Calculating the Quantum Kepler Length of a Particle

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class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81">arivero</span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-142844" data-lb-caption-desc="arivero · Feb 7, 2004 at 6:30 AM"> <article class="message-body js-selectToQuote"> <div > <div class="bbWrapper">One knows that in classical gravity a orbiting point sweeps equal areas at equal times. It can be seen that for macroscopic distances the area swept in a plank time is a lot greater than the minimum quantum of area, which is about (plank length)^2.<br /> <br /> Now, I ask, <i>given a particle of mass m, for which radius will a circular gravitational orbit around the particle to have the property of sweeping one plank area in exactly one plank time unit?</i><br /> <br /> Below that radius, it should be posible to use "plank time beats" to divide area into regions smaller that previous. So a fundamental break of physics will happen at "quantum kepler length of the particle m" ;-) <br /> <br /> Of course you know which other name this length receives, do you?<br /> <br /> <br /> [SPOILERS FOLLOW IN NEXT ANSWER. So padding inserted here]<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .<br /> .</div> </div> <div class="js-selectToQuoteEnd"> </div> <div class="googleads_fixed"> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-6580726045122001" crossorigin="anonymous"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-6580726045122001" data-ad-slot="3049969336" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-07T16:39:30-0600" data-time="1076193570" data-date-string="Feb 7, 2004" data-time-string="4:39 PM" title="Feb 7, 2004 at 4:39 PM">Feb 7, 2004</time> </div> </div> <footer class="message-footer"> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <div class="message-cell message-cell--main" id="post-physorg"> <a href="https://phys.org/physics-news/" target="_blank">Physics news</a> on Phys.org <ul class="phys_items"> <li><a href="https://phys.org/news/2025-02-unexpected-nucleus-prompts-reevaluation-atomic.html" target="_blank">Unexpected shape of lead-208 nucleus prompts reevaluation of atomic nuclei models</a></li> <li><a href="https://phys.org/news/2025-02-scientists-elusive-liquid-transition-deep.html" target="_blank">Scientists map elusive liquid-liquid transition point using deep neural network</a></li> <li><a href="https://phys.org/news/2025-02-links-disparate-pion-reactions-nuclear.html" target="_blank">New calculation links disparate pion reactions in nuclear physics</a></li> </ul> </div> <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-142964" id="js-post-142964" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/142964/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-142964"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T10:18:18-0600" data-time="1076170698" data-date-string="Feb 7, 2004" data-time-string="10:18 AM" title="Feb 7, 2004 at 10:18 AM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/142964/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #2 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-142964" data-lb-caption-desc="marcus · Feb 7, 2004 at 10:18 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by arivero </i><br /> <b>...\ ;-) <br /> <br /> Of course you know which other name this length receives, do you? </b> </div> </div> </blockquote><br /> compton wavelength<br /> nice</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-142983" id="js-post-142983" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/142983/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-142983"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T10:46:13-0600" data-time="1076172373" data-date-string="Feb 7, 2004" data-time-string="10:46 AM" title="Feb 7, 2004 at 10:46 AM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/142983/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #3 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-142983" data-lb-caption-desc="marcus · Feb 7, 2004 at 10:46 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by marcus </i><br /> <b>compton wavelength<br /> nice </b> </div> </div> </blockquote><br /> maybe a little discussion would be appropriate<br /> <br /> this is a really nice pensee<br /> <br /> (physics haiku?)<br /> <br /> in natural units the (reduced) compton a particle with mass M is 1/M<br /> <br /> the circular orbit velocity around such a particle is<br /> [tex]\sqrt{\frac{M}{R}}[/tex]<br /> <br /> so the rate area is swept out is<br /> <br /> [tex]R\sqrt{\frac{M}{R}}= \sqrt{MR}[/tex]<br /> <br /> setting that equal to one (as Alejandro requires) tells us<br /> that R = 1/M<br /> <br /> this is the (reduced) compton<br /> <br /> (when dealing with G = hbar = c = 1<br /> units one prefers the reduced wavelength which is the cyclic<br /> one divided by 2pi, as well as the angular format for frequency)</div> </div> <div class="js-selectToQuoteEnd"> </div> <div class="googleads_fixed"> <script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-6580726045122001" crossorigin="anonymous"></script>  <ins class="adsbygoogle" style="display:block" data-ad-client="ca-pub-6580726045122001" data-ad-slot="5961342082" data-ad-format="auto" data-full-width-responsive="true"></ins> <script> (adsbygoogle = window.adsbygoogle || []).push({}); </script> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" 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<time class="u-dt" dir="auto" datetime="2004-02-07T14:26:40-0600" data-time="1076185600" data-date-string="Feb 7, 2004" data-time-string="2:26 PM" title="Feb 7, 2004 at 2:26 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143057/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #4 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/8lpf16.5921/"> <meta itemprop="url" content="https://www.physicsforums.com/members/8lpf16.5921/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="5921"><span itemprop="name">8LPF16</span></span></span>     </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>191</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>0</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143057" data-lb-caption-desc="8LPF16 · Feb 7, 2004 at 2:26 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">How does the compton value relate to the Red/Orange line 655nm with no mass?<br /> <br /> LPF</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143064" id="js-post-143064" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143064/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143064"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T14:46:43-0600" data-time="1076186803" data-date-string="Feb 7, 2004" data-time-string="2:46 PM" title="Feb 7, 2004 at 2:46 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143064/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #5 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143064" data-lb-caption-desc="marcus · Feb 7, 2004 at 2:46 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">Alejandro something is catchy or piquant about the implied argument.<br /> I like it.<br /> Alejandro says, in effect, that a circular orbit cannot sweep out<br /> area at a rate that is <b>slower</b> than the Planck rate. He says it must be true for any circular orbit that:<br /> <br /> [tex]\sqrt{MR}> 1[/tex]<br /> <br /> because say the sweeping of area is slower than unity, say that it takes 3 time units to sweep out 1 area unit<br /> then one can divide the time interval up and this leads to<br /> being able to describe an area smaller than the area quantum.<br /> (one can use Planck "beats" to divide the indivisible)<br /> <br /> <br /> so he looks for a paradox<br /> <br /> he says fix some mass M and make the orbit radius R so small that<br /> <br /> [tex]\sqrt{MR}< 1[/tex]<br /> <br /> now the rate of sweeping of area is less than unity<br /> <b>what prevents this?</b><br /> <br /> and Alejandro discovers that what prevents this situation is that the orbit radius is less than the Compton for that mass.<br /> (the central gravitating body is being localized more restrictively than quantum mechnanics permits it to be localized---every particle is spread out by at least its compton)</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143075" id="js-post-143075" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143075/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143075"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T15:13:27-0600" data-time="1076188407" data-date-string="Feb 7, 2004" data-time-string="3:13 PM" title="Feb 7, 2004 at 3:13 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143075/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #6 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143075" data-lb-caption-desc="marcus · Feb 7, 2004 at 3:13 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by arivero </i><br /> <b>One knows that in classical gravity a orbiting point sweeps equal areas at equal times. It can be seen that for macroscopic distances the area swept in a plank time is a lot greater than the minimum quantum of area, which is about (plank length)^2.