Wednesday, June 25, 2014

Stray Physics Musings

* In the simple Platonic ideal, a black hole is a singularity from which not even light can escape.  In other words, photons can't cross the event horizon.  In this ideal, whether or not the matter and energy sucked up by a black hole had a net electric charge, the electric and magnetic fields generated by particles with electric charge would not escape the black hole because the photons that give rise to those fields would be trapped behind the event horizon.

Now, we know empirically, there is a strong magnetic field in the vicinity of Sagittarius A*,  the black hole at the center of the Milky Way.  The only way this could be possible in the Platonic ideal of a black hole is if the magnetic field is generated by the movement of charged particles just outside the event horizon as they are pulled toward the black hole.

Now, in an ad hoc blend of General Relativity reasoning and quantum mechanics reasoning, have concluded that black holes are leaky, and rather than preventing anything from escaping at all, actually emit Hawking radiation.  But, it doesn't necessarily follow that Hawking radiation is large contributor to the magnetic field around black holes that are observed.

* In principle, mesons and baryons have an infinite number of excited, higher energy states with higher masses than the ordinary versions of these hadrons.  It appears, in contrast, the fundamental fermions come in exactly three generations, rather than an infinite number, which means that an intuitive sense of higher generation fundamental fermions as excitations in the same sense as excited states of hadrons is probably flawed - unless the same process is at work but there is some competing factor that places an upper bound on the amount of excitation that a fundamental fermon can have, but not on a hadron (at least at the energy scales we can observe - one could image that there is exactly some fundamental number of excited states much greater than three that are possible for any given hadron at energies to high to observe).

Many factors argue in favor of exactly three generations with current experimental evidence.  There are direct lower limits on the possible mass of each of the four possible kinds of fourth generation fundamental fermions.  There are also strong theoretical considerations that require each generation to have a complete set of four fundamental fermions.

In ratio of limit to mass of third generation fermion, the bound is greatest in the case of the neutrinos.  The practical upper bound on the mass of the heaviest Standard Model neutrino rest mass eigenstate is on the order of 0.1 eV/c^2.  The lower bound on the mass of a fourth generation neutrino is about 45,000,000,000 eV/c^2.  The ratio of the two masses is 450,000,000,000 to 1.  This is profoundly greater than any of the ratios of masses between a particle of one generation and a particle of the next generation among the three generations of four kinds of Standard Model fermions.

* The Higgs field couples to the rest mass of massive Standard Model particles.  But, unlike gravity, it does not couple to mass arising from gluon fields in hadrons, to gluons, to photons, to kinetic energy, to angular momentum, to pressure, or any other quantity besides rest mass that gravity impacts in General Relativity.  Yet, since General Relativity describes gravity, and the gravitational effects of rest mass swamp all other sources of gravity in most circumstances, General Relativity must have some fairly deep relationships to the Higgs field.  But, the Higgs vacuum expectation value has no seeming correspondence to the cosmological constant aka dark energy.

* The most definitive evidence we have for dark matter comes from comparing the behavior of objects observed by astronomers with the behavior we would expect if only General Relativity applied.  I strongly suspect that this kind of evidence will be the most powerful means of ultimately discriminating between potential models explaining the mechanism of these effects.

For example, we are very near to having a detailed precision map of the shape of the Milky Way dark matter halo that is inferred from a clever method of exploiting the movement of a handful of very special stars which when measured precisely reveal this information in an elaborate variant on triangulation.  Increasingly precise measurements of the shape and size of the Milky Way's dark matter halo already permit quite precise estimates of the matter density of dark matter in the vicinity of our sun, which fixes on key parameter in direct dark matter detection experiments.  Knowing this from direct halo observations eliminates the model dependence of dark matter detection experiments that merely assume a theoretically estimated dark matter density in our vicinity.  Only the mass of individual dark matter particles and their cross section of interaction remain to be determined.

Current methods have come up empty in the GeV mass vicinity down to very low cross sections of interaction, and to move to lower mass candidates need to better distinguish and characterize neutrino and cosmic ray backgrounds, although good progress is being made on these fronts.  Of course, all is for naught if dark matter is genuinely collisionless, at least with matter other than other dark matter.

Accelerator experiments like the LHC also narrow the dark matter particle parameter space.  These experiments have likewise come up empty.  This strongly disfavors dark matter that interacts via any of the three Standard Model forces, again suggesting that it may be effectively collisionless if it is fermionic (the leading theory) except for Fermi contact forces (since fermions can't occupy the same space at the same time), and any dark matter specific interactions.  The lack of Standard Model forces or particles, or General Relativistic equation terms to explain dark matter is really frustrating.  We are missing something huge and we don't know why.

There are some hints at dark matter annihilation, but these are very model dependent and assume we know about all possible sources of cosmic ray signals when we don't.

Computer models that show what the universe would look like given various dark matter properties are also making great strides as greater computational power becomes available.

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