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  Is the Penrose Objective Reduction hypothesis falsified by the existense of macroscopic quantum systems?

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In Penrose's OR (Objective Reduction) hypothesis, the time taken for the wave function to collapse is roughly τ ≈ ℏ / E_G (https://en.wikipedia.org/wiki/Orchestrated_objective_reduction). This implies that more massive quantum systems will take a shorter time to collapse, since E_G tends to be larger. Isn't this idea falsified by the existence of macroscopic quantum systems such as superconductors that stay coherent for an indefinite period of time?



asked Jan 21, 2018 in Chat by ijt (0 points) [ no revision ]
recategorized Jan 22, 2018 by Dilaton

$E_G$ must be an exchanged energy during "observation" rather than the total energy, I guess (kind of the energy level width). I.e., by "observation" here I mean irreversible energy loss/gain, not just a "reflection energy" like in a resonator. Normally superconductors are isolated in this or that way to stay cold and to prevent the irreversible energy exchange.

Quoting from the Wikipedia article, "\(E_G\) is the gravitational self-energy or the degree of spacetime separation given by the superpositioned mass". As its name suggests, this self-energy is a property of the quantum system by itself, so I don't think your comment answers the question.

I think the phrase "$E_G$ is the gravitational self-energy or the degree of spacetime separation given by the superpositioned mass" is an awkward explanation (hypothesis) rather than a statement about some derived value of $E_G$.

OR is just a speculative thought research with vague and adjustable objects behaviors. Not really a common topic for PO ...

Vladimir, I found a specific formula on p. 340 of Shadows of the Mind. Using absolute units, consider a model system involving a spherical mass of radius \(a\) in a linear superposition of being in two non-overlapping locations. Then the reduction half life is on the order of \({1\over 20 \rho^2 a^5}\) where \(\rho\) is the density. Penrose goes on to give specific examples of half lifes for objects of various sizes and masses. A nucleon gets a reduction time of over ten million years. A speck of water of radius 10^{-3}cm gets less than a millionth of a second. I don't see a derivation of the formula in this book, but I'd guess there's something like it in one of the papers he references, for example Diósi, L. (1989). Models for universal reduction of macroscopic quantum fluctuations. Phys. Rev., A40, 1165-74.

I found an answer on p. 343 of Shadows of the Mind, in the chapter on Quantum Theory and Reality:

With superconductors, very little mass displacement occurs between the different superposed states. There is a significant momentum displacement instead, however, and the present ideas would need some further theoretical development in order to cover this situation.

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