Non-linear Replacements for QM

[Rade]

In another thread, PF member "SelfAdjoint" made the following comment:
...and indeed you see papers suggesting non-linear replacements for QM and nonlocal replacements for relativity...
I am interesting in reading such papers that "suggest" non-linear replacements for quantum mechanics (QM). Would anyone know of internet links ?
Also, I have a question, if in fact it can be shown that reality is non-linear (not unitary), would not such an experiment falsify QM as a valid theory, since by its definition QM requires that quantum realities be unitary ? Thanks for helping me better understand a very complex topic.

 

[vanesch]

I am interesting in reading such papers that "suggest" non-linear replacements for quantum mechanics (QM). Would anyone know of internet links ?

There are two "schools": some have a *reason* to have non-linear time evolution (the one that comes to mind is Penrose of course ; or look at the recent hype around Heim's theory), and others try to introduce small, made-up non-linear corrections to the Schroedinger equation in order to obtain a genuine collapse (Stamatescu for instance).

Also, I have a question, if in fact it can be shown that reality is non-linear (not unitary), would not such an experiment falsify QM as a valid theory, since by its definition QM requires that quantum realities be unitary ?

It is going to be difficult to differentiate between a (small) deviation of unitarity, and some error in the modelling of the experimental setup.
The idea would probably be to try to detect an expected quantum interference phenomenon, and observe that it doesn't appear.

For instance, look at Penrose's Felix experiment proposal, where he tries to show that, once a gravitational effect is introduced, quantum interference should disappear because of his postulated non-linearity which induces collapse. But *it is quite difficult, experimentally, to observe quantum interference* ! Any tiny uncontrolled effect can screw up the phase relations between the terms that should interfere, and destroy the coherence.
When you observe interference, there's no doubt: you've seen an effect. However, when you do not see interference, is it fundamental, or have you overlooked a perturbation in the experiment ?

 

[Rade]

Thank you Vanesch--I will google search Penrose Felix and Stamatescu, any others come to mind ?

 

[vanesch]

Careful pointed me out to a paper in which such kinds of discussion is helt. It is quite negative about MWI (but with no good argument!), but apart from that, it's a great read, and Leggett is after all a Nobel laureate.

http://www.physics.uiuc.edu/People/Faculty/profiles/Leggett/PhysicaC-2002.pdf