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Penrose's Gravitationally Induced State Reduction

by George Jones
Tags: gravitationally, induced, penrose, reduction, state
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George Jones
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Feb13-06, 09:47 AM
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Endnote 30.37 of Penrose's book The Road to Reality briefly outlines what Penrose calls "a more rigous justification" for his graviationally induced state reduction. The endnote concludes with "Details of this argument will be published later."

Penrose also alludes to this argument in a popular-level talk he gave at the Perimeter Institude.

Does anyone know if the argument has been published? It is not on the arxiv, nor can find it using scholar.google.com.

Regards,
George
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marcus
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Feb13-06, 09:58 AM
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Quote Quote by George Jones
...

Penrose also alludes to this argument in a popular-level talk he gave at the Perimeter Institude.

Does anyone know if the argument has been published? It is not on the arxiv, nor can find it using scholar.google.com.

Regards,
George
I have read mention of it, and know vaguely what you refer to, but I don't know of a rigorous exposition of the idea by Penrose.

Is it your impression that a rigorous presentation would involve re-working the foundations of quantum mechanics? (that may be a silly question, I don't understand the issues well enough to know if it is a good question)

I hope someone else can come up with an online source that elaborates on this---fraid I can't.
turbo
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Feb13-06, 10:28 AM
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Just Google on "Penrose" and "FELIX" and you'll get all kinds of links. His idea is that superposition of physical objects causes gravitational stresses in space-time, and that the larger the object, the greater the stress, and therefore the sooner the superposition must resolve, in accordance with the Heisenberg uncertainty principle. Superposition of macroscopic objects like Schrodinger's cat would create huge stresses, involving such a great amount of energy that the reduction of state would be practically instantaneous.

Here are some on-line lectures by Penrose on the subject.
http://www.rdegraaf.nl/index.asp?sND_ID=842142

George Jones
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Feb14-06, 04:56 PM
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Penrose's Gravitationally Induced State Reduction

Marcus: Penrose certainly believes that quantum theory needs a thorough reworking, but that is not what my question is about.

turbo-1: I was asking about something much more specific.

Thank you both for replying.

I have had a passing interest in Penrose's work for about eight months. The original reference for his ideas about gravity's role is

R. Penrose, "On Gravity's Role in Quantum State Reduction," General Relativity and Gravitation, 28(5), 1996, pp. 581-600.

This is reprinted as Chapter 13 of Physics Meets Philosophy at the Planck Scale.

Here's my take on his ideas about gravitationally induced state reduction.

Consider a single (extended) massive particle at rest, and two possible spatial positions of the particle, i.e., the particle is either "over here" (H) or "over there". Suppose the quantum states for "over here" and "over there" are stationary states [itex]\left| \Psi_{1} \right>[/itex] and [itex]\left| \Psi_{2} \right>[/itex], respectively. If the the same gravitational potential energy is associated with both positions (no change in "height"), the stationary states have the same energy [itex]E[/itex].

So,

[tex]i \hbar \frac{\partial}{\partial t} \left| \Psi_{1} \right> = E \left| \Psi_{1} \right>[/tex]

and

[tex]i \hbar \frac{\partial}{\partial t} \left| \Psi_{2} \right> = E \left| \Psi_{2} \right>.[/tex]

Now, suppose that the quantum state of the mass is the superposition

[tex]\left| \Psi \right> = c_{1} \left| \Psi_{1} \right> + c_{2} \left| \Psi_{1} \right>[/tex]

of "over here" and "over there". It would appear that [itex]\left| \Psi \right>[/itex] is also a stationary state with energy [itex]E[/itex], but Penrose says "Not so fast!"

The states [itex]\left| \Psi_{1} \right>[/itex] and [itex]\left| \Psi_{2} \right>[/itex] refer to different spacetimes - the spacetime for the "over here" state is curved over here, because the mass is over here, while the spacetime for the "over there" state is curved over there. Consequently, [itex]\partial / \partial t[/itex] for the "over here" spacetime and, [itex]\partial / \partial t[/itex] for the "over there" spacetime are different as timelike vectors and as quantum operators. Thus, the superposition is ill-defined.

Superpose anyway, and try to find a quantative measure of just how different the two [itex]\partial / \partial t[/itex] are. When taking the partial derivative with respect to [itex]t[/itex], spatial coordinates are held constant, so spatial variations cause changes in [itex]\partial / \partial t[/itex].

Thus, the spatial variation of some relevant quantity might serve as a measure of the ill-definedness of the superposition. What relevant quantity? For weak fields, maybe the difference between the Newtonian gravitation potentials for the two parts of the superposition, i.e., integrate over all space, the square (so plus and minus variations don't cancel) of the gradient (spatial variation) of the difference between the potentials.

Poisson's equation gives that this is proportional to the gravitational self-energy of the mass distribution that's left over when the two mass distributions are subtracted, which also seems like a good measure of just how different things are for the two spacetimes. This energy is then used to estimate, via the uncertainty principle, the time taken for state reduction.

It is here, I believe, that Penrose has had a new idea for further justification, and I was asking for details of this new "rigorous" idea.

Reduction to what state? Penrose claims that the states to which a "superposition" will reduce are solutions to the coupled system consisting of the Schrodinger equation including Newtonian gravitational potential energy together with Poisson's equation with the mass density represented by [itex]m \left| \psi \right|^2[/itex].

Penrose claims that this should be observable either by an experiment in space, or by a ground-based experiment being considered at the University of California. As Patrick Vanesch has said, if no decoherence is seen, everyone will interpret this as vindication for standard quantum mechanics. If decoherence is seen, then some people will claim that feedback with the environment is at work, not gravitationally induced state reduction.

http://arxiv.org/abs/quant-ph/0210001

Regards,
George
turbo
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Feb14-06, 05:54 PM
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I'm sorry to point you to lectures instead of relevant papers. Your initial query was not specific enough for me to determine the level of detail you expected. Your follow-up post is quite detailed, and I can tell you that I have not seen a Penrose paper addressing the points you raise, and I have been Googling him fairly regularly for over a year since I have been working on a private model of quantum gravitation. Penrose believes that the marriage of quantum theory and GR will be an even-handed one, and that both will have to be adjusted. So far, my inclination is that GR will have to absorb the bulk of the modifications. I hope he comes up with the rigorous interpretation - I'm anxious to see it.
A/4
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Mar1-06, 02:36 PM
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It should be noted that the idea of gravity-driven state collapse is not strictly Penrose's doing. It's been around for a while. In fact, Lagos Diosi came up with a virtually identical mechanism in the late 80s, several years before Penrose's Gen. Rel. Grav. paper.

There are also several recent publications that deal with this mechanism (the "Penrose-Diosi" formalism, as it's been called). These include:

Testing Gravity-Driven Collapse of the Wavefunction via Cosmogenic Neutrinos (Joy Christian)
http://arxiv.org/abs/quant-ph/0503001

Gravitationally-Induced Quantum Superpopsition Reduction with Large Extra Dimensions (J. R. Mureika)
http://arxiv.org/abs/gr-qc/0509082


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