<br /> <br /> Now, I ask, <i>given a particle of mass m, for which radius will a circular gravitational orbit around the particle to have the property of sweeping one plank area in exactly one plank time unit?</i><br /> <br /> Below that radius, it should be posible to use "plank time beats" to divide area into regions smaller that previous. So a fundamental break of physics will happen at "quantum kepler length of the particle m" ;-) <br /> <br /> Of course you know which other name this length receives, do you? </b> </div> </div> </blockquote><br /> If it is correct, Loop Quantum Gravity implies that the Planck quantities (the "natural units" as Planck called them) are <b>real features</b> of the environment<br /> that they are built into spacetime just as the speed of light (which is the Planck unit of speed) is built in.<br /> <br /> the theory pinpoints the place at which new physical effects can be expected, namely at Planck energy (2 billion joules)<br /> and it derives quantized spectrums for area and volume where<br /> the minimum measurable amounts of area and volume are order-one multiples of Planck area and Planck volume.<br /> <br /> among the new physical effects expected at Planck scale are<br /> modifications of Lorentz symmetry<br /> <br /> It now seems that these and other Planck scale effects may be possible to probe in the next few years leading to tests of LQG.<br /> If it checks out this will among other things infuse a greater sense of solidity into Planck units. There will be reason to think that they really are nature's units.<br /> <br /> Alejandro's puzzle (why can't area be swept out at slower than Planck unit rate?) is an example of a "Planck Parable", as I would call it.<br /> Or a "Planck units Haiku".<br /> <br /> I will try to think of another such story or puzzle, to respond in kind.<br /> <br /> If Loop Gravity develops successfully and tests out we will probably see more Planck haiku growing up as a kind of physics folklore.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143080" id="js-post-143080" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143080/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143080"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T15:26:31-0600" data-time="1076189191" data-date-string="Feb 7, 2004" data-time-string="3:26 PM" title="Feb 7, 2004 at 3:26 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143080/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #7 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143080" data-lb-caption-desc="marcus · Feb 7, 2004 at 3:26 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>The Wizard's Stove (a Loop Gravity parable)</b><br /> <br /> to understand this you need to go to the NIST website and look<br /> up Planck temperature<br /> or take my word for it that it is 1.4168e32 kelvin<br /> <br /> that is the temp T such that kT is Planck energy<br /> and if Planck energy is built into spacetime as an intrinsic<br /> threshold of some new effects<br /> then the temp is also (in the same way) a built in intrinsic feature of nature<br /> <br /> On that scale room temperature is about 2e-30<br /> and a nice oven temperature is about 3e-30<br /> (in fact if you work it out 3e-30 of the natural unit temperature<br /> is 425 kelvin, which is 305 Fahrenheit qualifying as a "slow to moderate" oven.<br /> <br /> Well in this short short story there is a Wizard who wants his stove to always be at 3e-30. Hope notation is clear, I mean 3x10<sup>-30</sup><br /> <br /> have to go for now, continue later</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143087" id="js-post-143087" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143087/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143087"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T15:54:02-0600" data-time="1076190842" data-date-string="Feb 7, 2004" data-time-string="3:54 PM" title="Feb 7, 2004 at 3:54 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143087/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #8 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143087" data-lb-caption-desc="marcus · Feb 7, 2004 at 3:54 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>the Wizard's Stove continued</b><br /> <br /> Once there was a Wizard who lived in a cave that he'd hollowed out in the core of a comet and the wizard was always cold<br /> He wanted a potbelly stove that always stayed at a steady temperature of 3E-30 natural. This would take the chill out of the cave and be convenient for baking.<br /> <br /> What he got to stoke the stove with is interesting. He got a supply of the usual kind of black holes each of which was always at the steady temperature of<br /> 3E-30 natural. (that is 425 kelvin or 152 celsius or fahrenheit 305 depending on which conventional human scale you like)<br /> <br /> the question is, what was the mass of each of the black holes.<br /> and how big were they?</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-143094" id="js-post-143094" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143094/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143094"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T16:33:41-0600" data-time="1076193221" data-date-string="Feb 7, 2004" data-time-string="4:33 PM" title="Feb 7, 2004 at 4:33 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143094/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #9 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143094" data-lb-caption-desc="arivero · Feb 7, 2004 at 4:33 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><br /> <br /> Yes, it is the typical Haiku one finds in elementary quantum mechanics book. Perhaps sometime we will see it in elementary LQG books :-) By the way, I had never seen it, but I do skip a lot of literature on this.<br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by marcus </i><br /> <b><br /> (physics haiku?)<br /> (when dealing with G = hbar = c = 1<br /> units one prefers the reduced wavelength which is the cyclic<br /> one divided by 2pi, as well as the angular format for frequency) </b> </div> </div> </blockquote><br /> It becomes even more rythmical if you allow for G, as then the one coming from plank length simplifies against the one coming from Newton universal gravitation law. At the end, Compton length contains, of course, m, h, and c, but no G around. As for author trickery, I confess that the paradox has been choosen a posteriori :-)<br /> <br /> I am -paying time- at a cybercafe now, so I hope that by monday the wizard will have all his charcoal supply issues solved!</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143122" id="js-post-143122" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143122/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143122"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T17:36:22-0600" data-time="1076196982" data-date-string="Feb 7, 2004" data-time-string="5:36 PM" title="Feb 7, 2004 at 5:36 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143122/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #10 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143122" data-lb-caption-desc="marcus · Feb 7, 2004 at 5:36 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by arivero </i><br /> <b>... I confess that the paradox has been choosen a posteriori :-)<br /> <br /> I am -paying time- at a cybercafe now, so I hope that by monday the wizard will have all his charcoal supply issues solved! </b> </div> </div> </blockquote><br /> A significant confession!<br /> <br /> the wizard reflected to himself that the temperature of the usual kind of black hole (that they sell for stoves) is<br /> <br /> [tex]\frac{1}{8\pi M}[/tex]<br /> <br /> where M is the mass of the hole</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143127" id="js-post-143127" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143127/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143127"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T17:40:52-0600" data-time="1076197252" data-date-string="Feb 7, 2004" data-time-string="5:40 PM" title="Feb 7, 2004 at 5:40 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143127/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #11 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143127" data-lb-caption-desc="marcus · Feb 7, 2004 at 5:40 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">at this time a tribe of gypsies was passing through the solar system telling fortunes, selling black holes and love potions, and stealing as gypsies always do.