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Critique of Quantum Optical Experimental Refutations of Bohr’s Principle of Complementarity, of the Wootters–Zurek Principle of Complementarity, and of the Particle–Wave Duality Relation

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Abstract

I argue that quantum optical experiments that purport to refute Bohr’s principle of complementarity (BPC) fail in their aim. Some of these experiments try to refute complementarity by refuting the so called particle–wave duality relations, which evolved from the Wootters–Zurek reformulation of BPC (WZPC). I therefore consider it important for my forgoing arguments to first recall the essential tenets of BPC, and to clearly separate BPC from WZPC, which I will argue is a direct contradiction of BPC. This leads to a need to consider the meaning of particle–wave duality relations and to question their fundamental status. I further argue (albeit, in opposition to BPC) that particle and wave complementary concepts are on a different footing than other pairs of complementary concepts.

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Notes

  1. See reference [51] for an early proposal for realisable intermediate experiments.

  2. This view was expressed by Prof. D. Bohm in private discussions during the years 1980 to 1985. Though I have never found a categoric statement in Bohr’s writings to support this view, there are indications in his writings pointing to this view, for example, Bohr writes, “...the appropriate physical interpretation of the symbolic quantum-mechanical formalism amounts only to predictions, of determinate or statistical character, pertaining to individual phenomena appearing under conditions defined by classical physical concepts.” [5, p. 238].

  3. In his article Drezet discusses the reality of trajectories and BPC in the context of arguing that the recently introduced Pusey, Barret and Rudolf (PBR) Theorem, concerned with ontic and epistemic hidden variable theories, does not preclude the causal interpretation (sometimes also referred to as Bohmian mechanics).

  4. Photons are bosons and are governed by the second quantized Maxwell equations. In the causal interpretation of boson fields, fundamental entities are purely fields; there are no boson particles. In this case WZPC cannot be given meaning based on this ontology.

  5. The R and S-fields defined by \(\psi =R\exp (iS/\hbar )\) are not independent of each other. Both play an equal part in determining a particles motion, the R-field through the quantum potential \(Q= -\hbar ^2/(2m)\nabla ^2 R/R\), and the S-field through the guidance formula \(v=\nabla S/m\).

  6. Actually, in computer models of the two-slit experiment [63–68] it is seen that trajectories never cross so that a particles path can be theoretically determined with certainty even when their is interference, and irrespective of whether the experiment is of an intermediate type or not.

  7. Drezet also makes this point in his two articles given in Refs. [72, 73]. In [73] Drezet discusses the duality relation in some detail in the context of arguing against Afshar’s claimed experimental refutation of BPC.

  8. We will not here take up the question of whether or not all measurements can ultimately be reduced to position measurement, but assume that this is the case.

  9. According to Bohm this requirement is needed so that \(H_I\) does not produce any uncontrollable changes in the observable Q, but only in observables that do not commute with Q. However, according to quantum theory, an arbitrary initial wave function cannot have a well defined eigenvalue of Q prior to measurement, unless it is an eigenstate of the observable being measured. It is the measurement process that changes the wave function into an eigenfunction of Q, with a corresponding definite eigenvalue q. In general, therefore, both the wave function and the value of Q is changed by a measurement. If this were not the case one could equally well envisage a mutually exclusive impulsive measurement that does not change the value of an observable P that does not commute with Q. This would imply that both Q and P have well defined values prior to measurement, whereas the wavefunction does not describe these values. This would constitute a variant of the EPR incompleteness argument. We conclude that Q and P cannot have definite values prior to measurement, unless the wave function is an eigenstate of one of them, in which case, only that observable will have a definite value.

  10. This differs from the EPR criteria for elements of reality, since in the EPR experiment the system is not an eigenstate of either of the non-commuting observables whose values are predicted with certainty.

  11. Though the R-field gives rise to the quantum potential, the S-field can also explain tunneling since the R and S-fields codetermine one another. See Ref. [63] for a computer model of quantum tunneling based on the causal interpretation.

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  1. School of Natural Sciences, Department of Physics, The University of Zambia, Lusaka, 10101, Zambia

    P. N. Kaloyerou

  2. Wolfson College, Linton Road, Oxford, OX2 6UD, UK

    P. N. Kaloyerou

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Kaloyerou, P.N. Critique of Quantum Optical Experimental Refutations of Bohr’s Principle of Complementarity, of the Wootters–Zurek Principle of Complementarity, and of the Particle–Wave Duality Relation. Found Phys 46, 138–175 (2016). https://doi.org/10.1007/s10701-015-9959-5

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