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.
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 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.
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.
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".
A single-particle multi-branched wave-function is studied. Usual which-path tests show that if the detector placed on one branch clicks, the detectors on the other branches remain silent. By the collapse postulate, after this click, the state of the particle is reduced to a single branch, the branch on which the detector clicked. The present article challenges the collapse postulate, claiming that when one branch of the wave-function produces a click in a detector, the other branches don't disappear. They can't produce clicks in detectors, but they are still there. An experiment different from which-path test is proposed, which shows that detectors are responsible for strongly decohering the wave-function, but not for making parts of it disappear. Moreover, one of the branches supposed to disappear may produce an interference pattern with a wave-packet of another particle.
The operations of many detection devices are usually explained in terms of the ionization tracks produced by classical charged particles. A wave-mechanical analysis does not seem to be available. Mott [Proc. R. Soc. London Ser. A 126, 79 (1929)] has shown that an incident \ensuremath{\alpha} wave emitted by a radioactive nucleus would be scattered by atoms primarily in directions almost forward. However, these scattered waves would appear over the entire sensitive region of the detector. The mechanism that produces a collapse of the wave function to a single track is analyzed here. The incident \ensuremath{\alpha} wave is written as a superposition of minimum-sized packets. Since it is linear, the Schr\"odinger equation for the system including an observer can be solved for each packet individually. After the minimum packets interact with the electrons in the detector, they cannot be recombined to form a plane wave. However, they can be combined in groups to form larger coherent packets interacting with the detector to form tracks. The size and shape of each coherent packet is determined by the properties of the medium that is ionized to produce its track. The track from each packet is seen by the observer and is associated with a state of his memory, recording only one track. Each such packet replaces the particle in the usual explanation. These are the packets required to predict the quantum jumps seen in the scattering of laser light from an isolated atom as I have discussed [Phys. Rev. A 45, 4925 (1992)]. The relation of the probability distribution of these tracks to the wave function is explained.