According to "the wave-particle non-dualistic interpretation of quantum mechanics at a single-qua... more According to "the wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level", the Schrodinger wavefunction is shown to be an instantaneous resonant spatial mode in which a quantum moves. To verify this key proposal, a modified Mach-Zehnder interferometer experiment with a single-particle source is proposed. A negative result of this experiment simply implies that the non-duality is wrong.
"Young's Double-Slit Experiment: What's Really Happening at a Single-Quantum Level?" - 2nd Webina... more "Young's Double-Slit Experiment: What's Really Happening at a Single-Quantum Level?" - 2nd Webinar FDP (Faculty Development Program) presentation on "Quantum Science and Technology" (QST) at Koneru Lakshmaia Education Foundation, KL University, Vijayawada, Andhra Pradesh, India, during 30--6-2021.
According to wave-particle non-dualistic interpretation of quantum mechanics, the initial/ global... more According to wave-particle non-dualistic interpretation of quantum mechanics, the initial/ global/overall phase associated with a quantum state vector is related to a particular eigenstate of an observable, resulting in the Born rule.
1st Webinar given on 29-062021, at the FDP (Faculty Development Program) on ``Quantum Science and Technology" (QST) at Koneru Lakshmaia Education Foundation, KL University, AP, India.
In quantum formalism, a discrepancy exists between Schrödinger's wavefunction and Born's rule, wh... more In quantum formalism, a discrepancy exists between Schrödinger's wavefunction and Born's rule, which is reconciled through a geometric derivation of Born's rule as a limiting case based on the relative frequency of detection. This derivation leverages the relationship between the global phase of the state vector and the specific eigenstate observed during quantum experiments. The naturally available Born's picture within Born's probabilistic interpretation not only demonstrates the equivalence of classical and quantum mechanical times but also elucidates various quantum enigmas. It provides a physical explanation for wavefunction collapse, leading to the statistical emergence of the Copenhagen interpretation, and facilitates the derivation of Malus' law for the transmission of a single photon through a polarizer. The longstanding measurement problem is addressed through the resolution of Schrödinger's cat paradox, subsequently resolving Wigner's friend and the Frauchiger-Renner paradoxes at the single-quantum level. Furthermore, Born's picture offers a clear resolution to the conundrum of quantum superposition, with a proposed experimental verification using a modified Mach-Zehnder interferometer. Significantly, this approach provides a causal explanation for Wheeler's delayed-choice experiment and resolves the fundamental mystery of quantum mechanics inherent in Young's double-slit experiment.
We propose an extremely simple experimental arrangement to simultaneously observe both wave and p... more We propose an extremely simple experimental arrangement to simultaneously observe both wave and particle behaviors, {\it i.e.}, wave-particle duality, of light and compare this technique with the results of the most recently done highly sophisticated experiment by L. Piazza {\it et al.} We also address about the basic question of whether Bohr's complementarity principle is really violated in these kinds of recent experiments or it is, indeed, being preserved inherently.
A unified approach, for solving a wide class of single and many-body quantum problems, commonly e... more A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from dealing with exactly and quasi-exactly solvable problems, the present approach makes transparent various properties of the familiar orthogonal polynomials and also the construction of their
According to "the wave-particle non-dualistic interpretation of quantum mechanics at a single-qua... more According to "the wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level", the Schrodinger wavefunction is shown to be an instantaneous resonant spatial mode in which a quantum moves. To verify this key proposal, a modified Mach-Zehnder interferometer experiment with a single-particle source is proposed. A negative result of this experiment simply implies that the non-duality is wrong.
"Young's Double-Slit Experiment: What's Really Happening at a Single-Quantum Level?" - 2nd Webina... more "Young's Double-Slit Experiment: What's Really Happening at a Single-Quantum Level?" - 2nd Webinar FDP (Faculty Development Program) presentation on "Quantum Science and Technology" (QST) at Koneru Lakshmaia Education Foundation, KL University, Vijayawada, Andhra Pradesh, India, during 30--6-2021.
According to wave-particle non-dualistic interpretation of quantum mechanics, the initial/ global... more According to wave-particle non-dualistic interpretation of quantum mechanics, the initial/ global/overall phase associated with a quantum state vector is related to a particular eigenstate of an observable, resulting in the Born rule.
1st Webinar given on 29-062021, at the FDP (Faculty Development Program) on ``Quantum Science and Technology" (QST) at Koneru Lakshmaia Education Foundation, KL University, AP, India.
