Halliday's blog
http://www.science20.com/theory_just_about_anything
Science 2.0® - Science for the next 2,000 yearsenWhat Is The Geometry Of Spacetime? — Wrap-Up: Why Does Any Of This Matter?
http://www.science20.com/theory_just_about_anything/what_iis_geometry_spacetime_%E2%80%94_wrapup_why_does_any_matter-127037
I'm sorry I've been away so long: The "press of life" got the "better of me". Sometimes, life just "gets in the way". (No excuses. I simply had other "things" that needed to take priority. Unfortunately, I don't see that changing any time soon. So, unfortunately, I cannot promise to have an especially active presence here for the foreseeable future.)<p>[Note: Since the creation of footnotes and cross references can be so tedious on this site, I shall go ahead and publish this version of this article without such, at first. However, I shall endeavor to add such in as I can find the time. I apologize for the lack of "polish" or completeness this will produce, at this time, but feel it will help me get this out to you in a more timely mann</p>
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<p><a href="http://www.science20.com/theory_just_about_anything/what_iis_geometry_spacetime_%E2%80%94_wrapup_why_does_any_matter-127037" target="_blank">read more</a></p>http://www.science20.com/theory_just_about_anything/what_iis_geometry_spacetime_%E2%80%94_wrapup_why_does_any_matter-127037#commentsPhysicsMon, 30 Dec 2013 20:36:38 +0000David Halliday127037 at http://www.science20.comWhat Is The Geometry Of Spacetime? — What Kinds Of Inner-Products/Metrics?
http://www.science20.com/theory_just_about_anything/what_geometry_spacetime_%E2%80%94_what_kinds_innerproductsmetrics-97160
We ended the second article in this series with the audacious claim that we have obtained the <a href="/uploads/328899205-494752366.m4a"><strong>METRIC</strong></a>.<a href="http://www.science20.com/theory_just_about_anything/what_geometry_spacetime_%E2%80%94_what_kinds_innerproductsmetrics-97160#footnote1" id="return1"><sup>1</sup></a> Quite frankly, I expected to hear a howl of protest to my brazen assertion that we had actually gotten so far. We certainly hadn't obtained anything quite like the usual matrix or tensor form of a metric, or even a "line element", nor had we seen how this has any relationship to the usual "strangeness" of the Special Theory of Relativity.<p>It is the issues/questions of the metric, its relationship to the inner or dot product, and what forms it </p>
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<p><a href="http://www.science20.com/theory_just_about_anything/what_geometry_spacetime_%E2%80%94_what_kinds_innerproductsmetrics-97160" target="_blank">read more</a></p>http://www.science20.com/theory_just_about_anything/what_geometry_spacetime_%E2%80%94_what_kinds_innerproductsmetrics-97160#commentsPhysicsMon, 26 Nov 2012 23:38:22 +0000David Halliday97160 at http://www.science20.comWhat Is The Geometry Of Spacetime? — What Is Space? — Inner-Product Spaces
http://www.science20.com/theory_just_about_anything/what_geometry_spacetime_%E2%80%94_what_space_%E2%80%94_innerproduct_spaces-89726
Since "spacetime" is simply a term for a space that has a component we call "time", we need only concentrate on spaces in a somewhat general sense. Now, as <a target="_blank" href="http://www.science20.com/profile/derek_potter">Derek Potter</a>, on this site, pointed out to me, <a target="_blank" href="http://www.science20.com/faze_space/blog/time_travel_paradoxes-87877#comment-106498">a little while ago</a>, "To us, a space is somewhere to put a box :)" So, let's take a short "detour" to address what we will mean by a space, in this series.<br />
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<p><a href="http://www.science20.com/theory_just_about_anything/what_geometry_spacetime_%E2%80%94_what_space_%E2%80%94_innerproduct_spaces-89726" target="_blank">read more</a></p>http://www.science20.com/theory_just_about_anything/what_geometry_spacetime_%E2%80%94_what_space_%E2%80%94_innerproduct_spaces-89726#comments