Imagine that a pair of photons are emitted from a central point (C) in space (see Figure 1) and propagate in opposite directions towards a polarization detector to the right (R) and to the left (L), each located a distance of one light-year from C. The method of photon production (a positronium source of correlated pairs of photons) guarantees that their polarizations will be the same. Both Bohr and Einstein would agree that if a photon-pair is produced and the detectors are both oriented vertically (as in Figure 1), a detection of a vertically-polarized photon at L in one year after photon-pair production will invariably correspond to a detection of a vertically-polarized photon at R. Similarly, neither detector will detect horizontally-polarized photons. Imagine now that the orientation of the left detector is rotated 30° clockwise in the plane perpendicular to the line from L to R, as in Figure 2. Quantum mechanics predicts that the proportion of a series of emissions of polarized light which match (both detected or both not detected) at L and R will be cos² (30°) = 0.75, meaning that in 3 cases of 4 there was a match, and in 1 case of 4, a photon was detected at L and not at R, or vice versa.

Bell's Theorem concerns a prediction about what should happen in the set-up of Figure 3, which is similar to Figure 2 except that the detector at R has been rotated 30° counterclockwise in the plane perpendicular to the line from L to R. Bell claimed that the locality assumption (i.e., the assumption that no signal can travel faster than the speed of light) dictates that the number of mismatches (i.e., errors) resulting from the instantaneous counterclockwise rotation at R (producing the Figure 3 set-up from the Figure 2 set-up) can be no more than twice the mismatches for Figure 2, ie. 2 cases in 4. The number of mismatches could be less, however, because mismatches (i.e., errors) of both ends could simulate a match (Bell's inequality). But in most experiments that have been performed, Bell's inequality is violated, in precisely the manner predicted by quantum mechanics, i.e., cos² (60°) = 0.25, meaning that in 1 case of 4 there is a match and in 3 cases of 4 a mismatch.

The first experiments to test Bell's inequality for photon polarizations were not sophisticated enough to preclude signals between the two photons L and R communicated at the speed of light. But apparatus used by Alan Aspect at the University of Paris in 1982 produced results that would require a signal many times the speed of light. However, the apparatus is not yet sophisticated enough to detect all but a small portion of the emitted photons. If Bell's inequality holds for all photons, it must be explained why the apparatus would select photons in precisely the manner predicted by quantum mechanics. It could also be asked whether oddities of photon spin (which is poorly understood) are well enough conceived that one can say with confidence that the experiment replicates EPR.

For a critique of the statistical methods of Aspect's experiment based on "subtraction of accidentals", see The Tangled Methods of Quantum Entanglement. For a critique questioning the timing constraints in Aspect's experiment see Does Bell's Inequality Principle rule out local theories of quantum mechanics.

But given that the experimental results are correct, that it replicates EPR and that Bell's inequality is violated, what does that say about the nature of reality? David Bohm has not rejected his belief in hidden variables or the incompleteness of quantum theory -- instead choosing to reject nonlocality -- believing that the signals are instantaneously communicated (faster than light). Others reject supraluminal communication and the objective determinateness of noncommuting observables of subatomic particles. One theorist even suggested that information from the first particle can travel backward in time to the point of the pair production and then travel forward in time to the second particle -- arriving at the precise moment of measurement. In any case, denying the simultaneous reality of position and momentum of an electron is not sufficient to guarantee its non-reality, insofar as its mass and charge can be determined to within any known experimental limits.

In their struggle to understand experiments, physicists may challenge anything and everything. They challenge linear time, induction, deductive logic, relativity, quantum theory, reality, causality, reason, etc. In a sense it is healthy to regard nothing as sacrosanct, but without reason & order science degenerates into incoherent babble. Laymen listening to the far-out speculations of desperate physicists tend to grasp at every bizzare hypothesis as proven fact. Some are excited by the idea that reality is as random, muddled, ambiguous, contradictory and subjective as their own thought processes. Physicists themselves sometimes confuse obscurity with profundity or mathematical agility with understanding. They lose humility, ceasing to believe in a vastness of undiscovered physical law beyond present knowledge. The ultimate challenge of being scientific is to retain imaginativeness, openmindedness, skepticism and an intolerance for contradiction within a single frame of mind.

The majority of physicists make no attempt to form models of reality, concerning themselves only with mathematical prediction -- although without an explicit metaphysical denial of the existence of objective reality (which would be a model of reality, e.g., the Copenhagen Interpretation). I think this approach indicates an implicit acceptance of both causality and of the objectivity of reality. I favor the idea that the so-called paradoxes of slits and circular apertures can be explained by particle-slit (particle-aperture) interaction n and a statistical interpretation. My second choice would be hidden variables -- not in the sense of particles, necessarily, but in the sense of undiscovered phenomena that currently make quantum theory incomplete. (See Is QM a complete theory?.)

---

Be first to comment this article

Only registered users can write comments.
Please login or register.

Powered by AkoComment Tweaked Special Edition v.1.4.6
AkoComment © Copyright 2004 by Arthur Konze - www.mamboportal.com
All right reserved