interpretations, part 1/4

It is time to write about something truly exciting, in other words it is time to write
about the interpretation problem of quantum theory. This is the 1st of 4 posts about it, the introduction if you will.

Some time ago, Chad Orzel wrote a blog post explaining decoherence and it shall be the starting point for us (he later wrote a more detailed explanation as response to a comment).

Consider a single photon in a Mach-Zehnder interferometer, which will end up at one of the two detecors D1 and D2.

If the interferometer is properly set up, the wave function W of the photon will be something like |1> + |2> (normalization coefficients are absorbed in the state vectors). Notice that W is symmetric in the two possible outcomes 1 and 2.

However, we know that when we do the experiment, only one of the detectors will click, either D1 or D2.

And so we have already all the ingredients together for the interpretation problem.

W: The wave function |1> + |2> is symmetric and prefers neither 1 or 2.

R: In reality, only one detector will click, either D1 or D2, and obviously one is preferred over the other.

As Chad explains, decoherence will eliminate to some extent the quantum interference between |1> and |2> and in this sense 'classical behavior' emerges; But this does not really solve our problem.

Even if the product between |1> and |2> or |D1> and |D2> is nearly zero, this does not elimiate the fact that W is symmetric and R is not. (Notice also, that decoherence will in general bring the product between |D1> and |D2> close to zero but not exactly zero and there is no sharp cut-off between quantum interference and classical behavior. But this is really not that important to our problem.)

By the way, please notice that the interpretation problem is a real problem (W does not match R); We are not talking about an 'interpretation problem' in the sense an art critic or a philosopher might use that phrase.

It is evident that every attempt to solve the interpretation problem must fall into one of three categories.

i) The problem is with W. The wave function is not a complete description of R. We will encounter this approach in part 2 of this series as hidden variables, etc.

ii) While W is complete, the problem is about what we mean with 'W describes R'. The Copenhagen interpretation, the ensemble interpretation and others belong here. I will discuss them in part 3.

iii) The most radical proposal is to assume that W is fine and our problem is with R; Reality is just not what we think it is. The many-worlds interpretation is the most important example and I will discuss it in the final part 4 of this series.

One more remark about the upcoming parts; While similar reviews often point to a favored interpretation and describe all others in a negative light, I will try something new and describe all interpretations as convincing and favorable as I can. I hope that this will increase the entertainment value.

continue to part 2.


Chris said...

4) The problem is assuming W and R must match up in the first place. W is a theory, R is a reality. W is imaginary, R is real. W has a vanishingly small percentage of the world's population agreeing on it, R has all but the deaf agreeing on it.

wolfgang said...

I think proposals that W and R do not (have to) match fall into category 2) which I will praise in part 3/4.

Neil B said...

I am the Neil B. mentioned above re Chad's post. For the record, before I move on to Part 4/4:
1. Chad responded directly to a blog post of mine, not a comment at his blog (altho I have commented before on that at his UP.)
2. Chad had to retract his claim that my math was wrong.
3. I recommend checking over my proposal directly, from my name link.