I have recently been reproached, by colleagues who are members of the competing ATLAS experiment, of misusing the word "see" in this blog, in the context of searches for physics signals. That was because I reported that CMS recently produced a very nice result where we measure the rate of H->bb decays in events where the Higgs boson recoils against a energetic jet; that signal is not statistically significant, so they could argue that CMS did not "see" anything, as I wrote in the blog title. 
The complex phase of a quaternion becomes apparent when a (complex) plane is put through its real axis and its imaginary part. In multiplication, quaternions do not commute. Thus, in general a b / a b.

The Hilbert Book Model contains a base model that is constructed from a quaternionic infinite dimensional separable Hilbert space and its unique non-separable companion that embeds its separable partner. The quaternionic number system exists in many versions that differ in the way that they are ordered. Cartesian and polar coordinate systems can define these orderings and let these versions act as parameter spaces. These parameter spaces can be represented by eigenspaces of special reference operators that reside in the separable Hilbert space. The operators connect the countable eigenvalues with an orthonormal base of eigenvectors. This procedure only applies the rational members of the number system.

With respect to the visual perception, the human optic tract closely resembles the visual tract of all vertebrates.

The Hilbert Book Model impersonates a creator (HBM). At the instant of the creation, the HBM stores all dynamic geometric data of his creatures in a read-only repository that consists of a combination of an infinite dimensional separable quaternionic Hilbert space and its unique non-separable companion that embeds its separable partner. The storage applies quaternionic eigenvalues of operators.

Quantum entanglement is a well observed but not well understood phenomena.  The frontier in this area has been to entangle systems at greater and greater distances.  Theoretically however it is poorly understood.  Susskind and Maldacena proposed the ER=EPR conjecture, which to oversimplify, states that entangled particles are connected by tiny wormholes(Maldacena and Susskind)  In this brief blog post I present a simple proof that the “non-locality” that experimentalist write of, and Susskind conjectured about solving via wormholes, can be explained with standard quantum mechanics and standard relativity.   What is new here is how we look at the spaces involved.


The base model of the Hilbert Book Model consists of an infinite dimensional separable Hilbert space and it's unique non-separable companion Hilbert space that embeds its separable companion. The version of the quaternionic number system that specifies the values of the inner product of these Hilbert spaces also defines the background parameter space of the base model. The rational values of this background parameter space form the eigenspace of a special reference operator that resides in the separable Hilbert space, and the full background parameter space is the continuum eigenspace of the companion reference operator in the non-separable Hilbert space.

The Hilbert Book Test Model is a purely mathematical model of the lower levels of the structure of physical reality. Its base consists of an infinite dimensional separable Hilbert space and its unique non-separable companion Hilbert space. Both Hilbert spaces use members of a version of the quaternionic number system to deliver the values of their inner products.

Since more than two centuries physics knows two categories of super-tiny objects that instruments cannot observe separately, but that obviously occur in huge quantities. If these super-tiny objects form coherent sets, then these sets constitute the objects that we currently consider as fundamental to quantum physics.

A new analysis by the ATLAS collaboration, based of the data collected in 13 TeV proton-proton collisions delivered by the LHC in 2016, finds an excess of X-->4 lepton events at a mass of 240 GeV, with a local significance of 3.6 standard deviations. The search, which targeted objects of similar phenomenology to the 125 GeV Higgs boson discovered in 2012, is published in ATLAS CONF-2017-058. Besides the 240 GeV excess, another one at 700 GeV is found, with the same statistical significance.