Probability and Causality – can they be reconciled in our understanding of the universe?

In last month’s Philosophy Now (July/August 2013) Raymond Tallis wrote an interesting and provocative article (as he often does) on the subject of probability and its relationship to quantum mechanics and causality (or not). He started off by referencing a talk he gave at the Hay Festival in Wales titled, ‘Has Physics Killed Philosophy?’ According to Tallis, no, but that’s neither the subject of his article nor this post.

Afterwards, he had a conversation with Raja Panjwani, who apparently is both a philosopher and a physicist as well as ‘an international chess champion’. They got to talking about how, in quantum mechanics, ‘causation has been replaced by probability’ unless one follows the ‘many-worlds’ interpretation of quantum mechanics, whereby every causal effect is realised in some world somewhere. One of the problems with the many-worlds view (not discussed by Tallis) is that it doesn’t account for the probability of an event occurring in ‘our world’ as dictated by Schrodinger’s equation and Born’s rule. (I’ve written an entire post on that subject if the reader is interested.)

David Deutsch, the best known advocate of the many-worlds interpretation, claims that the probabilities are a consequence of how many worlds there are for each quantum event, but if there are infinite possibilities, as the theory seems to dictate according to Feynman’s integral path method, then every probability is one, which would be the case if there were an infinite number of worlds. It has to be said that Deutsch is much cleverer than me, so he probably has an answer to that, which I haven’t seen.

Tallis’s discussion quickly turns to coin-tossing, as did his conversation with Panjwani apparently, to demonstrate to ordinary people (i.e. non-physicists) how probabilities, despite appearances to the contrary, are non-causal. In particular, Tallis makes the point, often lost on gamblers, that a long sequence of ‘Heads’ (for example) has no consequence for the next coin toss, which could still be equal probability ‘Head’ or ‘Tail’. But, assuming that the coin is ‘fair’ (not biased), we know that the probability of a long sequence of ‘Heads’ (or ‘Tails’) becomes exponentially less as the sequence gets longer. So what is the connection? I believe it’s entropy.

Erwin Schrodinger in his book (series of lectures, actually), What is Life? gives the example of shuffling cards to demonstrate entropy, which also involves probabilities, as every poker player knows. In other words, entropy, which is one of the fundamental laws of the universe, is directly related to probability. To take the classic example of perfume diffusing from a bottle into an entire room, what is the probability of all the molecules of the perfume ending up back in the bottle? Infinitesimal. In other words, there is a much, much higher probability of the perfume being evenly distributed throughout the entire room, gusts of wind and air-conditioning notwithstanding. Entropy is also linked to the arrow of time, but that’s another not entirely unrelated topic, which I may return to.

Tallis then goes on to discuss how each coin toss is finely dependent on the initial conditions, which is chaos theory. It seems that Tallis was unaware that he was discussing entropy and chaos theory, or, if he did, he didn’t want to muddy the waters. I’ve discussed this elsewhere in more detail, but chaos is deterministic yet unpredictable and seems to be entailed in everything from galactic formation to biological evolution. In other words, like entropy and quantum mechanics, it seems to be a fundamental factor in the universe’s evolvement.

Towards the end of his article, Tallis starts to talk about time and references physicist, Carlo Rovelli, whom he quotes as saying that there is ‘a possibility that quantum mechanics will become “a theory of the relations between variables, rather than a theory of the evolution of variables in time.”’ Now, I’ve quoted Rovelli previously (albeit second-hand from New Scientist) as claiming that at the basic level of physics, time disappears. The relevance of that assertion to this discussion is that causality doesn’t exist without time. Schrodinger’s time dependent equation is dependent on an ‘external clock’ and can only relate to ‘reality’ through probabilities. These probabilities are found by multiplying components of the complex equation with their conjugates, and, as Schrodinger himself pointed out, that is equivalent to solving the equation both forwards and backwards in time (ref: John Gribbin, Erwin Schrodinger and the Quantum Revolution, 2012).

So it is ‘time’ that is intrinsic to causality as we observe and experience it in everyday life, and time is a factor, both in entropy and chaos theory. But what about quantum mechanics? I think the jury is still out on that to be honest. The many-worlds interpretation says it’s not an issue, but John Wheeler’s ‘backwards in time’ thought experiment for the double-slit experiment (since been confirmed according to Paul Davies) says it is.

When I first read Schrodinger’s provocative and insightful book, What is Life? one of the things that struck me (and still does) is how everything in the universe seems to be dependent on probabilities, especially on a macro scale. Einstein famously said “God does not play with dice” in apparent frustration at the non-determinism inherent in quantum mechanics, yet I’d say that ‘God’ plays dice at all levels of nature and evolution. And causality seems to be a consequence, an emergent property at a macro level, without which we would not be able to make sense of the world at all.