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	<title>Comments on: String Wars Hit the MSM</title>
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	<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/</link>
	<description>Random samplings from a universe of ideas.</description>
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		<title>By: Not Even Wrong &#187; Blog Archive &#187; News From All Over</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23837</link>
		<dc:creator>Not Even Wrong &#187; Blog Archive &#187; News From All Over</dc:creator>
		<pubDate>Tue, 16 Jan 2007 20:59:48 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23837</guid>
		<description>[...] As mentioned here and at Cosmic Variance, the New Yorker recently actually ran a cartoon about the string theory controversy.Â  If that&#8217;s not an indication that something has made it into the zeitgeist, I don&#8217;t know what is.Â Â  Besides the New Yorker, string theory features in Zippy the Pinhead and recent Doonesbury cartoons, as well as one from Rodrigo Alonso entitled Pulling Strings that he sent me recently. [...]</description>
		<content:encoded><![CDATA[<p>[...] As mentioned here and at Cosmic Variance, the New Yorker recently actually ran a cartoon about the string theory controversy.Â  If that&#8217;s not an indication that something has made it into the zeitgeist, I don&#8217;t know what is.Â Â  Besides the New Yorker, string theory features in Zippy the Pinhead and recent Doonesbury cartoons, as well as one from Rodrigo Alonso entitled Pulling Strings that he sent me recently. [...]</p>
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		<title>By: Warren</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23838</link>
		<dc:creator>Warren</dc:creator>
		<pubDate>Tue, 16 Jan 2007 14:01:30 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23838</guid>
		<description>Maybe a final comment:

The string tension has nothing to do with a nucleus.  It is NOT the string coupling, which gives the coupling between different hadrons.  It is the tension that binds the quarks inside a single hadron.  This is the force that&#039;s stringy, as it&#039;s a constant, independent of separation, whereas the force between hadrons follows the usual Yukawa law.

If you really want to learn this stuff, you&#039;re not going to get it from a blog, especially from a quack like nc.  Any standard reference on particle physics will do; there are some written for laymen.  The string tension is understood not only by string theorists, but also by field theorists; it&#039;s a standard calculation in lattice QCD.

Please don&#039;t think that nc is a physicist.  (He only publishes in &quot;Electronics World&quot;?)  Anyone who has had even high-school physics would recognize that nc is a complete fake.  I have given references above, which anyone can look up.  For those of you who know no physics, I would suggest at least learning what &quot;significant digits&quot; means, to realize that no physicist would ever claim that using a 5-digit input would improve the rounding error in a calculation that also has an order-of-magnitude estimate as input.

Finally, there is nothing uncivil about calling a liar a liar.  On the contrary, allowing quacks like nc to repeatedly state lies &amp; self-contradictions would be far more uncivil.</description>
		<content:encoded><![CDATA[<p>Maybe a final comment:</p>
<p>The string tension has nothing to do with a nucleus.  It is NOT the string coupling, which gives the coupling between different hadrons.  It is the tension that binds the quarks inside a single hadron.  This is the force that&#8217;s stringy, as it&#8217;s a constant, independent of separation, whereas the force between hadrons follows the usual Yukawa law.</p>
<p>If you really want to learn this stuff, you&#8217;re not going to get it from a blog, especially from a quack like nc.  Any standard reference on particle physics will do; there are some written for laymen.  The string tension is understood not only by string theorists, but also by field theorists; it&#8217;s a standard calculation in lattice QCD.</p>
<p>Please don&#8217;t think that nc is a physicist.  (He only publishes in &#8220;Electronics World&#8221;?)  Anyone who has had even high-school physics would recognize that nc is a complete fake.  I have given references above, which anyone can look up.  For those of you who know no physics, I would suggest at least learning what &#8220;significant digits&#8221; means, to realize that no physicist would ever claim that using a 5-digit input would improve the rounding error in a calculation that also has an order-of-magnitude estimate as input.</p>
<p>Finally, there is nothing uncivil about calling a liar a liar.  On the contrary, allowing quacks like nc to repeatedly state lies &amp; self-contradictions would be far more uncivil.</p>
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		<title>By: Sean</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23834</link>
		<dc:creator>Sean</dc:creator>
		<pubDate>Sat, 13 Jan 2007 19:02:01 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23834</guid>
		<description>Okay, nc, I think this has been discussed with sufficient thoroughness.  Let&#039;s take anything else to your blog.</description>
		<content:encoded><![CDATA[<p>Okay, nc, I think this has been discussed with sufficient thoroughness.  Let&#8217;s take anything else to your blog.</p>
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		<title>By: nc</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23835</link>
		<dc:creator>nc</dc:creator>
		<pubDate>Sat, 13 Jan 2007 18:17:39 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23835</guid>
		<description>Just for the benefit of readers of comment #35, I don&#039;t call experimental data speculations.

