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<channel>
	<title>Comments for Azimuth</title>
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	<link>http://johncarlosbaez.wordpress.com</link>
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	<lastBuildDate>Sun, 19 May 2013 15:51:11 +0000</lastBuildDate>
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		<title>Comment on The Search For Budget-Conscious Life by John Baez</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28786</link>
		<dc:creator><![CDATA[John Baez]]></dc:creator>
		<pubDate>Sun, 19 May 2013 15:51:11 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28786</guid>
		<description><![CDATA[On a somewhat related note, the &lt;a href=&quot;http://imagination.ucsd.edu/starship/index.html&quot; rel=&quot;nofollow&quot;&gt;SETI Institute&lt;/a&gt; writes:

&lt;blockquote&gt;
Please join us on Wednesday May 22 at 10am PT for a SETI hangout with Gregory Benford (science fiction author) and Jill Tarter (Bernard Oliver Chair at the SETI Institute) on the Starship Century Symposium.

This symposium coordinated by the new Arthur C. Clarke Center for Human Imagination in collaboration with Gregory and James Benford, aims at presenting ideas from science and science fiction.

During this hangout hosted by Franck Marchis (Senior Planetary Astronomer at Carl Sagan Center of the SETI Institute) and moderated Adam Mann (WIRED),  we will discuss if we could build spaceships to explore the nearby galaxy and the contribution of the SETI research center to this project.
&lt;/blockquote&gt;]]></description>
		<content:encoded><![CDATA[<p>On a somewhat related note, the <a href="http://imagination.ucsd.edu/starship/index.html" rel="nofollow">SETI Institute</a> writes:</p>
<blockquote><p>
Please join us on Wednesday May 22 at 10am PT for a SETI hangout with Gregory Benford (science fiction author) and Jill Tarter (Bernard Oliver Chair at the SETI Institute) on the Starship Century Symposium.</p>
<p>This symposium coordinated by the new Arthur C. Clarke Center for Human Imagination in collaboration with Gregory and James Benford, aims at presenting ideas from science and science fiction.</p>
<p>During this hangout hosted by Franck Marchis (Senior Planetary Astronomer at Carl Sagan Center of the SETI Institute) and moderated Adam Mann (WIRED),  we will discuss if we could build spaceships to explore the nearby galaxy and the contribution of the SETI research center to this project.
</p></blockquote>
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		<title>Comment on The Search For Budget-Conscious Life by domenico</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28785</link>
		<dc:creator><![CDATA[domenico]]></dc:creator>
		<pubDate>Sun, 19 May 2013 15:30:20 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28785</guid>
		<description><![CDATA[I suppose that exist a natural production of spin singlet in some part of space.
In the EPR paradox the measure of Alice spin collapse the state of the Bob spin.
The spin of Alice is random, then the Bob spin is random (no communication possible).
Alice can collapse with quick ortogonal measure (x-axis or z-axis), then Bob measure a change in x-spin, and z-spin, measure.
I was thinking to a photon polarization (matter-antimatter annihilation), so that an astronomical measure can be simple (polarization transmission), but maybe I changed my mind.
Thank you for the clear demonstration.]]></description>
		<content:encoded><![CDATA[<p>I suppose that exist a natural production of spin singlet in some part of space.<br />
In the EPR paradox the measure of Alice spin collapse the state of the Bob spin.<br />
The spin of Alice is random, then the Bob spin is random (no communication possible).<br />
Alice can collapse with quick ortogonal measure (x-axis or z-axis), then Bob measure a change in x-spin, and z-spin, measure.<br />
I was thinking to a photon polarization (matter-antimatter annihilation), so that an astronomical measure can be simple (polarization transmission), but maybe I changed my mind.<br />
Thank you for the clear demonstration.</p>
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	<item>
		<title>Comment on Network Theory (Part 15) by Graph Laplacians &#124; Azimuth</title>
		<link>http://johncarlosbaez.wordpress.com/2011/10/26/network-theory-part-15/#comment-28784</link>
		<dc:creator><![CDATA[Graph Laplacians &#124; Azimuth]]></dc:creator>
		<pubDate>Sun, 19 May 2013 15:26:43 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=5945#comment-28784</guid>
		<description><![CDATA[As I&#8217;ve grown interested in network theory, I&#8217;ve gotten more and more interested in &#8216;graph Laplacians&#8217;. There&#039;s been some important progress on these recently...]]></description>
		<content:encoded><![CDATA[<p>As I&#8217;ve grown interested in network theory, I&#8217;ve gotten more and more interested in &#8216;graph Laplacians&#8217;. There&#8217;s been some important progress on these recently&#8230;</p>
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		<title>Comment on The Search For Budget-Conscious Life by John Baez</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28782</link>
		<dc:creator><![CDATA[John Baez]]></dc:creator>
		<pubDate>Sun, 19 May 2013 14:43:44 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28782</guid>
		<description><![CDATA[My point is just that it&#039;s much harder to colonize the Galaxy than send radio messages.   The dollar figures for a radio beacon versus colonizing Mars are just meant to illustrate this.

