The Nature of Consciousness

Piero Scaruffi

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These are excerpts and elaborations from my book "The Nature of Consciousness"

Of Symmetry and Asymmetry: Parity

The German physicist Otto Laporte first classified the wavefunctions as either even or odd, according to their symmetry and t discovered what appeared to be a principle of conservation of parity ("The structure of the iron spectrum", 1924): at the end of an atomic interaction the total parity of the involved wavefunctions is zero. If one of the involved wavefunctions switched from odd to even, then another one must have switched in the other direction. The Hungarian physicist Eugene Wigner showed that Laporte's rule was a consequence of the mirror image symmetry of the Schroedinger equation ("Some consequences of Schroedinger's theory for the term structures", 1927) and generalized the law of conservation to nuclear interactions. It felt reasonable to believe that the mirror image of a physical process should be identical in every way to the original one. Throughout the years there emerged doubts about the conservation of parity peaking with the work of Chinese-born physicists Chen Ning Yang and Tsung-Dao Lee ("Question of Parity Conservation in Weak Interactions", 1956) that led to the experimental confirmation by Chien-Shiung Wu.

Of Symmetry and Asymmetry: Gauge Theory

When James Maxwell turned electricity and magnetism into "field theories", he changed our perception of nature: not a set of observable particles that interact by touching each other, but a landscape of invisible fields that potentially extend to infinite. Energy, in particular, resides in the field: not only in the electrified and magnetic bodies but also in the space surrounding them. One fact that became apparent is that the same reality (in terms of quantities that we measure such as speed and electrical charge) can be implemented by different fields. A "gauge" transformation is any function that turns one field into another field whose observable quantities are the same, and the phenomenon is called "gauge invariance" or "gauge symmetry". If you can add a constant to one of the variables describing the field, and nothing changes in the quantities that you measure, then you are in the presence of gauge invariance. The concept of the gauge field was introduced by the German mathematician Hermann Weyl ("Gravitation and Electricity", 1918) while trying (unsuccessfully) to unify gravitation and electromagnetism. A decade later he succeeded in showing that Maxwell's theory in quantum mechanics is invariant (or "symmetric") under a gauge transformation ("Electron and Gravitation", 1929). He realized that one could derive Maxwell's electromagnetism purely from his old gauge principle. Gauge invariance constitutes a symmetry principle and that principle yields Maxwell's electromagnetism. (Incidentally, Weyl's "two-component spinor formalism" introduced in the same paper led him to foresee that conservation of parity, just formulated in 1924 by Otto Laporte, could be violated). Gauge fields were not used until Chen Ning Yang and Robert Mills ("Conservation of Isotopic Spin and Isotopic Gauge Invariance", 1954) generalized Weyl's electromagnetic gauge principle to the case of non-Abelian algebra, a particular case of Lie algebra, which eventually led to the unification of three of the fundamental forces. As Freeman Dyson wrote ("Unfashionable pursuits", 1983): "Quantum chromodynamics. is conceptually little more than a synthesis of Lie's group-algebras with Weyl's gauge fields." Weyl himself had shown the fundamental role played by Lie algebra in quantum mechanics ("Quantum Mechanics and Group Theory", 1927). The success of the Yang-Mills gauge theory led to the assumption that all fundamental forces are direct consequences of the properties of gauge symmetries.

Unification: In Search of Symmetry

Since the electric charge also varies with flavor, it can be considered a flavor force as well. Along these lines, Steven Weinberg  and Abdus Salam  (“A Model of Leptons”, 1967) unified the weak and the electromagnetic forces into one flavor force, and discovered a third flavor force, mediated by the Z quanta. The unified flavor force therefore admits four quanta: the photon, the W- boson, the W+ boson and the Z boson. These quanta behave like the duals of gluons: they are sensitive to flavor, not to color. All quanta are described by the so called "Yang-Mills field", which is a generalization of the Maxwell field (Maxwell's theory becomes a particular case of Quantum Flavor Dynamics: "Quantum Electrodynamics"). Note that the equations of the Yang-Mills field were discovered by Chen Ning Yang and Robert Mills way before anyone even conceived of gluons ("Conservation of Isotopic Spin and Isotopic Gauge Invariance”, 1954). They were just a mathematical generalization: Maxwell’s equations assume that there is only one kind of charge (the electric one), whereas the Yang-Mills equations allow for many.

The symmetry of the electroweak force (whereby the photon and the bosons get transformed among themselves) is not exact as in the case of Relativity (where time and space coordinates transform each other): the photon is mass-less, whereas bosons have mass. Only at extremely high temperatures the symmetry is exact. At lower temperatures a spontaneous breakdown of symmetry occurs.

This seems to be a general caprice of nature. At different temperatures symmetry breaks down: ferromagnetism, isotropic liquids, the electroweak force... A change in temperature can create new properties for matter: it creates magnetism for metals, it creates orientation for a crystal, it creates masses for bosons.

The fundamental forces exhibit striking similarities when their bosons are mass-less.  The three families of particles, in particular, acquire identical properties. This led scientists to believe that the “natural” way of being for bosons in a remote past was mass-less. How did they acquire the mass we observe today in our world? And why do they all have different masses? The Higgs mechanism gives fermions and bosons a mass.  Naturally it requires bosons of its own, the Higgs bosons (particles of spin 0).

Each interaction exhibits a form of symmetry, but unfortunately they are all different, as exemplified by the fact that quarks cannot turn into leptons. In the case of the weak force, particles (e.g., the electron and its neutrino) can be interchanged, while leaving the overall equations unchanged, according to a transformation called SU(2), meaning that one particle can be exchanged for another one. For the strong force (i.e., the quarks) the symmetrical transformation is SU(3), meaning that three particles can be shuffled around. For the electromagnetic force, it is U(1), meaning that only the electrical and magnetic component of the field can be exchanged for each other. Any attempt to find a symmetry of a higher order results into the creation of new particles. SU(5), for example (proposed by Howard Georgi and Sheldon Glashow in 1974), entails the existence of 24 bosons... but it does allow quarks and leptons to mutate into each other (five at the time), albeit at terribly high temperatures.

 


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