scholarly journals AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS

2012 ◽  
Vol 09 (05) ◽  
pp. 1250048 ◽  
Author(s):  
D. ACOSTA ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
J. M. ISIDRO ◽  
J. L. G. SANTANDER
Keyword(s):  
Quantum Mechanics ◽  
Quantum Mechanical ◽  
Entropy Flow ◽  
Planck’S Constant ◽  
Formal Derivation ◽  
Usual Quantum ◽  
Holographic Screen ◽  
Holographic Screens ◽  
Planck's Constant ◽  
Emergent Quantum Mechanics

Quantum mechanics emerges à la Verlinde from a foliation of ℝ3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantized in units of Boltzmann's constant kB. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on ℝ3. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Planck's constant ℏ from Boltzmann's constant kB.

scholarly journals The Enigma of the Muon and Tau Solved by Emergent Quantum Mechanics?

2019 ◽  
Vol 9 (7) ◽  
pp. 1471
Author(s):  
Theo van Holten
Keyword(s):  
Quantum Mechanics ◽  
Droplet Model ◽  
Matter Waves ◽  
Equilibrium Configurations ◽  
Self Consistent ◽  
Usual Quantum ◽  
Electron Models ◽  
Charged Leptons ◽  
Emergent Quantum Mechanics

This paper addresses the long-standing question of how it may be explained that the three charged leptons (the electron, muon and tau particle) have different masses, despite their conformity in other respects. In the field of Emergent Quantum Mechanics non-singular electron models are being revisited, and from this exploration has come a possible answer. In this paper a deformable droplet model is considered. It is shown how the model can be made self-consistent, whilst obeying the laws of momentum and energy conservation as well as Larmor’s radiation law. The droplet appears to have three different static equilibrium configurations, each with a different mass. Tentatively, these three equilibrium masses were assumed to correspond with the measured masses of the charged leptons. The droplet model was tuned accordingly, and was thereby completely quantified. The dynamics of the droplet then showed a “De Broglie-like” relation p = K / λ . Beat patterns in the vibrations of the droplet play the role of the matter waves of usual quantum mechanics. The value of K , calculated by the droplet theory, practically equals Planck’s constant: K ≅ h . This fact seems to confirm the correctness of identifying the three types of charged leptons with the equilibria of a droplet of charge.

scholarly journals On the Spectrum of the Local $${\mathbb {P}}^2$$ Mirror Curve

2020 ◽  
Vol 21 (11) ◽  
pp. 3479-3497
Author(s):  
Rinat Kashaev ◽  
Sergey Sergeev
Keyword(s):  
Spectral Problem ◽  
Bethe Ansatz ◽  
Quantum Mechanical ◽  
Planck’S Constant ◽  
Transcendental Equations ◽  
Del Pezzo ◽  
Planck's Constant ◽  
Quantum Mechanical Operator ◽  
Mechanical Operator

Abstract We address the spectral problem of the formally normal quantum mechanical operator associated with the quantised mirror curve of the toric (almost) del Pezzo Calabi–Yau threefold called local $${\mathbb {P}}^2$$ P 2 in the case of complex values of Planck’s constant. We show that the problem can be approached in terms of the Bethe ansatz-type highly transcendental equations.

scholarly journals A NOTE ON THE QUANTUM-MECHANICAL RICCI FLOW

2009 ◽  
Vol 24 (27) ◽  
pp. 4999-5006
Author(s):  
JOSÉ M. ISIDRO ◽  
J. L. G. SANTANDER ◽  
P. FERNÁNDEZ DE CÓRDOBA
Keyword(s):  
Quantum Mechanics ◽  
Configuration Space ◽  
Ricci Flow ◽  
Riemannian Metric ◽  
Quantum Mechanical ◽  
Two Dimensional ◽  
Conformally Flat ◽  
Flow Equations ◽  
Emergent Quantum Mechanics

We obtain Schrödinger quantum mechanics from Perelman's functional and from the Ricci-flow equations of a conformally flat Riemannian metric on a closed two-dimensional configuration space. We explore links with the recently discussed emergent quantum mechanics.