Eventually some civilization should arise that can spread through the Galaxy.   But we haven&#039;t seen that, so what should we do in the meantime?  It seems quite possible that only a tiny fraction of civilizations will reach the point of spreading through the Galaxy, while the rest die out before they do this.  If so, there may already be civilizations who have reached the point of being able to communicate across the Galaxy using radio waves, despite the apparent lack of Galaxy-colonizing ones.  If so, there&#039;s something easy we can do: listen for radio waves, while keeping in mind the constraints faced by primitive civilizations like our own.

&lt;blockquote&gt;
I feel that I am thinking biologically, and that I keep seeing physicists who are not thinking that way...
&lt;/blockquote&gt;

I don&#039;t agree with you.  I feel I&#039;m thinking like a detective trying to solve a mystery given the available clues.  Sure, it makes biological sense that a civilization will eventually colonize the Galaxy.  But what does that insight help us do?  For the most part is just puts us in the arms of the &lt;a href=&quot;http://en.wikipedia.org/wiki/Fermi_paradox&quot; rel=&quot;nofollow&quot;&gt;Fermi Paradox&lt;/a&gt;.  (Another physicist.  &lt;img src=&quot;http://math.ucr.edu/home/baez/emoticons/tongue2.gif&quot; alt=&quot;&quot; /&gt;) 

If we could find a really convincing solution to that, this would count as progress.  But it also pays to seek more evidence, and looking for radio signals is a cheap way to do this.  (So is &lt;a href=&quot;https://en.wikipedia.org/wiki/Extrasolar_planet&quot; rel=&quot;nofollow&quot;&gt;exoplanetology&lt;/a&gt;, but we&#039;re already putting a lot of effort into that.)

&lt;blockquote&gt;
Sending kids to Mars is silly...
&lt;/blockquote&gt;

I agree, and I &lt;a href=&quot;http://memetherapy.wordpress.com/2009/01/26/manned-vs-unmanned-spaceflight/&quot; rel=&quot;nofollow&quot;&gt;constantly inveigh&lt;/a&gt; against wasting resources this way.  My point in invoking Mars was to point out how hard it is to get there: and this is pathetically easy compared to getting to the next star.  So there could be plenty of civilizations that fizzle out before they leave their solar systems.  Maybe ours.]]></description>
		<content:encoded><![CDATA[<p>My point is just that it&#8217;s much harder to colonize the Galaxy than send radio messages.   The dollar figures for a radio beacon versus colonizing Mars are just meant to illustrate this.</p>
<p>Eventually some civilization should arise that can spread through the Galaxy.   But we haven&#8217;t seen that, so what should we do in the meantime?  It seems quite possible that only a tiny fraction of civilizations will reach the point of spreading through the Galaxy, while the rest die out before they do this.  If so, there may already be civilizations who have reached the point of being able to communicate across the Galaxy using radio waves, despite the apparent lack of Galaxy-colonizing ones.  If so, there&#8217;s something easy we can do: listen for radio waves, while keeping in mind the constraints faced by primitive civilizations like our own.</p>
<blockquote><p>
I feel that I am thinking biologically, and that I keep seeing physicists who are not thinking that way&#8230;
</p></blockquote>
<p>I don&#8217;t agree with you.  I feel I&#8217;m thinking like a detective trying to solve a mystery given the available clues.  Sure, it makes biological sense that a civilization will eventually colonize the Galaxy.  But what does that insight help us do?  For the most part is just puts us in the arms of the <a href="http://en.wikipedia.org/wiki/Fermi_paradox" rel="nofollow">Fermi Paradox</a>.  (Another physicist.  <img src="http://math.ucr.edu/home/baez/emoticons/tongue2.gif" alt="" />) </p>
<p>If we could find a really convincing solution to that, this would count as progress.  But it also pays to seek more evidence, and looking for radio signals is a cheap way to do this.  (So is <a href="https://en.wikipedia.org/wiki/Extrasolar_planet" rel="nofollow">exoplanetology</a>, but we&#8217;re already putting a lot of effort into that.)</p>
<blockquote><p>
Sending kids to Mars is silly&#8230;
</p></blockquote>
<p>I agree, and I <a href="http://memetherapy.wordpress.com/2009/01/26/manned-vs-unmanned-spaceflight/" rel="nofollow">constantly inveigh</a> against wasting resources this way.  My point in invoking Mars was to point out how hard it is to get there: and this is pathetically easy compared to getting to the next star.  So there could be plenty of civilizations that fizzle out before they leave their solar systems.  Maybe ours.</p>
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		<title>Comment on The Search For Budget-Conscious Life by Greg Egan</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28777</link>
		<dc:creator><![CDATA[Greg Egan]]></dc:creator>
		<pubDate>Sun, 19 May 2013 12:43:46 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28777</guid>
		<description><![CDATA[Since we haven&#039;t yet met anyone&#039;s kids, it seems perfectly reasonable to invest a modest amount of time and resources on SETI, and on thinking about different approaches to SETI.  I&#039;m sure it&#039;s a long shot, but it&#039;s massively premature to write it off as futile, least of all on the basis that Dyson spheres and Von Neumann machines are some kind of &quot;inevitable&quot; endpoint for every space-faring culture.]]></description>
		<content:encoded><![CDATA[<p>Since we haven&#8217;t yet met anyone&#8217;s kids, it seems perfectly reasonable to invest a modest amount of time and resources on SETI, and on thinking about different approaches to SETI.  I&#8217;m sure it&#8217;s a long shot, but it&#8217;s massively premature to write it off as futile, least of all on the basis that Dyson spheres and Von Neumann machines are some kind of &#8220;inevitable&#8221; endpoint for every space-faring culture.</p>
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		<title>Comment on The Search For Budget-Conscious Life by Graham Jones</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28772</link>
		<dc:creator><![CDATA[Graham Jones]]></dc:creator>
		<pubDate>Sun, 19 May 2013 09:54:09 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28772</guid>
		<description><![CDATA[The cost in $ for us now is not important. What matters is what kind of behaviour will be favoured (by their economics if you like, but ultimately by natural selection) among aliens with space travel and advanced technologies. The ERoEI of colonising a galaxy is quite big.

