<div dir="ltr"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><span style="font-family:arial,sans-serif">On Mon, Dec 5, 2016 at 11:47 PM, Adrian Tymes </span><span dir="ltr" style="font-family:arial,sans-serif"><<a href="mailto:atymes@gmail.com" target="_blank">atymes@gmail.com</a>></span><span style="font-family:arial,sans-serif"> wrote:</span><br></div><div class="gmail_extra"><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"></blockquote><br><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><span class="gmail-">
><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">></div> <font size="4">Well yes, change one thing and not the other and 2 identical things are no<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>longer identical. But it works both ways, rearranging the territory would<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>not affect the map. It seems to me that they both behave the same way to<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>perturbations, so what's the difference between them?</font></span></blockquote><span class="gmail-">
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</span><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Location, presumably, since 2 things can't occupy the same space at<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>the same time. </blockquote><div><br></div><div><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"><font size="4">Actually that isn't always true, it's only true for fermions, like protons neutrons and electrons, particles with half integer spin, they are the only ones that must obey the Pauli Exclusion Principle. Particles with integer spin, bosons like photons or the Higgs, don't need to obey Pauli and can overlap each other. Although not a fundamental particle a Helium-4 nucleus can under certain circumstances behave like a boson too because it's 2 protons and 2 neutrons spin in opposite directions and cancel out yielding a overall spin of zero, an integer. A neutral Helium-4 atom can sometimes behave like a Boson also because its 2 electrons spin in opposite directions. But for a Bose-Einstein Condensate to form all parts of the atom must be identical, and that can't happen if the external josseling of the atom is larger than the natural smeared out property all particles have due to their wavelike nature. So for Helium-4 to form a </font></div><font size="4"><span style="font-family:arial,helvetica,sans-serif">Bose-Einstein Condensate</span> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">you have to cool it way way down.</div></font></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">> </div>Until and unless you destroy the property of them<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>being independent things.<br></blockquote><br><font size="4">Yes<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">,</div> if you don't cool them enough and a<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Bose-Einstein Condensate<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>is not formed <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> then </div>you do indeed have two<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>independent things, but 2 things that have the exact same property of obeying the<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline"> </div>Pauli Exclusion Principle<div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">.</div> <div class="gmail_default" style="font-family:arial,helvetica,sans-serif;display:inline">S</div>o if you instantly exchanged the 2 things neither you nor the things would notice a difference.</font></div><div class="gmail_quote"><font size="4"><br></font></div><div class="gmail_quote"><div class="gmail_default" style="font-family:arial,helvetica,sans-serif"><font size="4">John K Clark</font></div><br> <div><br></div><div><br></div></div></div></div>