03)
This is all great stuff. Perhaps this will lead to an ontology that truly
captures the calculus for framing and context. (04)
Duane (05)
*******************************
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/
******************************* (06)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Peter P. Yim
Sent: Thursday, February 23, 2006 10:38 AM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] light cone - from wikipedia (07)
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 (08)
=ppy
-- (09)
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/
> *******************************
>
>
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