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	<title>Comments on: Boltzmann&#8217;s Universe</title>
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	<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/</link>
	<description>Random samplings from a universe of ideas</description>
	<pubDate>Tue, 07 Oct 2008 08:55:09 +0000</pubDate>
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		<title>By: The Boltzmann Brain Controversy &#171; In Other Words</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-311486</link>
		<dc:creator>The Boltzmann Brain Controversy &#171; In Other Words</dc:creator>
		<pubDate>Sun, 24 Feb 2008 21:09:59 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-311486</guid>
		<description>[...] and maybe even inspiring topic. Many more references can be found at :Cosmic Variance and again here, at Darwiniana (a very good synopsis, btw), and some original material at [...]</description>
		<content:encoded><![CDATA[<p>[...] and maybe even inspiring topic. Many more references can be found at :Cosmic Variance and again here, at Darwiniana (a very good synopsis, btw), and some original material at [...]</p>
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	</item>
	<item>
		<title>By: The lure of science pornography &#187; Undress Me Robot</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-310670</link>
		<dc:creator>The lure of science pornography &#187; Undress Me Robot</dc:creator>
		<pubDate>Fri, 15 Feb 2008 17:05:12 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-310670</guid>
		<description>[...] all reminds me of the (surprisingly mainstream) coverage of Boltzmann&#8217;s Brains. In explaining the silly idea in The New York Times, Dennis Overbye casually mentions this point: [...]</description>
		<content:encoded><![CDATA[<p>[...] all reminds me of the (surprisingly mainstream) coverage of Boltzmann&#8217;s Brains. In explaining the silly idea in The New York Times, Dennis Overbye casually mentions this point: [...]</p>
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	</item>
	<item>
		<title>By: Everyone's a Critic &#124; Cosmic Variance</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309577</link>
		<dc:creator>Everyone's a Critic &#124; Cosmic Variance</dc:creator>
		<pubDate>Wed, 30 Jan 2008 20:31:22 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309577</guid>
		<description>[...] response, of course, to the NYT story about Boltzmann&#8217;s Brain. George&#8217;s father Michael, a high-school science teacher, was moved to send it along (and gave [...]</description>
		<content:encoded><![CDATA[<p>[...] response, of course, to the NYT story about Boltzmann&#8217;s Brain. George&#8217;s father Michael, a high-school science teacher, was moved to send it along (and gave [...]</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Qubit</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309491</link>
		<dc:creator>Qubit</dc:creator>
		<pubDate>Tue, 29 Jan 2008 22:16:02 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309491</guid>
		<description>Maybe there is a killer virus that lurks in the universe, one that makes the odds of a boltzmann brain popping out of the ether at any point almost impossible. Viruses don’t have brains, but they do a great job of killing them and are a hell of a lot more likely to pop into existence than a brain. It’s not unconceivable that a type of virus removes all none real boltzman brains, leaving only evolved life forms possible. The nature of the universe is extremely violent and unforgiving; the universe simply has no time for things that are not real!  Of course there is a chance boltzman brain can get lucky, but you simply just have to look at conception in humans to realise that once in the egg, no other sperm can get in; then the odd of twins are statistically possible, but in universe terms very unlikely. 

