John von Neumann was the greatest mathematician of the 20th century, despite his life being cut short by cancer when he was just 53. He warrants extended discussion, because I have found when I mention his contribution to quantum mechanics, some people immediately dismiss him with a comment along the lines of “Sounds like Deepak Chopra. I feel pretty safe ignoring that.” As we will see below, a similarly dismissive reaction can come from people in positions of much greater authority, such as the author of a textbook on the metaphysics of quantum mechanics published by Oxford University Press – Quantum Ontology: A Guide to the Metaphysics of Quantum Mechanics by Professor Peter J Lewis (2016).
Von Neumann was about as far from a scientific heretic as could be imagined. He came from a wealthy Hungarian Jewish family, and was exceptionally gifted. At six he could divide two eight digit numbers in his head, and converse in ancient Greek. At eight he had mastered calculus. An interest in history prompted him to read through the whole of a 46-volume world history series. He attended the best school in Budapest, and his father hired private tutors to provide extra tuition in areas he displayed an aptitude for. These included the famous mathematician Gábor Szegő, who upon their first meeting was brought to tears by von Neumann's talent for producing instant solutions to complex mathematical problems. At 19 he was having mathematical papers published.
In his 34-year career, von Neumann authored over 150 papers, making numerous major contributions to mathematics, physics, computing and economics, and playing a key role in the development of computers, AI, game theory and the hydrogen bomb. At the time of his death he was America's greatest expert and authority on nuclear weapons, and was the originator of the MAD (mutually assured destruction) strategy to control the arms race. In 1999 the Financial Times named him Person of the Century, as representative of the 20th century's ideal that the power of the mind could shape the physical world (the double meaning here is unlikely to have been accidental).
In 1932, von Neumann's definitive mathematical analysis of quantum mechanics was published. The Mathematical Foundations of Quantum Mechanics is the closest thing quantum theory has to a bible. In it von Neumann mathematically proved that an “ordinary reality” cannot underlie the mathematical quantum facts. He showed that if electrons are ordinary objects, or constructed of ordinary objects, then the behaviour of these objects contradicts what quantum mechanics is telling us about reality.
Here is Lewis (p64) on von Neumann:
“...the worry is that at the end of the day there may be no good way to decide between [the competing solutions to the Measurement Problem], so the project of basing our ontology on our best physical theory will prove to be impossible, at least at this level of description.
However, there is another line of thought running through the history of quantum mechanics according to which there is no genuine underdetermination here. The measurement postulate has always sat uncomfortably with the rest of quantum mechanics. Von Neumann first explicitly formulated the measurement postulate as part of quantum mechanics, but he also claims that when the measurement postulate applies is arbitrary to a large extent, suggesting that it is not an objective physical process but something more closely connected to our situation in the world as observers. In that case, maybe the measurement postulate should never have been regarded as part of the physical theory itself; perhaps we should read the textbooks as saying that a system undergoing a measurement looks as if its state collapses to an eigenstate.”
So far, so good. But having pointed out von Neumann's claim that measurement is not an objective physical process but something more closely related to our status as observers, he does not go on to say anything about any relationship between consciousness and wave function collapse. Instead, he implies that this might mean that the collapse only “looks like” it happened, which leads him in the next sentence to the Many Worlds Interpretation. Von Neumann gets no other mention in Lewis' book, and the most important contemporary defender of this idea – Henry Stapp – isn't mentioned at all. It appears Lewis is leaving out von Neumann's interpretation entirely. The only mention of the theory that consciousness causes collapse anywhere in a book on quantum ontology is a claim on page 179 about Eugene Wigner, who defended and extended von Neumann's position in the 1950s. Wigner's view that consciousness causes the collapse, says Lewis, “falls short of being possible” because it “requires a deeply problematic interactionist dualism.” Lewis does not explain in the main text exactly what it is that he thinks is impossible, or why. He relegates it to a footnote: “One problem is that it seems utterly mysterious on this view how the ability to collapse wave functions could have evolved with the evolution of conscious beings, since evolution is a purely physical process. For further discussion see Chalmers The Conscious Mind 156 and 356.” This is a striking example of how deeply materialist assumptions shape the discourse: the view is dismissed not because it is incoherent, but because it conflicts with an unexamined, unquestioned belief about evolution being entirely physical. The von Neumann/Wigner/Stapp interpretation has been dismissed as impossible, on the grounds it is “utterly mysterious” how to square this idea with the evolution of conscious beings. But does materialistic science actually have any idea how consciousness evolved? No it does not, as Thomas Nagel had already pointed out four years before the publication of Lewis' book.