Macroscopic test of quantum mechanics versus stochastic electrodynamics

Local hidden variable theories are known to be inconsistent with quantum mechanics at the microscopic level, from the Bell inequalities @1#. Experimental tests at this level have decided in favor of quantum mechanics @2#, although there are still some experimental problems with low detection efficiency. The situation is different as particle numbers increase. There are no macroscopic tests of quantum measurement theory versus hidden variable theories. While it is possible to obtain Bell-type inequalities @3#, these are difficult to implement experimentally. However, it is in this region that quantum mechanical measurement theory is most open to question, as Bell @1# has most cogently pointed out. It is the purpose of this paper to demonstrate that an efficient test of quantum mechanics is possible, in a regime involving quantum correlations with large particle numbers. The test is a simple extension of a recent parametric oscillator Einstein-Podolsky-Rosen ~EPR! @4# experiment, which first demonstrated the EPR @5# paradox of quantum mechanics in its original form. That is, the experiment was the first to employ observables having the Heisenberg algebra of @ x̂ i , p̂ j#5\d i j , as used in the original EPR paper. Reid has recently shown @6# that this experiment is also intrinsically multiparticle in nature, since the quadrature operator measurements involve multiple particle detection. In testing quantum mechanics, it is useful to have an alternative as a comparison to the quantum mechanical predictions. We choose to compare quantum mechanical predictions with those of stochastic electrodynamics @7#—a classical theory with added vacuum fluctuations. This is known already to reproduce many features of quantum mechanics. In fact, theories of this type, in the guise of approximate Wigner @8# representations with a positive Wigner function, have been used in quantum optics @9# to obtain convenient approximations to quantum theory at large photon number. In this regime, the theory is sometimes called the semiclassical method @10#. Of course, we do not regard this as a practical alternative at small photon number, as it cannot violate the Bell inequality. However, stochastic electrodynamics is a possible alternative to quantum theory at large particle number. Either theory produces identical predictions for many experiments involving second-order correlations, including both squeezing ~quadrature noise reduction! and the original EPR proposal. An EPR experiment in its original form