James, a string theorist would be someone who claims a string tension of 16 tons for the strong nuclear force rather than 10 tons, without saying what nucleus is involved, its binding energy (which varies a lot, hence some elements have greater nuclear stability than others).  It might also be someone who insists that a 16 tons estimate (without any stated assumptions) is correct but 10 tons isn&#039;t, and then claims that empirical data is speculative.

A &quot;stringer&quot; could be someone who misquotes things deliberately, and holds on to a theory which is doesn&#039;t predict anything.</description>
		<content:encoded><![CDATA[<p>Just for the benefit of readers of comment #35, I don&#8217;t call experimental data speculations.</p>
<p>James, a string theorist would be someone who claims a string tension of 16 tons for the strong nuclear force rather than 10 tons, without saying what nucleus is involved, its binding energy (which varies a lot, hence some elements have greater nuclear stability than others).  It might also be someone who insists that a 16 tons estimate (without any stated assumptions) is correct but 10 tons isn&#8217;t, and then claims that empirical data is speculative.</p>
<p>A &#8220;stringer&#8221; could be someone who misquotes things deliberately, and holds on to a theory which is doesn&#8217;t predict anything.</p>
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		<title>By: James Wildspell</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23836</link>
		<dc:creator>James Wildspell</dc:creator>
		<pubDate>Sat, 13 Jan 2007 11:42:34 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23836</guid>
		<description>I came to this website/blog hoping to learn something. I have. Even highly educated physicists have a hard time being civil on message boards.

Edify me, please.
 1. What are &quot;stringers&quot;?
 2. Do all of you know who each other are in real life?
 3. If the answer to #2 is &quot;yes&quot;, would you be more likely to buy each other shots, or arm-wrestle?</description>
		<content:encoded><![CDATA[<p>I came to this website/blog hoping to learn something. I have. Even highly educated physicists have a hard time being civil on message boards.</p>
<p>Edify me, please.<br />
 1. What are &#8220;stringers&#8221;?<br />
 2. Do all of you know who each other are in real life?<br />
 3. If the answer to #2 is &#8220;yes&#8221;, would you be more likely to buy each other shots, or arm-wrestle?</p>
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		<title>By: Warren</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23821</link>
		<dc:creator>Warren</dc:creator>
		<pubDate>Fri, 12 Jan 2007 18:35:56 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23821</guid>
		<description>Here&#039;s some more experimental data (what nc calls &quot;speculations&quot;):  In the paper

http://arxiv.org/abs/nucl-th/0101056

&quot;The nucleon-nucleon interaction&quot; by R. Machleidt &amp; I. Slaus, the NNÏ€ coupling is given as about 14 (as I said above, but this reference is much more recent).  The result is found by fitting the data directly to exchanges of mesons between nucleons.  This is the paper cited by

http://arxiv.org/abs/nucl-th/0611096

&quot;The Nuclear Force from Lattice QCD&quot; by  N.Ishii, S.Aoki , &amp; T.Hatsuda, the paper that attempts to derive the experimental results from lattice QCD (the article Wilczek was so excited about).

