See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/341756038 Pandamaran Interpretation of Quantum Mechanics: The Second Interpretation Preprint · May 2020 CITATIONS READS 0 64 1 author: Andrew Das Arulsamy Institute of Interdisciplinary Science, Pandamaran, Malaysia 108 PUBLICATIONS 464 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Pancharatnam Phase View project All content following this page was uploaded by Andrew Das Arulsamy on 25 December 2020. The user has requested enhancement of the downloaded file. 1 Pandamaran Interpretation of Quantum Mechanics: The Second Interpretation Andrew Das Arulsamy Condensed Matter Group, Institute of Interdisciplinary Science, No. 24, level-4, Block C, Lorong Bahagia, Pandamaran, 42000 Port Klang, Selangor DE, Malaysia e-mail: [email protected] Abstract Interpreting quantum mechanics is a hard problem basically because it means explaining why and how the mathematics exploited to formulate wave-particle duality are related to obser- vations or reality. Consequently, interpretation of quantum mechanics should involve proper physical mathematics and physical logic, which is often not the case from the Copenhagen interpretation. Here, we shall revisit all the postulates of quantum mechanics with proper physics and physical logic and reconstruct them to establish the physically less-complex Pan- damaran interpretation of quantum mechanics. Keywords: Foundations of Quantum Mechanics; Copenhagen interpretation; Pandamaran interpretation. §1. Introduction Due to unsettled issues within the foundations of quantum mechanics, we have three main options for scientists to choose from when asked about the position of a ‘quantum’ particle before measurement.[1] A quantum particle here usually means an electron or a photon, which can be detected as free particles. The first is the realist position—After the measurement, it is found that the particle was at some point A. But quantum mechanics is incomplete because it clearly lacks the ability to predict that the particle was at point A before the measurement. This realist position was advocated by Einstein himself, but he was unable to defend it in an unambiguous manner where one such attempt is the well-known Einstein-Podolsky-Rosen (EPR) paradox.[2] The second position is known as the orthodox position—Before the measurement, the particle was not really anywhere such that quantum mechanics can only predict the probability distribution of the particle’s possible position. This probability distribution is unique in a sense that it implies the act of measurement forced the particle to take a stand and exposed its position at point A. Here, ‘taking a stand’ refers to the notion of wavefunction collapse (whatever the mechanism for this collapse is). This is the core Copenhagen-interpretation that was advocated, and enforced to be the truth by Bohr since 1925. The third one is called the agnostic position. This is also a valid position because where is the point in taking a side when quantum mechanics is unable to predict the position of that particle. Raman was an advocate of this position. This is the current situation with the foundations of quantum mechanics, and in the absence typeset using PTPTEX.cls hVer.0.9i 2 Andrew Das Arulsamy of additional technical arguments, we are not entirely sure which position is viable, let alone the truth. The primary aim of this work is to expose the new rules con- tained in the Pandamaran interpretation systematically, including the proper and consistent physics needed to take a firm stand on only one of the positions listed above, which should be automatic. We begin by revisiting the primary notion that is related to the wave-particle duality, which is the core quantum mechanical idea embedded in the Copenhagen interpretation that is responsible for the Heisenberg uncertainty principle. However, we shall not revisit the well-known Copenhagen postulates one-by-one, which can be obtained from Refs.,[1],[3],[4] instead, we shall re-evaluate and completely reconstruct the Copenhagen postulates with additional physics. The revised and the newly constructed postulates shall make up the Pan- damaran interpretation with consistent and unambiguous physics. 