<br /> <br /> So the wizard solved the following equation for the mass M, so that he could ask the gypsies for holes of that mass:<br /> <br /> <br /> [tex]\frac{1}{8\pi M} = 3*10^{-30}[/tex]</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget 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message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143129/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #12 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143129" data-lb-caption-desc="marcus · Feb 7, 2004 at 5:45 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">[tex]\frac{1}{8\pi M} = 3*10^{-30}[/tex] <br /> <br /> [tex]8\pi M = \frac{1}{3}*10^{30}[/tex] <br /> <br /> [tex]M = \frac{1}{24\pi}*10^{30}[/tex]</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143132" id="js-post-143132" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143132/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143132"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T17:49:06-0600" data-time="1076197746" data-date-string="Feb 7, 2004" data-time-string="5:49 PM" title="Feb 7, 2004 at 5:49 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143132/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #13 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143132" data-lb-caption-desc="marcus · Feb 7, 2004 at 5:49 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">this means that each piece of "stove charcoal"<br /> would be the size of a mote of dust and<br /> would have a mass about a twenty-thousandth of that of the earth<br /> <br /> and if it would not be too tedious I will work that out<br /> from the previously derived value of M</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-07T18:16:31-0600" data-time="1076199391" data-date-string="Feb 7, 2004" data-time-string="6:16 PM" title="Feb 7, 2004 at 6:16 PM" itemprop="dateModified">Feb 7, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143146" id="js-post-143146" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143146/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143146"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T18:15:39-0600" data-time="1076199339" data-date-string="Feb 7, 2004" data-time-string="6:15 PM" title="Feb 7, 2004 at 6:15 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143146/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #14 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143146" data-lb-caption-desc="marcus · Feb 7, 2004 at 6:15 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">the mass calculated was<br /> M = 1.3E28 Planck<br /> <br /> and the Earth's mass is<br /> 2.75E32 Planck<br /> <br /> that's why I said roughly a twenty-thousandth----1/20,000 Earth mass.<br /> <br /> ------if you like everything metric------<br /> the Planck mass unit is 22 micrograms as can be seen at NIST site,<br /> so that E9 Planck is 22 kilograms<br /> I get that in kilograms M = 29E19 kg = 2.9E20 kg.<br /> and that is, in fact, roughly a 20,000th of the mass of earth<br /> which is like about 6E24 kg.<br /> ----------------------------------------<br /> <br /> the radius of an ordinary kind of black hole is 2M<br /> so the ones for the Wizard's stove have a radius of<br /> 2.6E28<br /> this is the size of a tiny mote of dust or pollengrain<br /> because E28 is about one sixth of a micron<br /> so we are talking about half a micron radius or micron diameter</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-07T18:31:05-0600" data-time="1076200265" data-date-string="Feb 7, 2004" data-time-string="6:31 PM" title="Feb 7, 2004 at 6:31 PM" itemprop="dateModified">Feb 7, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-143156" id="js-post-143156" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/143156/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-143156"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-07T18:33:43-0600" data-time="1076200423" data-date-string="Feb 7, 2004" data-time-string="6:33 PM" title="Feb 7, 2004 at 6:33 PM" itemprop="datePublished">Feb 7, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/143156/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #15 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-143156" data-lb-caption-desc="marcus · Feb 7, 2004 at 6:33 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">black holes this size are always nice and warm<br /> in fact fahrenheit 305, OK for baking cornbread<br /> and homefry potatoes, macaroni-and-cheese,<br /> such as a wizard might want for supper.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-144017" id="js-post-144017" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144017/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144017"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-09T04:30:17-0600" data-time="1076322617" data-date-string="Feb 9, 2004" data-time-string="4:30 AM" title="Feb 9, 2004 at 4:30 AM" itemprop="datePublished">Feb 9, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144017/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #16 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144017" data-lb-caption-desc="arivero · Feb 9, 2004 at 4:30 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">Fine parable. I like this kind of effort to grasp the scale of the units and objects we use; in fact some months ago I did the example of putting the elementary particle masses in amu (atomic mass units) and then to look for the nucleus having the same weight!<br /> <br /> As you have completely given the answer to your history, let me to complete mine too. We have got Compton Length. Now, can we get quantum mechanics from it, using similar arguments?<br /> <br /> Yes, we can: the Bohr-Sommerfeld quantum condition can be formulated, at least for circles, via a a Newton(*)-Kepler principle: <i>any bound particle sweeps a multiple of Compton Area in a unit of Compton Time</i>. This principle does not need gravity; it works for any central force.<br /> <br /> The usual way, instead of this, is to use the obtained wavelength to check for destructive interference, most arguments in this line invoque De Broglie instead of Compton(**), so perhaps our whole thread could need a "fine tuning".<br /> <br /> [EDITED:] In fact, note that the argument here above does not depend of [tex]c[/tex]. Very much as the argumeng starting the thread does not depend of [tex]G[/tex]. <br /> <br /> (*)<a href="http://members.tripod.com/~gravitee/booki2.htm" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://members.tripod.com/~gravitee/booki2.htm</a><br /> (**) Indeed this was the point raised, subtly, by LPF earlier in the thread.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-10T08:46:16-0600" data-time="1076424376" data-date-string="Feb 10, 2004" data-time-string="8:46 AM" title="Feb 10, 2004 at 8:46 AM" itemprop="dateModified">Feb 10, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-144052" id="js-post-144052" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144052/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144052"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-09T06:24:50-0600" data-time="1076329490" data-date-string="Feb 9, 2004" data-time-string="6:24 AM" title="Feb 9, 2004 at 6:24 AM" itemprop="datePublished">Feb 9, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144052/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #17 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144052" data-lb-caption-desc="marcus · Feb 9, 2004 at 6:24 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by arivero </i><br /> <b>Fine parable. I like this kind of effort to grasp the scale... </b> </div> </div> </blockquote><br /> Glad you approve. "kepler length" was witty and subtle (but could be stated in very simple terms) and I wish we could have more idea-puzzles like that.<br /> the "wizard stove" idea actually did not come up to that level but was the best I could think of at the moment<br /> why are subtle presentations of the ideas so difficult to think of?<br /> (because the mind digs itself into ruts it can't get out of)<br /> think of more and maybe we will start a thread.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-144219" id="js-post-144219" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144219/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144219"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-09T11:34:54-0600" data-time="1076348094" data-date-string="Feb 9, 2004" data-time-string="11:34 AM" title="Feb 9, 2004 at 11:34 AM" itemprop="datePublished">Feb 9, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144219/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #18 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144219" data-lb-caption-desc="marcus · Feb 9, 2004 at 11:34 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>what the Moon thinks she weighs</b><br /> <br /> every lady has some idea of her weight--she may wonder if it is too much or too little, or she may be content with it, but she has some idea<br /> <br /> the moon thinks of her weight as a force<br /> measured by scales at her surface*<br /> <br /> Now Alejandro you were just talking about circular orbit speed.