[Paper Review] Where was the particle?

Sofia Wechsler|arXiv (Cornell University)|Jan 19, 2003

Quantum Mechanics and Applications10 references3 citations

TL;DR

This paper investigates the 'empty/full waves' hypothesis in quantum mechanics, which posits that a detector click results from a wave-packet carrying a property (termed 'full wave') rather than a localized particle. It shows that energy conservation implies full waves must follow continuous trajectories, leading to a counterfactual paradox in multi-particle contexts like Hardy's thought experiment. The study concludes that the hypothesis leads to contradictions with quantum predictions unless locality is relaxed, and ultimately argues it fails to resolve foundational quantum puzzles such as the 'before-before' loop.

ABSTRACT

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".

Motivation & Objective

• To assess the validity of the empty/full waves hypothesis, which attributes detector clicks to a property carried by a continuous wave-packet rather than a localized particle.
• To investigate whether the hypothesis can consistently explain counterfactual reasoning in quantum experiments, particularly in multi-particle systems like Hardy's thought-experiment.
• To determine whether the hypothesis offers a solution to foundational quantum puzzles such as the 'before-before' loop.
• To evaluate whether the hypothesis is compatible with energy conservation and continuous wave trajectories.

Proposed method

• Analyzes the energy conservation principle to derive that full waves must follow continuous trajectories from source to detector.
• Applies counterfactual reasoning to multi-particle quantum systems, particularly Hardy's thought-experiment involving an electron and a positron.
• Examines the implications of the empty/full waves hypothesis in scenarios with space-separated wave-function branches.
• Relaxes the locality requirement to test whether contradictions with quantum predictions can be resolved.
• Compares the hypothesis to local hidden variable theories, noting it cannot be proven or disproven with current evidence.
• Evaluates the hypothesis against known quantum paradoxes, including the 'before-before' loop.

Experimental results

Research questions

• RQ1 Can the empty/full waves hypothesis consistently explain detector clicks in multi-particle quantum systems without violating quantum predictions?
• RQ2 What are the implications of energy conservation for the trajectory of a full wave in quantum mechanics?
• RQ3 Does counterfactual reasoning within the empty/full waves framework lead to contradictions with quantum theory in Hardy-type experiments?
• RQ4 Can relaxing the locality condition resolve the contradictions arising from the hypothesis in multi-particle scenarios?
• RQ5 Does the empty/full waves hypothesis provide a solution to the 'before-before' loop paradox in quantum foundations?

Key findings

• Energy conservation enforces that full waves must follow continuous trajectories from the source to the detector, invalidating the idea of discontinuous or non-local wave-packet propagation.
• The combination of the empty/full waves hypothesis and counterfactual reasoning leads to a contradiction with quantum predictions in Hardy's thought-experiment.
• Relaxing the locality requirement resolves the contradiction, but this does not validate the hypothesis, as it remains untestable with current evidence.
• The hypothesis fails to resolve the 'before-before' loop paradox, indicating it does not offer a solution to foundational quantum puzzles.
• The empty/full waves hypothesis cannot be proven or disproven at present, and its compatibility with quantum mechanics remains an open question.