When a quantum object -- a particle as we call it in a non-rigorous way -- is described by a multi-branched wave- function, with the corresponding wave-packets occupying separated regions of the time-space, a frequently asked question is whether the quantum object is actually contained in only one of these wave-packets. If the answer is positive, then the other wave-packets are called in literature empty waves. The wave-packet containing the object is called a full wave, and is the only one that would produce a recording in a detector. A question immediately arising is whether the empty waves may also have an observable effect. Different works were dedicated to the elucidation of this question. None of them proved that the hypothesis of full/empty waves is correct - it may be that the Nature is indeed non-deterministic and the quantum object is not confined to one region of the space-time. All the works that proved that the empty waves have an effect, in fact, proved that if there exist full and empty waves, then the latter may have an observable effect. This is also the purpose and the limitation of the present work. What is shown here is that if the hypothesis is true, the empty waves have an influence. An experiment is indicated which reveals this influence. The analysis of the experiment is according to the quantum formalism. This experiment has the advantage of being more intuitive and practically more feasible than a previous proposal also in agreement with the quantum formalism. However, the presently proposed experiment also shows that the quantum theory is not in favor of the above hypothesis.
When a quantum object -- a particle as we call it in a non-rigorous way -- is described by a multi-branched wave- function, with the corresponding wave-packets occupying separated regions of the time-space, a frequently asked question is whether the quantum object is actually contained in only one of these wave-packets. If the answer is positive, then the other wave-packets are called in literature empty waves. The wave-packet containing the object is called a full wave, and is the only one that would produce a recording in a detector. A question immediately arising is whether the empty waves may also have an observable effect. Different works were dedicated to the elucidation of this question. None of them proved that the hypothesis of full/empty waves is correct - it may be that the Nature is indeed non-deterministic and the quantum object is not confined to one region of the space-time. All the works that proved that the empty waves have an effect, in fact, proved that if there exist full and empty waves, then the latter may have an observable effect. This is also the purpose and the limitation of the present work. What is shown here is that if the hypothesis is true, the empty waves have an influence. An experiment is indicated which reveals this influence. The analysis of the experiment is according to the quantum formalism. This experiment has the advantage of being more intuitive and practically more feasible than a previous proposal also in agreement with the quantum formalism. However, the presently proposed experiment also shows that the quantum theory is not in favor of the above hypothesis.
When a quantum system is described by a wave function consisting in a couple of wave-packets, each wave packet traveling on a separate path, a commonly asked question is why at a given time only one of the wave packets is able to trigger a click in a detector. In the second half of the last century many scientists considered the possibility that not all these wave-packets are identical. Namely, that there exist full waves and empty waves. The two types of waves were supposed to be identical in all the experiments, e.g. able to produce interference when meeting, however, the full wave was supposed to be able to trigger a detector, while the empty wave was supposed to leave the detector silent. The present text describes an experiment which, for explaining the results, seems to beg the hypothesis of full and empty waves.
When a quantum system is described by a wave function consisting in a couple of wave-packets, each wave packet traveling on a separate path, a commonly asked question is why at a given time only one of the wave packets is able to trigger a click in a detector. In the second half of the last century many scientists considered the possibility that not all these wave-packets are identical. Namely, that there exist full waves and empty waves. The two types of waves were supposed to be identical in all the experiments, e.g. able to produce interference when meeting, however, the full wave was supposed to be able to trigger a detector, while the empty wave was supposed to leave the detector silent. The present text describes an experiment which, for explaining the results, seems to beg the hypothesis of full and empty waves.
The hypothesis of empty/full waves considers that a click in a detector is triggered by a property carried by the wave-packet that impinges on that detector. Different authors call this property particle, but according to the terminology of this hypothesis, the term full wave is used in this text. The present article discusses the validity of the empty/full waves hypothesis. It is shown that the energy conservation principle imposes for a full wave a continuous trajectory from the source to the detector. That gives legitimacy to the question -- in case the wave function consists in a couple of space-separated branches -- which wave-packet was a full wave before the click in the detector, or, in other authors' terminology, where was the particle before the detector clicked. This question is a counterfactual question. In some multi-particle experiments, e.g. Hardy's thought-experiment with an electron and a positron, the combination of the empty/full waves hypothesis and counterfactual reasoning leads to a contradiction with the predictions of the quantum theory. However, it is shown here that this contradiction is solvable if the locality requirement is relaxed. To the difference from the local hidden variables, it is not possible to prove or disprove the idea of empty/ full waves, at least at present. But it is possible to ask whether this hypothesis offers a solution to the quantum puzzles. The answer is negative. For instance it offers no solution to the before-before loop. The question remains open whether the empty/full waves hypothesis is correct, or "God plays dice".
When a quantum system is described by a superposition of wave-packets, each wave-packet traveling on a separate path, a commonly asked question is why only one of the wave-packets is able to trigger a click in a detector. In the second half of the last century many scientists considered the possibility that not all these wave-packets are identical. Namely, that there exist “full waves” and “empty waves”. The two types of waves were supposed to be identical only in the sense that they are able to produce interference when crossing one another, however, the full wave was supposed to be able to trigger a click in a detector, while the empty wave was supposed to leave the detector silent. The present text describes an experiment in which, for explaining the results, it seems necessary to admit the existence of full and empty waves.
Whether the quantum mechanics (QM) is non-local is an issue disputed for a long time. The violation of the Bell-type inequalities was considered as proving this non-locality. However, these inequalities are constructed on a class of local hidden variables, which obey the calculus with positive probabilities. Such a calculus is rather suitable for billiard balls while the QM deals with wave-packets of complex amplitudes. There is no wonder that a calculus with positive numbers does not match a calculus with complex numbers. The present text describes a different model of hidden variables for entanglements, model that reproduces the quantum predictions in different experiments, and also explains why the QM is nonlocal. The model deals with waves, some of them full and the others empty, and the hidden variables mark which waves are full. The basic physical concept with which the model operates is joint amplitudes of probability, and not probabilities. The latter are a secondary concept, the probability of a combination of results being equal to the absolute square of sum of all the contributing joint amplitudes. Thus the non-locality appears: a) a joint amplitude ignores distance, it handles distant particles as if they were one single particle at one single place, b) joint amplitudes are complex numbers and the sum of several contributions may vanish, blocking the respective combination of wave-packets and therefore of results. Although showing the success of the model, this text does not advocate for full/empty waves. It is shown that this hypothesis works only as long as one does not consider moving observers, and does not compare their conclusions. The real purpose here is to point to a severe impasse: assuming the existence of a preferred frame contradicts the theory of relativity, while refuting the full/empty waves idea one runs into other insurmountable difficulties.
The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjoint regions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The quantum formalism did not explain until today the so-called “collapse” of the wave-function, i.e. the shrinking of the wave-function to one small region of the space, when a macroscopic object is encountered. This seems to happen in “which-way” experiments. A very appealing explanation for this behavior is the idea of a particle, localized in some limited part of the wave-function. The present article challenges the concept of particle. It proves in the base of a variant of the Tan, Walls and Collett experiment, that this concept leads to a situation in which the particle has to be simultaneously in two places distant from one another—situation that contradicts the very definition of a particle. Another argument is based on a modified version of the Afshar experiment, showing that the concept of particle is problematic. The concept of particle makes additional difficulties when the wave-function passes through fields. An unexpected possibility to solve these difficulties seems to arise from the cavity quantum electrodynamics studies done recently by S. Savasta and his collaborators. It involves virtual particles. One of these studies is briefly described here. Though, experimental results are needed, so that it is too soon to conclude whether it speaks in favor, or against the concept of particle.