None of the above people are &quot;stringers&quot;, so nc will need to invent a new epithet for them (or at least stop linking to their results).

(Sorry for not putting in the links, but the blog server is fighting me.)</description>
		<content:encoded><![CDATA[<p>Here&#8217;s some more experimental data (what nc calls &#8220;speculations&#8221;):  In the paper</p>
<p><a href="http://arxiv.org/abs/nucl-th/0101056" rel="nofollow">http://arxiv.org/abs/nucl-th/0101056</a></p>
<p>&#8220;The nucleon-nucleon interaction&#8221; by R. Machleidt &amp; I. Slaus, the NNÏ€ coupling is given as about 14 (as I said above, but this reference is much more recent).  The result is found by fitting the data directly to exchanges of mesons between nucleons.  This is the paper cited by</p>
<p><a href="http://arxiv.org/abs/nucl-th/0611096" rel="nofollow">http://arxiv.org/abs/nucl-th/0611096</a></p>
<p>&#8220;The Nuclear Force from Lattice QCD&#8221; by  N.Ishii, S.Aoki , &amp; T.Hatsuda, the paper that attempts to derive the experimental results from lattice QCD (the article Wilczek was so excited about).</p>
<p>None of the above people are &#8220;stringers&#8221;, so nc will need to invent a new epithet for them (or at least stop linking to their results).</p>
<p>(Sorry for not putting in the links, but the blog server is fighting me.)</p>
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		<title>By: Warren</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23822</link>
		<dc:creator>Warren</dc:creator>
		<pubDate>Fri, 12 Jan 2007 17:27:06 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23822</guid>
		<description>&lt;blockquote&gt;For the benefit of readers who prefer facts to speculations, my web site has shown the long range fall is an exponential drop in nuclear force at long ranges, for years. &lt;/blockquote&gt;

That&#039;s a good one.  How many years was that?  Yukawa found the fall-off in 1935.  To beat him you&#039;d have to be at least in your 90&#039;s.  From the photo at your web site, you&#039;re very well preserved.  But it&#039;s nice to see that Nature has published your results (although unfortunately under pseudonyms).  Maybe you should clue Wilczek in on your discovery.

&lt;blockquote&gt;There is a short range repulsion from the exchange of pions, and a longer range attraction (a force curve qualitatively like the Van der Waals force between molecules in chemistry).&lt;/blockquote&gt;

Wrong.  The Ï€ has spin 0, &amp; is therefore ALWAYS attractive.  It&#039;s also the lightest meson, &amp; therefore responsible for the longest range nuclear force.  It&#039;s the Ï, with spin 1,  that causes the repulsion.  And ALL the nuclear forces mediated by mesons are Van der Waals, residual from the fundamental strong force mediated by gluons between quarks &amp; gluons, whose color charges cancel in hadrons.

If you want to try something useful, here&#039;s a suggestion:  Try to redo your calculations including the exponential fall-off factor which you &quot;showed&quot; was there &quot;years ago&quot;, but inexplicably forgot in both of your above calculations (12 &amp; 31) &amp; see if you can get a consistent result, &amp; what new values you get for the &quot;string&quot; tension.</description>
		<content:encoded><![CDATA[<blockquote><p>For the benefit of readers who prefer facts to speculations, my web site has shown the long range fall is an exponential drop in nuclear force at long ranges, for years. </p></blockquote>
<p>That&#8217;s a good one.  How many years was that?  Yukawa found the fall-off in 1935.  To beat him you&#8217;d have to be at least in your 90&#8217;s.  From the photo at your web site, you&#8217;re very well preserved.  But it&#8217;s nice to see that Nature has published your results (although unfortunately under pseudonyms).  Maybe you should clue Wilczek in on your discovery.</p>
<blockquote><p>There is a short range repulsion from the exchange of pions, and a longer range attraction (a force curve qualitatively like the Van der Waals force between molecules in chemistry).</p></blockquote>
<p>Wrong.  The Ï€ has spin 0, &amp; is therefore ALWAYS attractive.  It&#8217;s also the lightest meson, &amp; therefore responsible for the longest range nuclear force.  It&#8217;s the Ï, with spin 1,  that causes the repulsion.  And ALL the nuclear forces mediated by mesons are Van der Waals, residual from the fundamental strong force mediated by gluons between quarks &amp; gluons, whose color charges cancel in hadrons.</p>
<p>If you want to try something useful, here&#8217;s a suggestion:  Try to redo your calculations including the exponential fall-off factor which you &#8220;showed&#8221; was there &#8220;years ago&#8221;, but inexplicably forgot in both of your above calculations (12 &amp; 31) &amp; see if you can get a consistent result, &amp; what new values you get for the &#8220;string&#8221; tension.</p>
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		<title>By: nc</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23823</link>
		<dc:creator>nc</dc:creator>
		<pubDate>Fri, 12 Jan 2007 13:42:29 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23823</guid>
		<description>&quot;Well, if you had read Yukawa&#039;s original paper on the subject, or any of the subsequent physics literature, you would have learned that a lot earlier. The fall-off is exponential.&quot;

