vegevore - Physics Page 1:
Abstract: From the mass of the lightest neutrino and
the temperature of the Cosmic Microwave Background,
the 'pH' of the vacuum of space-time is derived as the
negative logarithm of the ratio of the Cosmological
Constant (Quintessence) to the Planck density.
Details:
Heisenberg allows us to borrow energy from the vacuum for short times to form particle-antiparticle pairs. What is the density of those pairs at a given time? In other words: What is the 'pH' of the vacuum?
Consider pure water where we know that the pH is 7:
H2O ==> HO- + H+
At room temperature, only 1 in 10 000 000 molecules is ionized (reaction constant is 10-7), calculated as follows:
pH = Erequired / ( Ethermal * ln(10) )
= Eionization / ( k * T * ln(10) )
= 0.415 eV / ( 8.617E-5 eV/K * 298.6 oK * 2.302 )
= 7
Analogously, what fraction of the thermal vacuum is polarized to particle-antiparticle pairs, at the temperature of the Cosmic Microwave Background? For an electron-positron pair:
vacuum ==> e- + e+
pe = Erest mass / ( Ethermal * ln(10) )
= ( 2 * 0.511 MeV ) / ( 8.617E-5 eV/oK * 2.726 oK * 2.302 )
= 1.9E9
which is not a very interesting number. But recent evidence from Super-Kamiokande suggests that there is a lower mass particle, viz., the neutrino, with a mass in the range of 0.03 eV to 0.1 eV.
Consider this then, in particular, a mass of 0.033 eV as the lowest mass massive particle, that this can polarize the vacuum (polarization in the sense of weak charge, not electric charge):
pn = Eneutrinos / ( Ethermal * ln(10) )
= ( 2 * 0.033 eV ) / ( 8.617E-5 eV/oK * 2.726 oK * 2.302 )
= 123.
which is a more interesting number but does it really mean what its value suggests? What it is is the log of the fraction of the vacuum (viz., the Planck energy density) that is polarized; that fraction is the value of the Cosmological Constant. Of course, in reality what we have done is the opposite: we have derived the mass of the lightest neutrino from L, the Cosmological Constant, as inferred from recent data of type Ia Supernovae, i.e., that L is 72% of the critical density, eCrit.
In summary, we have:
L = ePlanck e 2 mn / k T
Addendum: As is readily apparent, this 'Cosmological Constant' in fact varies as a function of temperature: it is a quintessence.
14 VI 2001 Even more recent SN Ia data has confirmed quintessence.
31 XII 2001 Super-K has suffered a massive set-back with accidental destruction of most of it's PMT detectors.
(Discussion)