We give a definition of locality in quantum optics based upon Bell's work, and show that locality has been violated in no experiment performed up to now. We argue that the interpretation of the Wigner function as a probability density gives a very attractive local realistic picture of quantum optics provided that this function is nonnegative. We conjecture that this is the case for all states which can be realized in the laboratory. In particular, we believe that the usual representation of 'single photon states' by a Fock state of the Hilbert space is not correct and that a more physical, although less simple mathematically, representation involves density matrices. We study in some detail the experiment showing anticorrelation after a beam splitter and prove that it naturally involves a positive Wigner function. Our (quantum) predictions for this experiment disagree with the ones reported in the literature.
We give a definition of locality in quantum optics based upon Bell's work, and show that locality has been violated in no experiment performed up to now. We argue that the interpretation of the Wigner function as a probability density gives a very attractive local realistic picture of quantum optics provided that this function is nonnegative. We conjecture that this is the case for all states which can be realized in the laboratory. In particular, we believe that the usual representation of 'single photon states' by a Fock state of the Hilbert space is not correct and that a more physical, although less simple mathematically, representation involves density matrices. We study in some detail the experiment showing anticorrelation after a beam splitter and prove that it naturally involves a positive Wigner function. Our (quantum) predictions for this experiment disagree with the ones reported in the literature.
One of the Bell's assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., of the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of local realism. In this paper, Bell's inequality is derived in its traditional form, without resorting to the hypothesis of locality, the only assumption being that the probability distributions are nonnegative. These probability distributions are calculated, for a specific optical experiment, in the framework of quantum theory and it is shown that they can take on negative values. This can therefore be regarded as a rigorous proof that the hypothesis of locality is not relevant to violations of Bell's inequalities. The physical meaning of the obtained results is examined.
Abstract I revisit the Wigner (or Weyl–Wigner, WW) representation of the quantum electromagnetic field. I show that, assuming that Fock states are just mathematical concepts devoid of physical reality, WW suggests a realistic interpretation which turns out to be (classical) Maxwell theory with the assumption that there is a random radiation filling space, the vacuum field. I elucidate why, in sharp contrast, non-relativistic quantum mechanics of particles does not admit a realistic interpretation via WW. I interpret experiments involving entangled light beams within WW, in particular optical tests of Bell inequalities. I show that WW provides clues in order to construct local models for those experiments. I give arguments why Bell definition of local realism is not general enough.
Stochastic optics may be considered as simply a local realistic interpretation of quantum optics and, in this sense, it is a first step in the reinterpretation of the whole of quantum theory. However, as it is not possible to interpret all the details of quantum theory in a local realistic manner, as shown by Bell's theorem, minor changes are introduced in the formalism with the consequence that the new theory makes different predictions in some special cases. In stochastic optics, the quantum-operator formalism is simply considered a formal way of dealing with stochastic fields. In particular, the quantum zero point is taken as a real random electromagnetic radiation filling the whole of space. This radiation noise has the same nature as light signals, the only difference being the greater intensity of the latter. We assume that photon detectors have an intensity threshold just above the level of the noise, thus detecting only signals. Transmission of radiation through polarizers follows Malus's law, but the interplay of signal and noise leads quite naturally to the prediction that the detection probability of some signals is enhanced, which is known to be a necessary condition for the violation of the empirically tested Bell inequalities. In our view, correlated photon pairs are pairs of light signals supercorrelated in polarization, in the sense that, as well as the signal, the accompanying noise is also correlated. Thus stochastic optics allows predictions for the empirical correlations very close, but not identical, to the quantum ones. The theory is applied to the analysis of all experiments designed to test the Bell inequalities by measuring polarization correlations of photon pairs. The predictions agree with quantum optics and experiments within statistical errors, except for the Holt-Pipkin experiment. In this case, the experimental results agree with stochastic optical predictions within two standard deviations while violating quantum optics by four.
Over the past three decades or so, experiments of the type called Gedanken have become real. Recall the Schrödinger quote from Chapter 8: “… we never experiment with just one electron or atom or (small) molecule.” This is no longer true. We can do experiments involving single atoms or molecules and even on single photons, and thus it becomes possible to demonstrate that the “ridiculous consequences” alluded to by Schrödinger are, in fact, quite real. We have already discussed some examples of single-photon experiments in Chapter 6, and in Chapter 10 we shall discuss experiments performed with single atoms and single trapped ions. In the present chapter, we shall elaborate further on experimental tests of fundamentals of quantum mechanics involving a small number of photons. By fundamental tests we mean tests of quantum mechanics against the predictions of local realistic theories (i.e. hidden variable theories). Specifically, we discuss optical experiments demonstrating violations of Bell's inequalities, violations originally discussed by Bell in the context of two spin-one-half particles. Such violations, if observed experimentally, falsify local realistic hidden-variable theories. Locality refers to the notion, familiar in classical physics, that there cannot be a causal relationship between events with space-like separations. That is, the events cannot be connected by any signal moving at, or less than, the speed of light; i.e. the events are outside the light-cone. But in quantum mechanics, it appears that nonlocal effects, effects seemly violating the classical notion of locality in a certain restricted sense, are possible.
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward "subtraction" of the average ZPF intensity at the Wigner image of the detection process.
Regardless of past proposals (already disproved in experimental work by Brida et al), the Wigner picture of Parametric Down Conversion (works by Casado et al) can be interpreted as a local-realistic formalism, without the need to depart from quantum mechanical predictions at any step, at least for the relevant subset of QED-states. This involves reinterpreting the expressions for the detection probabilities, by means of an additional mathematical manipulation; though such manipulation seemingly provides enough freedom to guarantee consistency with the expectable, experimentally testable behavior of detectors, this is, in any case, irrelevant in relation to our main result, of a purely mathematical nature. Besides, the Wigner-PDC approach opens clear room to explain the elusive nature of a loop-hole free proof of the incompatibility of nature with that local-realism, without the need to assume hypothetical technological inefficiencies yet to overcome after several decades of experimental work. In relation to this, we also address the consequences of this framework in relation to typical Bell experiments. Additionally, we also propose an extremely simple interpretation on that apparently awkward subtraction of the average ZPF intensity at the Wigner image of the detection process.