Wavefunction real physical object?

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ChrisVer
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Here :
http://en.wikipedia.org/wiki/Penrose_interpretation

One reads:
Penrose's idea is a type of objective collapse theory. For these theories, the wavefunction is a physical wave, which experiences wave function collapse as a physical process, with observers not having any special role. Penrose theorises that the wave function cannot be sustained in superposition beyond a certain energy difference between the quantum states. He gives an approximate value for this difference: a Planck mass worth of matter, which he calls the "'one-graviton' level".[1] He then hypothesizes that this energy difference causes the wave function to collapse to a single state, with a probability based on its amplitude in the original wave function, a procedure derived from standard quantum mechanics. Penrose's "'one-graviton' level" criterion forms the basis of his prediction, providing an objective criteria for wave function collapse.[1] Despite the difficulties of specifying this in a rigorous way, he proposes that the basis states into which the collapse takes place are mathematically described by the stationary solutions of the Schrödinger–Newton equation.
I wouldn't be a liar to say that I understood almost nothing about this...what's the formulation behind it?
First of all, how can the wf be a physical wave? it corresponds to what? Also I find obscure the use of "observers not having any special role", that is not true even in the Copenhagen interpretation (where the "observer" is considered to be the interaction).
Then it says that the superposition cannot be sustained beyond certain energy difference between the quantum states. Now if I try to write it down mathematically, I'd say that a wf being in a superposition of (2) energy eigenstates:
[itex] | \psi > = a|1> + b|2>[/itex]
would need the energies [itex]E_{1}<E_{2}[/itex] and [itex]E_{2}- E_{1}= \Delta E \le E_{max} \equiv M_{Pl} [/itex], otherwise the wavefunction would collapse by itself? through what mechanism? There can't be any transition from 2 to 1, since [itex]<2|1>=0[/itex]. Also if the wavefunction is to describe a quantum particle,then it having energy equal to the Planck Mass is almost impossible.
Then, for some unknown reason, he thinks that [itex] \Delta E [/itex] will cause the collapse:
[itex] |\psi> \rightarrow |1> [/itex]
I don't understand how this solves the problem.
 

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Penrose talks about the energy differences and collapse in some of his papers with Stuart Hameroff. They are about the quantum origins of consciousness but if you want to ignore that he does go into the formulations of collapse.
 
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ChrisVer
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No,I am not really into studying consciousness stuff... I was just trying to understand, in his formalism, how can he reach the point where QM probabilistic world becomes the CM deterministic one [which I think is his main issue for calling QM an incomplete theory].
 
  • #5
atyy
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No,I am not really into studying consciousness stuff... I was just trying to understand, in his formalism, how can he reach the point where QM probabilistic world becomes the CM deterministic one [which I think is his main issue for calling QM an incomplete theory].
[STRIKE]When you say "his formalism", perhaps you could post specific peer-reviewed papers by Penrose so know what we are talking about?[/STRIKE] Edit: See the next post.

Or are you asking about real collapse theories in general? These generally predict deviations from quantum mechanics.

The most famous are the Ghirardi–Rimini–Weber (GRW) theory and Continuous Spontaneous Localization (CSL).

Here is a recent review of CSL by Pearle http://arxiv.org/abs/1209.5082.

There is a recent proposal to test CSL:

http://arxiv.org/abs/1405.2868
Optomechanical sensing of spontaneous wave-function collapse
Stefan Nimmrichter, Klaus Hornberger, Klemens Hammerer
Phys. Rev. Lett. 113, 020405 (2014)

Sabine Hossenfelder has a blog post about testing CSL http://backreaction.blogspot.com/2013/06/testing-spontaneous-localization-models.html, in which she points to another proposal to test the theory:

http://arxiv.org/abs/1305.6168
Are collapse models testable with quantum oscillating systems? The case of neutrinos, kaons, chiral molecules
M. Bahrami, S. Donadi, L. Ferialdi, A. Bassi, C. Curceanu, A. Di Domenico, B. C. Hiesmayr
Scientific Reports 3, 1952
 
Last edited:
  • #6
atyy
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Actually, the Nimmrichter, Hornberger and Hammerer paper linked above has explicit comments on the Diosi-Penrose model in the section containing Eq 11-13 just before their conclusion.

They reference:
http://www.sciencedirect.com/science/article/pii/0375960187906815
A universal master equation for the gravitational violation of quantum mechanics
L. Diósi

http://journals.aps.org/pra/abstract/10.1103/PhysRevA.40.1165
Models for universal reduction of macroscopic quantum fluctuations
L. Diósi

http://link.springer.com/article/10.1007/BF02105068?LI=true
On Gravity's role in Quantum State Reduction
Roger Penrose
 
  • #7
stevendaryl
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It's something assigned to a point in space hence like an EM field can be considered real.
I'm sure you know this, but one obstacle to interpreting the wave function as a field like the EM field is that in general the wave function lives in configuration space, rather than physical space. If you have [itex]N[/itex] particles, the wave function is a function on [itex]3N[/itex] dimensional space, rather than [itex]3[/itex] dimensional space.
 
  • #8
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I'm sure you know this, but one obstacle to interpreting the wave function as a field like the EM field is that in general the wave function lives in configuration space, rather than physical space. If you have [itex]N[/itex] particles, the wave function is a function on [itex]3N[/itex] dimensional space, rather than [itex]3[/itex] dimensional space.
Yes - that's why you need something like the things I mentioned a bit later.

Thanks
Bill
 

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