For the benefit of readers who prefer facts to speculations, my web site has shown the long range fall is an exponential drop in nuclear force at long ranges, for years.  For the complete picture, you take a look at the curve here: http://www.nature.com/nature/journal/v445/n7124/fig_tab/445156a_F1.html

There is a short range repulsion from the exchange of pions, and a longer range attraction (a force curve qualitatively like the Van der Waals force between molecules in chemistry).

Frank Wilczek notes: &quot;Our description of how the atomic nucleus holds together has up to now been entirely empirical. Arduous calculations starting from the theory of the strong nuclear force provide a new way into matter&#039;s hard core.&quot;

- http://www.nature.com/nature/journal/v445/n7124/full/445156a.html</description>
		<content:encoded><![CDATA[<p>&#8220;Well, if you had read Yukawa&#8217;s original paper on the subject, or any of the subsequent physics literature, you would have learned that a lot earlier. The fall-off is exponential.&#8221;</p>
<p>For the benefit of readers who prefer facts to speculations, my web site has shown the long range fall is an exponential drop in nuclear force at long ranges, for years.  For the complete picture, you take a look at the curve here: <a href="http://www.nature.com/nature/journal/v445/n7124/fig_tab/445156a_F1.html" rel="nofollow">http://www.nature.com/nature/journal/v445/n7124/fig_tab/445156a_F1.html</a></p>
<p>There is a short range repulsion from the exchange of pions, and a longer range attraction (a force curve qualitatively like the Van der Waals force between molecules in chemistry).</p>
<p>Frank Wilczek notes: &#8220;Our description of how the atomic nucleus holds together has up to now been entirely empirical. Arduous calculations starting from the theory of the strong nuclear force provide a new way into matter&#8217;s hard core.&#8221;</p>
<p>- <a href="http://www.nature.com/nature/journal/v445/n7124/full/445156a.html" rel="nofollow">http://www.nature.com/nature/journal/v445/n7124/full/445156a.html</a></p>
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		<title>By: Warren</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23824</link>
		<dc:creator>Warren</dc:creator>
		<pubDate>Fri, 12 Jan 2007 12:43:58 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23824</guid>
		<description>For the benefit of nc, who claims not to be talking to &quot;stringers&quot;:  You said,

&lt;blockquote&gt;instead of making claims/attacks which aren&#039;t actually backed up by evidence.&lt;/blockquote&gt;

The spins &amp; masses of observed particles aren&#039;t evidence?  Your lies are progressively more transparent.  Then you said,

&lt;blockquote&gt;The two protons are on average ~10^{-15} m apart.&lt;/blockquote&gt;

...again order of magnitude, and then immediatley contradicted yourself by saying

&lt;blockquote&gt;Notice that you can quote intermediate results in a calculation to more precision than the final result, to avoid the problem of what are called &#039;intermediate rounding errors&#039; which string theorists haven&#039;t heard about.&lt;/blockquote&gt;

There is absolutely no advantage to giving one input to more precision (5 decimal places!!), while another input is only an order of magnitude estimate.  And now the masterpiece:

&lt;blockquote&gt;Hence, by this calculation the strong force needed is not 3 tons (which assumed a force ratio of 137) but only about o.09 tons.&lt;/blockquote&gt;

by which you reveal that the person you are arguing against is actually yourself!

