# Tau Function Squared

## Tuesday, November 17, 2015

### Anyons from M-theory

For many years I espoused the idea of "anyons in the microtubule", formed from (hypothetical) delocalized electrons subjected to the magnetic field of the action potential. Privately I also had notions of these electrons somehow condensing into a "brane" wrapping around the cylinder... Now Cumrun Vafa shows how it's done.

## Monday, August 24, 2015

### Nuclear bioqubits

It's a-priori outlandish - and I still prefer electrons in the microtubule - but good enough to blog: phosphorus nuclei as the qubits of the quantum brain. Just like Australia's quantum computer!

## Friday, January 17, 2014

### Orch OR latest

I see Hameroff and Penrose have a major new article about their theory that conscious states are quantum states in microtubules, and that the dynamics of conscious states is due to "orchestrated objective reduction"; and there are a number of commentary articles too. I will make my own comment, just as soon as I can read it all.

## Wednesday, March 20, 2013

### Deligne's prize

The eminent mathematician Pierre Deligne just won the Abel Prize. He first won fame for proving the last of the Weil conjectures, which in turn implied the truth of a conjecture by Ramanujan concerning his tau function. The tau function has a special relationship to 24-dimensional spaces that makes it a frequent ingredient in the probability-amplitude formulae of string theory. But much of string theory descends from M-theory, in which the one-dimensional string is revealed to be a two-dimensional "M2-brane".

Although strings and branes live in high-dimensional spaces, one often concerns oneself with the interior of these objects - one-dimensional for strings, two-dimensional for M2-branes - and describes their interior physics using a similarly low-dimensional field theory.

Now, note that the microtubule has a one-dimensional approximation (as a line) and a two-dimensional approximation (as a cylinder). The propagation of certain degrees of freedom within the shell of the microtubule may therefore have an approximate description in terms of a one- or two-dimensional field theory.

Back in the mid-1990s, Nanopoulos et al proposed to describe microtubules in a one-dimensional approximation (neglecting the radial dimension of the cylinder) using a string worldsheet theory. To my knowledge, no-one ever proposed a holographic uplift of this approximation to a brane worldvolume theory - but this is unsurprising given that the worldvolume theory of the M2-brane wasn't even discovered until the next decade.

Also in the 2000s, it became a common thing to apply string theory, via the AdS/CFT duality, to condensed matter physics; the string models are not exact descriptions of their microscopic physics, but rather offer a model, computationally tractable thanks to the duality, of the quantum-thermodynamic class to which the system of interest belongs.

It would certainly be interesting if, say, a holographic uplift of Weil cohomology played a role in describing the quantum fluctuations of the microtubule according to an effective brane theory. I can even imagine the Ramanujan tau function playing a specific role, as the building block of a fudge factor which gives this effective theory the nice properties (like conformality) of a genuine M-theoretic model, thereby making the physics calculable...

Although strings and branes live in high-dimensional spaces, one often concerns oneself with the interior of these objects - one-dimensional for strings, two-dimensional for M2-branes - and describes their interior physics using a similarly low-dimensional field theory.

Now, note that the microtubule has a one-dimensional approximation (as a line) and a two-dimensional approximation (as a cylinder). The propagation of certain degrees of freedom within the shell of the microtubule may therefore have an approximate description in terms of a one- or two-dimensional field theory.

Back in the mid-1990s, Nanopoulos et al proposed to describe microtubules in a one-dimensional approximation (neglecting the radial dimension of the cylinder) using a string worldsheet theory. To my knowledge, no-one ever proposed a holographic uplift of this approximation to a brane worldvolume theory - but this is unsurprising given that the worldvolume theory of the M2-brane wasn't even discovered until the next decade.

Also in the 2000s, it became a common thing to apply string theory, via the AdS/CFT duality, to condensed matter physics; the string models are not exact descriptions of their microscopic physics, but rather offer a model, computationally tractable thanks to the duality, of the quantum-thermodynamic class to which the system of interest belongs.

It would certainly be interesting if, say, a holographic uplift of Weil cohomology played a role in describing the quantum fluctuations of the microtubule according to an effective brane theory. I can even imagine the Ramanujan tau function playing a specific role, as the building block of a fudge factor which gives this effective theory the nice properties (like conformality) of a genuine M-theoretic model, thereby making the physics calculable...

## Friday, January 11, 2013

### Phonon antennae

One of the problems for quantum biology - if you are looking for quantum coherence at the scale of tissues, and not just within a single macromolecule - is, how is quantum coherence created and sustained at those scales? There seem to be two options regarding the mode of interaction: photons and phonons. That is, electromagnetism, and quantized mechanical vibration.

In this regard, the concept of a "phonon antenna", introduced by the quantum biology group at Ulm, looks important - as a type of physical structure that would be an important causal nexus in phonon-induced mesoscopic quantum coherence.

In this regard, the concept of a "phonon antenna", introduced by the quantum biology group at Ulm, looks important - as a type of physical structure that would be an important causal nexus in phonon-induced mesoscopic quantum coherence.

## Saturday, September 22, 2012

### Australian quantum computing

We take a break from biology to bring you the Australian single-atom qubit.

By my understanding, the Australian effort to create a solid-state quantum computer (by doping a silicon chip with addressable phosphorus atoms), which is ten years old, had foundered in recent years; but the enterprise was saved and revived by Michelle Simmons. It's now her job to make sure the world isn't overrun by unfriendly Australian quantum AI. Good luck, Professor Simmons!

By my understanding, the Australian effort to create a solid-state quantum computer (by doping a silicon chip with addressable phosphorus atoms), which is ten years old, had foundered in recent years; but the enterprise was saved and revived by Michelle Simmons. It's now her job to make sure the world isn't overrun by unfriendly Australian quantum AI. Good luck, Professor Simmons!

## Monday, September 3, 2012

### Spin chains as the conceptual bridge

There is a different sort of tau function which appears in the theory of integrable systems, and it may be more appropriate for what I have in mind. Thus we have, on the one hand, "Classical tau-function for quantum spin chains", and on the other hand, "Pseudo-spin model for the cytoskeletal microtubule surface".

(Also see: "A spin chain primer".)

(Also see: "A spin chain primer".)

Subscribe to:
Posts (Atom)