<br /> The moon knows the circular orbit speed right down at her surface<br /> and she thinks of it in Planck terms (that is as a fraction of the speed of light) because that is natural<br /> she thinks of every physical quantity that way, in those units.<br /> <br /> what is the relation between her weight and the fourth power of that speed?<br /> <br /> ----------------------<br /> <br /> * it is hard to imagine the moon standing on bathroom scales placed on her own surface, but she thinks of the force which is her weight as<br /> a million times what one millionth of her would weigh on scales at her surface. or perhaps a billion times a billionth, I'm not sure which.<br /> <br /> --------------------<br /> EDIT: hello A. using edit button as suggested to clarify problem.<br /> the key thing is "she thinks of every physical quantity in Planck terms" so the question is, what is the relation between two numbers:<br /> the fourth power of the surface orbit speed and her weight (both expressed in the Planck system of units). no big deal, kind of a silly problem actually, I should solve it probably just as a check that I am stating it right. what I like is the moon having an idea of her own weight.<br /> ---------------------<br /> MORE EDIT: well,you didnt take me up on this one, so I will say the answer.<br /> They are the same number.<br /> in Planck units the circ orbit velocity at surface is<br /> [tex]\sqrt{\frac{GM}{Rc^2}}[/tex]<br /> you see I divided the dimensionful speed by c to get the speed as a fraction of c<br /> And so the fourth power of the speed is<br /> [tex](\frac{GM}{Rc^2})^2[/tex]<br /> this is the same as her weight at her own surface<br /> [tex](\frac{GM^2}{R^2})[/tex]<br /> divided by the unit of force belonging to Planck units<br /> [tex]\frac{c^4}{G}[/tex]</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-09T13:45:42-0600" data-time="1076355942" data-date-string="Feb 9, 2004" data-time-string="1:45 PM" title="Feb 9, 2004 at 1:45 PM" itemprop="dateModified">Feb 9, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-144262" id="js-post-144262" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144262/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144262"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-09T12:59:06-0600" data-time="1076353146" data-date-string="Feb 9, 2004" data-time-string="12:59 PM" title="Feb 9, 2004 at 12:59 PM" itemprop="datePublished">Feb 9, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144262/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #19 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144262" data-lb-caption-desc="arivero · Feb 9, 2004 at 12:59 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">I believe you have not stated the question rightly; even in plank units, the first equation (orbital velocity) gives the velocity as the square root of $M_earth/R_orbit$ while the second one gives the force as the square of $M_moon/R_moon$... Ok Ok I see.. I get you are intending to use the same Mass and same Radius in both equations, but -to me- it is not rightly stated, probably due to stress (a hard monday, as I see from other threads). You are referring to the "orbital" velocity of a stone thrown across the surface of the moon. And, actually, you only ask for G=1, neither c and h are needed.<br /> <br /> In any case, it is fully classical gravity so we are hitting the off-topic wall :-(<br /> <br /> [edited 10/Feb] Well, I see, you could try to connect it with the other quantization puzzles we have set up, but it seems too far fetched :-(</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-10T08:38:28-0600" data-time="1076423908" data-date-string="Feb 10, 2004" data-time-string="8:38 AM" title="Feb 10, 2004 at 8:38 AM" itemprop="dateModified">Feb 10, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-144310" id="js-post-144310" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144310/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144310"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-09T14:05:47-0600" data-time="1076357147" data-date-string="Feb 9, 2004" data-time-string="2:05 PM" title="Feb 9, 2004 at 2:05 PM" itemprop="datePublished">Feb 9, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144310/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #20 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144310" data-lb-caption-desc="arivero · Feb 9, 2004 at 2:05 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>addenda</b><br /> <br /> I have found this link<br /> <br /> <a href="http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_plancklt.html" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_plancklt.html</a><br /> <br /> which gives a interesting operational definition of Planck time.<br /> <br /> There mass and time of Planck are defined as the quantitues simultanesly compatible with uncertainty principle and with gravitational collapse equation. IE a mass of plank spreaded in a plank volume takes a time of plank to collapse gravitationally into a point.<br /> <br /> He says it is adapted from P. Coles' 1999 dictionary.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-144329" id="js-post-144329" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144329/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144329"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-09T14:42:37-0600" data-time="1076359357" data-date-string="Feb 9, 2004" data-time-string="2:42 PM" title="Feb 9, 2004 at 2:42 PM" itemprop="datePublished">Feb 9, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144329/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #21 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144329" data-lb-caption-desc="marcus · Feb 9, 2004 at 2:42 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>Let's try for more Loop Gravity fables!</b><br /> <br /> Alejandro, thanks for the link<br /> if that collapse-time business is from Cole's dictionary then<br /> I prefer your definition of the "kepler length" of something.<br /> It would make a better dictionary<br /> <br /> Or a better "modern physics bestiary"<br /> <br /> Let's try for more LQG fables.<br /> <br /> What I like, one thing I like, about Loop Gravity is that<br /> LQG and the Planck units are<br /> <b>mutually validating</b></div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-144335" id="js-post-144335" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144335/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144335"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-09T14:48:37-0600" data-time="1076359717" data-date-string="Feb 9, 2004" data-time-string="2:48 PM" title="Feb 9, 2004 at 2:48 PM" itemprop="datePublished">Feb 9, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144335/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #22 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144335" data-lb-caption-desc="marcus · Feb 9, 2004 at 2:48 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by marcus </i><br /> <br /> LQG and the Planck units are<br /> <b>mutually validating</b> </div> </div> </blockquote><br /> what I mean is in LQG one finds that<br /> space (area and volume) is quantized and it turns out<br /> that the quantization is precisely at Planck scale<br /> <br /> so that confirms that the Planck units are a good<br /> idea of units built into nature.<br /> <br /> On the other hand Planck units lend some<br /> confirmation to Loop gravity because they keep coming up<br /> in the equations in and around the theory.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-144699" id="js-post-144699" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144699/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144699"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-10T04:24:59-0600" data-time="1076408699" data-date-string="Feb 10, 2004" data-time-string="4:24 AM" title="Feb 10, 2004 at 4:24 AM" itemprop="datePublished">Feb 10, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144699/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #23 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144699" data-lb-caption-desc="arivero · Feb 10, 2004 at 4:24 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">I disagree. As a mathematical aparatus, LQG does not worry about which fundamental length to choose; the theory does not depend of a concrete value. It does not turn up that quantization uses this scale, it is simply that physical intuition has suggested people to use Planck length. Examples as the one I provided in this thread are not usual in LQG treatises. Of course, I could be missing some reference... no time to read everything :-)<br /> <br /> Personally, I am against the natural system of units, because people get used to neglect the h and the c from formulae even when they are describing approximations. For instance the fermionic lagrangian has a h multiplying it, thus it is obvious why there is not classical limit for fermions... but if you forget to put it, some students will have one or two bad days until they do the dimensional adjustment.