Sending kids to Mars is silly (though it may happen http://www.independent.co.uk/news/science/video-over-600-people-sign-up-to-live-on-mars-8594348.html). The whole idea of living on the surface of a planet is silly for organisms that have space travel. There is so much more energy and material available for organisms that fragment planets and live on the pieces.

It&#039;s weird. I feel that I am thinking biologically, and that I keep seeing physicists who are not thinking that way, and yet I&#039;m really only putting together two ideas from physicists 50 odd years ago (Von Neumann probes, Dyson sphere).

As for messages across vast time scales: apart from the funeral pyre, I saw their kids before I saw their message.]]></description>
		<content:encoded><![CDATA[<p>The cost in $ for us now is not important. What matters is what kind of behaviour will be favoured (by their economics if you like, but ultimately by natural selection) among aliens with space travel and advanced technologies. The ERoEI of colonising a galaxy is quite big.</p>
<p>Sending kids to Mars is silly (though it may happen <a href="http://www.independent.co.uk/news/science/video-over-600-people-sign-up-to-live-on-mars-8594348.html" rel="nofollow">http://www.independent.co.uk/news/science/video-over-600-people-sign-up-to-live-on-mars-8594348.html</a>). The whole idea of living on the surface of a planet is silly for organisms that have space travel. There is so much more energy and material available for organisms that fragment planets and live on the pieces.</p>
<p>It&#8217;s weird. I feel that I am thinking biologically, and that I keep seeing physicists who are not thinking that way, and yet I&#8217;m really only putting together two ideas from physicists 50 odd years ago (Von Neumann probes, Dyson sphere).</p>
<p>As for messages across vast time scales: apart from the funeral pyre, I saw their kids before I saw their message.</p>
]]></content:encoded>
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	<item>
		<title>Comment on The Search For Budget-Conscious Life by John Baez</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28752</link>
		<dc:creator><![CDATA[John Baez]]></dc:creator>
		<pubDate>Sun, 19 May 2013 01:32:07 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28752</guid>
		<description><![CDATA[On my G+ post about this issue there was a commenter who was convinced that quantum entanglement allowed for faster-than-light communication.  I told him it just doesn&#039;t work like that, but it seemed to bounce off him.  I suppose for someone who hasn&#039;t thought about this much, it&#039;s a fact that requires either a lengthy argument or some acceptance of &#039;authority&#039;. 

[EDIT: oh, now I see Greg has given the lengthy argument!  Thanks!]

