{"id":96,"date":"2017-05-28T15:09:36","date_gmt":"2017-05-28T22:09:36","guid":{"rendered":"http:\/\/einstein-cartan.org\/wp\/?page_id=96"},"modified":"2020-08-11T17:02:52","modified_gmt":"2020-08-12T00:02:52","slug":"graphs","status":"publish","type":"page","link":"https:\/\/einstein-cartan.org\/wp\/graphs\/","title":{"rendered":"Graphs"},"content":{"rendered":"<p><span style=\"color: #000000;\">We present here some plots of our central equation as a function of the variable <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=r_x+&#038;bg=ffffff&#038;fg=000&#038;s=1&#038;c=20201002\" alt=\"r_x \" class=\"latex\" \/> , which\u00a0gives a multiple of our <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=r_t+%3D+%282%5Cpi%2F%5Csqrt%7B%5Calpha%7D%29%5C%2Cl_P+&#038;bg=ffffff&#038;fg=000&#038;s=1&#038;c=20201002\" alt=\"r_t = (2&#92;pi\/&#92;sqrt{&#92;alpha})&#92;,l_P \" class=\"latex\" \/>.<\/span><\/p>\n<p style=\"text-align: center;\"><img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=f%28r_x%29+%3D+&#038;bg=ffffff&#038;fg=000&#038;s=1&#038;c=20201002\" alt=\"f(r_x) = \" class=\"latex\" \/> <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=%C2%A0%5Cfrac%7B%5Calpha%5Chbar+c%7D%7B8%5Cpi%5C%2Cl_P%28%5Cfrac%7B2%5Cpi%7D%7B%5Csqrt%7B%5Calpha%7D%7D%29r_x%7D+-+%5Cfrac%7B3%5Cpi%5Chbar+c%7D%7B2%5C%2Cl_P%28%5Cfrac%7B2%5Cpi%7D%7B%5Csqrt%7B%5Calpha%7D%7Dr_x%29%5E3%7D+&#038;bg=ffffff&#038;fg=000&#038;s=2&#038;c=20201002\" alt=\"\u00a0&#92;frac{&#92;alpha&#92;hbar c}{8&#92;pi&#92;,l_P(&#92;frac{2&#92;pi}{&#92;sqrt{&#92;alpha}})r_x} - &#92;frac{3&#92;pi&#92;hbar c}{2&#92;,l_P(&#92;frac{2&#92;pi}{&#92;sqrt{&#92;alpha}}r_x)^3} \" class=\"latex\" \/><\/p>\n<p style=\"text-align: center;\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"309\" data-permalink=\"https:\/\/einstein-cartan.org\/wp\/graphs\/frtrx2graph1\/\" data-orig-file=\"https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph1.jpg?fit=639%2C498&amp;ssl=1\" data-orig-size=\"639,498\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"frtrx2graph1\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph1.jpg?fit=639%2C498&amp;ssl=1\" class=\"aligncenter size-full wp-image-309\" src=\"https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph1.jpg?resize=639%2C498&#038;ssl=1\" alt=\"\" width=\"639\" height=\"498\" srcset=\"https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph1.jpg?w=639&amp;ssl=1 639w, https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph1.jpg?resize=300%2C234&amp;ssl=1 300w\" sizes=\"auto, (max-width: 639px) 100vw, 639px\" \/><\/p>\n<p><span style=\"color: #000000;\">In the above plot, <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=r_x+&#038;bg=ffffff&#038;fg=000&#038;s=1&#038;c=20201002\" alt=\"r_x \" class=\"latex\" \/> ranges from 1 to 10.\u00a0 We can see that we have\u00a0a maximum at around\u00a05.56 x 10^13 GeV right before <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=2%5C%2Cr_x&#038;bg=ffffff&#038;fg=000&#038;s=0&#038;c=20201002\" alt=\"2&#92;,r_x\" class=\"latex\" \/>.<\/span><\/p>\n<p style=\"text-align: center;\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" data-attachment-id=\"310\" data-permalink=\"https:\/\/einstein-cartan.org\/wp\/graphs\/frtrx2graph2\/\" data-orig-file=\"https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph2.jpg?fit=636%2C486&amp;ssl=1\" data-orig-size=\"636,486\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"frtrx2graph2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph2.jpg?fit=636%2C486&amp;ssl=1\" class=\"aligncenter size-full wp-image-310\" src=\"https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph2.jpg?resize=636%2C486&#038;ssl=1\" alt=\"\" width=\"636\" height=\"486\" srcset=\"https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph2.jpg?w=636&amp;ssl=1 636w, https:\/\/i0.wp.com\/einstein-cartan.org\/wp\/wp-content\/uploads\/2019\/01\/frtrx2graph2.jpg?resize=300%2C229&amp;ssl=1 300w\" sizes=\"auto, (max-width: 636px) 100vw, 636px\" \/><\/p>\n<p><span style=\"color: #000000;\">In the above plot we have expanded the horizontal axis out to 100 times <img decoding=\"async\" src=\"https:\/\/s0.wp.com\/latex.php?latex=r_t+&#038;bg=ffffff&#038;fg=000&#038;s=1&#038;c=20201002\" alt=\"r_t \" class=\"latex\" \/>.\u00a0 This makes it easier to see that the right hand solution asymptotically approaches zero.\u00a0 This is the positive solution responsible for the Compton wavelength while the left hand slope gives the observed fermion masses.\u00a0 If higher energy fermions do exist, then we can see that they are limited to energies near the GUT scale.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present here some plots of our central equation as a function of the variable , which\u00a0gives a multiple of our . In the above plot, ranges from 1 to 10.\u00a0 We can see that we have\u00a0a maximum at around\u00a05.56 x 10^13 GeV right before . In the above plot we have expanded the horizontal [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-96","page","type-page","status-publish","hentry"],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/P80P78-1y","jetpack-related-posts":[],"_links":{"self":[{"href":"https:\/\/einstein-cartan.org\/wp\/wp-json\/wp\/v2\/pages\/96","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/einstein-cartan.org\/wp\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/einstein-cartan.org\/wp\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/einstein-cartan.org\/wp\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/einstein-cartan.org\/wp\/wp-json\/wp\/v2\/comments?post=96"}],"version-history":[{"count":35,"href":"https:\/\/einstein-cartan.org\/wp\/wp-json\/wp\/v2\/pages\/96\/revisions"}],"predecessor-version":[{"id":371,"href":"https:\/\/einstein-cartan.org\/wp\/wp-json\/wp\/v2\/pages\/96\/revisions\/371"}],"wp:attachment":[{"href":"https:\/\/einstein-cartan.org\/wp\/wp-json\/wp\/v2\/media?parent=96"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}