Monday, April 30, 2007

Non-local realism

Curiosity always draws the student of color perception to revisit the advances in the research of the physiology facilitating color vision. The student learns about particles of light called photons hitting like a billiard ball (activating) a rhodopsin protein, isomerizing it, and then producing a phototransduction cascade resulting in the cell membrane to hyperpolarize and cut off the neurotransmitter to the second order neurons in the retina. Yet, when the stimulus is studied, it is not a particle but an electromagnetic wave. What is the correct visualization of a photon, what is a photon's realism?

Albert Einstein, the Swiss student who in 1905 came up with the photon concept in his paper Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, later in life stated "Gott würfelt nicht," God does not play dice. By this he meant that quantum theory does not provide a complete description of physical reality, because quantum theory only gives probabilistic predictions of individual events. In the seminal 1935 EPR paper with Podolsky and Rosen, Einstein wrote "while we have thus shown that the wavefunction does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible."

Such models of physical realism, suggesting that the results of observations are consequence of the properties carried by physical systems, are called hidden-variable theories. The idea is that all measurement outcomes depend on pre-existing properties of objects that are independent of the measurement. The limitation of quantum theory then would be that we do not know all variables, they are hidden from us.

Another important concept is that of locality, which prohibits any influences between events in space-like separated regions. Think of it in terms of Maxwell's equations, where the electric and magnetic fields are plane waves travelling at a constant speed, which is the speed of light. If there is causality between two non-local events, the time delay must be larger than the time light takes to travel from the first to the second event.

An example of non-local effect is the quantum phenomenon of entanglement, where, for example, a Ti:sapphire femtosecond laser pumps a type 2 beta-barium-borate (BBO) crystal, which in virtue of its optical birefringence produces two photons sharing the same wave function. The two photons can be directed in two separate arms of an instrument, becoming non-local. Yet, because they share the same wave function, when one photon's state changes, the other photon's state must also change at the same time, which is a non-local effect; the two photons appear to have a simultaneous non-local reality.

entanglement

Many years after the EPR paper, some physicists still debate on the photon's reality. For example, every two years the SPIE still has a conference on "The Nature of Light: What Are photons?" However, for most scientists active in the field, this question is not asked. In fact, experimentally observable quantum correlations demonstrate that intuitive features of realism must be abandoned.

This is shown beautifully in a recent article by Gröblacher et al. in the 19 April issue of Nature, An experimental test of non-local realism, which is published in two parts, an experimental part in the printed journal and a theoretical part in an online supplement. The supplement shows elegantly how to construct an explicit non-local hidden-variable model. The experimental part then shows how to build an experimental set-up for testing non-local hidden-variable theories. The salient, and tricky, part of the experimental plan—in which pairs of polarization entangled photons are generated via spontaneous down-conversion as mentioned above—is in how to determine the two-photon visibilities so that the hypothesis is proven.

Where does this leave you when you are trying to understand color perception? Abandon realistic descriptions of photons. You only need a good mathematical model, and everything you need to know about visual stimulation by photons is included in the color matching functions. Even when you need to consider conditions like color vision deficiencies, you can do it by manipulating appropriately the color matching functions, without requiring a realistic description of photransduction.

Thank you to Dmitri Boiko for the pointer to the Nature article.

PS: Links contributed in the comments: