Tuesday, June 25, 2013

Is the wavefunction ontological or epistemological?

Part 1: The EPR argument

Quantum mechanics is a fascinating subject, extremely rich in mathematical, physical, philosophical, and historical content. Studying quantum mechanics is school with its classical problems of solving the hydrogen atom is only the very first step in a long journey. The quantum foundation area with its diversified views is an equally fascinating domain. At first sight, it looks like the majority of the current interpretations are “obviously” misguided except for your own, whatever that may be, and all other interpretations must be rooted into classical prejudices. However this is not the case and it takes some time and effort to fully appreciate and accept all points of views in interpreting quantum mechanics.

Into all this mix, I am proposing yet another quantum mechanics interpretation, and I will attempt to show that quantum mechanics is actually intuitive and it all follows from clear physical principles in a reconstruction program. Since the principle names the theory (e.g the theory of relativity got its name form the relativity principle), I will call quantum mechanics: the theory of elliptic composability and I will show that all primitive concepts like for example ontology and epistemology has to be adjusted to their corresponding composability class. In particular the quantum wavefunction is neither ontological nor epistemological, meaning it is not “parabolic-ontological” not “parabolic-epistemological” but it will be shown to be “elliptic-ontological”.

I will start this journey following arguments in historical fashion, and I will start with the EPR argument. I have no clear idea how many parts this series will contain, probably around 10 but I will keep an open format.

At the dawn of quantum mechanics, Bohr struggled with its interpretation, and the ideas of complementarity and uncontrollable disturbances was a major part of the discussion. Today this is no longer the case dues to advances in understanding of the mathematical structure of quantum mechanics. Even today most textbooks are painting the wrong picture of the uncertainty principle due to sloppy mathematical formulation and this probably deserves a post of its own for clarification.

For the EPR argument suffices to state that one cannot measure simultaneously with perfect accuracy both the position and the momentum of elementary particles. Then Einstein, Podolski, and Rosen argued along the following lines: what if I have a system which disintegrates into subsystem 1 and subsystem 2 and we measure position on subsystem 1 and momentum on subsystem 2. If the original system was initially at rest, conservation of momentum implies that measuring the momentum of subsystem 2 implies we know with absolute precision the momentum of subsystem 1. But wait a minute, on subsystem 1 we measure with perfect accuracy the position as well so it seems that we succeeded on beating the uncertainty principle. Quantum mechanics does not allow that which means quantum mechanics must be incomplete.

The whole argument holds provided two critical assumptions hold as well:

  • “If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.” 
  • “On the other hand, since at the time of measurement the two systems no longer interact, no real change can take place in the second system in consequence of anything that may be done to the first system.” 

Both assumptions are actually wrong and later on, John Bell refuted the EPR conclusion based on the second assertion (that of locality). Arguing on similar lines with Bell, one can show that the first assumption is invalid as well.

The remote effect due to local measurement is called quantum steering and while it cannot be used to send signals faster than the speed of light, it does change the remote state. Such effects were observed in actual experiments. In the elliptic composability quantum mechanics reconstruction project it is easy to understand its root cause:

In classical or quantum mechanics, observables play a dual role, that of observables and of generators. But while in classical mechanics (parabolic composability) the observables for a total system factorizes neatly into a product of observables for each subsystem, in quantum mechanics (elliptic composability) observables and generators are mixed together and the factorization is not possible in general (see Fig 3 in http://arxiv.org/pdf/1303.3935v1.pdf) . In other words, the system becomes “entangled”.

In the next post I will show Bell's refutation of EPR argument based on locality.

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