But I blame the news media for confusing people in the first place.]]></description>
		<content:encoded><![CDATA[<p>On my G+ post about this issue there was a commenter who was convinced that quantum entanglement allowed for faster-than-light communication.  I told him it just doesn&#8217;t work like that, but it seemed to bounce off him.  I suppose for someone who hasn&#8217;t thought about this much, it&#8217;s a fact that requires either a lengthy argument or some acceptance of &#8216;authority&#8217;. </p>
<p>[EDIT: oh, now I see Greg has given the lengthy argument!  Thanks!]</p>
<p>But I blame the news media for confusing people in the first place.</p>
]]></content:encoded>
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		<title>Comment on The Search For Budget-Conscious Life by Greg Egan</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28750</link>
		<dc:creator><![CDATA[Greg Egan]]></dc:creator>
		<pubDate>Sun, 19 May 2013 01:26:24 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28750</guid>
		<description><![CDATA[It might be fun to work through the example of quantum &quot;teleportation&quot;, to see why you need a classical message as well as an entangled pair.  (The following is adapted from &quot;Quantum Theory:  Concepts and Methods&quot; by Asher Peres.)

Let A and B be two spin-(1/2) particles in the entangled state:

  $latex \psi_{AB} = (u_A d_B - d_A u_B) / \sqrt{2}$

where $latex \{u_P, d_P\}$ are the spin-up and spin-down states for particle P.

Let X be a spin-(1/2) particle in an unknown state:

  $latex \psi_X = \alpha u_X + \beta d_X$

giving a total state for the three particles:

  $latex \psi_{XAB} = (\alpha u_X + \beta d_X) (u_A d_B - d_A u_B) / \sqrt{2}$

or, expanding this out:

  $latex \psi_{XAB} = (\alpha u_X u_A d_B - \alpha u_X d_A u_B +
              \beta d_X u_A d_B -  \beta d_X d_A u_B) / \sqrt{2}$

Suppose Alice has particle A of the entangled pair, along with particle X that she wants to &quot;teleport&quot; to Bob, while Bob has particle B.

Alice performs a measurement on X and A that resolves their state into one of the following four orthonormal states:

  $latex e_{00} = (u_X d_A - d_X u_A) / \sqrt{2}$

  $latex e_{01} = (u_X d_A + d_X u_A) / \sqrt{2}$

  $latex e_{10} = (u_X u_A - d_X d_A) / \sqrt{2}$

  $latex e_{11} = (u_X u_A + d_X d_A) / \sqrt{2}$

Given the result of that measurement, if Bob performs the correct operation on particle B for each possible outcome, that will guarantee that after he&#039;s done so, any subsequent measurements on B&#039;s spin degree of freedom will be identical to those you&#039;d get for the original state of particle X.

How does this work?  You can rewrite $latex \psi_{XAB}$ as:

$latex \psi_{XAB} = (e_{00} (-\alpha u_B - \beta d_B) +
    e_{01} (-\alpha u_B + \beta d_B) + $
$latex \hbox{\qquad \qquad \qquad} e_{10} ( \alpha d_B + \beta u_B) +
    e_{11} ( \alpha d_B - \beta u_B)) / 2$

The four states for particle B on the RHS can all be transformed by an appropriate operation into:

  $latex \alpha u_B + \beta d_B$

up to an overall phase, either by doing nothing or by measuring a spin, i.e. $latex U_{nn}$ applied to the term following $latex e_{nn}$ will always yield $latex \alpha u_B + \beta d_B$ if you choose:

  $latex U_{00} = - I$

  $latex U_{01} = - \sigma_z$

  $latex U_{10} =   \sigma_x$

  $latex U_{11} = i \sigma_y$

So &lt;i&gt;after&lt;/i&gt; Bob receives a classical two-bit message from Alice telling him which of the $latex e_{nn}$ she measured particles X and A to be in, he can then perform the corresponding unitary operation $latex U_{nn}$ on particle B ... and the result will be that particle B will end up in the same state as particle X was in initially!

