Thursday, December 18, 2008

Quantum Decoherence

Quantum Decoherence looks to be an idea that has a lot going for it. In fact it seems to tie up so many lose ends that I find the notion extremely attractive myself. As an explanation of the apparent sudden and random discontinuous changes of the quantum mechanical state vector decoherence is just so neat. This web site sums up the theoretical attractions of decoherence theory. I have reproduced some of these attractions below (with my additional comments in brackets):

No additional classical concepts are required for a consistent quantum description. (A sharp distinction between macroscopic classical systems and microscopic quantum mechanical systems does not exist)

There are no particles (The universal ontology is a uniform one of waves only. The cosmos doesn't contain any dirty gritty bits, only smooth voluptous waves)

There are no quantum jumps (No probabilistic discontinuous jumps of the state vector)

There is but ONE basic framework for all physical theories: quantum theory (No extra physics is needed to account for quantum jumps; we have the physics already in the form of various wave equations - we just need to apply these equations to the measurement of quantum systems with macroscopic systems)

There is no time at a fundamental level (That is, because all quantum equations are reversible, the cosmos is in principle reversible and time is an artifact of boundary conditions, end of story; in fact end of story telling as well)

Finally the Decoherence web site adds:

It is a direct consequence of the Schrödinger equation, but has nonetheless been essentially overlooked during the first 50 years of quantum theory.

What a deal. It’s hard to resist. No new theory; just the correct and insightful application of quantum equations, an application that’s been overlooked for the last 50 years. The whole thing leads to a seamless, ‘in principle’ smooth and deterministic physics with no need to lash on any ad hoc random jumps of the state vector. On this view the randomness of quantum theory is not absolute but only apparent. It is a product of the entanglement of quantum systems with the chaos of macroscopic objects used to measure quantum phenomena thus leading to the apparent, repeat apparent, random changes in state of microscopic systems.

One question I need to look into is this: What does decoherence theory say about the case of not detecting a particle in a designated state? The failure to detect a particle in a state means that it must be in the orthogonal complementary state, which is in fact a superposition of many states. Can entanglement account for the apparent jump in state associated with not detecting a particle?

Decoherence theory has the touch and feel of a winner, especially as its reduction of explanatory entities is very much in the spirit of Occam’s razor.

However, I have my doubts. I have long noted the analogues between quantum theory and the probability envelopes of random walk and I am now fixated on the idea that probability envelopes of a special quantum kind are incarnated as a “real” world ontology. These analogues suggest that we go the whole hog and expect these envelopes to behave like other probability envelopes when a change in information occurs: that is the envelope “collapses” or at least suddenly changes its form under certain circumstances. I may well be backing the wrong horse, but the reason why I take the application of these analogues seriously is indicated below. In the following I note the parallels between quantum envelopes and conventional probability envelopes. In the following I use ‘real’ probability envelopes and not complex envelopes. So for a state represented by |p) we have |p) = (p| .

If we have two probability envelopes or ‘states’ |p) and |q) each of which pertains to one of two separate (= ‘orthogonal’) coordinates then the state of the composite system is a two dimensional probability envelope that effectively can be represented by the ‘outer product’ |p)|q), as in quantum mechanics proper.

Imagine that we have a particle in a probability state represented by the envelope |p) and we have another probability envelop on the same coordinate which is some kind of detecting ‘field’ or state, |q), that is capable of capturing the particle in state |p). Under these conditions the probability of the particle being captured by the detecting state is equal to the inner product, or ‘intersection’, (p|q) as in quantum mechanics proper.

The algebra of quantum envelopes looks suspiciously like a kind of probability calculus but with real probabilities being replaced by “complex probabilities”.

The foregoing “state algebra” doesn’t produce any dynamics: that can be added with Schrödinger’s equation; as I have suggested in my book this equation has a close relation to the random walk diffusion equation.

To my mind quantum theory is too closely related to random walk and probability calculus to dismiss the notion of real collapses (and discontinuous changes of state). This need not be the Copenhagen type collapse which posits the presence of an observer. In my interpretation of quantum theory, the presence of a “detecting” or “capturing” state is sufficient for a possible collapse or a sudden change of state according to probability. I’ll be frank and admit that I’m expecting the collapses to be real because otherwise I’m confounded by the similarities with probability calculus. I’ll candidly admit that I’m applying an anthropomorphism in expecting the similarities of quantum theory with probability calculus and random walk not to be wasted. For me decoherence is an anticlimax, a solution by those who have either lost the plot or couldn’t see it in the first place; it cuts across my expectation of uncovering a meaningful, coherent story. (Although, of course, decoherence has its own cluster of alluring points as I have indicated above)

These ideas are, of course, highly speculative, kooky and frankly look to be rather dangerous conjectures to back. But then I’ve no reputation to lose. In contrast decoherence is the safe solution, the tidy deterministic solution; it’s the solution that we know in our hearts to be the likely one if we believe the universe to be a relatively prosaic closed system and not open-ended. In my opinion it’s the solution for the boys and not the men. However, if experimental work does skew the evidence toward the decoherence picture then count me out; I’ll have to concede and admit that the world is more boring than I expected!

Which theories we tend to support, need I say, is not merely a function of experimental data, (which in any case is often not a sufficient sample to settle the matter), but also a function of idiosyncrasies in our background, our sense of analogy, our feel for elegance, what we are expecting to see, and even what we are hoping for. Vested interests and group identification also have a role here.These motivational factors have, needless to say, connections with background agendas, world views, hopes and aspirations. I don’t think it is wrong to have these background hopes and views, it’s only human; but it is well to be aware of them and how they are subtly influencing one’s hopes and expectations and how one interprets the data. Do not let these background influences hide in the subconscious. Be prepared to face them, challenge them, change them, and above all never, never, never, be the slave of them and allow them to string you along. If a world view betrays you and fails as an interpretive structure in the face of contra indicators, throw it away as you would a broken tool. Never fall for the fidiest trap.

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