1.1. Rationale for the Second Interpretation Physically, the Heisenberg uncertainty principle is a consequence of wave-particle duality. Here, we should note that the Heisenberg uncertainty only applies for r ≤ ∆r, or when the observation scale, r is within the probability distribution of a quantum particle, ∆r. Therefore, if r>∆r, then the Heisenberg uncertainty is inapplicable because we can identify the position of the particle or the position of the wave packet or the position of the particle’s or wave packet’s distribution function. Here, we elaborate and apply this Heisenberg uncertainty principle and describe how it is actually related to one’s ability to know both the momentum and the position of a quantum particle. However, unlike the momentum–position Heisenberg uncertainty discussed above and elsewhere, we cannot determine or predict all the spin components of a quantum particle for all or any scales or range of observation, either for r ≤ ∆r or for r>∆r. For example, r is the range of observation or the region of observation that is defined within l and r. In particular, l ⊙ r implies ⊙ is an atomic hydrogen with its outer circle (with radius r) representing an electron wave packet surrounding the proton, · in the center. In this case, ∆r = πr2, while r denotes the region between r left and right. Therefore, for r>∆ , we can know the position of the particle, which is defined by the Bohr radius, but the position is not known at a given Cartesian coordinate (x,y,z) because such a point-like position does not exist for any electron. The above new interpretation of Heisenberg uncertainty principle, which limits its validity, belongs to the Pandamaran interpretation that shall be exposed in the following section. But first, we shall observe the generalized Heisenberg uncertainty relation, which is fully valid for Copenhagen interpretation, but only valid in a limited sense in Pandamaran interpretation. The generalized Heisenberg uncertainty relation is given by,[1] ~ σ σ ≥ , (1.1) A B 2 2 2 where σA and σB are the statistical standard deviations for the observables, A and ~ B, respectively. Here, σAσB is positive definite by definition and therefore, − 2 is automatically excluded. Pandamaran Interpretation of Quantum Mechanics 3 The Heisenberg uncertainty principle means that there is an Heisenberg uncer- tainty relation for every pair of non-commuting operators, such that their respective pair of observables are known as incompatible observables. Such a pair of incom- patible observables or incompatible eigenvalues do not have a common or shared eigenfunctions. For example, the complete set of eigenfunctions for the position op- erator,x ˆ is not the same as the complete set of eigenfunctions for the momentum operator,p ˆ. Note this, we will not always label all the operators with a hat. In contrast, the observables for commuting operators permit the complete set of eigen- 2 functions for L to be the same as for Lz where their eigenfunctions are denoted by ml 2 Yl . In other words, L and Lz have the complete set of common and simultaneous eigenfunctions, while such a situation cannot occur for x and p because x and p are incompatible observables. We have to wonder why incompatible observables have to mean that we cannot observe or measure them simultaneously? In particular, if we could measure the position (x) of an electron accurately, then it is not possible to measure its momentum (p) as accurately as x, and vice versa. The proper answer to this question is only given in the so-called Pandamaran interpretation. Copenhagen interpretation assumes the answer to be due to the notion known as the wavefunction collapse. For example, according to Copenhagen interpretation, once the measurement on the position of an electron is made, then the act of measurement collapses the said wavefunction to a narrow spike and the information about its momentum is lost forever. If we happen to measure the momentum first, then the wavefunction collapses into a proper wave with a well-defined wavelength, and the information about the electron’s position is lost forever. The reason why the above incompatibility is not observed for compatible ob- servables is because the collapsed wavefunction for compatible observables carry the information for both observables. For example, if we measure L2 of an electron in an eigenstate, we can still measure Lz for another electron in the same eigenstate be- cause both electrons shared the same eigenstate, and both operators shared the same ml eigenfunction, Yl . For compatible observables, the wavefunction collapse mecha- nism remains the same. This is a physically false statement because we can do the same for x (measure x for one electron in a eigenstate) and p (measure p for another electron in the same eigenstate) even if the wavefunction-collapse mechanism for x and p differs. For example, can we measure both ~2l(l+1), the eigenvalue for L2 of an electron in an eigenstate, and measure again the eigenvalue for Lz, ~ml for another electron in the same eigenstate? such that we do not measure one eigenvalue and calculate the other? If this is possible, then we can definitely do the same for x and p. In 2 2 particular, we just need to make these switches L −→ xˆ, Lz −→ pˆ, ~ l(l + 1) −→ x and ~ml −→ p in the above sentence. There is another possibility for us to consider in our attempt to save the Copen- hagen’s wavefunction-collapse scenario. Can we measure both of these compatible 2 eigenvalues, ~ l(l + 1) and ~ml simultaneously from the same electron in an eigen- 2 state? The answer is definitely yes because both ~ l(l+1) and ~ml are automatically determined if we could measure l alone.