But Bob can&#039;t do anything until he receives the message from Alice telling him the result of her measurement.  Nothing is &quot;teleported&quot; until he performs the correct, matching operation himself, and he can&#039;t know what that is until he has heard from Alice.]]></description>
		<content:encoded><![CDATA[<p>It might be fun to work through the example of quantum &#8220;teleportation&#8221;, to see why you need a classical message as well as an entangled pair.  (The following is adapted from &#8220;Quantum Theory:  Concepts and Methods&#8221; by Asher Peres.)</p>
<p>Let A and B be two spin-(1/2) particles in the entangled state:</p>
<p>  <img src='http://s0.wp.com/latex.php?latex=%5Cpsi_%7BAB%7D+%3D+%28u_A+d_B+-+d_A+u_B%29+%2F+%5Csqrt%7B2%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;psi_{AB} = (u_A d_B - d_A u_B) / &#92;sqrt{2}' title='&#92;psi_{AB} = (u_A d_B - d_A u_B) / &#92;sqrt{2}' class='latex' /></p>
<p>where <img src='http://s0.wp.com/latex.php?latex=%5C%7Bu_P%2C+d_P%5C%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;{u_P, d_P&#92;}' title='&#92;{u_P, d_P&#92;}' class='latex' /> are the spin-up and spin-down states for particle P.</p>
<p>Let X be a spin-(1/2) particle in an unknown state:</p>
<p>  <img src='http://s0.wp.com/latex.php?latex=%5Cpsi_X+%3D+%5Calpha+u_X+%2B+%5Cbeta+d_X&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;psi_X = &#92;alpha u_X + &#92;beta d_X' title='&#92;psi_X = &#92;alpha u_X + &#92;beta d_X' class='latex' /></p>
<p>giving a total state for the three particles:</p>
<p>  <img src='http://s0.wp.com/latex.php?latex=%5Cpsi_%7BXAB%7D+%3D+%28%5Calpha+u_X+%2B+%5Cbeta+d_X%29+%28u_A+d_B+-+d_A+u_B%29+%2F+%5Csqrt%7B2%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;psi_{XAB} = (&#92;alpha u_X + &#92;beta d_X) (u_A d_B - d_A u_B) / &#92;sqrt{2}' title='&#92;psi_{XAB} = (&#92;alpha u_X + &#92;beta d_X) (u_A d_B - d_A u_B) / &#92;sqrt{2}' class='latex' /></p>
<p>or, expanding this out:</p>
<p>  <img src='http://s0.wp.com/latex.php?latex=%5Cpsi_%7BXAB%7D+%3D+%28%5Calpha+u_X+u_A+d_B+-+%5Calpha+u_X+d_A+u_B+%2B+++++++++++++++%5Cbeta+d_X+u_A+d_B+-++%5Cbeta+d_X+d_A+u_B%29+%2F+%5Csqrt%7B2%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;psi_{XAB} = (&#92;alpha u_X u_A d_B - &#92;alpha u_X d_A u_B +               &#92;beta d_X u_A d_B -  &#92;beta d_X d_A u_B) / &#92;sqrt{2}' title='&#92;psi_{XAB} = (&#92;alpha u_X u_A d_B - &#92;alpha u_X d_A u_B +               &#92;beta d_X u_A d_B -  &#92;beta d_X d_A u_B) / &#92;sqrt{2}' class='latex' /></p>
<p>Suppose Alice has particle A of the entangled pair, along with particle X that she wants to &#8220;teleport&#8221; to Bob, while Bob has particle B.</p>
<p>Alice performs a measurement on X and A that resolves their state into one of the following four orthonormal states:</p>
<p>  <img src='http://s0.wp.com/latex.php?latex=e_%7B00%7D+%3D+%28u_X+d_A+-+d_X+u_A%29+%2F+%5Csqrt%7B2%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='e_{00} = (u_X d_A - d_X u_A) / &#92;sqrt{2}' title='e_{00} = (u_X d_A - d_X u_A) / &#92;sqrt{2}' class='latex' /></p>
<p>  <img src='http://s0.wp.com/latex.php?latex=e_%7B01%7D+%3D+%28u_X+d_A+%2B+d_X+u_A%29+%2F+%5Csqrt%7B2%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='e_{01} = (u_X d_A + d_X u_A) / &#92;sqrt{2}' title='e_{01} = (u_X d_A + d_X u_A) / &#92;sqrt{2}' class='latex' /></p>
<p>  <img src='http://s0.wp.com/latex.php?latex=e_%7B10%7D+%3D+%28u_X+u_A+-+d_X+d_A%29+%2F+%5Csqrt%7B2%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='e_{10} = (u_X u_A - d_X d_A) / &#92;sqrt{2}' title='e_{10} = (u_X u_A - d_X d_A) / &#92;sqrt{2}' class='latex' /></p>
<p>  <img src='http://s0.wp.com/latex.php?latex=e_%7B11%7D+%3D+%28u_X+u_A+%2B+d_X+d_A%29+%2F+%5Csqrt%7B2%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='e_{11} = (u_X u_A + d_X d_A) / &#92;sqrt{2}' title='e_{11} = (u_X u_A + d_X d_A) / &#92;sqrt{2}' class='latex' /></p>
<p>Given the result of that measurement, if Bob performs the correct operation on particle B for each possible outcome, that will guarantee that after he&#8217;s done so, any subsequent measurements on B&#8217;s spin degree of freedom will be identical to those you&#8217;d get for the original state of particle X.</p>
