Roger Penrose has a remarkable intuition and he has made audacious proposals which as such have been wrong. This is the fate of pioneers. The following proposals are familiar to me.
- Penrose introduced the notion of twistors. This has led to to dramatic successes in the understanding of N=4 SYMs but there are still profound problems: in particular, all particles should be massless and these SYMs are unrealistic also otherwise. Also a subset of Feynman diagrams can be twistorialized. Twstor approach fails also in the curved space-time of general relativity.
The TGD solution would be simple: the twistor structure of the twistor space of the space-time surface is induced from that of H=M4×CP2 or M8 providing dual descriptions of physics in TGD Universe. 4-D twistor structure exists only in these cases if one requires that twistor spaces involved have Kähler structure: the mathematical existence of quantum TGD requires this. TGD is therefore unique.
8-dimensionality replaces 4-D masslessness with 8-D masslessness and particles can be massive in 4-D sense. Twistor fields are replaced with 6-D surfaces in 12-D twistor space of H or MM8 having induced twistor structure. This predicts dynamical length scale dependent cosmological constant and its value at long scales approaches to zero and the sign is correct.
- Penrose proposed that consciousness and gravitation are somehow related. To me the proposal - known as Orch OR - dees not make sense mathematically.
But the proposal as such is very reasonable: gravitation is the only long range interaction which is not screened and one expects quantum coherence in arbitrarily long scales and the coherence of living matter impossible in biology as mere chemistry framework requires this. The coherence of living matter would be induced coherence, not real quantum coherence. Dark matter in the TGD sense as large heff&get; h phases would induce it.
- Penrose proposed that classical physics makes sense somehow and that quantum measurement could reduce to a deterministic process which he called Orch OR. He was wrong but his intuition was correct.
However, classical physics is an exact part of quantum physics in the zero energy ontology (ZEO) of TGD. In ZEO quantum state can be regarded as a superposition of preferred extremals (space-time surfaces) and quantum jumps replace this superposition with a new one. This solves the basic paradox of quantum measurement theory.
- Penrose proposed that the universe dies (big crunch and re-incarnate (big bang) in a well-defined sense. As far I know, there is no empirical evidence for this.
In ZEO of TGD bringing in consciousness this really occurs. In death (in universal sense) conscious entity dies and reincarnates with an opposite arrow of time - this is essential for getting rid of the paradox of quantum measurement theory - Universe is full of these conscious entities in various scales are repeating this process and evolving more and more complex and intelligence incarnation by incarnation.
This can happen even for stars and galaxies and formation of blackholes might be this kind of process: instead of an expansion a contraction occurs and might be expansion in reverse time direction for the sub-cosmology involved (TGD predicts Russian doll cosmology).
The dissipation of the time reversed system looks like extraction of energy from the environment and self-organization instead of decay. In living matter this sequence of incarnations corresponds to breathing. Metabolic energy feed would be sucking of metabolic energy. This allows to avoid heat death predicted by the standard thermodynamics postulating a single time arrow.