Book Review: West With the Night, Beryl Markham

West With the Night is the autobiography of Beryl Markham, a pioneering aviator of pre WW2 Africa. This remarkable autobiography dates to 1942 and is so beautifully written that if you know someone who loves flying you should pick them up a copy. As usual, let me introduce the book by a few quotes:
From the time [...]

Berry ( or Pancharatnam-Berry or quantum ) phase.

Classically, if a vector is parallel transported around a closed circuit on a curved space, it returns with its orientation altered. A drawing modified from the one at the a review of Berry’s Geometric Phase on the web page of Nicola Manini (assistant professor at Milan University) shows the classical effect:

In the drawing above, when [...]

Test post. Ignore.

Is this coming from the future???

Koide formulas and Qubit / Qutrit MUBs

Recently we’ve been discussing Mutually Unbiased Bases or MUBs on this blog. This has not been for any particular interest in pure mathematics, but instead in their application to a preon theory of the elementary particles, and the E8 quantum numbers. The relationship is rather long and difficult to explain. All the major pieces are [...]

Jay Yablon on Tensors and Symmetry

My approach to elementary particles is to try to build them up from a Clifford algebra assumed to have something to do with spacetime. This is inherently geometric, but it is not the only way to do geometry. A similarity is that both of us end up relating the three spatial dimensions to color. (Forgive [...]

MUBs, Preons, and Lisi’s E8 model

If a Hilbert space is d-dimensional, we expect that the number of elementary particles we can describe with it is d. For example, a Pauli spinor is 2-dimensional and electrons come in two states, spin-up and spin-down. The Dirac spinors are 4-dimensional and the related theory describes electrons plus their antiparticles, and therefore 4 states.
So [...]

Love = Negative Energy

Perhaps due to a lack of details regarding his or their martyrdom, the Catholic Church pulled Saint Valentine from its liturgical veneration in 1969. Since that time, the holiday has expanded world-wide to areas that have never heard of early Roman martyrs. What a descent. From ecstatic religious devotion to a crude worshipping at the [...]

MUBs and Symmetry Breaking

One can obtain a Hilbert space from a wide variety of physical situations. Suppose we are to use a Hilbert space to model elementary particles, for instance. One the one hand, we’d like to have our model cover as many particles as possible. But to do this, we may have to assume a symmetry that [...]

Qutrit Mutually Unbiased Bases (MUBs)

Mutually Unbiased Bases are sets of bases for a Hilbert space that are “unbiased:” the transition probabilities between any two states from different bases are equal. For a Hilbert space of dimension 3 (i.e. qutrits), the transition probability is 1/3. The operator space of a Hilbert space of dimension n is n^2, in this case [...]

The Generalized Pauli Group

I’ve been watching Perimeter Institute lectures again, and one that dips into the stuff I’m working came up. In addition to the lecture, there is an acrobat file that contains the slides and photos of the blackboard. This is 124 pages long and it is these pages that I will reference.
Applications of the generalized Pauli [...]

Contemporaneity and Density Matrices

I’m continuing to watch the Perimeter Institute lectures and watching the latest one, Dynamic Time: The “Missing Link” in the Search for a Unified Theory? by Avshalom Elitzur, has influenced me to type up my version of the ontology of quantum mechanics.
As Elitzur states, the central conundrum is to ask the question, “what is the [...]

Fundamental Bohmian Density Matrices

I’ve been listening to Perimeter Institute lectures and came upon one by Roderich Tumulka that was interesting enough that I looked up his papers. They are voluminous. One that applies more or less directly to the area I play in is this one: On the Role of Density Matrices in Bohmian Mechanics quant-ph/0311127, by Detlef [...]