Jonah Bossewitch	PHI 327

March 6, 1996	Chad Mohler

Red Light, Green Light, 1-2-3

The innocent mathematical assertions that known as "Bell's inequalities" are responsible for generating more confusion than most mathematical assertions could ever dream of causing. Perhaps this confusion stems from the fact that these irreproachable assertions have been brutally violated in the hands of renegade physicists. In fact, an entire family of experiments have been proposed and/or performed that seem to confirm the violation of these inequalities. However, before we jump to any radical conclusions that would force us to completely restructure our world view, we had better be cautious and thorough. What do Bell's inequalities really assert? How are they violated? Is this a paradox? What, if anything, follows from their violation?

When considering Bell's inequalities, it is crucial to consider that most mathematical propositions do not stand alone. Almost all mathematical assertions are grounded in underlying assumptions (explicit, as well as implicit) that form the foundation of those assertions. Mathematical assertions that start with the same assumptions, and still manage to contradict each other, are called paradoxes. However, there are many apparent paradoxes that can be resolved by determining if there are any relevant assumptions that were not shared by both assertions. The only way to fully appreciate the violation of Bell's inequalities, is to consider both the nature of Bell's inequalities, and the assumptions behind their derivation.

Bell's inequalities are derived using classical probability theory which relies upon the following three assumptions: (a) Every correlation can be explained by a common cause, (b) Nothing, including messages, may travel faster than the speed of light, and (c) The universe is not conspiring against us, so the experimental settings are really random. These assumptions combined with the perfect correlations observed when the settings are the same entail the prediction that p(1;2) + p(2;3) >= p(1;3) (a.k.a. Bell's inequalities).

Fortunately, (or else the world would not exist as we now know it) the experimental data that has been gathered indicates that there is a entire class of devices that do not obey these inequalities. The original thought experiment was proposed by EPR, but Aspect was the first to carry out actual experiments with real life devices in 1981. The results reported showed that p(1;2) + p(2;3) were significantly less than p(1;3), in a definitive and puzzling violation of Bell's inequalities. How can we account for the perfect correlations when the settings are equal, and at the same time explain the behavior of the machine when the settings are not equal?!? In the words of David Mermin, "this is the conundrum posed by the device."

After describing an abstract device that demonstrates the EPR paradox, Mermin remarks that his "aim is only to state the conundrum of the device, not to resolve it." However, he later claims that "It is not the Copenhagen interpretation of quantum mechanics that is strange, but the world itself," and this statement hardly sounds neutral. Mermin also claims that value definiteness does not hold for either quantum or macroscopic objects. He tries to convince us that the violation of Bell's inequalities implies that "the moon is not there when nobody looks," and that "Einstein's position [values are definite, but QM is incomplete] now appears to be violated by nature." Mermin is clearly pushing the Copenhagen interpretation (i.e. one possible resolution) without providing a convincing argument for it, or ever admitting that he is preaching a possibility, not a truth.

Mermin dismisses alternative interpretations of quantum mechanics as "trivial", and pretentiously mocks eastern mysticism, as well as anybody who doesn't agree with him (know- nothing-ism). The fact of the matter is that it is perfectly reasonable to reject different classical assumptions than the ones that the Copenhagen gang rejected, since the empirical data is consistent with many versions of what is going on behind the scenes.

For example, to make the "wholeness of nature argument" less vague, we can draw an analogy to computer science. In computer science we can speak about local or global variables. Local variables may only be accessed from within a particular function, but global variables can be read or changed by anybody, anywhere. If the Universe employed a mechanism analogous to global variables (e.g. all photons are the manifestation of a single, "spirit" photon), then the message the particles carry could be a function of that global variable. In this interpretation, signals may travel faster than light, but particles have definite values, and correlated events do have common causes. So, according to this interpretation, I am still entitled to believe that the moon is actually there when I'm not looking at it, and the angels can relax on their pin.

The intricate mysteries of the EPR paradox and the violation of Bell's inequalities are very complex, and I do not intend to resolve this conundrum either. But, it is important to be aware of the locations of the holes in a theory, so that you can make a well informed leap of faith. Mermin chooses to leap in one direction, but there are others paths are logically valid. Besides, if the moon isn't there when I'm not looking at it, where does the man in the moon go?

(PS -	In response to Mermin's challenge to the reader, I was wondering about the validity of Wigner's simplification. What if the color that lights up is not solely a function of the particle, but also a function of the state of the detector, where the state of the detector incorporates its setting (Color = f(particle, detector))? Say that there was also a preexisting relationship between the states of the two detectors (R(d1, d2)) that produced the probability outcomes observed. Wouldn't this explain the data? While this possibility might be unlikely, isn't it possible?)