You could tell your self in the past this, if you found a way; but you would end up leading yourselves into an un-real universe, once you passed the point you sent the information to yourselves in the past, you would not know what to do next. Unless you told yourselves what to do and that would be like creating a big polo mint in space and driving through the hole! Where would that get you?</description>
		<content:encoded><![CDATA[<p>Maybe there is a killer virus that lurks in the universe, one that makes the odds of a boltzmann brain popping out of the ether at any point almost impossible. Viruses don’t have brains, but they do a great job of killing them and are a hell of a lot more likely to pop into existence than a brain. It’s not unconceivable that a type of virus removes all none real boltzman brains, leaving only evolved life forms possible. The nature of the universe is extremely violent and unforgiving; the universe simply has no time for things that are not real!  Of course there is a chance boltzman brain can get lucky, but you simply just have to look at conception in humans to realise that once in the egg, no other sperm can get in; then the odd of twins are statistically possible, but in universe terms very unlikely. </p>
<p>You could tell your self in the past this, if you found a way; but you would end up leading yourselves into an un-real universe, once you passed the point you sent the information to yourselves in the past, you would not know what to do next. Unless you told yourselves what to do and that would be like creating a big polo mint in space and driving through the hole! Where would that get you?</p>
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	<item>
		<title>By: Starts With A Bang! &#187; Brain-damaged arguments and Boltzmann Brains</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309412</link>
		<dc:creator>Starts With A Bang! &#187; Brain-damaged arguments and Boltzmann Brains</dc:creator>
		<pubDate>Tue, 29 Jan 2008 03:26:30 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309412</guid>
		<description>[...] make sure you understand the Boltzmann Brain proposal (and for another, less scathing of it, see Sean Carroll&#8217;s post over at cosmic [...]</description>
		<content:encoded><![CDATA[<p>[...] make sure you understand the Boltzmann Brain proposal (and for another, less scathing of it, see Sean Carroll&#8217;s post over at cosmic [...]</p>
]]></content:encoded>
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	<item>
		<title>By: Lawrence B. Crowell</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309136</link>
		<dc:creator>Lawrence B. Crowell</dc:creator>
		<pubDate>Fri, 25 Jan 2008 02:36:22 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309136</guid>
		<description>To discuss quantum fluctuations I am going to texify some here.  I hope I make no errors.  Often when I do this I have to repair errors I make in doing this, but there is no preview.  So here goes.

If you have a state psi(t) it will evolve into a state psi(t + &#38;t) by the Schrodinger equation
[tex]i\hbar\frac{\partial\psi(t)}{\partial t}~=~H\psi(t)[/tex]
where I will from now set hbar to one.  The Hamiltonian H defines a unitary time development operator U(t) with
[tex]&#124;\psi(t_0~+~t)\rangle~=~e^{-iH(t_0~+~t)}&#124;\psi(t_0)\rangle[/tex]
where the unitary operator is the exponential term on the right.  We then consider the overlap of a state and its time development some small increment of time
[tex]\langle\psi(t)&#124;\psi(t~+~\delta t)\rangle~=~\langle\psi(t)&#124;e^{-iH\delta t}&#124;\psi(t)\rangle[/tex]
which with the Taylor theorem gives
[tex]\langle\psi(t)&#124;\psi(t~+~\delta t)\rangle~\simeq~\langle\psi(t)&#124;(1~-~iH\delta t~-~\frac{1}{2}H^2\delta t^2&#124;\psi(t)\rangle[/tex]
This is the overlap between a state and its time development into the future.  Now what we do is to take the modulus square of this to get
[tex]&#124;\langle\psi(t)&#124;\psi(t~+~\delta t)\rangle&#124;^2~\simeq~(1~-~\Big(\langle\psi(t)&#124;H^2&#124;\psi(t)~-~&#124;\langle\psi(t)&#124;H&#124;\psi\rangle^2\Big)\delta t^2[/tex]
The last two terms on the right are 
[tex]
(\langle~H^2~\rangle~-~\langle~H~\rangle^2)\delta t^2,
[/tex]
with some compression of notation.  The term in the parenthesis is the square of
[tex]
\Delta H~=~\sqrt{\langle~H^2~\rangle~-~\langle~H~\rangle^2}
[/tex]
Now this is the Heisenberg uncertainty principle for the whole package in the modulus squared is 
[tex]
\Delta H\delta t/\hbar~=~\sqrt{\langle~H^2~\rangle~-~\langle~H~\rangle^2})\delta t/\hbar.
[/tex]
This says that if I sample the system in a short time I will get a range of possible values for the energy of the system.

As a digression this has some interesting properties, for this is the metric of the Fubini-Study space and the fibration over the projective Hilbert space.

The quantum fluctuation is physically the result of sampling or measuring the system.  Quantum mechanics is contrary to popular belief a completely deterministic physics.  The Schr{\"o}dinger wave equation is completely deterministic.  But since the wave is complex valued, and there is this fibration given by the unitary operator over the projective Hilbert space what we measure in real variables has this range of possible outcomes.

In thermodynamics there are also fluctuations, and a formula for them based on the deBroglie wavelength.  It is analogous to this, but where one has to look at Fokker-Planck equations or Langevin processes.  These are similar to quantum fluctuations, but are really different physics.  

