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<blockquote data-quote="Rosco..Jones" data-source="post: 48515" data-attributes="member: 2729"><p><span style="color: #808000">"Just one singularity approximately the "size of an electron" would weigh about the same as our Moon."</span></p><p></p><p>Hardt, Your killing me. The base size "micro" singularity is one Planck mass in size. Singularity size increases in Planck mass quantities. I don't have the interest to calculate the mass required for a <span style="color: #c0c0c0"><a href="http://en.wikipedia.org/wiki/Schwarzschild_radius" target="_blank"><span style="color: #c0c0c0">Schwarzschild radius</span></a></span> (event horizon) equal to the electron radius. Anyway, there was never any mention of the size if the singularities used in JT's TM.</p><p></p><p>I think that you were looking at the micro black holes used in the TM as you would the massive stellar black holes. Gravity at the Planck distances involved does not act the same as it does at macro distances.</p><p></p><p>"Contrarily to conventional black holes which are solutions of gravitational field equations of the general theory of relativity, quantum gravity black holes incorporate quantum gravity effects in the vicinity of the origin, where classically a curvature singularity occurs."</p><p></p><p><span style="color: #c0c0c0"><a href="http://en.wikipedia.org/wiki/Planck_mass" target="_blank"><span style="color: #c0c0c0">Planck mass</span></a></span> 2.176 (13) × 10−8 kg</p><p></p><p><span style="color: #c0c0c0"><a href="http://en.wikipedia.org/wiki/Planck_length" target="_blank"><span style="color: #c0c0c0">Planck length </span></a></span><a href="http://en.wikipedia.org/wiki/Planck_length" target="_blank"><span style="color: #c0c0c0">1.616 (97) × 10−35 m</span></a></p><p><span style="color: #c0c0c0"><span style="color: #c0c0c0">(event horizon)</span></span></p><p></p><p>Electron mass <span style="color: #c0c0c0"> <a href="http://en.wikipedia.org/wiki/Orders_of_magnitude_%28mass%29#10-25_kg_or_less" target="_blank"><span style="color: #c0c0c0">9.109×10−31</span></a></span> kg</p><p></p><p>Electron's radius is 10−22 m</p><p></p><p>Reference: Earth mass 8.87×10−3m</p><p><span style="color: #c0c0c0"><span style="color: #c0c0c0">event horizon</span></span></p><p></p><p>"The Kerr–Newman metric defines a black hole with an event horizon only when the following relation is satisfied: a^2+Q^2 <= M^2</p><p></p><p>An electron's <em>a</em> and <em>Q</em> (suitably specified in <a href="http://en.wikipedia.org/wiki/Geometrized_units" target="_blank">geometrized units</a>) both exceed its mass <em>M</em>, in which case the metric has no event horizon and thus there can be no such thing as a <a href="http://en.wikipedia.org/wiki/Black_hole_electron" target="_blank">black hole electron</a> — <span style="color: #ff6600">only a <a href="http://en.wikipedia.org/wiki/Naked_singularity" target="_blank"><span style="color: #ff6600">naked</span></a> spinning ring singularity</span>. Such a metric has several seemingly unphysical properties, such as the ring's violation of the <a href="http://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis" target="_blank">cosmic censorship hypothesis</a>, <span style="color: #ff6600">and also appearance of causality-violating <u><a href="http://en.wikipedia.org/wiki/Closed_timelike_curve" target="_blank"><span style="color: #ff6600"><u><u><span style="color: #ff9900">closed timelike curves</span></u></u></span></a></u> in the immediate vicinity of the ring.</span>"</p></blockquote><p></p>
[QUOTE="Rosco..Jones, post: 48515, member: 2729"] [COLOR=#808000]"Just one singularity approximately the "size of an electron" would weigh about the same as our Moon."[/COLOR] Hardt, Your killing me. The base size "micro" singularity is one Planck mass in size. Singularity size increases in Planck mass quantities. I don't have the interest to calculate the mass required for a [COLOR=#c0c0c0][URL='http://en.wikipedia.org/wiki/Schwarzschild_radius'][COLOR=#c0c0c0]Schwarzschild radius[/COLOR][/URL][/COLOR] (event horizon) equal to the electron radius. Anyway, there was never any mention of the size if the singularities used in JT's TM. I think that you were looking at the micro black holes used in the TM as you would the massive stellar black holes. Gravity at the Planck distances involved does not act the same as it does at macro distances. "Contrarily to conventional black holes which are solutions of gravitational field equations of the general theory of relativity, quantum gravity black holes incorporate quantum gravity effects in the vicinity of the origin, where classically a curvature singularity occurs." [COLOR=#c0c0c0][URL='http://en.wikipedia.org/wiki/Planck_mass'][COLOR=#c0c0c0]Planck mass[/COLOR][/URL][/COLOR] 2.176 (13) × 10−8 kg [COLOR=#c0c0c0][URL='http://en.wikipedia.org/wiki/Planck_length'][COLOR=#c0c0c0]Planck length [/COLOR][/URL][/COLOR][URL='http://en.wikipedia.org/wiki/Planck_length'][COLOR=#c0c0c0]1.616 (97) × 10−35 m[/COLOR][/URL] [COLOR=#c0c0c0][COLOR=#c0c0c0](event horizon)[/COLOR][/COLOR] Electron mass [COLOR=#c0c0c0] [URL='http://en.wikipedia.org/wiki/Orders_of_magnitude_%28mass%29#10-25_kg_or_less'][COLOR=#c0c0c0]9.109×10−31[/COLOR][/URL][/COLOR] kg Electron's radius is 10−22 m Reference: Earth mass 8.87×10−3m [COLOR=#c0c0c0][COLOR=#c0c0c0]event horizon[/COLOR][/COLOR] "The Kerr–Newman metric defines a black hole with an event horizon only when the following relation is satisfied: a^2+Q^2 <= M^2 An electron's [I]a[/I] and [I]Q[/I] (suitably specified in [URL='http://en.wikipedia.org/wiki/Geometrized_units']geometrized units[/URL]) both exceed its mass [I]M[/I], in which case the metric has no event horizon and thus there can be no such thing as a [URL='http://en.wikipedia.org/wiki/Black_hole_electron']black hole electron[/URL] — [COLOR=#ff6600]only a [URL='http://en.wikipedia.org/wiki/Naked_singularity'][COLOR=#ff6600]naked[/COLOR][/URL] spinning ring singularity[/COLOR]. Such a metric has several seemingly unphysical properties, such as the ring's violation of the [URL='http://en.wikipedia.org/wiki/Cosmic_censorship_hypothesis']cosmic censorship hypothesis[/URL], [COLOR=#ff6600]and also appearance of causality-violating [U][URL='http://en.wikipedia.org/wiki/Closed_timelike_curve'][COLOR=#ff6600][U][U][COLOR=#ff9900]closed timelike curves[/COLOR][/U][/U][/COLOR][/URL][/U] in the immediate vicinity of the ring.[/COLOR]" [/QUOTE]
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