&lt;blockquote&gt;Obviously the strong force doesn&#039;t have a sudden cutoff at its range limit, but falls more gradually so the strength of coupling varies with distance.&lt;/blockquote&gt;

Well, if you had read Yukawa&#039;s original paper on the subject, or any of the subsequent physics literature, you would have learned that a lot earlier.  The fall-off is exponential.

&lt;blockquote&gt;It&#039;s a pity discussions can&#039;t focus on the physics, but result in people calling calculations rubbish without first checking them!&lt;/blockquote&gt;

So, why didn&#039;t you check your calculation earlier?  And when will you check mine?  Have you even read it yet?  Do you know what &quot;string tension&quot; means?  Do you know what &quot;string&quot; means?  How can you claim to give a valid result for the string tension when you claim strings don&#039;t exist?  How can you respond to these disproofs of your arguments when you claim to not be talking to &quot;stringers&quot;?  These and more humorous absurdities in our next episode...</description>
		<content:encoded><![CDATA[<p>For the benefit of nc, who claims not to be talking to &#8220;stringers&#8221;:  You said,</p>
<blockquote><p>instead of making claims/attacks which aren&#8217;t actually backed up by evidence.</p></blockquote>
<p>The spins &amp; masses of observed particles aren&#8217;t evidence?  Your lies are progressively more transparent.  Then you said,</p>
<blockquote><p>The two protons are on average ~10^{-15} m apart.</p></blockquote>
<p>&#8230;again order of magnitude, and then immediatley contradicted yourself by saying</p>
<blockquote><p>Notice that you can quote intermediate results in a calculation to more precision than the final result, to avoid the problem of what are called &#8216;intermediate rounding errors&#8217; which string theorists haven&#8217;t heard about.</p></blockquote>
<p>There is absolutely no advantage to giving one input to more precision (5 decimal places!!), while another input is only an order of magnitude estimate.  And now the masterpiece:</p>
<blockquote><p>Hence, by this calculation the strong force needed is not 3 tons (which assumed a force ratio of 137) but only about o.09 tons.</p></blockquote>
<p>by which you reveal that the person you are arguing against is actually yourself!</p>
<blockquote><p>Obviously the strong force doesn&#8217;t have a sudden cutoff at its range limit, but falls more gradually so the strength of coupling varies with distance.</p></blockquote>
<p>Well, if you had read Yukawa&#8217;s original paper on the subject, or any of the subsequent physics literature, you would have learned that a lot earlier.  The fall-off is exponential.</p>
<blockquote><p>It&#8217;s a pity discussions can&#8217;t focus on the physics, but result in people calling calculations rubbish without first checking them!</p></blockquote>
<p>So, why didn&#8217;t you check your calculation earlier?  And when will you check mine?  Have you even read it yet?  Do you know what &#8220;string tension&#8221; means?  Do you know what &#8220;string&#8221; means?  How can you claim to give a valid result for the string tension when you claim strings don&#8217;t exist?  How can you respond to these disproofs of your arguments when you claim to not be talking to &#8220;stringers&#8221;?  These and more humorous absurdities in our next episode&#8230;</p>
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		<title>By: nc</title>
		<link>http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/comment-page-1/#comment-23825</link>
		<dc:creator>nc</dc:creator>
		<pubDate>Fri, 12 Jan 2007 11:21:25 +0000</pubDate>
		<guid isPermaLink="false">http://blogs.discovermagazine.com/cosmicvariance/2007/01/06/string-wars-hit-the-msm/#comment-23825</guid>
		<description>For the benefit of people interested in physics, here&#039;s an alternative calculation of strong nuclear force strength, for anybody interested in &lt;i&gt;physics&lt;/i&gt;, instead of making claims/attacks which aren&#039;t actually backed up by evidence.  Helium-4 has two protons and two neutrons.  The two protons are on average ~10^{-15} m apart.