Lawrence B. Crowell</description>
		<content:encoded><![CDATA[<p>To discuss quantum fluctuations I am going to texify some here.  I hope I make no errors.  Often when I do this I have to repair errors I make in doing this, but there is no preview.  So here goes.</p>
<p>If you have a state psi(t) it will evolve into a state psi(t + &amp;t) by the Schrodinger equation<br />
<img src='/latexrender/pictures/da576b7a2a43ab5c26affde110f826ac.gif' title='i\hbar\frac{\partial\psi(t)}{\partial t}~=~H\psi(t)' alt='i\hbar\frac{\partial\psi(t)}{\partial t}~=~H\psi(t)' align=absmiddle/><br />
where I will from now set hbar to one.  The Hamiltonian H defines a unitary time development operator U(t) with<br />
<img src='/latexrender/pictures/e1bbd65ae8fc3db35ccc26bdf7e744b5.gif' title='|\psi(t_0~+~t)\rangle~=~e^{-iH(t_0~+~t)}|\psi(t_0)\rangle' alt='|\psi(t_0~+~t)\rangle~=~e^{-iH(t_0~+~t)}|\psi(t_0)\rangle' align=absmiddle/><br />
where the unitary operator is the exponential term on the right.  We then consider the overlap of a state and its time development some small increment of time<br />
<img src='/latexrender/pictures/3a15207dd385eb73b9c3aef0d25db038.gif' title='\langle\psi(t)|\psi(t~+~\delta t)\rangle~=~\langle\psi(t)|e^{-iH\delta t}|\psi(t)\rangle' alt='\langle\psi(t)|\psi(t~+~\delta t)\rangle~=~\langle\psi(t)|e^{-iH\delta t}|\psi(t)\rangle' align=absmiddle/><br />
which with the Taylor theorem gives<br />
<img src='/latexrender/pictures/1feb03ee870376492f2d75df907889d7.gif' title='\langle\psi(t)|\psi(t~+~\delta t)\rangle~\simeq~\langle\psi(t)|(1~-~iH\delta t~-~\frac{1}{2}H^2\delta t^2|\psi(t)\rangle' alt='\langle\psi(t)|\psi(t~+~\delta t)\rangle~\simeq~\langle\psi(t)|(1~-~iH\delta t~-~\frac{1}{2}H^2\delta t^2|\psi(t)\rangle' align=absmiddle/><br />
This is the overlap between a state and its time development into the future.  Now what we do is to take the modulus square of this to get<br />
<img src='/latexrender/pictures/ccbb24593b187aa94944aff45a407803.gif' title='|\langle\psi(t)|\psi(t~+~\delta t)\rangle|^2~\simeq~(1~-~\Big(\langle\psi(t)|H^2|\psi(t)~-~|\langle\psi(t)|H|\psi\rangle^2\Big)\delta t^2' alt='|\langle\psi(t)|\psi(t~+~\delta t)\rangle|^2~\simeq~(1~-~\Big(\langle\psi(t)|H^2|\psi(t)~-~|\langle\psi(t)|H|\psi\rangle^2\Big)\delta t^2' align=absmiddle/><br />
The last two terms on the right are<br />
<img src='/latexrender/pictures/6c198f26a653138c396db94befb98e05.gif' title='&#13;&#10;(\langle~H^2~\rangle~-~\langle~H~\rangle^2)\delta t^2,&#13;&#10;' alt='&#13;&#10;(\langle~H^2~\rangle~-~\langle~H~\rangle^2)\delta t^2,&#13;&#10;' align=absmiddle/><br />
with some compression of notation.  The term in the parenthesis is the square of<br />
<img src='/latexrender/pictures/ef2c765129fc7daea587b57520a698fd.gif' title='&#13;&#10;\Delta H~=~\sqrt{\langle~H^2~\rangle~-~\langle~H~\rangle^2}&#13;&#10;' alt='&#13;&#10;\Delta H~=~\sqrt{\langle~H^2~\rangle~-~\langle~H~\rangle^2}&#13;&#10;' align=absmiddle/><br />
Now this is the Heisenberg uncertainty principle for the whole package in the modulus squared is<br />
<img src='/latexrender/pictures/e3fa3092aa8d8371aac63fa0cac4003f.gif' title='&#13;&#10;\Delta H\delta t/\hbar~=~\sqrt{\langle~H^2~\rangle~-~\langle~H~\rangle^2})\delta t/\hbar.&#13;&#10;' alt='&#13;&#10;\Delta H\delta t/\hbar~=~\sqrt{\langle~H^2~\rangle~-~\langle~H~\rangle^2})\delta t/\hbar.&#13;&#10;' align=absmiddle/><br />
This says that if I sample the system in a short time I will get a range of possible values for the energy of the system.</p>
<p>As a digression this has some interesting properties, for this is the metric of the Fubini-Study space and the fibration over the projective Hilbert space.</p>
<p>The quantum fluctuation is physically the result of sampling or measuring the system.  Quantum mechanics is contrary to popular belief a completely deterministic physics.  The Schr{\&#8221;o}dinger wave equation is completely deterministic.  But since the wave is complex valued, and there is this fibration given by the unitary operator over the projective Hilbert space what we measure in real variables has this range of possible outcomes.</p>
<p>In thermodynamics there are also fluctuations, and a formula for them based on the deBroglie wavelength.  It is analogous to this, but where one has to look at Fokker-Planck equations or Langevin processes.  These are similar to quantum fluctuations, but are really different physics.  </p>
<p>Lawrence B. Crowell</p>
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	<item>
		<title>By: Qubit</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309123</link>
		<dc:creator>Qubit</dc:creator>
		<pubDate>Thu, 24 Jan 2008 22:03:31 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309123</guid>
		<description>I can live my life backwards through time, while every one else lives forwards through time and we can all see the exact same history of the world. I dont think am real enough and am probably dead already because my life is improbable. 

