What follows is most likely among the wrongest wrongs a wronger ever wronged. I know little about this subject, but that won’t stop me from wielding my philosophical scimitar like a berserker. Where angels fear to tread, and so on:
The Statistician to the Stars tweeted a link to this essay in Wired, about whether quantum mechanics are probabilistic (Copenhagen Interpretation) or deterministic (Broglie-Bohm theory). This topic has been on my mind due to the fine essay about the philosophy explored in the Matrix movies in the initial issue of the Sci Phi Journal (get your copies here) by David Kyle Johnson.
In this essay, Dr. Johnson mentions that the universe is not deterministic – is not caused – at a quantum level. What he means is that, unlike the larger-scale physical world, we can’t begin from a known state and know, according to natural laws, what will happen next. For an example of a deterministic event: Galileo climbs the tower of Pisa, and drops a 1lbs lead sphere from the top. We know – meaning, we can confidently predict within a very small margin of error – that the ball will fall at 32’/sec^2, and, adjusting for wind, air resistance and the Coriolis Effect, exactly where the ball will land. We know this because the behavior of a ball dropped through the air near the surface of the earth has been Determined to our satisfaction – we have cooked up a series of mathematical models that, when applied to the motions of bodies under gravity through a gas, provide gratifyingly consistent and useful results.
This is the sort of things that gives bad scientists a big head, and tends to make even good scientists believe that the mathematics *are* the real world. No, the mathematics, in an inexplicably beautiful way, *describe* the real world. In one of his lectures, the great Richard Feynman, after filling a couple blackboards with complex math, paused to reflect that, after all, a couple of bodies were going around each other – the math seemed far more complex that the behavior is was meant to describe. The thing to keep in mind is that the ultimate referent, the thing to which our beliefs may be true, is the physical thing, and not the math that describes it.
Now we come to quantum measurements. Niels Bohr and a group of other brilliant men concocted some very useful formulas for describing the behaviour of sub-atomic phenomena. These formulas have been developed further into the Standard Model of physics that every student of physics learns. The Standard Model is the backbone of all current nuclear physics.
But the equations of the Standard Model are probabilistic, not deterministic. To go back to our Pisa example above, it would be like saying that there’s a 75% chance that the ball will land within a given circle 10′ in diameter, but 25% of the time, it won’t – every once in a while, it’ll even land in Florence or on Mars or somewhere in the Tadpole Galaxy. The math tells you it’s very unlikely to land in another galaxy, but you can’t entirely rule it out.
And that’s how things are said to work in the subatomic world: all you know is how likely it is that Outcome A will obtain. You just can’t determine in advance that you’ll certainly get Outcome A – you might, you might even get it 99.9% of the time, but you might not. Unlike the falling ball, it isn’t just a matter of there being other factors we just don’t know about that caused the ball to move too fast or too slow or miss its target – nope, it is the nature of sub-atomic reality that we can’t determine the outcome in advance.
Here’s where it gets logically and philosophically tricky: Dr. Johnson, along with almost all physicists, says that this means that the behaviors of, say, electrons are uncaused. It isn’t the case of the most useful math being probabilistic, but the reality being deterministic – nope, the claim is that reality really, truly is a matter of chance, that an electron, somehow, isn’t in any one place or traveling along any one particular vector, until we ‘collapse the wave function’ by measuring it.
Here we point out, as logicians as well as philosophers, that we have completely reified the math: we have let the math tell reality how it has to be. Is there an experiment or a logic exercise that would allow us to decide which, if either, of the following statements is true?
1. Events at a quantum level are uncaused.
2. Events at a quantum level may be caused, but, if so, we don’t know how.
This is the equivalent of distinguishing between “they certainly look uncaused” and “we sure are having trouble seeing the cause, if it exists.” Note that the math doesn’t figure into it.
It might be argued – I think it has been – that Occam’s Razor favors #1: what we see is what we get, we don’t see cause, therefore it isn’t there. The counter argument: contrary to old Bill Occam, you’re adding to the physical world the assumption that an additional class of beings exist, ones without cause. It would be simpler to assume one class of objects, but merely say we don’t know the causes of some of them.
Bottom line: we can’t say that we *know* even in the limited and hedged scientific sense, that quantum events are uncaused. Maybe, maybe not. To assert this is the equivalent of claiming to have proved a universal negative. As is so often the case, logically and philosophically, the right answer is: we don’t know.
The article from Wired shows that some scientists are working under the assumption that quantum events are caused, and are providing math and experimental results to show how it might work. The only interesting part, one that Kuhn predicted, is that the practitioners of Normal Science aren’t all that interested in examining their models.