What is probability? At school we learn a little about chance – we learn for instance that the possibility of rolling a 2 on a fair die is one chance in six. What we don't learn is the deeper meaning of probability, that it is a judgement or estimate that emerges, rationally or semi-rationally, from a person's knowledge and ignorance of a situation or system, that it is subjective rather than objective. This perspective is generally known as Bayesian probability. In tonight's post, I want to talk a little about this view of probability, and then about quantum physics. I want then to venture into more flakey territory, to suggest a way the supernatural can interact with the natural world. Tonight's post follows on from another post I wrote a couple of years ago called "Free Will and Supernatural Causation".
Suppose you have on the table in front of you a shuffled deck of cards face down. You reach over and turn the top card over. The top card may or may not be the Queen of Hearts but you have no idea if it is or not until you flip the card. All you know before you flip it is that the Queen of Hearts occurs once and once only in the pack. Prior to turning it over you can make an estimate of the probability the card will the Queen of Hearts; assuming that there are no jokers in the pack, the probability is one chance in fifty-two. This is a reasonable estimate given your limited knowledge of the situation or system. Suppose however you know more, know that the top half of the pack is all red cards. In this case, you can revise the possibility – it is now one chance in twenty-six. Suppose you know that the top thirteen cards are all hearts. You can again revise the probability – it is now one chance in thirteen. Suppose you know that the top two cards are the Queen of Hearts and the Ace of Spades – now the most rational estimate of the chance of picking your wanted card immediately is just one in two. Suppose you know, for sure, that the Ace is on top. In this case the chance of picking the Queen of Hearts is simply zero. If you know however, for sure, that the Queen of Hearts is on top, the chance of flipping it is a certainty, unity, 100%. The more knowledge you have of the order of cards in the pack, the 'better' you can estimate the probability of turning over that one particular card.
We can consider the relationship of knowledge and ignorance, on the one hand, to probability on the other, by considering another hypothetical scenario. Suppose you buy a Lotto ticket every week, hoping to become an instant millionaire. A friend, condescendingly, seeks to dampen your enthusiasm by saying, "You know, you're more like to get killed in a car accident tomorrow than win Lotto first division." In a sense, your friend is telling the truth – statistically, some number of New Zealanders are killed on the roads every day but it is not every week that a New Zealander wins first division in Lotto. But it is only true in a limited sense. Your friend's estimate of the relative probabilities is grounded on the idea that New Zealanders are all the same, all indistinguishable, and does not take into account the specifics of your particular situation. Suppose that you bought a hundred lotto tickets a couple of days ago but have no intention of leaving your third floor apartment tomorrow, perhaps because you've suffered a broken leg. Given this additional information, your friends statement must be regarded as false; you do indeed have more chance of winning Lotto than being killed in a car accident. What this example shows among other things is that the fundamental philosophic axiom that statements must either be true or false runs into difficulties when the statements concern probabilities, because any estimate of probability is a conjecture based on limited information which can be revised as more information comes to light.
There is an old argument in philosophy, related to the arguments around the existence or non-existence of free will, that if the universe is deterministic and evolves according to deterministic laws, and if one possesses perfect knowledge of a particular system, one should be able to predict perfectly its future developments. Future events will all have a probability of either 1 or 0. In a deterministic universe, it only makes sense to make an estimate of probability if we only have limited knowledge, are partly ignorant. If we know everything about the present state of a system, we would know everything about its future. An evaluation of probability requires some ignorance; one must lack some information. It would be nice to say that the more knowledge we have of a situation or system, the closer our estimate of a future event's probability comes to either zero or one, but as the examples above demonstrate, the relationship between knowledge and certainty is not simple and very far from linear.
Of course, as I discussed in the other post, physicists today believe in fact that we do not live in a deterministic universe, that the universe is in key respects underdetermined. This has been for close to a hundred years the dominant position with respect to interpretations of quantum physics. The idea of probability is central to all quantum physics, the idea that we cannot know facts for sure when dealing with particles, but only possibilities. At this point, I want to bring up Schrodinger's cat, a thought experiment readers may be familiar with. It's interesting. Just in case, I'll recapitulate its basic ideas.
In 1935, Schrodinger presented the following thought experiment, an experiment in which a cat is put in a box with a piece of uranium that has a fifty-fifty chance of decaying during the period the cat is ensconced within the box. If it decays, a gun will go off, killing the cat. Schrondinger argued that, until the box is opened and the scientist looks inside, the two states "Cat-alive" and "Cat-dead" both exist simultaneously. The cat is alive and dead at the same time. However, when the scientist opens the box, 'wave-function collapse' occurs and one particular state wins out over the other. Schrodinger's purpose in posing this thought experiment was not to present a realistic picture of quantum physics but rather to show that the dominant interpretations of quantum physics current in his day must be wrong if they yielded such an absurd result as a consequence. However, physicists since have run with it – one interpretation of quantum physics that readers might have heard is the idea of a multiverse, that whenever a system can go in more than one direction multiple universes branch off, each of them enacting a different possibility. In this case, when the scientist opens the box, an even number of universes branch off, half of them expressing the 'cat-alive' possibility and the other half the 'cat-dead' possibility. These different universes don't subsequently interact. More recently, the popular theory among physicists to deal with the 'measurement problem', the problem of wave-function collapse, is known as decoherence, a theory I don't fully comprehend but which I understand to be only a partial solution to this problem.
