- #1

ChrisVer

Gold Member

- 3,347

- 448

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

One reads:

I wouldn't be a liar to say that I understood almost nothing about this...what's the formulation behind it?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.

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.