<p>How does this work?  You can rewrite <img src='http://s0.wp.com/latex.php?latex=%5Cpsi_%7BXAB%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;psi_{XAB}' title='&#92;psi_{XAB}' class='latex' /> as:</p>
<p><img src='http://s0.wp.com/latex.php?latex=%5Cpsi_%7BXAB%7D+%3D+%28e_%7B00%7D+%28-%5Calpha+u_B+-+%5Cbeta+d_B%29+%2B+++++e_%7B01%7D+%28-%5Calpha+u_B+%2B+%5Cbeta+d_B%29+%2B+&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;psi_{XAB} = (e_{00} (-&#92;alpha u_B - &#92;beta d_B) +     e_{01} (-&#92;alpha u_B + &#92;beta d_B) + ' title='&#92;psi_{XAB} = (e_{00} (-&#92;alpha u_B - &#92;beta d_B) +     e_{01} (-&#92;alpha u_B + &#92;beta d_B) + ' class='latex' /><br />
<img src='http://s0.wp.com/latex.php?latex=%5Chbox%7B%5Cqquad+%5Cqquad+%5Cqquad%7D+e_%7B10%7D+%28+%5Calpha+d_B+%2B+%5Cbeta+u_B%29+%2B+++++e_%7B11%7D+%28+%5Calpha+d_B+-+%5Cbeta+u_B%29%29+%2F+2&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;hbox{&#92;qquad &#92;qquad &#92;qquad} e_{10} ( &#92;alpha d_B + &#92;beta u_B) +     e_{11} ( &#92;alpha d_B - &#92;beta u_B)) / 2' title='&#92;hbox{&#92;qquad &#92;qquad &#92;qquad} e_{10} ( &#92;alpha d_B + &#92;beta u_B) +     e_{11} ( &#92;alpha d_B - &#92;beta u_B)) / 2' class='latex' /></p>
<p>The four states for particle B on the RHS can all be transformed by an appropriate operation into:</p>
<p>  <img src='http://s0.wp.com/latex.php?latex=%5Calpha+u_B+%2B+%5Cbeta+d_B&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;alpha u_B + &#92;beta d_B' title='&#92;alpha u_B + &#92;beta d_B' class='latex' /></p>
<p>up to an overall phase, either by doing nothing or by measuring a spin, i.e. <img src='http://s0.wp.com/latex.php?latex=U_%7Bnn%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='U_{nn}' title='U_{nn}' class='latex' /> applied to the term following <img src='http://s0.wp.com/latex.php?latex=e_%7Bnn%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='e_{nn}' title='e_{nn}' class='latex' /> will always yield <img src='http://s0.wp.com/latex.php?latex=%5Calpha+u_B+%2B+%5Cbeta+d_B&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='&#92;alpha u_B + &#92;beta d_B' title='&#92;alpha u_B + &#92;beta d_B' class='latex' /> if you choose:</p>
<p>  <img src='http://s0.wp.com/latex.php?latex=U_%7B00%7D+%3D+-+I&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='U_{00} = - I' title='U_{00} = - I' class='latex' /></p>
<p>  <img src='http://s0.wp.com/latex.php?latex=U_%7B01%7D+%3D+-+%5Csigma_z&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='U_{01} = - &#92;sigma_z' title='U_{01} = - &#92;sigma_z' class='latex' /></p>
<p>  <img src='http://s0.wp.com/latex.php?latex=U_%7B10%7D+%3D+++%5Csigma_x&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='U_{10} =   &#92;sigma_x' title='U_{10} =   &#92;sigma_x' class='latex' /></p>
<p>  <img src='http://s0.wp.com/latex.php?latex=U_%7B11%7D+%3D+i+%5Csigma_y&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='U_{11} = i &#92;sigma_y' title='U_{11} = i &#92;sigma_y' class='latex' /></p>
<p>So <i>after</i> Bob receives a classical two-bit message from Alice telling him which of the <img src='http://s0.wp.com/latex.php?latex=e_%7Bnn%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='e_{nn}' title='e_{nn}' class='latex' /> she measured particles X and A to be in, he can then perform the corresponding unitary operation <img src='http://s0.wp.com/latex.php?latex=U_%7Bnn%7D&amp;bg=ffffff&amp;fg=333333&amp;s=0' alt='U_{nn}' title='U_{nn}' class='latex' /> on particle B &#8230; and the result will be that particle B will end up in the same state as particle X was in initially!</p>
<p>But Bob can&#8217;t do anything until he receives the message from Alice telling him the result of her measurement.  Nothing is &#8220;teleported&#8221; until he performs the correct, matching operation himself, and he can&#8217;t know what that is until he has heard from Alice.</p>
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		<title>Comment on The Search For Budget-Conscious Life by John Baez</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28748</link>
		<dc:creator><![CDATA[John Baez]]></dc:creator>
		<pubDate>Sun, 19 May 2013 00:59:30 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28748</guid>
		<description><![CDATA[Long-range interstellar travel is a lot harder than making a radio beam that could communicate across the galaxy.  The Benfords calculate we could do the latter now for 10  billion dollars:

