I originally intended to write something about dreams today but have decided to postpone that post and instead elaborate in this post on the ideas I pitched a couple of days ago. Sometimes in this blog I come back to a problem repeatedly, revising my position, as in the series of essays I wrote about Neil Gaiman's comic book storyline A Game of You; although I could just leave my musings about quantum theory in the form I presented them in the previous post, I thought I would try to clarify my position and show that, although it looks flakey, this position is defensible. It is a strange position. I am arguing, in effect, that quantum physics allows for the possibility of supernatural causation, that Einstein and others (like Bohm) were correct in supposing that quantum physics requires a hidden-variable theory, but that they were wrong in believing science capable of discovering and elaborating such a theory. In today's post I want to talk about this in more depth. Bear with me.
The heart of my argument is the justifiable supposition that any estimate of probability is subjective rather than objective. An estimate of probability exists in the mind of a knower rather than being a fact about reality existing in the outside world. In the previous essay, I discussed the example of a shuffled pack of cards and I want to return to this example and look at it from a different perspective. Suppose we have a pack of cards and in the same room four people who have different degrees of knowledge about the sequence of cards in the pack. The question asked of them is "What is the probability of drawing the Queen of Hearts from the top of the pack?" Person A knows only that the pack is an ordinary pack minus jokers; he or she estimates the probability of drawing a Queen of Hearts as being 1/54. Person B knows more; he or she knows that the top twenty-six cards are all red. Consequently, Person B estimates the probability as being 1/26. Person C knows that the top thirteen cards are all hearts and consequently estimates the probability as being 1/13. Person D, with god-like omniscience, knows the precise order of cards in the pack and knows for sure that the top card is the Queen of Hearts. Consequently, he or she estimates the probability as being a certainty, 100%.
Which of the four is correct? It seems that the four individuals are increasingly more accurate, that the first is least accurate and the last most accurate. If we assume the Law of the Excluded Middle to be right (the axiom that propositions must either be true or false), it seems that Person D's estimate is true and that Person A's estimate must be false. More charitably, however, we could say that Person A's estimate is the best guess he or she can make given the information available to him or her. Although they are making increasingly accurate guesses, Persons A through C cannot be said to be making true statements. Only Person D is in a position to make a true statement regarding the card because he or she is omniscient– and of course it is worth noting that his or her estimate is no longer really an estimate of probability, but rather of certainty. If a person is omniscient, he or she knows for sure whether future events or outcomes will occur or not; it is no longer an issue of probability. From a traditional logical perspective, then, any proposition stating the probability of a future event, a probability given as something other than one or zero, is either false or meaningless. Is the future predetermined or not? Interestingly, David Foster Wallace grappled with the same problem when he was a student, the problem of Fate, although he approached it from a different angle. (Read Wallace's book Fate, Time, and Language for his thoughts.) Wallace weighed in in favour of free will and opposed the notion of Fate, but I have argued in the past the opposite, that Fate does in fact exist and that free will doesn't.
When quantum physics was first developed in the early decades of the twentieth century, when the wave-particle duality of light and matter was first proposed, no-one had any theory at first to make sense of this duality. In 1928, Max Born made a radical suggestion: that reality is indeterminate and that the equations of quantum physics can be construed as assigning probabilities to events and quantities. The probabilistic interpretation of quantum physics has ever since been central to most accepted views of quantum physics – although de Broglie, Einstein and later Bohm challenged it. The Schrodinger Equation and Dirac equation provide us with possibilities about the energies, momenta ,and positions of particles rather than certainties because reality itself is, in a sense, uncertain. It is precisely this position that I wish to critique. The fatal mistake I think quantum physicists made then and have continued to make ever since is that they have misunderstood the nature of probability. The physicists have treated uncertainty as being an objective fact about the universe – when in fact uncertainty is subjective, is a quality of a knowing mind when confronted with the universe. And yet, with only few exceptions, physicists have continued to cling to the idea that quantum physics presents an objective picture of reality, that uncertainty is objective rather than subjective.
In the previous post, I described the Schrodinger's Cat paradox and will do so again now as an aid in presenting my counter-theory. The paradox is beautiful, profound, and important. Schrodinger imagines the following situation. A cat is put in a sealed box with a piece of uranium that has a 50% chance of decaying over a certain period. If the uranium decays, a gun goes off, killing the cat. Schrodinger argues that, according to standard interpretations of quantum physics, the cat is described by a superposition of two states: the poor creature is both alive and dead at the same time. It is only when the scientist opens the box and observes the cat that one state is confirmed. This moment, this observation when the box is opened, brings about something known as 'wave function collapse'. Schrodinger's intention in posing this problem was to show the deficiencies of the standard probabilistic interpretations, to show what happens when the ideas of quantum physics, which are normally applied only to microscopic systems, are applied to macroscopic situations. He sought to show that the orthodox interpretation of quantum physics must be false if it yields such an absurd conclusion. However radical advancements in Chaos Theory have shown that microscopic events can have macroscopic effects, ("A butterfly flapping its wings in South America can cause a hurricane in Europe") and so the objection that quantum physics is inapplicable to macroscopic systems can be challenged.
