The system studied is the brain and cyclotron resonance of protons in "brain water" is involved. The goal was to find whether there exists evidence for macroscopic quantum entanglement. The work was based on the proposal that some quantum coherent, non-classical, third party, say quantum gravitation, could mediate quantum entanglement between protons of brain water. NMR methods based on so-called multiple quantum coherence (MQC) act as an entanglement witness.

One source of theoretical inspiration for the work of Kerskens and Perez was the article "Spin Entanglement Witness for Quantum Gravity" of Bose et al (see this).

In the proposal of Bose et al for generating entanglement by quantum gravitational interaction between mesoscopic objects a superposition of two locations for the objects is required. It is assumed that it is possible to correlate the locations with spin values. Entanglement would be generated by different phases, which evolve to different pairs of components of objects and measurement of spin would demonstrate the presence of entanglement.

Mechanisms generating quantum coherence in scales of at least 10 meters and giving rise to a superposition of locations are needed but are difficult to imagine in the standard view of quantum gravitation.

In TGD, the mechanism would be different. Gravitational Planck constant ℏ_{gr}= Gm/v_{0} associated with Earth-test particle interaction could generate quantum coherence in even brain scale and gravitational Compton length Λ_{gr}= GM_{/}v_{0} ∼ .45 meters, where v_{0}∼ c a velocity parameter characterizes the lower bound for the quantum gravitational coherence scale. The analogs of magnetized states assignable to microscopic objects of size scale 10^{-4} meters take the role of spins and spin-spin interaction generates the entanglement, which is detected by measuring the spin of either object just as in the case of ordinary spins.

Classical interactions, be their gauge or gravitational interactions, cannot generate entanglement whereas their quantum counterparts do so in scales smaller than the scale of quantum coherence.

- The first open question is whether quantum gravitation is able to generate quantum coherence in long length scales such as the scale of the brain. The fact that gravitation has infinite range and is unscreened might allow this. This however requires a new view of quantum gravitation.
A gravitational 2-particle interaction or interaction induced by quantum gravitation is needed to entangle the systems. If spins or possibly magnetizations are in question, the entanglement can be detected by spin measurements as done in the experiment. The interaction must be such that it can be distinguished from ordinary magnetic interactions.

- If objects with mass above Planck mass behave like quantum coherent particles with respect to quantum gravitation rather than consisting of small quantum coherent units such as elementary particles, the gravitational fine structure constant α
_{gr}=GM_{1}M_{2}/ℏ between objects satisfying M_{1}M_{2}>m_{Pl}^{2}becomes strong and one expects that the situation becomes non-perturbative.The condition M

_{1}= M_{2}= m_{Pl}is satisfied for a water blob of radius ≈ 10^{-4}meters and corresponds to the size of a large neuron (see this and this). The gravitational interaction energy GM_{1}M_{2}/d for distance d≈ 10^{-4}m is about 10^{-2}eV and of the same order of magnitude as thermal energy. - In the interferometer experiment a much larger phase difference could be generated in the TGD framework but the problem is that it is difficult to imagine a mechanism for creating a superposition of 2 locations of mesoscopic or even microscopic objects.
- It is also difficult to imagine a mechanism creating 1-1 correlation between location and spin direction (analogous to entanglement associated with spin and angular momentum).

**The notion of gravitational Planck constant**

The basic problem is what makes the quantum coherence scale so long.

- In the TGD framework, the non-perturbative character motivates a generalization of the Nottale's hypothesis stating that the gravitational Planck constant ℏ
_{gr}= GMm/v_{0}, v_{0}<c a velocity parameter. ℏ_{eff}=nh_{0}=ℏ_{gr}would be associated with gravitational flux tubes to which interacting masses M and m are attached, and would replace ℏ with the gravitational fine structure constant α_{gr}= GMm/ℏ >1 meaning that Mm>m_{Pl}^{2}is true. One could say that Nature is theoretician friendly and makes perturbation theory possible. This applies also to other interactions.The gravitational Compton length Λ

_{gr}= GM/v_{0}does not depend on the mass m at all. For the mass of order Planck mass assignable to a large neuron one has Λ_{gr}=L_{Pl}/v_{0}, which is of order Planck length. Much longer quantum coherence scale is however required. - In the case of the Earth, the basic gravitationally interacting pairs would be Earth mass and particles of various masses. The gravitational Compton length Λ
_{gr,E}= GM_{E}/v_{0}does not depend on the small mass and is about .45 cm for v_{0}∼ c favored by TGD applications. By the way, this scale corresponds to the size of a snowflake (see this).Λ

_{gr,E}∼ .45 cm defines a minimum value for the gravitational quantum coherence scale but much larger coherence lengths, say of order Earth radius, are possible. The size scale of the brain or even body would define a natural scale of quantum coherence. For objects with a size of order of a large neuron, the gravitational interaction could be quantal in scales of the brain, and actually in the scales of the magnetic bodies assignable to the organism. - Earth-particle interactions can induce quantum coherence in the scale of the brain and the masses could be taken to be of the order of Planck mass so that they would correspond to water blob with size of 10, so that their distance could be larger than d. This raises the hope that the effects of quantum gravitation quantum coherent in cell length scale or even longer scales could be measured although the interaction itself is extremely weak for elementary particles.
- For r= 10
^{-4}meters, M=M_E would give E∼ e^{2}/4 × 10^{2}eV ∼ 2.5 eV. For r=5× 10^{-4}meters this would give E≈ .01 eV, roughly the thermal energy at the physiological temperature.

**A possible TGD based mechanism generating spin entanglement**

These considerations suggest a TGD based mechanism for the generation of spin entanglement, which is not directly based on quantum gravitational interaction but on microscopic and even macroscopic qravitionally induced quantum coherence making possible a generalization of the spin-spin interaction as a way to generate entanglement.

- "Spin" should correspond to an analogy of macroscopic magnetization rather than to individual spin. Spin-spin interaction between "mesoscopic" quantum coherent particles characterized by ℏ
_{gr}and having mass about Planck mass generates the entanglement, which can be detected by measuring the "spin" of either particle. As a consequence also the "spin" of the other particles is determined and one has a standard situation demonstrating that the particles were entangled before the measurement.Large value of the energy due to the large value of ℏ

_{gr}could mean that one has a dark Bose-Einstein condensate like state with a large number of ordinary particles, say protons at the gravitational flux tube representing the quantal magnet behaving like spin.In the TGD framework, Galois confinement provides a universal mechanism for the formation of many-particle bound states from virtual particles with possibly momenta with components in an extension of rationals . The total momentum would have integer components using the unit defined by the size scale of causal diamond (CD).

- The dark cyclotron energy E
_{c}=ℏ_{gr}eB/m= Λ_{gr}eB, Λ_{gr}= GM/v_{0}of a mesoscopic particle whose particles are associated with (touching) the dark monopole flux tubes of the Earth's gravitational field, does not depend on its mass and is large.The magnetic field created by this kind of particle would correspond in the Maxwellian picture to a field B ∝ ℏ

_{gr}e/mr^{3}. This would give for the magnetic interaction energy of the mesoscopic particles the estimate E≈ μ_{1}μ_{2}/r^{3}= e^{2}Λ_{gr}^{2}/r^{3}.

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

## No comments:

Post a Comment