Fractal time crystals and quantum time crystals: Why Frank’s adventure to advance Winfree failed?

“I am fumbled to an interest in maps among rings, and products of rings….the ring idea constitutes the skeleton, the bare bones….. only one variable the phase, only one observable, the phase…….singularities happen only in models not in the real world”. A Winfree 1977

“Singularity is almost invariably a clue”. Sherlock Holmes

“Information of the universe is not written in the “bing” but in the silence between the “bings””.

We all know about the crystal of matter, however, we all got excited to hear that matter could also form a crystal. Frank took the term “time crystal” in his 2012 PRL paper, used by A Winfree way back in 1977 (The geometry of biological time, Second edition 2003, just after his death in 2002). He even used the same phrase “ring device” taken from Winfree, and used the concept of “tick” (page 79, GBT) to edit this “ring device” to generate spontaneously a new “ring device” or a new clock. When we read the book by Winfree, it appears as if Frank was largely inspired by that book and copied everything therein. Winfree argued that (p 79) if a neuron is kept under a constant bias or kept in a calcium deficient solution, it fires spontaneously and rhythmically (Guttman et al 1979). Thus, spontaneous rhythms are born with a “tick”.

Winfree talked about material crystals that make life, like virus. To him, life is a time cycle and crystals of time cycles or rhythms is a life, every single event of life, like birth and death of a living cell, ovulation, everything is like a ring, it returns to the initial state. Mitosis cycle is considered to be a simple clock (Campbell 1964, GBT) Surprisingly we also believe in that. Nature makes time crystals and the materials take the form so that it can sing the music properly in the most feasible way. Frank wanted to provide a more concrete physical presentation of the Winfree’s work, but failed miserably. Nesting of clocks are more important and Frank did not get it at all from Winfree’s work, because nesting was largely missing. A vivid copy of Winfree’s work is found in Brain Rhythm book by G. Buzsaki, but, he merely tried to establish the very old Winfree’s concept with more examples. Nested rhythms came many times, but, a proper mathematical structure of nesting was never born. Our contribution is exactly there. We took “phase singularity” suggested by Winfree and used that as a generic tool to integrate information and proposed a new information theory which rejects the existing Integrated Information Theory (IIT) proposed by Coch and others.

Say, a pendulum is oscillating periodically, Frank Wilczek will call it a time crystal, because time is fixed like atoms are fixed in a crystal, of course it can have a classical and a quantum version. The similarity between Winfree’s proposal and Frank’s argument is enormous. Winfree talked rigorously about the dynamics in the ring, so did Frank, but Winfree said explicitly that this ring may not be a real ring and he emphasized that repeatedly, while Frank wanted to see it in real system as a pendulum. If the diameter of its time cycle changes i.e. pendulum moves a shorter distance, then, they will call it a spontaneous time symmetry breaking. Now, why the pendulum will change its oscillation diameter, if there is no friction. Spontaneous property of the system, so they call it, spontaneous symmetry breaking (SSB). The point is that changing the diameter of a circle is fine, but when the proposal comes that all materials making the ring or the time cycle need to be frozen in the ground state and at the same time moving, this is utter nonsense. This is like considering that a particle is moving and stopping at the same time. Frank suggested that in superconducting ring put a thrust to the ionic motions and they will rotate in a circular path, then, in the ground state (even after thrust they remain in the ground state, nonsense!) they will change the rotation speed characteristically. So, we can say, that time symmetry is breaking!

If we consider the ring as a cavity resonator, then what happens in a cavity resonator we all know, we will get a fundamental frequency and then its harmonics, obviously, shall we say that in every single cavity resonator in the universe time symmetry is spontaneously broken? No, we cannot say that kind of nonsense, because spontaneous birth of a clock or spontaneous symmetry breaking is driven by a human choice, or free will. We are externally applying a force or an energy, then use of the word “spontaneous” is a crime. This is “induced”. Monroe et al has claimed (ArXiv first experimental evidence of time crystal) that they have experimentally realized time crystal in a superconducting ring, however, by that logic every single guitar string is a time crystal. Because the time profile would look similar and “melting of the crystal”, is a mere imagination

The mistake made by Frank was that he did not consider “phase singularity” suggested by A Winfree. He have gone into extensive details to prove that there truly exists a “phase singularity”, his list is rich in examples, and he himself did several experiments to establish that. Actually, phase singularity concept was introduced by Brady 1975 (p81) Moreover, he came up with several observations which could change the way we topologically represent the rhythms. Phase reset, amplitude reset are two examples that one must take into consideration. He never put these parameters into a mathematical perspective. However, he did suggest that there is a self-similarity in phase integration. Phi = Phi + 1. Change in the amplitude of a rhythm changes the phase of other interconnected rhythms. The grammar of topological treatment of rhythms or time cycles or clocks were never established. Though Winfree suggested the birth of a singularity due to the change in higher phase (page 52, Geometry of biological time), and every point of singularity is a screw axis. Whenever there is a decomposition of “bing” a expansion of the information sphere generates a spiral or helical motion radially outward. Because there is a full rotation of the circle as all system points reset their clock. So, clock reset with external motion is the origin of movement in the time cycle network. This is the origin of helix in nature, if we include Winfree findings (WinFree 1973a) with ours philosophically. This is beautiful to see that every time environment changes something, the effect builds a singularity and that singularity causes all associated clocks to reset and thus, allowing a helical growth. This should be the construction route of a time crystal. It’s mathematics and conceptual provisions are much more profound than Frank’s time crystal.

And we did develop the grammar very extensively, we told that there will be a “bing” at the point of “phase singularity” and these bings, hold geometric information. Winfree’s phase reset study showed that after reset if we plot phase 0 points we get Archimedes spiral. Thus, the development of e, pi and phi with i was inherently evident in Winfree’s analysis. The time crystals if we really want to build, it will be a vortex jelly (page 69, The geometry of time). One could find that this rotation is quantized, thus, quantization is a classical process, as it should be, however, continuously, the new singularities are born and resetting the clocks would happen all over the information network or 3D phase sphere. Of course clock reset is localized, but the domain of localization is redefined every time. Thus, uncertainty and superposition of several ways of resetting the amplitude or clock remain there, giving birth to quantum jelly of time, a true analogue of time

The Winfree’s journey into the concept of black hole and astrophysics leads us to a point (page 69-71, The geometry of time) where we could discuss the correlation between CTC (close time cycle loop and the time crystal). CTC is much closer to what Frank has been arguing ( CTC has a history of nearly a century (1927 van Stockum first made the solution of Einstein’s field equation, which represents a infinitely long cylinder made of rigidly and rapidly rotating dust). It would really have been wonderful of Frank could adopt his time crystal from CTC not from Winfree’s time ring. Because time ring and time crystal of Winfree survives only when we enter inside the singularity and find another world, so it will become a fractal crystal of time neither classical nor quantum as such.

Franck took everything from Winfree but “singularity”, had he taken that, he would not have to get into a blunder of adventures.

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