In quantum formalism, a discrepancy exists between Schrödinger's wavefunction and Born's rule, wh... more In quantum formalism, a discrepancy exists between Schrödinger's wavefunction and Born's rule, which is reconciled through a geometric derivation of Born's rule as a limiting case based on the relative frequency of detection. This derivation leverages the relationship between the global phase of the state vector and the specific eigenstate observed during quantum experiments. The naturally available Born's picture within Born's probabilistic interpretation not only demonstrates the equivalence of classical and quantum mechanical times but also elucidates various quantum enigmas. It provides a physical explanation for wavefunction collapse, leading to the statistical emergence of the Copenhagen interpretation, and facilitates the derivation of Malus' law for the transmission of a single photon through a polarizer. The longstanding measurement problem is addressed through the resolution of Schrödinger's cat paradox, subsequently resolving Wigner's friend and the Frauchiger-Renner paradoxes at the single-quantum level. Furthermore, Born's picture offers a clear resolution to the conundrum of quantum superposition, with a proposed experimental verification using a modified Mach-Zehnder interferometer. Significantly, this approach provides a causal explanation for Wheeler's delayed-choice experiment and resolves the fundamental mystery of quantum mechanics inherent in Young's double-slit experiment.
We propose an extremely simple experimental arrangement to simultaneously observe both wave and p... more We propose an extremely simple experimental arrangement to simultaneously observe both wave and particle behaviors, {\it i.e.}, wave-particle duality, of light and compare this technique with the results of the most recently done highly sophisticated experiment by L. Piazza {\it et al.} We also address about the basic question of whether Bohr's complementarity principle is really violated in these kinds of recent experiments or it is, indeed, being preserved inherently.
A unified approach, for solving a wide class of single and many-body quantum problems, commonly e... more A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from dealing with exactly and quasi-exactly solvable problems, the present approach makes transparent various properties of the familiar orthogonal polynomials and also the construction of their
We elaborate upon a new method of solving linear differential equations, of arbitrary order, whic... more We elaborate upon a new method of solving linear differential equations, of arbitrary order, which is applicable to a wide class of single and multi-variate equations. Our procedure separates the operator part of the equation under study in to a part containing a function of the Euler operator and constants, and another one retaining the rest. The solution of the equation is then obtained from the monomials (or the monomial symmetric functions, for the multi-variate case), which are the eigenfunctions of the Euler operator. Novel exponential forms of the solutions of the differential equations enable one to analyze the underlying symmetries of the equations and explore the algebraic structures of the solution spaces in a straightforward manner. The procedure allows one to derive various properties of the orthogonal polynomials and functions in a unified manner. After showing how the generating functions and Rodriguez formulae emerge naturally in this method, we briefly outline the generalization of the present approach to the multi-variate case.
The Calogero model (CM) and the Calogero-Sutherland model (CSM) are quantum many-particle systems... more The Calogero model (CM) and the Calogero-Sutherland model (CSM) are quantum many-particle systems in one-dimension with a non-trivial pair-wise inverse square interactions among any arbitrarily chosen pair of particles. The CM is defined in a space spanned by the unbounded set of real numbers, whereas the CSM is on a closed set of real numbers defined on a circle. Therefore, the CSM can be derived as a special case from the CM. In the present thesis, I have, along with my Ph.D Advisor, mapped both the CM and CSM to the corresponding free particle systems by means of similarity transformations. In order to construct such similarity transformations, I discovered a new method to solve linear differential equations of arbitrary order.
A magician, seems to be analogous to quantum mechanics, throws the spectators into a bewildering ... more A magician, seems to be analogous to quantum mechanics, throws the spectators into a bewildering surprise by exhibiting a magic trick similar to the quantum superposition. The trick appears to be strange, weird and counter-intuitive like the quantum superposition, as long as the underlying secret behind its working is unknown. In the present article, the mystery of quantum superposition is demystified at a single-quantum level. Also, the counterfactual reality and the causality in Young's double-slit and Wheeler's delayed-choice experiments are pointed out, respectively.
``Can Nature be intrinsically probabilistic at fundamental level?'' - The answer cannot be ``yes... more ``Can Nature be intrinsically probabilistic at fundamental level?'' - The answer cannot be ``yes'', but ...
Quantum mechanics is revealing a profound and remarkable property of spacewhere the quantum pheno... more Quantum mechanics is revealing a profound and remarkable property of spacewhere the quantum phenomena happen.
Using the quantum formalism, a question-"Why particle ontology is unavoidable in quantum mechanic... more Using the quantum formalism, a question-"Why particle ontology is unavoidable in quantum mechanics?"-is analyzed. The frequently outspoken inference, "particle appears to be fuzzy and spread out, i.e., it seems to be at multiple states at once", is shown to be inconsistent with respect to quantum formalism.
A new 'wave-particle non-dualistic interpretation at a single-quantum level' is presented by show... more A new 'wave-particle non-dualistic interpretation at a single-quantum level' is presented by showing the physical nature of Schrödinger's wavefunction as an 'instantaneous resonant spatial mode' to which a particle's motion is confined. The initial phase associated with a state vector is identified as related to a particular eigenstate of an observable and hence, the Born rule is derived as a limiting case of the relative frequency of detection along with an augmentation of a geometrical interpretation. This derivation automatically resolves the measurement problem. The Copenhagen interpretation is shown to be the statistical average of the non-dualistic interpretation. The position eigenvalues of a moving particle's eigenstate lie on a classical path of least action-resulting in the equality of quantum mechanical and classical times. This equality reveals the emergence of classical world from the underlying quantum world. "What's really happening?" in Young's double-slit experiment is explained at a single-quantum level. An interference experiment is proposed to verify the instantaneous nature of the wavefunction.