I would like to develop the Schrodinger's Cat thought experiment in the following way. Suppose the experiment takes place under the guidance of three scientists – a chief scientist, an assistant, and an assistant to the assistant. Prior to opening the box we have not one but four universes – the universe of the cat, and three universes each of which belongs to one of the scientists. In the first universe, let us suppose that the cat is definitely alive. In the other three, the cat is both alive and dead at the same time. The assistant to the assistant opens the box and checks on the condition of the cat. Wave function collapse occurs – in his universe the cat is now definitely alive. We now have two universes in which the cat is definitely alive and two universes in which the cat is in a superposition of both states. The assistant to the assistant tells the assistant. Again wave function collapse occurs. We now have three universes in which the cat is definitely alive and one in which its vitality is still in doubt. The assistant tells the chief scientist and, again, wave function collapse occurs. In all four universes the cat is now definitely alive. Somehow all four universes, each of which represents a state of knowledge in the consciousness of a living being about the 'real' 'objective' world, have come into alignment.
In this thought experiment, I have asserted that the collapse of a particular wave function occurs not once but multiple times, once for every conscious individual observing or learning about the state of the particular system of interest. This runs completely counter to every established theory of quantum physics I know. According to most physicists, who are not only rational but possessed of 'sound common sense', wave function collapse only ever occurs once. The state of the cat passes once, permanently, from the unknown into the known. This common-sense tenet overlooks the fact that knowledge can only exist in the mind of a knower and that there is more than one knower in the world. Yet physicists continue to ignore this subjectivity. In the previous post, I briefly mentioned that the popular theory of wave function collapse today is 'decoherence' – decoherence is an attempt to ground wave function collapse in objective reality rather than in subjective perception. Decoherence theories propose that wave function collapse occurs when the microscopic system of interest interacts with its environment, interacts with macroscopic systems such as the apparatus used to measure the properties of the microscopic system. I lack the mathematical education to fully elucidate decoherence theories but the difference, in a nutshell, between my theory and decoherence is that decoherence theories propose that wave function collapse occurs when a system interacts with other physical systems, whereas I am proposing that wave function collapse occurs when a system interacts with a conscious mind. Although I lack the physics training to present a mathematical proof, I don't need one. If probability is of its nature subjective, it makes sense to suppose that wave function collapse is also subjective.
I want to draw attention to a curious feature of the examples I have given. With respect to the 'pack of cards' thought experiment, although three of the four observers are initially in doubt as to whether the Queen of Hearts is on top, when the card is flipped all four agree that it is. With respect to the Schrodinger's cat thought experiment, although three of the four sentient beings involved are initially in doubt about whether the cat is alive or dead, all eventually agree that the cat is alive. This is not intuitively obvious. If every person inhabits a different universe, I might believe Elvis is dead and you might believe he is alive, and we might both be right. If everything is subjective, then there is no such thing as objective truth. This line of thought leads to postmodernism, to the conclusion that all truth is relative. It could also lead to the idea that truth is a matter of consensus and that there is nothing outside 'consensus reality', what some philosophers have termed 'intersubjectivity'. The alternative to the idea that reality is in this radical sense fragmentary, subjective, is the idea that there are 'hidden variables' at work, an idea I discussed in the previous post. Einstein himself believed in a 'hidden variable' theory of quantum physics. In the previous post I suggested that such hidden variable theories may be eternally beyond the grasp of rational science; the hidden variables at play might be supernatural. Perhaps the only viable alternative to postmodernism is some form of mysticism.
The question I am really asking in this post is much older than quantum physics. Since the ancient Greeks people have posed the problem, "If a tree falls in the forest and no-one is around, does it make a sound?" The postmodern answer is simply, "No". Reality only exists in the minds of knowers. The hidden variable answer is, "Yes" – but only perhaps because a transcendental knower exists who knows everything. This is of course a mystical answer but sometimes seems to me the only answer.
I hope this post is clear enough; I fear that my writing style today is inadequate to the ideas that I am trying to express. If it is still unclear, read this post and the previous one again and maybe it will become clearer. I hope so, anyway,
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