Friedman: An Eloquent Expression of the Future

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	Friedman: An Eloquent Expression of the Future

ouyangwulong

8-31-2007 12:42 AM

2310 views

tags:

physics, cosmology, humanity, relationships

ouyangwulong says:

Though it has been criticized because of its ties to general relativity, this equation strikes me as highly poetic. Friedman expresses in mathematic formula this reality, that our fate is a balance of two forces: the inertia pulling us apart, and the critical mass and attractive forces pulling us together. If we slip apart, there is the slow and lonely Cold Death, but if attraction prevails we are trapped in the stifling and claustrophobic Big Crunch.

Whatever the scientific validity of it, this equation expresses a fundamental truth I see mirrored in my own life...

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8-31-2007 7:14 AM

debbyski

OMG OW! My average IQ is now suffering a massive migrane. *LOL*

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<div style="margin: 12px 0px; font-family: arial; color: #333333; background: #ffffff; border: solid 4px #e5e5e5; width: 100%; clear: left;"><div class="CM_CTB_Content_Wrap" style="margin: 0px; padding: 0px;background-color: #ffffff;"><div style="border-bottom: solid 1px #dcdcdc; white-space: nowrap; margin-bottom: 8px; background-color: #eeeeee ;background-image: url(http://clipmarks.com/images/source-bg.gif); background-repeat: repeat-x; height: 24px; line-height: 24px; vertical-align: middle; padding-bottom: 4px; color: #666666; font-size: 10px;" ><a href="http://clipmarks.com/clip-to-blog/" title="see clips that are hot right now"><img src="http://content.clipmarks.com/blog_embed/177a616b-14de-4d0f-87f5-0a4b0de4d5d1/19FAAA89-DC5D-4866-AA1B-1738BE628AB0/" alt="" width="19" height="19" border="0" style="vertical-align: middle; margin: 0px 4px; display: inline; border: none; float:none;" /></a>clipped from <a title="http://en.wikipedia.org/w/index.php?title=Friedmann_equations&oldid=154167662" href="http://en.wikipedia.org/w/index.php?title=Friedmann_equations&oldid=154167662" style="font-size: 11px;">en.wikipedia.org</a></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Friedmann_equations&oldid=154167662">The <B>Friedmann equations</B> are a set of equations in <A title="Physical cosmology" href="http://en.wikipedia.org/wiki/Physical_cosmology" linkindex="52" set="yes">cosmology</A> that govern the <A title="Metric expansion of space" href="http://en.wikipedia.org/wiki/Metric_expansion_of_space" linkindex="53" set="yes">expansion of space</A> in <A title="Homogeneity" href="http://en.wikipedia.org/wiki/Homogeneity" linkindex="54">homogeneous</A> and <A title="Isotropy" href="http://en.wikipedia.org/wiki/Isotropy" linkindex="55" set="yes">isotropic</A> models of the universe within the context of <A title="General relativity" href="http://en.wikipedia.org/wiki/General_relativity" linkindex="56" set="yes">general relativity</A>. </blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Friedmann_equations&oldid=154167662"><div align="center"><img src="http://content8.clipmarks.com/blog_cache/en.wikipedia.org/img/73BF5F47-A8FF-49D5-B117-0387ABAB8E3A" alt="H^2 \equiv \left(\frac{\dot{a}}{a}\right)^2 = \frac{8 \pi G \rho + \Lambda}{3} - K\frac{c^2}{a^2}" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Friedmann_equations&oldid=154167662"><div align="center"><img src="http://content9.clipmarks.com/blog_cache/en.wikipedia.org/img/D25403F2-CFD2-4DE7-8C83-938F073D6C1E" alt="3 \, \frac{\ddot{a}}{a} =  \Lambda - 4 \pi G \left(\rho + \frac{3p}{c^2}\right)" /></div></blockquote><div