A polynomial power series is constructed for the one-sided step function using a modified Taylor ... more A polynomial power series is constructed for the one-sided step function using a modified Taylor series, whose derivative results in a new representation for Dirac δ-function.
A new `wave-particle non-dualistic interpretation at a single-quantum level' is presented by show... more 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. It's shown that the non-dualistic interpretation statistically yields the 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 the correctness of the non-dualistic interpretation.
The inner-product, < ψ|ψ >, between a state vector, |ψ > and its dual, < ψ|, is thoroughly analyz... more The inner-product, < ψ|ψ >, between a state vector, |ψ > and its dual, < ψ|, is thoroughly analyzed using the recently developed 'wave-particle non-dualistic interpretation of quantum mechanics'; here, |ψ > is a solution of the Schrödinger wave equation. Using this analysis, ``questions about what decides whether a photon is to go through or not and how it changes its direction of polarization when it does go through a polarizing filter" - a statement by Prof. Dirac - is unambiguously explained.
A new 'wave-particle non-dualistic interpretation at a single-quantum level' is presented by show... more A new 'wave-particle non-dualistic interpretation at a single-quantum level' is presented by showing the physical nature of Schrödinger's wave function as an 'in-stantaneous 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.
According to non-dualistic interpretation of quantum mechanics, the initial/ global/overall phase... more According to non-dualistic interpretation of quantum mechanics, the initial/ global/overall phase associated with a quantum state vector is related to a particular eigenstate of an observable. This phase gives raise to a "tube" like geometrical structure, associating the state vector and the tube branches into several smaller tubes. The total number of smaller tubes is equal to the total number of eigen-states of the observable; each branch is associated with a particular eigenstate. The cross-sectional area of the initial tube is equal to the sum of cross-sectional areas of all tubes, resulting in the Born rule and also in the conservation of probability in quantum mechanics. 2
According to `the wave-particle non-dualistic interpretation of quantum mechanics at a single-qua... more According to `the wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level' (NI), the SchrÖdinger wave function is proposed/shown to be an instantaneous resonant spatial mode in which a quantum moves. To verify this key proposal, a modified Mach-Zehnder interferometer experiment with a single-particle source is proposed. A negative result of this experiment simply implies that the NI is wrong.
A new 'wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level'... more A new 'wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level' is presented by interpreting the Schrödinger 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.
Schrödinger's cat and Wigner's friend paradoxes are analyzed using the 'wave-particle non-dualist... more Schrödinger's cat and Wigner's friend paradoxes are analyzed using the 'wave-particle non-dualistic interpretation of quantum mechanics at a single-quantum level' and are shown to be non-paradoxes within the quantum formalism. Then, the extended version of Wigner's friend thought experiment, proposed in a recent article titled, "Quantum theory cannot consistently describe the use of itself ", Nature Communications 9, 3711 (2018), by Frauchiger and Renner (FR) is considered. In quantum mechanics, it's well-known that, statistically observing a large number of identical quantum systems at some particular quantum state, which results in Born's probability, and merely inferring its presence in the same quantum state with the same probability yield distinct physical phenomena. If this fact is not taken care while interpreting any experimental outcomes, then FR type paradoxes pop up. 'What an astonishingly self-consistent the Quantum Theory is!'-is explicitly worked out in the case of FR gedankenexperiment. The present work shows the importance of single-quantum phenomenon for the non-paradoxical interpretation of statistically observed experimental outcomes.
The main ideas of the wave-particle non-dualistic interpretation of quantum mechanics are elucida... more 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 unambigu-ously explain Hanbury Brown-Twiss effect, at the level of individual quanta, for the two-particle coincidence detection.
Using a newly proposed 'wave-particle non-dualistic interpretation' of the quantum formalism, Boh... more Using a newly proposed 'wave-particle non-dualistic interpretation' of the quantum formalism, Bohr's principle of complementarity is analyzed in the context of the single-slit diffraction and the Afshar's experiments-at the single-quantum level. The fundamental flaw in the Afshar's argument is explicitly pointed out.
A new 'wave-particle non-dualistic interpretation' at the single-quantum level, existing within t... more A new 'wave-particle non-dualistic interpretation' at the single-quantum level, existing within the quantum formalism, is presented by showing the Schrödinger wave function as an '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.
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Videos by N Gurappa
1st Webinar given on 29-062021, at the FDP (Faculty Development Program) on ``Quantum Science and Technology" (QST) at Koneru Lakshmaia Education Foundation, KL University, AP, India.
Papers by N Gurappa
1st Webinar given on 29-062021, at the FDP (Faculty Development Program) on ``Quantum Science and Technology" (QST) at Koneru Lakshmaia Education Foundation, KL University, AP, India.