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-144772" id="js-post-144772" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144772/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144772"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-10T08:50:00-0600" data-time="1076424600" data-date-string="Feb 10, 2004" data-time-string="8:50 AM" title="Feb 10, 2004 at 8:50 AM" itemprop="datePublished">Feb 10, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144772/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #24 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144772" data-lb-caption-desc="arivero · Feb 10, 2004 at 8:50 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>compton length and Zitterbewegung</b><br /> <br /> Perhaps Zitterbewegung is the most general effect that depens on compton wavelength. There was some comment about it in the past, and I even started a thread recently at the Quantum zone of the forum,<br /> <br /> <a href="https://www.physicsforums.com/showthread.php?s=&threadid=13365" class="link link--internal">https://www.physicsforums.com/showthread.php?s=&threadid=13365</a></div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-10T08:52:29-0600" data-time="1076424749" data-date-string="Feb 10, 2004" data-time-string="8:52 AM" title="Feb 10, 2004 at 8:52 AM" itemprop="dateModified">Feb 10, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-144881" id="js-post-144881" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/144881/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-144881"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-10T11:46:43-0600" data-time="1076435203" data-date-string="Feb 10, 2004" data-time-string="11:46 AM" title="Feb 10, 2004 at 11:46 AM" itemprop="datePublished">Feb 10, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/144881/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #25 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-144881" data-lb-caption-desc="marcus · Feb 10, 2004 at 11:46 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">A.R. this is slightly off-topic perhaps, having to do with the<br /> article you mentioned with the quote from Lucretius<br /> and the "relational" pivotal idea<br /> <br /> Rovelli recaps those ideas in his book pages 150-155<br /> which are section 5.6 "Relational interpretation of quantum theory"<br /> 5.6.1 "The observer observed"<br /> 5.6.2 "Facts are interactions"<br /> he illustrates this section with a drawing of Archimedes<br /> or Galileo (who can tell the difference) that it looks like he himself<br /> drew it, or someone in his family who is not an artist. The man is fearless<br /> <br /> anyway I am glad he did not let drop the ideas of that 1998 article<br /> you cited, but updated and included them in the book</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-145935" id="js-post-145935" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/145935/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-145935"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-12T09:54:31-0600" data-time="1076601271" data-date-string="Feb 12, 2004" data-time-string="9:54 AM" title="Feb 12, 2004 at 9:54 AM" itemprop="datePublished">Feb 12, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/145935/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #26 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-145935" data-lb-caption-desc="arivero · Feb 12, 2004 at 9:54 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by arivero </i><br /> By the way, I had never seen it, but I do skip a lot of literature on this. </div> </div> </blockquote><br /> Doing a bit of literature search, a first surprising point is that the recent paper of Markopoulou and Smolin does not use this trick but simply prefers to postulate the existence of a stocastic phenomena.<br /> <a href="http://xxx.unizar.es/abs/gr-qc/0311059" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://xxx.unizar.es/abs/gr-qc/0311059</a><br /> <br /> The "trialogue", at formula 4.2 from Veneziano, uses gravitational force <b>between strings</b> to underline that G and c could be more fundamental than h. <br /> <a href="http://xxx.unizar.es/abs/physics/0110060" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://xxx.unizar.es/abs/physics/0110060</a><br /> <br /> Also Novikov/Zeldovich are quoted pointing out that plank length and c should be enough in quantum gravity, because G and h appear always (or at least in the Einstein Hilbert action), as a product [tex]\sqrt{Gh}[/tex].</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-145951" id="js-post-145951" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/145951/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-145951"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-12T10:40:40-0600" data-time="1076604040" data-date-string="Feb 12, 2004" data-time-string="10:40 AM" title="Feb 12, 2004 at 10:40 AM" itemprop="datePublished">Feb 12, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/145951/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #27 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-145951" data-lb-caption-desc="marcus · Feb 12, 2004 at 10:40 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by arivero </i><br /> <b>Doing a bit of literature search, a first surprising point is that the recent paper of Markopoulou and Smolin does not use this trick but simply prefers to postulate the existence of a stocastic phenomena.<br /> <a href="http://xxx.unizar.es/abs/gr-qc/0311059" target="_blank" class="link link--external" rel="nofollow ugc noopener">http://xxx.unizar.es/abs/gr-qc/0311059</a><br /> ...<br /> because G and h appear always (or at least in the Einstein Hilbert action), as a product [tex]\sqrt{Gh}[/tex]. </b> </div> </div> </blockquote><br /> Your university at Zaragoza has its own arXiv mirror site!<br /> <br /> You refer to<br /> "Quantum Theory from Quantum Gravity"<br /> by Fotini Markopoulou and Lee Smolin<br /> <br /> I am not sure what to think about this article. How can the very quantum theory itself arise from spin networks?<br /> is the network or graph of adjacency relations such a mathematically rich structure that it can give rise to quantum theory? I did not know what to make of the abstract:<br /> <br /> "We provide a mechanism by which, from a background independent model with <b>no quantum mechanics</b>, quantum theory arises<br /> in the same limit in which spatial properties appear.<br /> <br /> Starting with an arbitrary abstract graph as the microscopic model of spacetime..."<br /> <br /> any clarification about what they are trying to do?</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-145984" id="js-post-145984" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/145984/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-145984"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-12T11:52:14-0600" data-time="1076608334" data-date-string="Feb 12, 2004" data-time-string="11:52 AM" title="Feb 12, 2004 at 11:52 AM" itemprop="datePublished">Feb 12, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/145984/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #28 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-145984" data-lb-caption-desc="arivero · Feb 12, 2004 at 11:52 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">There are about 20 mirrors of arxiv around the world (so, will it survive meteorite clash?). Zaragoza happens to have the spanish one. It is remotelly supported from the original, so no maintenance needed.<br /> <br /> It seems that M & S point out that if a stochastic trembling in coordinaates is postulated, then plank constant and schoedinger equation follow. Not surprising to us in this thread. But they do not take risk about the origin of the trembling.<br /> <br /> From a fundamental point of view, surely they are just remarking that unification of quantum theory and general relativity is supposed to be a new theory, so both regimes should emerge in the appropiate limits. No news here neither.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="Orion1" data-content="post-146388" id="js-post-146388" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/146388/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-146388"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-13T04:14:10-0600" data-time="1076667250" data-date-string="Feb 13, 2004" data-time-string="4:14 AM" title="Feb 13, 2004 at 4:14 AM" itemprop="datePublished">Feb 13, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/146388/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #29 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/orion1.5562/"> <meta itemprop="url" content="https://www.physicsforums.com/members/orion1.5562/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="5562"><span class="username--style11" itemprop="name">Orion1</span></span></span>     </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>973</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>3</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-146388" data-lb-caption-desc="Orion1 · Feb 13, 2004 at 4:14 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>Kepler's Length...</b><br /> <br /> Problem:<br /> <br /> given a particle of mass m, for which radius will a circular gravitational orbit around the particle to have the property of sweeping one plank area in exactly one plank time unit?<br /> <br /> <br /> <br /> <br /> Kepler's Second Law:<br /> [tex]\frac{dA}{dt} = \frac{L}{2m} = K_k[/tex]<br /> <br /> Planck Area: (circle)<br /> [tex]dA = \pi r_p^2 = \frac{\pi \hbar G}{c^3}[/tex]<br /> <br /> Planck Time: (period)<br /> [tex]dt = t_p = 2 \pi \sqrt{ \frac{ \hbar G}{c^5}[/tex]<br /> <br /> Angular Momentum:<br /> [tex]L = mrv[/tex]<br /> <br /> [tex]v = \sqrt{ \frac{Gm}{r_1}}[/tex]<br /> <br /> [tex]L = mr_1 \sqrt{ \frac{Gm}{r_1}}[/tex]<br /> <br /> integral:<br /> [tex]\frac{\pi r_p^2}{t_p} = \frac{r_1}{2} \sqrt{ \frac{Gm}{r_1}}[/tex]<br /> <br /> [tex]r_1 = \frac{4}{Gm} \left( \frac{ \pi r_p^2}{t_p} \right)^2[/tex]<br /> <br /> Solution #1:<br /> Compton Wavelength:<br /> [tex]r_1 = \frac{\hbar}{mc} = \overline{ \lambda}[/tex]<br /> <br /> Planck Mass:<br /> [tex]m = m_p = \sqrt{ \frac{\hbar c}{G}}[/tex]<br /> <br /> Solution #2:<br /> Planck Radius:<br /> [tex]r_1 = \sqrt{ \frac{ \hbar G}{c^3}} = \overline{ \lambda}[/tex]<br /> <br /> [tex]K_k = 2.422*10^{-27} m^2s^{-1}[/tex]<br /> [tex]L = \hbar ![/tex]<br /> <br /> [/color]</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-13T05:53:41-0600" data-time="1076673221" data-date-string="Feb 13, 2004" data-time-string="5:53 AM" title="Feb 13, 2004 at 5:53 AM" itemprop="dateModified">Feb 13, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-146451" id="js-post-146451" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/146451/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-146451"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-13T09:29:20-0600" data-time="1076686160" data-date-string="Feb 13, 2004" data-time-string="9:29 AM" title="Feb 13, 2004 at 9:29 AM" itemprop="datePublished">Feb 13, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/146451/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #30 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-146451" data-lb-caption-desc="marcus · Feb 13, 2004 at 9:29 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">there are actually two masses in the picture<br /> and arivero referred to the central mass<br /> (in which case the mass of the satellite is assumed<br /> negligible, making the angular momentum of the orbit<br /> hard to determine)<br /> but this analysis is very much in a good spirit and<br /> the right direction!<br /> Orion please try it where you have a pair of particles<br /> of equal mass circling each other<br /> maybe they are each m/2 so the combined mass is m<br /> or they could each be m.<br /> I am just waking up so not sure if this is a sensible reply<br /> but it might be.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-146471" id="js-post-146471" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/146471/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-146471"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-13T10:22:45-0600" data-time="1076689365" data-date-string="Feb 13, 2004" data-time-string="10:22 AM" title="Feb 13, 2004 at 10:22 AM" itemprop="datePublished">Feb 13, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/146471/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #31 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-146471" data-lb-caption-desc="arivero · Feb 13, 2004 at 10:22 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><br /> <br /> <blockquote data-attributes="" data-quote="" data-source="" class="bbCodeBlock bbCodeBlock--expandable bbCodeBlock--quote js-expandWatch"> <div class="bbCodeBlock-content"> <div class="bbCodeBlock-expandContent js-expandContent "> <i>Originally posted by Orion1 </i> <br /> Solution #1:<br /> Compton Wavelength:<br /> [tex]r_1 = \frac{\hbar}{mc} = \overline{ \lambda}[/tex]<br /> <br /> Planck Mass:<br /> [tex]m = m_p = \sqrt{ \frac{\hbar c}{G}}[/tex]<br /> <br /> Solution #2:<br /> Planck Radius:<br /> [tex]r_1 = \sqrt{ \frac{ \hbar G}{c^3}} = \overline{ \lambda}[/tex]<br /> <br /> [tex]K_k = 2.422*10^{-27} m^2s^{-1}[/tex]<br /> [tex]L = \hbar ![/tex] </div> </div> </blockquote><br /> The "standard", or at least majoritary, definition for Planck length is "the compton length of a mass of plank". I supposse that you are pointing out that this particular case has a total gravitational action of exactly [tex]h[/tex]. Is it?<br /> <br /> In any case I think it is more important to stress that the Compton Length answer happens <i>for any mass</i>.<br /> <br /> Also, it is usually told that [tex]m_p[/tex] is the case where Swartzchild radius and Compton radius coincide. Not sure about the meaning of this, here.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="Orion1" data-content="post-146880" id="js-post-146880" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/146880/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-146880"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-14T03:36:41-0600" data-time="1076751401" data-date-string="Feb 14, 2004" data-time-string="3:36 AM" title="Feb 14, 2004 at 3:36 AM" itemprop="datePublished">Feb 14, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/146880/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #32 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/orion1.5562/"> <meta itemprop="url" content="https://www.physicsforums.com/members/orion1.5562/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="5562"><span class="username--style11" itemprop="name">Orion1</span></span></span>     </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>973</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>3</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-146880" data-lb-caption-desc="Orion1 · Feb 14, 2004 at 3:36 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>Binary Systems...</b><br /> <br /> <br /> <br /> Compton Radius/Wavelength:<br /> [tex]r_1 = \frac{\hbar}{mc} = \overline{ \lambda}[/tex]<br /> <br /> The Compton Radius is only a solution for a Keplerian-Planck System, for which m<<M.<br /> <br /> As m approaches M in magnitude, the system becomes binaric, and all keplerian laws fail and no longer apply.<br /> <br /> Kepler's Laws function only as derivatives to the Binary Theorem, therefore are not actually 'laws'.<br /> <br /> Solutions to binary systems requires a modification to Newtons Gravitational Law using a center of mass integration. <br /> <br /> [tex]dt_1 = dt_2[/tex]<br /> <br /> [tex]\frac{dA}{dt} = K_k = 2.422*10^{-27} m^2s^{-1}[/tex]<br /> <br /> Orion1 Binary System Theorem:<br /> [tex]\frac{dA}{dt} = \frac{Gm_2^3t_1}{4 \pi (m_1 + m_2)^2 r_1} = K_k[/tex]<br /> <br /> [tex]r_1 = \frac{Gm_2^3t_1}{4 \pi K_k (m_1 + m_2)^2}[/tex]<br /> <br /> Limit t<sub>1</sub> = t<sub>p</sub> (period)<br /> [tex]r_1 = \frac{Gm_2^3}{2 K_k (m_1 + m_2)^2} \sqrt{ \frac{\hbar G}{c^5}}[/tex]<br /> <br /> Limit m<sub>1</sub> = m<sub>2</sub> = m<sub>p</sub> <br /> r<sub>1</sub> = 2.538*10^-35 m<br /> r<sub>p</sub> = 1.616*10^-35 m<br /> <br /> <br /> <br /> Also, it is usually told that [tex]m_p[/tex] is the case where Swartzchild radius and Compton radius coincide.<br /> [/color]<br /> <br /> Compton Radius:<br /> [tex]r_c = \frac{\hbar}{mc} = \overline{ \lambda}[/tex]<br /> <br /> Schwarzschild Radius:<br /> [tex]r_s = \frac{2Gm}{c^2}[/tex]<br /> <br /> [tex]r_c = r_s[/tex]<br /> <br /> [tex]\frac{\hbar}{mc} = \frac{2Gm}{c^2}[/tex]<br /> <br /> Compton-Schwarzschild Mass:<br /> [tex]m_{cs} = \sqrt{ \frac{ \hbar c}{2G}[/tex]<br /> <br /> Close, but negative.