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In an interview with Nautilus's Steve Paulson, Penrose uses an example from quantum computing to explain that qubits of information remain in multiple states until coming together into an instantaneous calculation, called “quantum coherence," making a large number of things act together in one quantum state.
Here's where Penrose's theory draws upon the work of Hameroff by saying that this quantum coherence takes place in protein structures called “microtubules". These microtubules reside inside the neurons in our brains and can store and process information and memory. Penrose and Hameroff think that microtubules are quantum devices that are orchestrating our conscious awareness.
This theory is not appreciated by everyone in the scientific community, with many critics saying the brain is too “warm, wet, and noisy" and cannot sustain a quantum process. Another physicist, Max Tegmark, even calculated that the brain cannot possibly think as fast as this idea requires. Hawking is also not on board, suggesting Penrose should stick with his field of expertise.
Yet, a 2013 study by Japanese scientists added some proof to the theory by Penrose and Hameroff as researchers detected vibrations in the microtubules. Penrose and Hameroff then proposed that by focusing brain stimulation on these vibrations one could conceivably “benefit a host of mental, neurological, and cognitive conditions."