May 16, 2005

part 5 - interpretation

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So now we have a little quantum background, let's just dig a little deeper into this concept of quantum reality. This stuff is a little higher level than our previous stuff so it should go more quickly. There are really two parts to this. First think about what we've shown. If we think of the quantum particle before we observe it, it is best represented by a wave of possibilities. After we observe it, it's best represented as a particle. This big wave of possibilities condenses to a single possibility.

If we were to ask what is the nature of this pre-observational possibility, this is commonly referred to as the quantum interpretation question. In other words how do we interpret what the quantum possibility wave, Psi, says about the reality of the 'thing' (let's call it a quon as the author does) we are concerned with? In yet anotherphrasing, what does the probability wave (Psi) tell us about the factual situation of an unmeasured quon?

If we were to ask when do these set of possibilities become a single possiblity, this is commonly called the quantum measurement question. This conversion of possibilities to a single possibilities is commonly referred to as when the wave function collapses.

Let's focus on the first part - the interpretation part. We talked about a few different interpretations at to what the wave function says about reality but lets focus on the two extreme cases - the Copenhagen interpretation and the Realist interpretation. Let's lay out their stances on this subject.

Bohr and Heisenberg are the key players of the Copenhagen interpretation. They feel that quantum theory gives a full account of the facts. Let's lay out what this means - sometimes known as the orthodox ontology. They say that there is nothing more to know about the situation. It's not that there's a more adequate representation of the facts than quantum theory and we aren't smart enough to know it or good enough to measure it. There is no more accurate representation than quantum theory. Why one quon hits here and one hits there is unknowable. The two electrons were identical before hitting. Identical in every sense of the word, yet they hit different positions on our screen. The knowledge we lack to determine exactly where the quon hits is simply not there to be known. This is referred to as quantum ignorance. Measured differences arise from quantum randomness - a total black box. You can see why someone at this point might resort to philosophy or spiritual resources to come to grips with this.

Einstein is the key player in the Realist camp. There were lots but he was the most aggressive in pushing this line of thought. Einstein says, 'fine quantum theory works but it does not have a full account of the facts or the mechanism by which a quon hits here or there.' You are missing something. Note that Einstein is not saying we can necessarily determine what that missing thing is, only that it exists. The quon is somewhere in particular before it hits the screen. That is why theories that try to debunk quantum as a full account of the facts are referred to as hidden variable theories. Einstein says that quons are not identical. Quantum theory is a statistical description and a necessarily incomplete description of a quon. Something about the quon distinguishes it from another and that is why the quon hits somewhere different. Our relationship to the quon as an observer is one of classical ignorance.

There actually are theories to describe this hidden variable. The most simple is the pilot wave. A wave that effectively guides the quons in ways that result in wavelike properties before observation and particle like properties after observation.

All these hidden variable theories have 3 common attributes by their very nature:

  1. All particles must be 'connected' to every other particle in the universe - Sounds like a deal killer but it's not a big worry for scientists. Gravity connects everything in the universe. The sun has some, albeit small, influence on a sun trillions of miles away.
  2. This hidden variable must be entirely invisible - Sounds like a deal killer as well but again it's not that big of a problem. Quarks are effectively impossible to separate and measure. They are inferred through behavior in experiments to the point that we believe them to exist with a high degree of probability.
  3. The hidden variable must transmit its control over a quon's attributes (position, momentum, etc.) faster than the speed of light. Ouch. That is a bad one. Hard to swallow.
At any rate there is something unsatisfactory with this pilot wave approach. It certainly seems contrived doesn't it? Nevertheless it could be legitimate. John Bell showed this influence in point 3 had to go faster than light - had to be superluminal. Bell used this fact to do something utterly amazing. He created an inequality from this fact that if it could be experimentally measured would show that either Einstein or Bohr was correct. We'll get to that much later.

Let me give the ending away because you'll probably figure this out from what I've said previously. Just when we get to the end of our story about Bell's inequality and we think one of those two interpretations has won, there will be a maddening loophool that won't actually allow anyone to declare victory. However, it will seriously make one side upset at the possibilities that support their theory. Suspense in science - who knew?

At any rate understand the takeaways here. Either quantum theory is a full account of facts and we as observers of the universe are constrained about what we can experimentally measure about it or a hidden variable theory explains all this and it has some ridiculous sounding requirements. Either way things are strange.

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