<br /> [/color]</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-14T04:25:03-0600" data-time="1076754303" data-date-string="Feb 14, 2004" data-time-string="4:25 AM" title="Feb 14, 2004 at 4:25 AM" itemprop="dateModified">Feb 14, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="marcus" data-content="post-146960" id="js-post-146960" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/146960/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-146960"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-14T09:45:40-0600" data-time="1076773540" data-date-string="Feb 14, 2004" data-time-string="9:45 AM" title="Feb 14, 2004 at 9:45 AM" itemprop="datePublished">Feb 14, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/146960/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #33 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/marcus.66/"> <meta itemprop="url" content="https://www.physicsforums.com/members/marcus.66/" /> <div class="message-userDetails"> <span class="message-name"><a href="/members/marcus.66/" class="username " dir="auto" data-user-id="66" data-xf-init="member-tooltip"><span itemprop="name">marcus</span></a></span>    <div class="post-badges"> <div class="post-badge badge-university" data-xf-init="tooltip" title="Verified Expert in Science and Math"> <i class="fa--xf fal fa-university" aria-hidden="true"></i><span> Science Advisor</span> </div> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> <div class="post-badge badge-heart" data-xf-init="tooltip" title="Memorial: Member has Passed"> <i class="fa--xf fal fa-heart" aria-hidden="true"></i><span> Dearly Missed</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>24,753</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>792</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-146960" data-lb-caption-desc="marcus · Feb 14, 2004 at 9:45 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper">Hi Orion<br /> you said:"Also, it is usually told that [planck mass] is the case where Swartzchild radius and Compton radius coincide."<br /> <br /> I have never heard that, what I have read has been that Planck mass is the case where <b>half</b> the Schwarzschild radius and the Compton wavelength coincide.<br /> <br /> if you have a link to something online with the alternative definition you could post it, then anyone who is curious about the different defintion could check it out<br /> <br /> but it is just a factor of two that we are worrying about<br /> <br /> half the Schw. is GM/c^2<br /> <br /> and that has to equal the Compton, which in reduced or angular format is hbar c/Mc^2<br /> <br /> So one sets the two equal and solves<br /> <br /> GM/c^2 = hbar c/Mc^2<br /> <br /> I will try to put this in LaTex, to match your clear writing.<br /> <br /> [tex]\frac{GM}{c^2} = \frac{\hbar c}{Mc^2}[/tex]<br /> <br /> [tex]M^2 = \frac{\hbar c}{G}[/tex]</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-14T09:52:54-0600" data-time="1076773974" data-date-string="Feb 14, 2004" data-time-string="9:52 AM" title="Feb 14, 2004 at 9:52 AM" itemprop="dateModified">Feb 14, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="arivero" data-content="post-147001" id="js-post-147001" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/147001/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-147001"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-14T11:39:49-0600" data-time="1076780389" data-date-string="Feb 14, 2004" data-time-string="11:39 AM" title="Feb 14, 2004 at 11:39 AM" itemprop="datePublished">Feb 14, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/147001/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #34 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/arivero.81/"> <meta itemprop="url" content="https://www.physicsforums.com/members/arivero.81/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="81"><span itemprop="name">arivero</span></span></span>   <span class="threadstarter" data-xf-init="tooltip" title="Thread Starter"><i class="fal fa-user-edit"></i></span>  <div class="post-badges"> <div class="post-badge badge-star" data-xf-init="tooltip" title="Click to Support PF"> <i class="fa--xf fal fa-star" aria-hidden="true"></i><span> Gold Member</span> </div> </div>  </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>3,481</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>175</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-147001" data-lb-caption-desc="arivero · Feb 14, 2004 at 11:39 AM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>factor2</b><br /> <br /> Sorry marcus it was me who raised the sloopy definition; there is a factor 2 (even 4) around all the thread, but I am not worried at this level; we are playing sort of dimensional analysis.<br /> <br /> Orion, note that the initial setup does not ask for a whole revolution. Area law forks for a sector of the circle too. Answers are the same, although to look for a complete revolution is an interesting particular case, hmm.</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-14T11:51:00-0600" data-time="1076781060" data-date-string="Feb 14, 2004" data-time-string="11:51 AM" title="Feb 14, 2004 at 11:51 AM" itemprop="dateModified">Feb 14, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article>  <article class="message message--post js-post js-inlineModContainer " data-author="Orion1" data-content="post-147166" id="js-post-147166" itemscope itemtype="https://schema.org/Comment" itemid="https://www.physicsforums.com/posts/147166/"> <meta itemprop="parentItem" itemscope itemid="https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/" /> <span class="u-anchorTarget" id="post-147166"></span> <div class="message-header"> <header class="message-attribution message-attribution--split"> <ul class="message-attribution-main listInline "> <li class="u-concealed"> <time class="u-dt" dir="auto" datetime="2004-02-14T21:05:19-0600" data-time="1076814319" data-date-string="Feb 14, 2004" data-time-string="9:05 PM" title="Feb 14, 2004 at 9:05 PM" itemprop="datePublished">Feb 14, 2004</time> </li> </ul> <ul class="message-attribution-opposite message-attribution-opposite--list "> <li> <span style="cursor:pointer;" data-xf-init="share-tooltip" data-href="/posts/147166/share" aria-label="Share" role="button" rel="nofollow"> <i class="fa--xf fal fa-share-alt" aria-hidden="true"></i> </span> </li> <li> #35 </li> </ul> </header> </div> <div class="message-inner"> <div class="message-cell message-cell--user"> <section class="message-user" itemprop="author" itemscope itemtype="https://schema.org/Person" itemid="https://www.physicsforums.com/members/orion1.5562/"> <meta itemprop="url" content="https://www.physicsforums.com/members/orion1.5562/" /> <div class="message-userDetails"> <span class="message-name"><span class="username " dir="auto" data-user-id="5562"><span class="username--style11" itemprop="name">Orion1</span></span></span>     </div> <div class="message-userExtras"> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-comments fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Messages"></i></dt> <dd>973</dd> </dl> <dl class="pairs pairs--justified"> <dt><i class="fa--xf fal fa-thumbs-up fa-fw" aria-hidden="true" data-xf-init="tooltip" title="Reaction score"></i></dt> <dd>3</dd> </dl> </div> <span class="message-userArrow"></span> </section> </div> <div class="message-cell message-cell--main"> <div class="message-main js-quickEditTarget"> <div class="message-content js-messageContent"> <div class="message-userContent lbContainer js-lbContainer " data-lb-id="post-147166" data-lb-caption-desc="Orion1 · Feb 14, 2004 at 9:05 PM"> <article class="message-body js-selectToQuote"> <div itemprop="text"> <div class="bbWrapper"><b>Orion1 Binary Theorem...</b><br /> <br /> <br /> the initial setup does not ask for a whole revolution. Area law forks for a sector of the circle too.<br /> [/color]<br /> <br /> <br /> [tex]dt_1 = dt_2[/tex]<br /> <br /> [tex]\frac{dA}{dt} = K_k = 2.422*10^{-27} m^2s^{-1}[/tex]<br /> <br /> Orion1 Binary System Theorem:<br /> [tex]r_1 = \frac{4(m_1 + m_2)^2}{Gm_2^3} \left( \frac{dA}{dt} \right)^2[/tex]<br /> <br /> [tex]r_1 = \frac{}{Gm_2^3} \left( 2(m_1 + m_2) \left( \frac{dA}{dt} \right) \right)^2[/tex]<br /> <br /> [tex]r_1 = \frac{ (2K_k(m_1 + m_2))^2}{Gm_2^3} [/tex]<br /> <br /> Limit m<sub>1</sub> = m<sub>2</sub> = m<sub>p</sub><br /> r<sub>1</sub> = 6.464*10^-35 m<br /> r<sub>p</sub> = 1.616*10^-35 m<br /> r<sub>1</sub> = 4r<sub>p</sub><br /> <br /> <br /> Below that radius, it should be posible to use "plank time beats" to divide area into regions smaller that previous. So a fundamental break of physics will happen at "quantum kepler length of the particle m"<br /> [/color]<br /> <br /> [tex]\frac{dA}{dt} = \frac{}{2} \sqrt{ \frac{\hbar G}{c}} = K_k = 2.422*10^{-27} m^2s^{-1}[/tex]<br /> <br /> Planck Mass Fusion:<br /> Limit m<sub>1</sub> = m<sub>2</sub> = m<sub>p</sub><br /> Limit r<sub>1</sub> = r<sub>p</sub><br /> [tex]\frac{dA}{dt} = \frac{ \sqrt{Gm_2^3r_p}}{2(m_1 + m_2)} = \frac{}{4} \sqrt{ \frac{\hbar G}{c}} = K_1 = 1.211*10^{-27} m^2s^{-1}[/tex]<br /> <br /> Planck-Compton Radius: r<sub>1</sub> = r<sub>p</sub><br /> [tex]r_p = \frac{\hbar}{m_pc} = \overline{ \lambda_p}[/tex]<br /> <br /> Gravitation 'quantum shutdown' below the Planck Radius: r<sub>1</sub> <= r<sub>p</sub> <br /> <br /> r<sub>1</sub> <= r<sub>p</sub> <br /> [tex]\frac{ \sqrt{m_2^3r_1}}{(m_1 + m_2)} = \frac{}{2} \sqrt{ \frac{\hbar }{c}}[/tex] <br /> <br /> r<sub>1</sub> <= r<sub>p</sub> <br /> [tex]\frac{m_2^3}{(m_1 + m_2)^2} = \frac{ \hbar}{4cr_1}[/tex]<br /> <br /> r<sub>1</sub> <= r<sub>p</sub> <br /> [tex]r_1 = \frac{ \hbar (m_1 + m_2)^2}{4cm_2^3}[/tex]<br /> <br /> [/color]</div> </div> <div class="js-selectToQuoteEnd"> </div> </article> </div> <div class="message-lastEdit"> Last edited: <time class="u-dt" dir="auto" datetime="2004-02-15T05:31:26-0600" data-time="1076844686" data-date-string="Feb 15, 2004" data-time-string="5:31 AM" title="Feb 15, 2004 at 5:31 AM" itemprop="dateModified">Feb 15, 2004</time> </div> </div> <footer class="message-footer"> <div class="message-microdata" itemprop="interactionStatistic" itemtype="https://schema.org/InteractionCounter" itemscope> <meta itemprop="userInteractionCount" content="0" /> <meta itemprop="interactionType" content="https://schema.org/LikeAction" /> </div> <div class="reactionsBar js-reactionsList "> </div> <div class="js-historyTarget message-historyTarget toggleTarget" data-href="trigger-href"></div> </footer> </div> </div> </div> </article> </div> </div> <div class="block-outer 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class="structItem-parts"> </ul> </div> </div> <div class="structItem-cell structItem-cell--meta" title="First message reaction score: 0"> <dl class="pairs pairs--justified"> <dt>Replies</dt> <dd>8</dd> </dl> <dl class="pairs pairs--justified structItem-minor"> <dt>Views</dt> <dd>783</dd> </dl> </div> </div> <div class="structItem structItem--thread is-prefix91 is-locked js-inlineModContainer js-threadListItem-1061460" data-author="kodama"> <div class="structItem-cell structItem-cell--main" data-xf-init="touch-proxy"> <div class="structItem-title"> <span class="prefix inter" dir="auto">I</span> <a href="/threads/two-recent-tests-of-loop-quantum-gravity-theory.1061460/" class="" data-tp-primary="on" data-xf-init="preview-tooltip" data-preview-url="/threads/two-recent-tests-of-loop-quantum-gravity-theory.1061460/preview">Two recent tests of loop quantum gravity theory</a> </div> <div class="structItem-minor"> <ul class="structItem-parts"> <li class="structItem-startDate"><time 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</div> </div> <div class="structItem-cell structItem-cell--meta" title="First message reaction score: 0"> <dl class="pairs pairs--justified"> <dt>Replies</dt> <dd>11</dd> </dl> <dl class="pairs pairs--justified structItem-minor"> <dt>Views</dt> <dd>2K</dd> </dl> </div> </div> <div class="structItem structItem--thread is-prefix91 is-locked js-inlineModContainer js-threadListItem-1060884" data-author="HighPhy"> <div class="structItem-cell structItem-cell--main" data-xf-init="touch-proxy"> <div class="structItem-title"> <span class="prefix inter" dir="auto">I</span> <a href="/threads/wave-particle-duality-and-double-slit-experiment.1060884/" class="" data-tp-primary="on" data-xf-init="preview-tooltip" data-preview-url="/threads/wave-particle-duality-and-double-slit-experiment.1060884/preview">"Wave-particle duality" and double-slit experiment</a> </div> <div class="structItem-minor"> <ul class="structItem-parts"> <li class="structItem-startDate"><time class="structItem-latestDate u-dt" dir="auto" datetime="2024-03-17T17:28:12-0500" data-time="1710714492" data-date-string="Mar 17, 2024" data-time-string="5:28 PM" title="Mar 17, 2024 at 5:28 PM">Mar 17, 2024</time></li>  </ul> <span class="structItem-pageJump"> <a href="/threads/wave-particle-duality-and-double-slit-experiment.1060884/page-2">2</a> </span> <ul class="structItem-parts"> </ul> </div> </div> <div class="structItem-cell structItem-cell--meta" title="First message reaction score: 0"> <dl class="pairs pairs--justified"> <dt>Replies</dt> <dd>36</dd> </dl> <dl class="pairs pairs--justified structItem-minor"> <dt>Views</dt> <dd>5K</dd> </dl> </div> </div> <div class="structItem structItem--thread is-locked js-inlineModContainer js-threadListItem-985048" data-author="frostysh"> <div class="structItem-cell structItem-cell--main" data-xf-init="touch-proxy"> <div class="structItem-title"> <a href="/threads/i-with-understanding-keplers-second-law.985048/" class="" data-tp-primary="on" data-xf-init="preview-tooltip" 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Are you sure you want to submit this form?", attach: "Attach files", rich_text_box: "Rich text box", close: "Close", link_copied_to_clipboard: "Link copied to clipboard.", text_copied_to_clipboard: "Text copied to clipboard.", loading: "Loading…", you_have_exceeded_maximum_number_of_selectable_items: "You have exceeded the maximum number of selectable items.", processing: "Processing", 'processing...': "Processing…", showing_x_of_y_items: "Showing {count} of {total} items", showing_all_items: "Showing all items", no_items_to_display: "No items to display", number_button_up: "Increase", number_button_down: "Decrease", push_enable_notification_title: "Push notifications enabled successfully at Physics Forums: Science Discussion, Homework Help, Articles", push_enable_notification_body: "Thank you for enabling push notifications!", pull_down_to_refresh: "Pull down to refresh", release_to_refresh: "Release to refresh", refreshing: "Refreshing…" }); </script> <form style="display:none" hidden="hidden"> <input type="text" name="_xfClientLoadTime" value="" id="_xfClientLoadTime" title="_xfClientLoadTime" tabindex="-1" /> </form>  <script type="application/ld+json"> { "@context": "https://schema.org", "@type": "WebPage", "url": "https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/", "mainEntity": { "@type": "DiscussionForumPosting", "@id": "https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/", "headline": "Calculating the Quantum Kepler Length of a Particle", "datePublished": "2004-02-07T12:30:21+00:00", "keywords": "Kepler, Length, Particle, Quantum", "url": "https://www.physicsforums.com/threads/calculating-the-quantum-kepler-length-of-a-particle.14007/", "articleSection": "Beyond the Standard Models", "author": { "@type": "Person", "@id": "https://www.physicsforums.com/members/arivero.81/", "name": "arivero", "url": "https://www.physicsforums.com/members/arivero.81/" }, "interactionStatistic": [ { "@type": "InteractionCounter", "interactionType": "https://schema.org/ViewAction", "userInteractionCount": 25307 }, { "@type": "InteractionCounter", "interactionType": "https://schema.org/CommentAction", "userInteractionCount": 65 }, { "@type": "InteractionCounter", "interactionType": "https://schema.org/LikeAction", "userInteractionCount": 0 } ], "dateModified": "2004-02-07T22:39:30+00:00", "articleBody": "One knows that in classical gravity a orbiting point sweeps equal areas at equal times. It can be seen that for macroscopic distances the area swept in a plank time is a lot greater than the minimum quantum of area, which is about (plank length)^2.\r\n\r\nNow, I ask, given a particle of mass m, for which radius will a circular gravitational orbit around the particle to have the property of sweeping one plank area in exactly one plank time unit?\r\n\r\nBelow that radius, it should be posible to use \"plank time beats\" to divide area into regions smaller that previous. So a fundamental break of physics will happen at \"quantum kepler length of the particle m\" ;-) \r\n\r\nOf course you know which other name this length receives, do you?\r\n\r\n\r\n[SPOILERS FOLLOW IN NEXT ANSWER. So padding inserted here]\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n.\r\n." }, "publisher": { "@type": "Organization", "name": "Physics Forums: Science Discussion, Homework Help, Articles", "alternateName": "Physics Forums", "description": "Join Physics Forums, where students, scientists, and enthusiasts come together to explore and discuss the current understanding and practice of various scientific fields.", "url": "https://www.physicsforums.com", "logo": "https://www.physicsforums.com/styles/physicsforums/images/physics-forums-logo-og.png" } } </script> <script type="text/javascript" src="https://www.physicsforums.com/copyright.js" defer></script> <script> function parseNewPost(postid) { var newpost = document.getElementById("js-post-" + postid), npa = [newpost]; MathJax.typeset(npa); } function parsePreview() { var preview = document.getElementsByClassName("xfPreview"); MathJax.typeset(preview); } function parseNewConversationPost(postid) { var newpost = document.getElementsByClassName("convMessage-" + postid); MathJax.typeset(newpost); } function parseNewProfilePost(postid) { var newpost = document.getElementById("js-profilePost-" + postid), npa = [newpost]; MathJax.typeset(npa); } function parseTooltip() { MathJax.typeset(); } </script> </body> </html>

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Calculating the Quantum Kepler Length of a Particle