style="height: 2px; font-size: 2px; background: #dcdcdc; border-bottom: solid 1px #f5f5f5; margin: 2px 4px;"></div><blockquote style="text-align: left; padding: 0px 8px; margin: 4px 0px 8px 0px; background: transparent; border: none;" cite="http://en.wikipedia.org/w/index.php?title=Friedmann_equations&oldid=154167662"><P>where <SPAN class="texhtml">Λ</SPAN> is the <A title="Cosmological constant" href="http://en.wikipedia.org/wiki/Cosmological_constant" linkindex="64" set="yes">cosmological constant</A> possibly caused by <A title="Vacuum energy" href="http://en.wikipedia.org/wiki/Vacuum_energy" linkindex="65" set="yes">vacuum energy</A>, <SPAN class="texhtml"><I>G</I></SPAN> is the <A title="Gravitational constant" href="http://en.wikipedia.org/wiki/Gravitational_constant" linkindex="66">gravitational constant</A>, <SPAN class="texhtml"><I>c</I></SPAN> is the speed of light, <SPAN class="texhtml"><I>a</I></SPAN> is the <A title="Scale factor (Universe)" href="http://en.wikipedia.org/wiki/Scale_factor_%28Universe%29" linkindex="67" set="yes">scale factor</A>, and <SPAN class="texhtml"><I>K</I></SPAN> is the <A title="Gaussian curvature" href="http://en.wikipedia.org/wiki/Gaussian_curvature" linkindex="68" set="yes">Gaussian curvature</A> when <SPAN class="texhtml"><I>a</I> = 1</SPAN> (i.e. today). If the <A title="Shape of the universe" href="http://en.wikipedia.org/wiki/Shape_of_the_universe" linkindex="69" set="yes">shape of the universe</A> is <A title="Shape of the universe" href="http://en.wikipedia.org/wiki/Shape_of_the_universe#Spherical_Universe" linkindex="70" set="yes">hyperspherical</A> and <SPAN class="texhtml"><I>R</I></SPAN> is the radius of curvature (<SPAN class="texhtml"><I>R</I><SUB>0</SUB></SPAN> in the present-day), then <SPAN class="texhtml"><I>a</I> = <I>R</I> / <I>R</I><SUB>0</SUB></SPAN>. Generally, <IMG src="http://upload.wikimedia.org/math/5/8/4/584c2c96e76ca82e57086486a8982050.png" alt="K \over a^2" class="tex" /> is the <A title="Gaussian curvature" href="http://en.wikipedia.org/wiki/Gaussian_curvature" linkindex="71">Gaussian curvature</A>. If <SPAN class="texhtml"><I>K</I></SPAN> is positive, then the universe is hyperspherical. If <SPAN class="texhtml"><I>K</I></SPAN> is zero, then the universe is <A title="Shape of the universe" href="http://en.wikipedia.org/wiki/Shape_of_the_universe#Flat_Universe" linkindex="72">flat</A>. If <SPAN class="texhtml"><I>K</I></SPAN> is negative, then the universe is <A title="Shape of the universe" href="http://en.wikipedia.org/wiki/Shape_of_the_universe#Hyperbolic_Universe" linkindex="73">hyperbolic</A>. Note that <SPAN class="texhtml">ρ</SPAN> and <SPAN class="texhtml"><I>p</I></SPAN> are in general functions of <SPAN class="texhtml"><I>a</I></SPAN>. The <A title="Hubble parameter" href="http://en.wikipedia.org/wiki/Hubble_parameter" linkindex="74">Hubble parameter</A>, <SPAN class="texhtml"><I>H</I></SPAN>, is the rate of expansion of the universe.</P></blockquote></div><div style="margin: 0px 6px 6px 4px;"><table style="font-size: 11px;border-spacing: 0px;padding: 0px;" cellpadding="0" cellspacing="0" width="100%"><tr><td style="background:transparent;border-width:0px;padding:0px;">&nbsp;</td><td align="right" style="background:transparent;border-width:0px;padding:0px;width:107px" width="107"><a href="http://clipmarks.com/share/19FAAA89-DC5D-4866-AA1B-1738BE628AB0/blog/" title="blog or email this clip"><img src="http://content6.clipmarks.com/images/c2b-foot.png" border="0" alt="blog it" width="107" height="17" style="border-width:0px;padding:0px;margin:0px;" /></a></td></tr></table></div></div>

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