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Thursday, 31 January 2013

Some things ... cannot be learned quickly

There are some things which cannot be learned quickly,
and time, which is all we have,
must be paid heavily for their acquiring.
They are the very simplest things,
and because it takes a man’s life to know them
the little new that each man gets from life
is very costly and the only heritage he has to leave.

- Ernest Hemingway (From A. E. Hotchner, Papa Hemingway, Random House, NY, 1966)

Sunday, 27 January 2013

Elementary particles and quantum geometry

Black holes are formed due to the gravitational collapse of matter - ordinary matter, consisting of the particles and excitations of the Standard Model that we know and love. These include electrons, photons, neutrinos, quarks, mesons etc, and their respective anti-particles. General Relativity tells us that the properties of (macroscopic) black holes are universal, in that they do not depend on the precise fraction of each particle species in the initial "mixture".

A black hole formed from the collapse of a non-rotating cloud of $ n$ electrons and $ n$ positrons will be neutral, non-rotating and of mass $ 2n m_e$, where $ m_e$ is the electron mass. Let us refer to this black hole as $ bh(n,e^-; n,e^+)$ or $ bh_e$ for short. A black hole formed from the collapse of cloud of $ m$ neutrinos and $ m$ anti-neutrinos, where $ m * m_{\nu} = n * m_e$ ($ m_{\nu}$ being the mass of a neutrino). According to our labeling scheme, this black hole will be labeled as $ bh(m,\nu;m,\bar\nu)$ or $ bh_{\nu}$ for short. Both black holes have the same mass $ M = n * m_e = m * m_{\mu} $ and thus the same horizon area $ A = GM/c^2$.

... and so it begins

Welcome to my blog, gentle readers. Here you will be exposed to all manner of speculation and conjecture on my part. Those with an enhanced sensitivity to non-rigorous reasoning might occasionally experience a feeling akin to motion sickness. I urge such rigor-bound passengers to depart at the earliest exit. To the rest, welcome aboard. Happy trails!