&lt;blockquote&gt;
We find the optimum total capital costs for a galactic-scale Beacon to be in the range of 10$B.  The Apollo project cost about 300 B$ in current dollars, and large science today, such as the Large Hadron Collider, International Linear Collider and ITER fusion reactor, are of order 10 B$. This suggests that galactic-scale Beacons are plausible luxuries.
&lt;/blockquote&gt;

Even sending your kids to Mars would cost more!

The Benfords suggest a number of possible reasons why civilizations might bother to send messages:

&lt;blockquote&gt;
Human history suggests that there are two major categories of long-term messages that finite, mortal beings send across vast time scales:

• &lt;b&gt;Kilroy Was Here.&lt;/b&gt; These can be signatures verging on graffiti. Names chiseled into walls have survived from ancient times. More recently, we sent compact disks on interplanetary probes, often bearing people’s names and short messages that can endure for millennia.

• &lt;b&gt;High Church.&lt;/b&gt; These are designed for durability, to convey the culture’s highest achievements. The essential message is this was the best we did; remember it.

Thinking broadly, high-power transmitters might be built for wide variety of goals other than two-way communication driven by curiosity. For example:

• &lt;b&gt;The Funeral Pyre.&lt;/b&gt; A civilization near the end of its life announces its existence.

• &lt;b&gt;Ozymandias.&lt;/b&gt; Here the motivation is sheer pride; the beacon announces the existence of a high civilization, even though it may be extinct, and the beacon tended by robots. This recalls the classic Percy Bysshe Shelly lines:

&lt;i&gt;And on the pedestal these words appear:
&#039;My name is Ozymandias, King of Kings;
Look on my works, Ye Mighty, and despair!’
Nothing beside remains. Round the decay
of that colossal wreck, boundless and bare,
The lone and level sands stretch far away.&lt;/i&gt;

• &lt;b&gt;Help!&lt;/b&gt; Quite possibly societies that plan over time scales ~1000 years will foresee physical problems and wish to discover if others have surmounted them. An example is a civilization whose star is warming (as ours is), which may wish to move their planet outward with gravitational tugs. Many others are possible.

• &lt;b&gt;Leakage Radiation.&lt;/b&gt; These are unintentional, much like objects left accidentally in ancient sites and uncovered long after. They do carry messages, even if inadvertent: technological fingerprints. These can be not merely radio and television broadcasts radiating isotropically, which are fairly weak, but deep space radar and beaming of energy over solar system distances. This includes “industrial” spaceship launchers, beam-driven sails, “planetary defense” radars scanning for killer asteroids, and cosmic power beaming driving interstellar starships with beams of lasers, millimeter or microwaves. There are many ideas about such uses already in the literature (Benford &amp; Benford, 2006).