Although I am not a professional physicist, I have thought about this problem for many years now, and have for a long time believed that there is simple route out of the mess. Many quantum physicists believe indeterminacy to be a feature of the universe. But perhaps it is simply a feature of what we can know about the universe. The Hesienberg uncertainty principle states that it is impossible to know simultaneously the precise position and momentum of a particle but this does not necessarily mean that the particle lacks a precise position and momentum. Rather it may be that it is impossible for any human being to know it. The Schrodinger and Dirac equations do not describe reality, they describe what can be known about reality, set limits on that knowledge. Let's return to the Schrodinger's cat thought experiment for a bit to illustrate this idea. Surely, even if the scientist doesn't know if the cat is dead or alive, the cat itself must know? It seems we have two universes, not in the multiverse sense, but in the sense that there is universe known to the cat, and a universe known to the scientist. In the first universe the cat is either alive or dead; it is only in the scientist's universe that the cat is both alive and dead at the same time. Suppose the scientist deputises an assistant to open the box; suppose that the assistant finds the cat alive. We now have three universes: the cat's universe, in which it is definitely alive, the assistant's universe, in which the cat is definitely alive, and the scientist's universe, in which the cat is dead and alive at the same time – until the assistant informs the chief scientists of its condition. There is a different universe for every observing consciousness; the equations only describe what can be known by any particular individual or group, rather than revealing the inner truth of reality.
In proposing this interpretation of quantum physics, that the equations describe what can be known rather than all of what is out there, I am simply bringing the notion of probability back to its roots. Any estimate is kind of semi-rational guess based on limited information, on knowledge and ignorance, is at heart subjective. Perhaps quantum physics sets limits not only on what we know, but what it is possible to know.
When Schrodinger posed his thought experiment, he did so in order to draw attention to the absurdities of contemporary interpretations of quantum. Schrodinger in fact believed that the universe was indeed deterministic and that the current theory was incomplete. At the time, he believed in what is called a hidden-variable theory. Albert Einstein himself also believed in a hidden-variable theory, saying in a letter once, "I am convinced that God does not play dice!" In 1932, the genius mathematician John von Neumann presented a proof that no hidden variable theory could account for quantum mechanics, that no hidden variable theory could be true. Today, however, largely because of the work of John Bell in the 'sixties, we know that hidden variable theories are indeed possible so long as they are non-local, so long as they allow information to be transmitted from one system to another faster than the speed of light (contrary to the Special Theory of Relativity). So Einstein gets his hidden-variable theory but at the price of finding it irreconcilable with his Special Theory of Relativity.
I myself believe in a hidden variable theory and would now like to set out my own opinion. The universe is deterministic. Therefore we simply must accept some kind of hidden-variable theory. This theory, as Bell showed, must be non-local – meaning that whether on not the cat survives its internment in the box may well depend on stuff transpiring on the other side of the planet or on the other side of the galaxy. Aside from this non-locality, it is impossible to know the details of these hidden variables. When such hidden-variable theories were first proposed by people like de Broglie back in the 'thirties, it was assumed that even if science lacked the capacity to explore and delineate such hidden variable theories at the time, in the future science would be capable of doing so. I am not so sure. Perhaps the Schrondinger and Dirac equations set fixed limits on what humans can know scientifically. Perhaps knowledge of this core aspect of reality is only available through revelation, through mystical experience.
It is possible, arguably, that the hidden variables in any hidden variable theory are the actions of a supernatural entity or entities, perhaps God (if we suppose only one such supernatural agent), perhaps an array of spirits and ghosts who interact with matter via the grey area of quantum indeterminacy. The old adage has it that "God moves in mysterious ways" and perhaps human lives and human civilisation is guided by higher beings. We cannot prove the existence of the supernatural – this is why Kierkegaard speaks of the "leap of faith". The knowledge of reality provided by science is inevitably circumscribed and perhaps we need to look outside science for answers. The supernatural lies outside the purview of reason. Perhaps, if Schrodinger's cat survives its captivity, it's because a guardian angel is looking our for it and ensuring the uranium doesn't decay. And if it gets killed... well, perhaps there is a reason for that too. If estimates of probability arise from ignorance and quantum physics draws a line beyond which science cannot go, perhaps we must look to sources of knowledge outside the scientific method. I know I sound flakey suggesting this but no-one can prove me wrong.
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