What they dont tell you at school is that it is possable to produce an imaginary black hole in your mind, information on its own is enough to do this. This is called frame setting, it makes your life real and observed up to that point. While you live on like being born again; in other words you exist in every single point in the universe as a real object. Then you simply are a universe at that point. Everthing before it simply is your imagination, that has become real. You surround the universe like a dyson sphere; like around a star and then you take everthing you need to carry on you life as yourself and nothing more. Doing this is the same as an animal that has no concious ablity to understand that its giving birth.

If I got something wrong then its your fault, because you used me to do it! You cant expect me to get "everything" right. Your frame is the one I set and unless you are "Your" then you can dismiss this as nonsense. 
Its not wrong anyway, its entropy is just too high at the begining to be right, it needs to be a lot lower. The universe is not real, its proably a simulation and that really does suck!

Look left see blue "Think way of the mushroom!", "Eyes forward!", "A cat see's with two eyes", look right? "I cant remember?" 

Do it yourselves next time!

If you dont understand this, then ignore it! And don't comment!</description>
		<content:encoded><![CDATA[<p>I can live my life backwards through time, while every one else lives forwards through time and we can all see the exact same history of the world. I dont think am real enough and am probably dead already because my life is improbable. </p>
<p>What they dont tell you at school is that it is possable to produce an imaginary black hole in your mind, information on its own is enough to do this. This is called frame setting, it makes your life real and observed up to that point. While you live on like being born again; in other words you exist in every single point in the universe as a real object. Then you simply are a universe at that point. Everthing before it simply is your imagination, that has become real. You surround the universe like a dyson sphere; like around a star and then you take everthing you need to carry on you life as yourself and nothing more. Doing this is the same as an animal that has no concious ablity to understand that its giving birth.</p>
<p>If I got something wrong then its your fault, because you used me to do it! You cant expect me to get &#8220;everything&#8221; right. Your frame is the one I set and unless you are &#8220;Your&#8221; then you can dismiss this as nonsense.<br />
Its not wrong anyway, its entropy is just too high at the begining to be right, it needs to be a lot lower. The universe is not real, its proably a simulation and that really does suck!</p>
<p>Look left see blue &#8220;Think way of the mushroom!&#8221;, &#8220;Eyes forward!&#8221;, &#8220;A cat see&#8217;s with two eyes&#8221;, look right? &#8220;I cant remember?&#8221; </p>
<p>Do it yourselves next time!</p>
<p>If you dont understand this, then ignore it! And don&#8217;t comment!</p>
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	<item>
		<title>By: Daryl McCullough</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309119</link>
		<dc:creator>Daryl McCullough</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:33:28 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309119</guid>
		<description>Sorry, I don't see how any of your comments are relevant. To say that some reaction is only possible at such and such an energy scale is a &lt;em&gt;probabilistic&lt;/em&gt; statement. What it means is that without that energy, the transition becomes &lt;em&gt;much&lt;/em&gt; less likely. But the probability never goes to zero unless the transition violates a conserved quantity.</description>
		<content:encoded><![CDATA[<p>Sorry, I don&#8217;t see how any of your comments are relevant. To say that some reaction is only possible at such and such an energy scale is a <em>probabilistic</em> statement. What it means is that without that energy, the transition becomes <em>much</em> less likely. But the probability never goes to zero unless the transition violates a conserved quantity.</p>
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	<item>
		<title>By: Hal S</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309117</link>
		<dc:creator>Hal S</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:14:24 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309117</guid>
		<description>ie supermassive black holes and spiral galaxies</description>
		<content:encoded><![CDATA[<p>ie supermassive black holes and spiral galaxies</p>
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	</item>
