**Brief summary and criticism of Penrose-Diosi model**

A natural starting point idea would be that ordinary quantum coherence induces quantum gravitational coherence.

- Quantum superposition of 3-geometries dictated by mass distributions of particles defined by particle wave functions. The wave function of the many-particle system is a superposition over configurations with localized particles and each configuration corresponds to a superposition of gravitational potentials defining gravitational self-energy.
- In general relativity, this superposition corresponds to a point in the space of 3-geometries, the superspace of Wheeler consisting of 3-geometries. Therefore quantum gravitation is unavoidable and quantum coherence for matter dictates that for the gravitation. Therefore ordinary quantum theory forces quantum gravitation in the counterpart of the superspace.
In this view, the rate of quantum gravitational dehorence corresponds to the rate of ordinary quantum coherence: this conforms with Einstein's equations and Equivalence Principle.

- It is essential that one has a many-particle system. For a single particle system the gravitational self-energy is the same for all positions of the particle and does not depend on the wave function at all. Even for many particle systems, the superposition of shifted systems have the same gravitational binding energy.
In the Penrose-Diosi model, it is however proposed that the above argument works for single particle and gravitational interaction energy is estimated by assigning to wave function an effective 2-particle system.

The underlying reason for this assumption is the idea that the notion of wave function and therefore also wave function collapse somehow reduces to classical gravitation.

**Could one measure the rate of gravitational quantum decoherence
in the Penrose-Diosi model?**

In the Penrose-Diosi model (see this), the quantum gravitational coherence can in principle be detected by measuring the rate for gravitational quantum decoherence.

- Quantum gravitational decoherence for a wave function representing a superposition of mass distribution and a shifted mass distribution is considered.
The idea is gravitational quantum coherence could be detected if the corresponding quantum decoherence occurs faster than other forms of decoherence. The basic objection is that the Equivalence Principle states that the two decoherences are one and the same thing.

If the gravitational coherence time is short enough but not too short, this might be possible. Limits for the decoherence time τ

_{gr}are proposed and are between millisecond and second: these are biologically relevant time scales. - Gravitational quantum decoherence time τ
_{gr}is estimated by applying Uncertainty Principle: τ_{gr}=ℏ/Δ E_{gr}. Δ E_{gr}is the difference between the gravitational self-energy for a system and a shifted system.One has actually a superposition of different classical configurations each inducing a classical gravitational field. Wave functions for particles of

*many-particle state*define the gravitational superposition. Gravitational superposition coded by a wave function for a large number of particles. In this case, gravitational binding energies E_{gr Δ Egr between 2 different quantum states are well-defined. }One could take atomic physics as a role model in the calculation of the change of the gravitational potential energy. Coulomb energy would be replaced with gravitational potential energy.

- With a motivation coming from the notion of gravitational wave function collapse, one however considers
*single particle*states obtained as a superposition of Ψ(r) and its shift Ψ(r+d). In this case, the gravitational interaction energy is not well-defined unless one defines it as a gravitational self-interaction energy, which however does not depend on the position of the particle at all and is same for local state and the bilocal state.Penrose suggests that the difference between gravitational interaction energies makes sense and can be estimated

*classically*using effective mass densities m|Ψ^{2}|(r) and m|Ψ(r+d)|^{2}instead of Ψ(r) and Ψ(r+d)^{*}. One seems to think that one has effectively a two-particle system and calculates the gravitational interaction energy for it. To me this looks like treating a delocalized single-particle state as a two-particle state. - The situation could be simplified for a superposition of a macroscopic quantum state, say B-E condensate, and its shift. One could try to detect decoherence time τ for this situation. Now however the fact that B-E condensate is effectively a single particle, suggests that the change of the gravitational self-interaction energy vanishes.
- It turns out that it is not possible to find parameter values which would allow a test in the framework of recent technology.
The intuitive idea is that the gravitational SFRs localizing the wave functions effectively induce instantaneous shifts of particles. For charged particles this induces accelerated motion and emission of radiation. This radiation might be detectable. The implicit assumption is however that a single particle state effectively behaves like a 2-particle state as far as gravitation is considered.

No evidence for this radiation and therefore for gravitational SFRs is found.

- The reduction to a single particle case does not make sense in standard quantum physics (Penrose suggests something different). The gravitational self-interaction energy is the same for both shifted single particle states for any single particle wave function. For many-particle states the situation would change.
- The radiation should have wavelength λ of order of the shift parameter d. d is expected to correspond to atom size or nuclear or nucleon size in the case of atoms. The energies for photons would be above 10
^{4}eV. These energies are suspiciously large. Much larger shifts would be required but these are not plausible for the proposed mechanism. - Why shifted mass distributions are assumed? Even in the case of many-particle systems the gravitational self-interaction energy does not depend on wave function if the system is only shifted. The reason is that the relative positions of particles are not changed in the shift.
If one uses many-particle states, a superposition of scaled mass distributions would be more natural in the standard quantum physics framework. A coherent, easy-to-calculate, change of the gravitational interaction energy. A possible connection with density changing phase transitions, such as melting and boiling, emerges. Water is a key substance in living systems!

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

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