Today on arXiv, a paper appeared, modestly titled Some conjectures about the mechanism of poltergeist
Poltergeist accounts concern at least four kinds of strange spontaneous manifestations, such as burning of materials, failures of electric equipments, rapping noises and movements of objects. A simple analysis of phenomenology of these disturbances shows that they might have a common origin, that is, a reduction in strength of molecular bonds due to an enhancement in polarization of vacuum which decreases the actual electron charge. Arguments based on Prigogine’ nonequilibrium thermodynamics are proposed, which show how transformations in brain of some pubescent children or young women might be the cause of these effects.
The article goes on to discuss modifications of the quantum vacuum as allowing objects to catch on fire. Enjoy.
I’ve finally just now figured out how to combine the quark / lepton weak hypercharge and weak isospin quantum numbers with the generation numbers. This should allow the Koide mass formula to be extended to the quarks!
The weak hypercharge and weak isospin quantum numbers for the elementary fermions are:
, with the quantum numbers for the antiparticles with opposite handedness given by the negatives of the above.
The Koide mass formulas for the charged and neutral leptons can be derived from making the assumption that these particles are color neutral composite particles built from three preons that I’ve usually called “snuarks” and they are taken from a set of three mutually unbiased bases for the Pauli algebra.
In the density matrix language, a particle is not represented by a state vector, but instead by a state matrix. A state matrix gives the transition amplitudes for the states that are bound together. The diagonal entries correspond to the amplitude for the propagation of one of the snuarks without change. The off diagonal entries give amplitudes for the various ways a snuark can switch states. Consequently, in the language of quarks and gluons, the off diagonal entries represent the gauge bosons of the theory while the diagonal entries give the valence quarks. Using “r,g,b” as the indices for the matrix, the (r,g) entry gives the amplitude for transitions from G to R; in the quark / gluon language, this would be the action of a R/G gluon.
Is this coming from the future???
Kea kindly pointed out to me that the Perimeter Institute just put on the web a lecture on density matrices and the foundations of quantum mechanics. The lecturer is Christopher Fuchs, and the duration is an hour and a quarter. As a promoter of density matrix theory, I thought I would discuss it here.
The lecture begins with the contribution of the foundations of quantum mechanics to the descent into insanity of John Forbes Nash some 50 years ago. Fuchs shared my view that quantum probabilities are not “non commutative generalizations” of classical probabilities, but his analysis is based on the assumption that quantum states should be written entirely in probability form. In this I disagree.
For those who don’t know what this is about, quantum states are usually represented by “state vectors” which are vectors in a Hilbert space. One can manipulate these state vectors by applying operators to them. That is, an “operator” is a linear transformation that maps the various state vectors to new state vectors. When one operates on a state vector, therefore one gets a new vector. To compute a probability, one takes two vectors and uses the inner product of the Hilbert space to multiply them. This gives a complex number. The probabiliy is the square of the absolute value of that complex number.
WordPress’s management software reports that this blog has steadily increased its readership this year, with each month better than the previous:
Happy New Year to the readers.
My resolution is to be more professional about physics in 2008. And hopefully to retire.
The previous few posts showed how a density matrix formalism gives a variety of quantum mechanics that naturally supports an interpretation of quantum states as symmetry operators on the quantum states. The method for doing this required ignoring the gauge bosons in bound states. For example, beginning with a complicated Feynman diagram for a bound state:
we simplified it by trimming off all the guage bosons and particle / anti-particle pairs created from gauge bosons. What’s left is just the valence fermions. We mark the points where these valence fermions change state with black dots and have:
This sort of thing will really annoy the old folks. It was the method we used to extend Koide’s charged lepton mass formula to the neutrinos. It may have something to do with the triality trick that Garrett Lisi used to fit the standard model particles to E8, and eventually we will return to the subject. But for now, I’d like to discuss the application of these trimmed diagrams as I was originally exposed to them; as a generic method of giving mass to massless particles. But first, a word about the philosophy behind the “new physics.”
In the previous post we showed how we can take the left to right snuark mass interaction, and combine it with the right to left interaction, to make a left to right to left interaction, which we will somewhat abusively call a “LRL propagator”. The reason for calling it a propagator is because we are going to ignore the gauge bosons; they’re pre gravitons and carry very little energy so they don’t matter much anyway. What’s left is fermions going in and fermions going out, just like a propagator. This was a Feynman diagram of order 6. That is, the coupling constant “iq” shows up 6 times.
The LRL propagators came in 4 types, two of which were identical. We wrote them separately for each of the three fermion lines. Each of these lines ended up with a vertex and a complex coupling constant. These complex coupling constants are scalars, so we may as well combine the three of them into a single scalar coupling constant. Putting the LRL propagators back together, the four cases are:
An idempotent is an element of an algebra that is unchanged when it is squared, . In an algebra, the “primitive” idempotents are those that cannot be written as sums of nonzero idempotents. In a sense, these are like primes. In the density matrix formulation of quantum mechanics, the particle states are primitive idempotents.
My aunt, Frances Vick was honored by the Texas Folklore Society this past week in San Antonio, largely for publishing many Texas folklore books over the years.
When I was a boy, an inevitable consequence of tramping around in the East Texas pasture and woods was that one would end up with ticks. Ticks are small blood sucking insects that tend to pick out the most sensitive parts of ones body, stick a barbed thingy in and glue themselves on for a few days. If you have difficult imagining this, perhaps photos and movies will help explain. When one finds a tick on oneself, there is a presecribed series of events that are required to remove them. If one simply grabs them, then the head is left in your skin and it will fester badly.