Quantum Bayesian Networks

January 22, 2013

Causality and Quantum Mechanics

Filed under: Uncategorized — rrtucci @ 4:39 pm

This blog is a travelogue of sorts for a globe trekker of sorts (me). It’s a Captain’s log for my tiny one man boat. Here is my newest entry.

These are exciting times for this traveller. In the past few weeks, I’ve been gearing up for my next trip, in which I plan to visit the country of Causality. It’s a huge country, so one could easily get lost in it. To prevent that from happening to me, I’ll be doing a journey that has been done before with much success. I’ll be retracing the steps of an earlier, very famous and intrepid, Bayesian networks explorer, Captain Judea Pearl, who has done for Causality what Captain Cook did for the Pacific.

One can often reverse some of the arrows of a Bayesian net without changing the full probability distribution that the net represents. This leads some people to say that Bayesian networks are not causal. I like to say instead that the basic theory of B nets, all by itself, is causally incomplete. Judea Pearl has taught us that one can build a super-structure on top of that basic foundation, to address causality issues more fully. The object of the superstructure is to compare at least two B Nets, the original one and another one obtained from the first by doing an “intervention” or “operation, or “surgery” on it. Pearl has even devised a “calculus” for that superstructure.

Here are some references recounting captain Pearl’s Pacific/Causality voyages:

Wikipedia has two entries (here and here) on Causality that are pretty good.

The importance of Causality, or the big C, has been recognized by mankind for thousands of years in fields as diverse as: religion, philosophy, logic, history, jurisprudence, psychology, medicine, pharmacology, epidemiology, mathematical probability and statistics, and physics.

C is a type of bond that connects, in varying degrees, two events across time, or two statements in an if-then clause in logic, or two events in probability theory.

In physics, which is my gig, C is everywhere you look. It could be called Nature’s Hammer.

C is virtually synonymous, or at least joined at the hip, with what we call a force. In Newtonian mechanics, a force causes an acceleration. The force is the cause and the acceleration is the effect. A force by any other name is still a cause. The force of a punch to the gut or a hammer crushing glass. The force of a giant maelstrom pulling a sea vessel, like a twig, inexorably towards its center. All manifestations of C. Since forces are a major concern in physics, C is too. But its relationship to force is not the only reason why physicists are enamored with C.

C often relates two events close in time and space. So any temporal phenomenon in physics, which is just about everything in physics, is deeply related to C. For example, in special relativity, which tells us how the clocks in different inertial frames are related, C is there. It’s lurking beneath the surface, in all that talk about simultaneity of events, light cones, spacelike and timelike intervals and frame dependance of observations. Other examples of phenomena related to C because of their temporal nature: the Second Law of thermodynamics, and processes with feedback. As in the case of special relativity, C is good at imposing restrictions on what a system can do.

And then, as is its wont, quantum mechanics throws a spanner into the C works. Quantum mechanics supercedes our classical ideas of what C is and how it should behave. Purely classical physics is based on differential equations with initial and/or boundary conditions. These seem to imply that nature and C are deterministic. That C is merely the hand of destiny. But then quantum mechanics tells us that no, nature and C have an inescapable, intrinsic probabilistic aspect to them. But it gets worse. Quantum mechanics tells us that nature and C are not just gambling with an ordinary probability theory, but with a probability theory based on complex amplitudes, and that makes it rife with quantum entanglement and coherence weirdness (and richness). And God only knows how C will manifest itself in our final theory of quantum gravity, but it’s certain to be in an interesting way, full of flair and panache.

C and quantum mechanics are both ubiquitous topics in Physics, so these two topics are likely to overlap in many ways, some already known, others awaiting to be discovered.

So far, Captain Pearl has not done much exploring of C in quantum mechanics. He has not sailed his uniquely outfitted man of war, the HMS Bayesian Networks, too close to those shores yet. This is a great opportunity for quantum information theory and quantum computing explorers.

Causality a work!
dominoes

Bullet ripping through Jack of Hearts. High speed photography by MIT's Harold (Doc) Edgerton.

Bullet ripping through Jack of Hearts. High speed photography by MIT’s Harold (Doc) Edgerton.

Artist Harry Clarke's 1919 illustration for "A Descent into the Maelström"

Artist Harry Clarke’s 1919 illustration for “A Descent into the Maelström”

Wikipedia entry for Edgar Allan Poe’s short story “Descent into the Maelstrom” here

1 Comment »

  1. Your ship is sailing so fast it is hard to keep up even when just following you from a thousand miles away looking through an inverted telescope.

    Comment by siteadmin — January 22, 2013 @ 5:08 pm


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