Quantum flute

Quantum flute

It is amazing how fast experimental discoveries, which look mysterious in the standard physics framework but are readily explainable in the TGD framework, are emerging recently.

Now University of Chicago physicists have invented a “quantum flute” that, like the Pied Piper, can coerce photons to move together in a way that’s never been seen before. The discovery is described in Physical Review Letters and Nature Physics (see this and this).

The system, devised in the lab of Assoc. Prof. Schuster, consists of a long cavity made in a single block of metal, designed to trap photons at microwave frequencies. The cavity is made by drilling offset holes like holes in a flute. One can send one or more wavelengths to the “flute” and each wavelength creates a note coding for quantum information. The interactions of notes are then controlled by a superconducting electrical circuit.

The real surprise was the interaction of photons. In quantum electrodynamics (QED) the interaction of photons is extremely weak. When photons achieve critical total energy, the situation changes dramatically. One can say that photons interact, not pairwise as usually, but all at the same time. Photon state behave like a Bose-Einstein condensate of bound state.

Galois confinement as a universal mechanism for the formation of bound states

TGD involves M⁸-H duality in an essential manner. M⁸-H duality relates differential geometric and number theoretic descriptions of quantum physics and is analogous to Langlands duality. Number theoretical vision, involving classical number fields, extensions of rationals, and extensions of p-adic number fields induced by them, is essential for understanding the physical correlates of cognition (see this) but has led to a breakthrough in the understanding of also ordinary physics (see this and this).

1. The number theoretic side of the M⁸-H duality predicts Galois confinement as a universal mechanism for the formation of bound states from the dark variants of ordinary particles characterized by effective Planck constant h_eff=nh₀≥h: integer n has interpretation as the dimension of extension of rationals induced by a polynomial and serves as a measure of algebraic complexity defining evolutionary level and a kind of IQ for the system.
2. Galois confinement states that physical bound states are Galois singlets transforming trivially under the Galois group of a polynomial P determining space-time region if M⁸-H duality holds true. There is (more than) an analogy with hadrons, which are color singlets. Galois confinement is central in TGD inspired quantum biology and also allows us to understand various nanoscopic and macroscopic quantum phenomena of condensed matter physics.

For instance, Cooper pairs would represent on a lowest level in a hierarchy and there is evidence for 4-fermion analogs of Cooper pairs (see this).

In particular, N photons can form bound states in which they behave like a single particle. This bound state is a more general state than Bose-Einstein condensate since photons need not have identical quantum numbers. These many-photon states described in the article could be states of this kind. These N-photon states are very similar to the dark 3N- photon states proposed to represent genes consisting of N codons with codon represented as dark photon triplet.

Galois confinement and statistics

Even the quantum entangled 2-photon states emitted in some decays of atoms could be Galois confined bound states and entanglement in general could correspond to Galois confinement. This would solve a (I do not now how well-known) problem related to statistics.

1. If the symmetry of the 2-photon state | 1> | -1>+| -1> | 1> created in decay of atom is symmetric due to statistics as physical photon exchange, one cannot measure the spin of the other photon since the outcome | 1> | -1> or | -1> | 1> violates statistics as a symmetry under exchange of particles!
2. The solution of the problem is quantum field theoretic realization of statistics, which only says that creation operators for photons commute and can be changed, not the photons. Exchange symmetry for photons is a stronger symmetry and true only for bound states (see this). The correlate for the bound state property at the level of H=M⁴× CP₂ would be the presence of the flux tube pair connecting photons and splitting in quantum measurement by reconnection to a pair of U-shaped flux tubes.
3. The same applies to Slater determinants for fermions assumed in atomic and molecular physics. The Slater determinants are completely antisymmetric and this antisymmetry is assumed to hold true for bound states such as atoms and molecules. Indeed, one cannot measure the states of, say, electrons of an atom without destroying the atom.
4. The exchange symmetry of particles instead of creation operators can be true only for bound states, since otherwise quantum measurement of elementary particle states would not be possible. This assumption saves also from the strange conclusion that the particles in my body are possessed by all systems of the Universe (see this).
5. Galois singletness could be a universal mechanism for the formation of bound states consisting at the fundamental level of dark quarks with momenta having components which are algebraic integers in an extension of rationals determined by some polynomial P.
6. A natural question is whether Galois singletness, instead of the singletness with respect to the permutation group, might define a number theoretic generalization of the strong exchange symmetry of bound states in TGD. Note that the maximal Galois group for a polynomial of order n is S_n.

A couple of remarks are in order.

1. In TGD, the QFT realization of exchange symmetry holds true. The fermionic oscillator operators are associated with the spinor harmonics quark spinors in H=M⁴× CP₂. And due the flatness of M⁴ there are no problems encountered in general relativity related to the definition of positive and negative energies.
2. Simple Galois groups having no normal subgroups are physically very special and correspond to prime factors in the maximal functional decomposition of a polynomial in terms of lower degree polynomials (see this). Number theoretical vision is essential for understanding the physical correlates of cognition and this leads to a vision about cognitive measurement cascades decomposing irrep of Galois group to a product of irreps of its factors (see this).

See the article TGD and condensed matter or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

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