	<item>
		<title>By: Hal S</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309116</link>
		<dc:creator>Hal S</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:12:15 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309116</guid>
		<description>The universe evolves through the process of diffusion...some bound states are only producable at energy scales larger than what we see today</description>
		<content:encoded><![CDATA[<p>The universe evolves through the process of diffusion&#8230;some bound states are only producable at energy scales larger than what we see today</p>
]]></content:encoded>
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	<item>
		<title>By: Daryl McCullough</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309115</link>
		<dc:creator>Daryl McCullough</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:11:27 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309115</guid>
		<description>Hal S,

Your conclusion does not follow from that. The &lt;em&gt;average&lt;/em&gt; energy density for the entire universe may be decreasing with time, but that doesn't imply that local densities might not increase.</description>
		<content:encoded><![CDATA[<p>Hal S,</p>
<p>Your conclusion does not follow from that. The <em>average</em> energy density for the entire universe may be decreasing with time, but that doesn&#8217;t imply that local densities might not increase.</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Hal S</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309114</link>
		<dc:creator>Hal S</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:09:55 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309114</guid>
		<description>All stable heavy elements must have been produced in large stars through nucleosynthesis, therefore we have permanent record that there was some large star that existed before our own solar system</description>
		<content:encoded><![CDATA[<p>All stable heavy elements must have been produced in large stars through nucleosynthesis, therefore we have permanent record that there was some large star that existed before our own solar system</p>
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	<item>
		<title>By: Daryl McCullough</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309112</link>
		<dc:creator>Daryl McCullough</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:04:47 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309112</guid>
		<description>Somehow, my definition of the transition amplitude A disappeared. But it's just the element: A(t) = .</description>
		<content:encoded><![CDATA[<p>Somehow, my definition of the transition amplitude A disappeared. But it&#8217;s just the element: A(t) = .</p>
]]></content:encoded>
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	<item>
		<title>By: Hal S</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309111</link>
		<dc:creator>Hal S</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:03:47 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309111</guid>
		<description>This is actually rather neat.

We know that fundamental forces unify at higher energies, and we know the universe is expanding and energy density is decreasing.  Thus we have a permanent record of the fact that the universe had a higher energy density early in its evolution</description>
		<content:encoded><![CDATA[<p>This is actually rather neat.</p>
<p>We know that fundamental forces unify at higher energies, and we know the universe is expanding and energy density is decreasing.  Thus we have a permanent record of the fact that the universe had a higher energy density early in its evolution</p>
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	<item>
		<title>By: Daryl McCullough</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309110</link>
		<dc:creator>Daryl McCullough</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:02:29 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309110</guid>
		<description>Hal S,

Please don't post any more urls without explaining why you think that any of them are relevant. Why are any of those web pages relevant?</description>
		<content:encoded><![CDATA[<p>Hal S,</p>
<p>Please don&#8217;t post any more urls without explaining why you think that any of them are relevant. Why are any of those web pages relevant?</p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Daryl McCullough</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309109</link>
		<dc:creator>Daryl McCullough</dc:creator>
		<pubDate>Thu, 24 Jan 2008 21:01:16 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309109</guid>
		<description>Here's a more mathematically precise claim about what is possible from fluctuations.

