Can the M theory/ string theory coexist with the penrose interpretation of quantum mechanics?
The "interpretation" of Penrose's is not really an interpretation of Quantum Mechanics; more of modifying Quantum Mechanics -- https://en.wikipedia.org/wiki/Penrose_interpretation -- to allow for objective collapse due to gravity.
So is that a yes or no?
If string theory doesn't modify QM, then the answer is no.
It does remind me superficially of Smolin's "Principle of Maximal Variety", .
If I'm not mistaken, then Penrose theory requires a classical spacetime (or at least one that is very strongly superselected), as the gravitational field and the particle configuration cannot be entangled in any way. If they were, the linearity of the evolution would not allow for any form of collapse or state separation.
That means no theory of quantized gravitation qualifies, including Supergravity, M-Theory (strings), Loop quantum gravity, etc. The only framework that matches is in fact quantum field theory on curved spacetime, which is what practically all of Penrose's (and Hawking's for that matter) calculations are based on.
As I understood it Smolin wasn't starting off talking about quantized QM Gravity per se. Though I think a unit of measure was implied in his attempt to connect QM and GR via the metric "similarity of views" a metric orthogonal to classical locality.
This seems consistent with Penrose' proposal that there is some maximum "elasticity" to space-time curvature? In what dimension is this elasticity defined? Smolin seems to be suggesting it is a function of the measure of distance across the non-space time dimensions. Or inverting that, the measure of difference in non gravitational dimensions is derivable from some specific sense of the elasticity of spacetime - as I understand it this is sort of Penrose.
From http://lanl.arxiv.org/pdf/1506.02938v1.pdf p3-4
"In the microscopic causal geometry underlying nature, two systems can interact if they are within a distance R in the metric hij . There are two ways this can happen. It can happen when they are nearby in the emergent macroscopic notion of spatial geometry. When two people stand next to each other and scan a landscape they see similar views. But two microscopic systems can also be very far apart in the macroscopic geometry and still have a similar view of their surroundings. When this happens there are a new kind of interactions between them
A brief quote from The wiki page on Penrose's interpretation, sounds a lot like Smolin, or vice versus.
"Accepting that wavefunctions are physically real, Penrose believes that matter can exist in more than one place at one time. In his opinion, a macroscopic system, like a human being, cannot exist in more than one place for a measurable time, as the corresponding energy difference is very large. A microscopic system, like an electron, can exist in more than one location significantly longer (thousands of years), until its space-time curvature separation reaches collapse threshold."
Separate names with a comma.