QUANTUM GEOMETRY

Time Portal: A Glimpse of the Future

Alternate view:

It would not greatly surprise me if the Higgs boson is never found. It may (a) not exist; or, (b) exist, but be something like a concerted specific interaction of three photons in different dimensions. In the latter case would it ever be recognizable as something other than “photons” ? The Higgs mechanism may be needed to explain the origin of mass, but does the Higgs mechanism require a Higgs particle? Probably not. Suppose, for instance, that the Higgs mechanism involves, rather than a particle, an operator, which alone, through its functioning, results in the scalar Higgs field. This view will be addressed in more detail in future posts.

Conventional view:  

In particle physics, the Higgs mechanism is the process that gives mass to elementary particles. The particles gain mass by interacting with the Higgs field that permeates all space. More precisely, the Higgs mechanism endows gauge bosons in a gauge theory with mass through absorption of Nambu–Goldstone bosons arising in spontaneous symmetry breaking.

In the standard model, the phrase “Higgs mechanism” refers specifically to the generation of masses for the W^±, and Z weak gauge bosons through electroweak symmetry breaking. Although the evidence for the electroweak Higgs mechanism is overwhelming, experiments have yet to discover the single Higgs boson predicted by the standard model. The Large Hadron Collider at CERN is currently searching for Higgs bosons, and attempting to understand the electroweak Higgs mechanism.

The Higgs mechanism was incorporated into modern particle physics by Steven Weinberg and Abdus Salam, and is an essential part of the standard model. 

[en.wikipedia.org/wiki/Higgs_mechanism]

Many thanks to Sven Sauer for his wonderful fantasy landscape above. More on the artist and his work can be found here»

Philosopher in Meditation

After my resounding failure to create a true maximal mandala of the hexagrams in two dimensions I concluded it was time to move on to three. My dalliance with a spherical approach has already been referenced. Clearly I needed a handle of some sort that I could grasp with my mind and that would successfully carry the endeavor into the third dimension.

I eventually came up not with one but two: the kinship system of the nuclear family described in the I Ching and the coordinate system of René Descartes. Strange bedfellows that these may seem, they strangely lead to the same result. Just an accident of circumstance or is there a significant hidden meaning here? We shall soon enough see. I opt for the latter, but then I am privy to the outcome, aren’t I.

There is, of course, that famous Shakespeare quote from The Tempest, “… misery acquaints a man with strange bedfellows.” But more appropriate here I think is what Shakespeare has Polonius say in Hamlet, “Though this be madness, yet there is method in’t.” Then, too, there is that challenging coincidence(?) of the common usage of the term/concept “hexagram” by both the I Ching and group theory.

Art credit: Philosopher in Meditation, the traditional title of an oil painting in the Musée du Louvre, Paris, that has long been attributed to the 17th-century Dutch artist Rembrandt.

Dimension in Antiquity

Did the ancients view the world in terms of dimension? If they did, was it a three-dimensional world they saw as we do or was it a different kind of world, one unknown to us? I think long before Descartes codified our view of dimension in his analytic geometry, humankind was thinking in terms of dimension, but my guess is, in a way quite different than we moderns do. 

Before the invention of writing there was little or no impetus to see the world linearly or in terms of two dimensions. Cave art even was of greater dimension than two because the “canvas” was not flat, the stone walls of the cave having natural undulations.

Yet for the ancients time must have been at least as important a dimension as any space dimension. They would have been acutely aware of the seasons, the moon phases, the cycle of day and night, the cycle of birth and death. They surely knew of both cyclic and sequent change. They were thinking about spacetime long before Minkowski and Einstein. 

Space would have also been viewed in very concrete terms - - - not as length, breadth and height, but as “the way to the river,” “the place where hunting is good,” “where our friends are located, where our enemies.” These natural forms of “measurement” would have had both distance and direction components. The distance component would likely have been thought of largely in terms of time and practicality - - - e.g., “how long to reach the destination,” “how much water and food to bring along.”

Ultimately, I think dimension would have been “understood” as any one or combination of a myriad of concrete reference parameters. Where particle physicists conceive of quantum numbers as dimensions alongside the dimensions of space and time and modern mathematicians think of dimension in abstract terms as infinite-dimensional function spaces whose vectors are functions, the ancients did something quite analogous, only in concrete rather than abstract terms. 

A few words about dimension

In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it (for example, the point at 5 on a number line). A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it (for example, to locate a point on the surface of a sphere you need both its latitude and its longitude). The inside of a cube, a cylinder or a sphere is three-dimensional because three co-ordinates are needed to locate a point within these spaces.

In physical terms, dimension refers to the constituent structure of all space (cf. volume) and its position in time (perceived as a scalar dimension along the t-axis), as well as the spatial constitution of objects within – structures that have correlations with both particle and field conceptions, interact according to relative properties of mass, and which are fundamentally mathematical in description. These or other axes may be referenced to uniquely identify a point or structure in its attitude and relationship to other objects and occurrences. Physical theories that incorporate time, such as general relativity, are said to work in 4-dimensional “spacetime”, (defined as a Minkowski space). Modern theories tend to be “higher-dimensional” including quantum field and string theories. The state-space of quantum mechanics is an infinite-dimensional function space.

The concept of dimension is not restricted to physical objects. High-dimensional spaces occur in mathematics and the sciences for many reasons, frequently as configuration spaces such as in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space we live in.

[en.wikipedia.org/wiki/Dimension]

The Direct Route

If only I’d thought of using intersecting spheres instead of intersecting circles for the mandala I would have had the most direct route to cracking the code and I could have accomplished this in the mid to late 60s instead of the late 70s to early 80s. But this was not to be. Well, actually the thought did occur to me briefly - - - sort of like, “I really ought to try this approach with spheres,” - - - but visualizing the mandala in 3 dimensions this way was for me an insurmountable hurdle at the time (and, to be honest, still is to this day.) Remember, this was before the days of the personal computer, and drawing the figure on paper, if even possible, seemed much too cumbersome and daunting a task. Truth be told though, intersecting spheres could have led to a valid result.

Crop Circle showing a variation of the Flower of Life

Photo Credit: Lucy Pringle

This space reserved for a future entry if needed.