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Young’s Double-Slit and Wheeler’s Delayed-Choice Experiments at a Single-Quantum Level: Wave-Particle Non-Duality

Nakka Gurappa

Published Nov 1, 2020• 0 citations
OpenAlex

Abstract

A new `wave-particle non-dualistic interpretation at a single-quantum level' is presented by showing the physical nature of Schrodinger's wave function as an ‘instantaneous resonant spatial mode’ to which a particle's motion is confined. The initial phase associated with a state vector is identified to be related to a particular position eigenstate of the particle and hence, the equality of quantum mechanical time to classical time is obtained; this equality automatically explains the emergence of classical world from the underlying quantum world. Derivation of the Born rule as a limiting case of the relative frequency of detection is provided for the first time, which automatically resolves the measurement problem. Also, the Born rule derivation is supplemented with a geometrical interpretation. `What’s really going on' in Young's double-slit and Wheeler's delayed-choice experiments is explained at a single-quantum level. Also, an interference experiment is proposed to verify the correctness of the non-dualistic interpretation.

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A new wave-particle non-dualistic interpretation at a single-quantum level' is presented by showing the physical nature of Schrodinger's wave function as an ‘instantaneous resonant spatial mode’ to which a particle's motion is confined. The initial phase associated with a state vector is identified to be related to a particular position eigenstate of the particle and hence, the equality of quantum mechanical time to classical time is obtained; this equality automatically explains the emergence of classical world from the underlying quantum world. Derivation of the Born rule as a limiting case of the relative frequency of detection is provided for the first time, which automatically resolves the measurement problem. Also, the Born rule derivation is supplemented with a geometrical interpretation. What’s really going on' in Young's double-slit and Wheeler's delayed-choice experiments is explained at a single-quantum level. Also, an interference experiment is proposed to verify the correctness of the non-dualistic interpretation.
A new `wave-particle non-dualistic interpretation at a single-quantum level' is presented by showing physical nature of Schrodinger's wave function as an ‘instantaneous resonant spatial mode’ to which a particle's motion is confined. The initial phase associated with a state vector is identified to be related to a particular position eigenstate of particle and hence, equality of quantum mechanical time to classical time is obtained; this equality automatically explains emergence of classical world from underlying quantum world. Derivation of Born rule as a limiting case of the relative frequency of detection is provided for first time, which automatically resolves measurement problem. Also, Born rule derivation is supplemented with a geometrical interpretation. It's shown that non-dualistic interpretation statistically yields Copenhagen interpretation. ``What’s really going on? in Young's double-slit experiment is explained at a single-quantum level. Also, an interference experiment is proposed to verify correctness of non-dualistic interpretation.
A new `wave-particle non-dualistic interpretation' at the single-quantum level, existing within the quantum formalism, is presented by showing the Schr\odinger wave function as an `{\it instantaneous resonant spatial mode}' where a particle moves. For the first time, the position eigenstate of a particle is identified to be related to the absolute phase of the wave function in such a way that its position eigen values always lie on a classical trajectory, proving that the `time parameter' is common to both classical and quantum mechanics. It's brought into light that the quantum formalism demands a different kind of boundary conditions to be imposed to the wave function unlike classical formalism and hence naturally yields the Born rule as a limiting case of the relative frequency of detection. This derivation of the Born rule automatically resolves the measurement problem. Also, these boundary conditions immediately expound Bohr's principle of complementarity at a single quantum level. Further, the non-duality naturally contains the required physical mechanism to elucidate why the Copenhagen interpretation is experimentally so successful. The single-quantum phenomenon is then used to unambiguously explain what's really going on in the Young double-slit experiment as anticipated by Feynmann and the same is again used to provide a causal explanation of Wheeler's delayed-choice experiment.
A new wave-particle non-dualistic interpretation for the quantum formalism is presented by proving that the Schrödinger wave function is an `{\it instantaneous resonant spatial mode}' in which the quantum particle moves. The probabilities in quantum mechanics arise only for the observer's perspective due to the nature of doing experiments but they do not exist in Nature. In other words, quantum mechanics itself is not a probabilistic theory. This view-point is proved by deriving the Born's rule by showing it to be equal to the experimentally observed relative frequencies. Also, it is shown that the classical and quantum mechanical times are one and the same. By identifying the already inherently existing mechanism for the collapse of wave function within the quantum formalism, the present interpretation naturally proves why the Copenhagen interpretation is very successful in explaining the experimental outcomes. The Young's double-slit experiment, the Wheeler's delayed choice experiment and the Afshar's experiment are unambiguously explained at a single quantum level. Both `measurement problem' and `retrocausality' are absent in the present non-dualistic interpretation of quantum mechanics.
The Schrödinger's wave function can naturally be realized as an 'instantaneous resonant spatial mode' in which quantum particle moves and hence the Born's rule is derived after identifying its origin. This realization facilitates the visualization of `what's really going on?' in the Young's double-slit experiment which is known to be the central mystery of quantum mechanics. Also, an actual mechanism underlying the `spooky-action-at-a-distance', another mystery regarding the entangled quantum particles, is revealed. Wheeler's delayed choice experiments, delayed choice quantum eraser experiment and delayed choice entanglement swapping experiments are unambiguously and naturally explained at a single quantum level. The reality of Nature represented by the quantum mechanical formalism is conceptually intuitive and is independent of the measurement problem.
A new 'wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level' is presented by interpreting the Schrodinger wave function as an 'instantaneous resonant spatial mode' (IRSM) to which a quantum is confined and moves akin to the case of a test particle in the curved space-time of the general theory of relativity. This union of the wave and particle natures into a single entity is termed as non-duality. Using quantum formalism, the IRSM is shown to induce dual-vectors at the boundaries and interacts according to the inner-product. The overall phase associated with the state vector, which never contributes to the inner-product, is related to a particular eigenstate of an observable where the particle resides. This eigenstate becomes the natural outcome during observation of a single-quantum's single event. Observation over a large number of identical quanta, differing only by overall phases, results in the relative frequency of detection which yields Born's rule as a limiting case proving the absence of measurement problem in quantum mechanics. The non-duality not only provides the actual mechanism for the 'wave function collapse' but also statistically becomes equivalent to the Copenhagen interpretation. An explicit derivation for the Born rule using individual quantum events is provided by considering an example of spin-1/2 particles in the Stern-Gerlach experiment. In this regard, a generalized representation for the SU (2) algebra, facilitating the description of single-quantum events, is constructed without any deviations from the quantum formalism.
The main ideas of the wave-particle non-dualistic interpretation of quantum mechanics are elucidated using two well-known examples, viz., (i) a spin-1/2 system in the Stern-Gerlach experiment and (ii) Young's double-slit experiment, representing the cases of observables with discrete and continuous eigenvalues, respectively. It's proved that only Born's rule can arise from quantum formalism as a limiting case of the relative frequency of detection. Finally, non-duality is used to unambiguously explain Hanbury Brown-Twiss effect, at the level of individual quanta, for the two-particle coincidence detection.