The mass of two protons, two electrons and two neutrons is 4.0323 amu, while the measured mass of a helium atom is 4.0026 amu.  This mass defect is 0.0063 amu ~ 9.42*10^{-13} Joules of nuclear binding energy (by E=mc^2).  &lt;i&gt;Notice that you can quote intermediate results in a calculation to more precision than the final result, to avoid the problem of what are called &#039;intermediate rounding errors&#039; which string theorists haven&#039;t heard about.&lt;/i&gt;

The strong nuclear binding energy keeping two protons distance &lt;i&gt;x&lt;/i&gt; apart is equivalent to &lt;i&gt;E = {Integral of the force with respect to distance moved in direction of force} = Integral between distance s and infinity of [(q^2)/(4*Pi*Epsilon*x^2)} dx = (q^2)/(4*Pi*Epsilon*s).&lt;/i&gt;  Putting in the binding energy 9.42*10^{-13} Joules calculated above and the distance of &lt;i&gt;s&lt;/i&gt;~10^{-15} m tells us that the effective square of the strong charge &lt;i&gt;q^2&lt;/i&gt; needed is &lt;i&gt;q^2 = 4*Pi*Epsilon*s*E&lt;/i&gt; = 1.05*10^{-37}.  This is directly proportional to force, and is 4.08 times the square of the charge of the proton.

Hence, by this calculation the strong force needed is not 3 tons (which assumed a force ratio of 137) but only about o.09 tons.  Obviously the strong force doesn&#039;t have a sudden cutoff at its range limit, but falls more gradually so the strength of coupling varies with distance.  It&#039;s a pity discussions can&#039;t focus on the physics, but result in people calling calculations rubbish without first checking them!</description>
		<content:encoded><![CDATA[<p>For the benefit of people interested in physics, here&#8217;s an alternative calculation of strong nuclear force strength, for anybody interested in <i>physics</i>, instead of making claims/attacks which aren&#8217;t actually backed up by evidence.  Helium-4 has two protons and two neutrons.  The two protons are on average ~10^{-15} m apart.</p>
<p>The mass of two protons, two electrons and two neutrons is 4.0323 amu, while the measured mass of a helium atom is 4.0026 amu.  This mass defect is 0.0063 amu ~ 9.42*10^{-13} Joules of nuclear binding energy (by E=mc^2).  <i>Notice that you can quote intermediate results in a calculation to more precision than the final result, to avoid the problem of what are called &#8216;intermediate rounding errors&#8217; which string theorists haven&#8217;t heard about.</i></p>
<p>The strong nuclear binding energy keeping two protons distance <i>x</i> apart is equivalent to <i>E = {Integral of the force with respect to distance moved in direction of force} = Integral between distance s and infinity of [(q^2)/(4*Pi*Epsilon*x^2)} dx = (q^2)/(4*Pi*Epsilon*s).</i>  Putting in the binding energy 9.42*10^{-13} Joules calculated above and the distance of <i>s</i>~10^{-15} m tells us that the effective square of the strong charge <i>q^2</i> needed is <i>q^2 = 4*Pi*Epsilon*s*E</i> = 1.05*10^{-37}.  This is directly proportional to force, and is 4.08 times the square of the charge of the proton.</p>
<p>Hence, by this calculation the strong force needed is not 3 tons (which assumed a force ratio of 137) but only about o.09 tons.  Obviously the strong force doesn&#8217;t have a sudden cutoff at its range limit, but falls more gradually so the strength of coupling varies with distance.  It&#8217;s a pity discussions can&#8217;t focus on the physics, but result in people calling calculations rubbish without first checking them!</p>
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