Let &#124;Psi&#62; and &#124;Phi&#62; be two different states of a quantum system involving many, many particles. Then the prediction of quantum mechanics is that the probability that the system, when put in state &#124;Psi&#62; at time 0 will be found in state &#124;Phi&#62; at a later time t is given by

P = &#124;A&#124;^2

where A =  is the transition amplitude and where H is the Hamiltonian.

The question is: under what circumstances do we expect the transition amplitude A to be zero for all values of t? Well, certainly A will always be zero if Phi and Psi have different eignvalues for conserved quantities. But if that's &lt;i&gt;not&lt;/i&gt; the case; if Phi and Psi have the same values for charge, total momentum, total energy, total angular momentum, etc., then I would think that A would be nonzero for most values of t.</description>
		<content:encoded><![CDATA[<p>Here&#8217;s a more mathematically precise claim about what is possible from fluctuations.</p>
<p>Let |Psi&gt; and |Phi&gt; be two different states of a quantum system involving many, many particles. Then the prediction of quantum mechanics is that the probability that the system, when put in state |Psi&gt; at time 0 will be found in state |Phi&gt; at a later time t is given by</p>
<p>P = |A|^2</p>
<p>where A =  is the transition amplitude and where H is the Hamiltonian.</p>
<p>The question is: under what circumstances do we expect the transition amplitude A to be zero for all values of t? Well, certainly A will always be zero if Phi and Psi have different eignvalues for conserved quantities. But if that&#8217;s <i>not</i> the case; if Phi and Psi have the same values for charge, total momentum, total energy, total angular momentum, etc., then I would think that A would be nonzero for most values of t.</p>
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	</item>
	<item>
		<title>By: Hal S</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309108</link>
		<dc:creator>Hal S</dc:creator>
		<pubDate>Thu, 24 Jan 2008 20:57:55 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309108</guid>
		<description>http://en.wikipedia.org/wiki/Bound_state</description>
		<content:encoded><![CDATA[<p><a href="http://en.wikipedia.org/wiki/Bound_state" rel="nofollow">http://en.wikipedia.org/wiki/Bound_state</a></p>
]]></content:encoded>
	</item>
	<item>
		<title>By: Hal S</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309107</link>
		<dc:creator>Hal S</dc:creator>
		<pubDate>Thu, 24 Jan 2008 20:52:33 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309107</guid>
		<description>http://en.wikipedia.org/wiki/Diffusion</description>
		<content:encoded><![CDATA[<p><a href="http://en.wikipedia.org/wiki/Diffusion" rel="nofollow">http://en.wikipedia.org/wiki/Diffusion</a></p>
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	</item>
	<item>
		<title>By: Daryl McCullough</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309106</link>
		<dc:creator>Daryl McCullough</dc:creator>
		<pubDate>Thu, 24 Jan 2008 20:38:26 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309106</guid>
		<description>Hal S,

I don't believe that you are correct. The laws of physics don't in any way say that there must remain a record of past evolution.</description>
		<content:encoded><![CDATA[<p>Hal S,</p>
<p>I don&#8217;t believe that you are correct. The laws of physics don&#8217;t in any way say that there must remain a record of past evolution.</p>
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	</item>
	<item>
		<title>By: Hal S</title>
		<link>http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309105</link>
		<dc:creator>Hal S</dc:creator>
		<pubDate>Thu, 24 Jan 2008 20:31:43 +0000</pubDate>
		<guid isPermaLink="false">http://cosmicvariance.com/2008/01/14/boltzmanns-universe/#comment-309105</guid>
		<description>There will be an evolution to this process, and entropy will increase, but again as outlined in 48, you can never get rid of all the correlations, and there will be some finite record of this evolution</description>
		<content:encoded><![CDATA[<p>There will be an evolution to this process, and entropy will increase, but again as outlined in 48, you can never get rid of all the correlations, and there will be some finite record of this evolution</p>
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