Posner qubits: spin dynamics of entangled Ca ₉ (PO ₄ ) ₆ molecules and their role in neural processing

Abstract

<jats:p> It has been suggested that <jats:sup>31</jats:sup> P nuclear spins in Ca <jats:sub>9</jats:sub> (PO <jats:sub>4</jats:sub> ) <jats:sub>6</jats:sub> molecules could form the basis of a quantum mechanism for neural processing in the brain. A fundamental requirement of this proposal is that spins in different Ca <jats:sub>9</jats:sub> (PO <jats:sub>4</jats:sub> ) <jats:sub>6</jats:sub> molecules can become entangled and remain so for periods (estimated at many hours) that hugely exceed typical <jats:sup>31</jats:sup> P spin relaxation times. Here, we consider the coherent and incoherent spin dynamics of Ca <jats:sub>9</jats:sub> (PO <jats:sub>4</jats:sub> ) <jats:sub>6</jats:sub> arising from dipolar and scalar spin-spin interactions and derive an upper bound of 37 min on the entanglement lifetime under idealized physiological conditions. We argue that the spin relaxation in Ca <jats:sub>9</jats:sub> (PO <jats:sub>4</jats:sub> ) <jats:sub>6</jats:sub> is likely to be much faster than this estimate. </jats:p>

Quantum effects in the brain: A review

“…The hypothesis is this: that phosphorus nuclear spin might function as a neural qubit to allow for quantum processing to play a role in cognition [84][85][86] 198,201 . However, they argue that these extended times are partly due to experimental control of the coherent spin dynamics, a condition that Fisher does not take into account 198 . In their analysis of Posner spin dynamics they take a number of other factors into account such as dipolar and scalar couplings within Posner molecules as well as the Zeeman interaction of the phosphorus spins with the geomagnetic field 198 .…”

“…However, they argue that these extended times are partly due to experimental control of the coherent spin dynamics, a condition that Fisher does not take into account 198 . In their analysis of Posner spin dynamics they take a number of other factors into account such as dipolar and scalar couplings within Posner molecules as well as the Zeeman interaction of the phosphorus spins with the geomagnetic field 198 . With these as the dominant relaxation pathway they arrive at a relaxation time of 37 minutes, as opposed to Fisher's shortest estimation of approximately a day.…”

“…He identifies a possible molecule as the Posner molecule 197 , thought to be involved in the formation of hydroxyapatite, an important constituent of bone tissue[198][199][200] . A Posner molecule is, simplistically, a distorted cube with a calcium ion at each vertice, a ninth at the centre and a phosphate ion on each of the six faces of the cube198 . The entangled phosphate spins then result in entangled Posner molecules 84 .Fisher estimates that for phosphorus spins in Posner molecules coherence times could be as long as hours84 or, in a later paper, 21 days 85 .…”

The Dynamical Ensemble of the Posner Molecule is not Symmetric

“…[4][5][6][7] More recently, it has been proposed that the 31 P nuclear spins within PMs can exhibit long-lived entanglement, and that this could play an important role in nervous excitation via synaptic Ca 2+ ion release. [8][9][10] These and other studies 11 have subsequently explored PMs as potential "neural qubits", drawing upon the fact that nuclear spin coherence times associated with these systems have been found to be exceptionally large per theoretical estimates. Such studies have suggested or assumed that the prototypical structure for the PM is one with an S 6 molecular point group symmetry, at least on average.…”

“…12 Certain molecular symmetries can render the six 31 P nuclei magnetically equivalent (e.g., S 6 ), resulting in a small number of unique scalar (J) couplings (e.g., three unique coupling constants for S 6 ). 11 Understandably, other molecular symmetries could treat groups of 31 P nuclei as distinct, thus, resulting in a larger number of pertinent scalar couplings. 13 As the ability of the system to sustain long-lived spin coherences is starkly related to the asymmetry in the coupling network, [14][15][16][17][18] the spin physics of PMs is inherently linked to the molecule's point group symmetries.…”