• &lt;b&gt;Join Us.&lt;/b&gt; Religion may be a galactic commonplace; after all, it is here. Seeking converts is common, too, and electromagnetic preaching fits a frequent meme.﻿
&lt;/blockquote&gt;]]></description>
		<content:encoded><![CDATA[<p>Long-range interstellar travel is a lot harder than making a radio beam that could communicate across the galaxy.  The Benfords calculate we could do the latter now for 10  billion dollars:</p>
<blockquote><p>
We find the optimum total capital costs for a galactic-scale Beacon to be in the range of 10$B.  The Apollo project cost about 300 B$ in current dollars, and large science today, such as the Large Hadron Collider, International Linear Collider and ITER fusion reactor, are of order 10 B$. This suggests that galactic-scale Beacons are plausible luxuries.
</p></blockquote>
<p>Even sending your kids to Mars would cost more!</p>
<p>The Benfords suggest a number of possible reasons why civilizations might bother to send messages:</p>
<blockquote><p>
Human history suggests that there are two major categories of long-term messages that finite, mortal beings send across vast time scales:</p>
<p>• <b>Kilroy Was Here.</b> These can be signatures verging on graffiti. Names chiseled into walls have survived from ancient times. More recently, we sent compact disks on interplanetary probes, often bearing people’s names and short messages that can endure for millennia.</p>
<p>• <b>High Church.</b> These are designed for durability, to convey the culture’s highest achievements. The essential message is this was the best we did; remember it.</p>
<p>Thinking broadly, high-power transmitters might be built for wide variety of goals other than two-way communication driven by curiosity. For example:</p>
<p>• <b>The Funeral Pyre.</b> A civilization near the end of its life announces its existence.</p>
<p>• <b>Ozymandias.</b> Here the motivation is sheer pride; the beacon announces the existence of a high civilization, even though it may be extinct, and the beacon tended by robots. This recalls the classic Percy Bysshe Shelly lines:</p>
<p><i>And on the pedestal these words appear:<br />
&#8216;My name is Ozymandias, King of Kings;<br />
Look on my works, Ye Mighty, and despair!’<br />
Nothing beside remains. Round the decay<br />
of that colossal wreck, boundless and bare,<br />
The lone and level sands stretch far away.</i></p>
<p>• <b>Help!</b> Quite possibly societies that plan over time scales ~1000 years will foresee physical problems and wish to discover if others have surmounted them. An example is a civilization whose star is warming (as ours is), which may wish to move their planet outward with gravitational tugs. Many others are possible.</p>
<p>• <b>Leakage Radiation.</b> These are unintentional, much like objects left accidentally in ancient sites and uncovered long after. They do carry messages, even if inadvertent: technological fingerprints. These can be not merely radio and television broadcasts radiating isotropically, which are fairly weak, but deep space radar and beaming of energy over solar system distances. This includes “industrial” spaceship launchers, beam-driven sails, “planetary defense” radars scanning for killer asteroids, and cosmic power beaming driving interstellar starships with beams of lasers, millimeter or microwaves. There are many ideas about such uses already in the literature (Benford &amp; Benford, 2006).</p>
<p>• <b>Join Us.</b> Religion may be a galactic commonplace; after all, it is here. Seeking converts is common, too, and electromagnetic preaching fits a frequent meme.﻿
</p></blockquote>
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		<title>Comment on The Search For Budget-Conscious Life by Greg Egan</title>
		<link>http://johncarlosbaez.wordpress.com/2013/05/18/the-search-for-budget-conscious-intelligent-life/#comment-28747</link>
		<dc:creator><![CDATA[Greg Egan]]></dc:creator>
		<pubDate>Sun, 19 May 2013 00:29:20 +0000</pubDate>
		<guid isPermaLink="false">http://johncarlosbaez.wordpress.com/?p=15863#comment-28747</guid>
		<description><![CDATA[The only applications I know of for quantum entanglement in communications are encryption and (the unfortunately named) quantum &quot;teleportation&quot;, and in both cases the possession of entangled pairs by the communicating parties needs to be accompanied by a channel of classical information.  So even if interstellar civilisations are making use of entangled pairs, that will necessarily be &lt;i&gt;in addition to&lt;/i&gt; some form of signal transmission.

That signal might well be very hard to detect for ordinary, private communications, but there might also be cultures who are making a deliberate effort to attract attention, but have a limited energy budget for that purpose.

Natural astrophysical sources of entangled particles are unlikely to be very useful for communications.  If Alice receives some positrons from a natural source of pair production and Bob receives electrons from the same source, even if some of the particles they receive happen to be entangled (which in itself is unlikely unless they have access to the entire output of the source), they&#039;ll have no way of knowing which are entangled with which.  Since they need to send things to each other anyway, they&#039;d be much better off manufacturing and distributing their own entangled pairs.]]></description>
		<content:encoded><![CDATA[<p>The only applications I know of for quantum entanglement in communications are encryption and (the unfortunately named) quantum &#8220;teleportation&#8221;, and in both cases the possession of entangled pairs by the communicating parties needs to be accompanied by a channel of classical information.  So even if interstellar civilisations are making use of entangled pairs, that will necessarily be <i>in addition to</i> some form of signal transmission.</p>
<p>That signal might well be very hard to detect for ordinary, private communications, but there might also be cultures who are making a deliberate effort to attract attention, but have a limited energy budget for that purpose.</p>
<p>Natural astrophysical sources of entangled particles are unlikely to be very useful for communications.  If Alice receives some positrons from a natural source of pair production and Bob receives electrons from the same source, even if some of the particles they receive happen to be entangled (which in itself is unlikely unless they have access to the entire output of the source), they&#8217;ll have no way of knowing which are entangled with which.  Since they need to send things to each other anyway, they&#8217;d be much better off manufacturing and distributing their own entangled pairs.</p>
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