Mass gap problem and Planck constant

2021 ◽  
Vol 34 (3) ◽  
pp. 385-388
Author(s):  
Amrit S. Šorli ◽  
Štefan Čelan
Keyword(s):  
Quantum Mechanics ◽  
Einstein Relation ◽  
Planck Constant ◽  
Planck’S Constant ◽  
Mass Gap ◽  
Planck's Constant

The mass gap problem is about defining the constant that defines the minimal excitation of the vacuum. Planck’s constant is defining the minimal possible excitation of the vacuum from the point of quantum mechanics. The mass gap problem can be solved in quantum mechanics by the formulation of the photon’s mass according to the Planck‐Einstein relation.

Heisenberg, Bohr, Robertson, and the Uncertainty Principle

2020 ◽  
pp. 133-156
Author(s):  
Jim Baggott
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Laboratory Experiments ◽  
Space Time ◽  
Spectral Lines ◽  
Planck’S Constant ◽  
Classical Space ◽  
Planck's Constant

From the outset, Heisenberg had resolved to eliminate classical space-time pictures involving particles and waves from the quantum mechanics of the atom. He had wanted to focus instead on the properties actually observed and recorded in laboratory experiments, such as the positions and intensities of spectral lines. Alone in Copenhagen in February 1927, he now pondered on the significance and meaning of such experimental observables. Feeling the need to introduce at least some form of ‘visualizability’, he asked himself some fundamental questions, such as: What do we actually mean when we talk about the position of an electron? He went on to discover the uncertainty principle: the product of the ‘uncertainties’ in certain pairs of variables—called complementary variables—such as position and momentum cannot be smaller than Planck’s constant h (now h / 4π‎).

New test of quantum mechanics: Is Planck’s constant unique?

1991 ◽  
Vol 66 (3) ◽  
pp. 256-259 ◽  
Author(s):  
Ephraim Fischbach ◽  
Geoffrey L. Greene ◽  
Richard J. Hughes
Keyword(s):  
Quantum Mechanics ◽  
Planck’S Constant ◽  
Planck's Constant

Fringes decorating anticaustics in ergodic wavefunctions

1989 ◽  
Vol 424 (1867) ◽  
pp. 279-288 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Energy Range ◽  
Probability Density ◽  
Integrable Systems ◽  
Chaotic Systems ◽  
Planck’S Constant ◽  
Diffraction Patterns ◽  
Definition Of ◽  
Planck's Constant

The probability density Π is calculated for quantum eigenstates near spatial boundaries of classically chaotic regions. By contrast with integrable systems, for which the classical Π diverges on classical boundaries, which are caustics, in chaotic systems the classical Π does not diverge but vanishes abruptly in a way that depends on the number of freedoms N ; the boundaries are anticaustics. Quantum mechanics softens anticaustics, to give Π in terms of a set of canonical diffraction patterns, one for each N ; these are studied in detail. The appropriate definition of Π involves averaging over eigenstates in an energy range larger than O ( h ) but smaller than O ( h ⅔ ) (where h is Planck’s constant), that is over a range of ∆ N states near the N th, where N 1-1 / N ≪ ∆ N ≪ N 1-⅔ N .

scholarly journals Quantum Harmonic Analysis of the Density Matrix

Quanta ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 74 ◽  
Author(s):  
Maurice A. De Gosson
Keyword(s):  
Density Matrix ◽  
Harmonic Analysis ◽  
Quantum Mechanical ◽  
Mixed States ◽  
Density Matrices ◽  
Planck’S Constant ◽  
Planck's Constant

We will study rigorously the notion of mixed states and their density matrices. We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This review has been written having in mind two readerships: mathematical physicists and quantum physicists. The mathematical rigor is maximal, but the language and notation we use throughout should be familiar to physicists.Quanta 2018; 7: 74–110.

scholarly journals Why space could be quantised on a different scale to matter

2021 ◽  
Author(s):  
Matthew J. Lake
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Mechanical ◽  
Material Objects ◽  
Simple Argument ◽  
Planck’S Constant ◽  
Mechanical Effects ◽  
Quantum Mechanical Effects ◽  
Planck's Constant ◽  
The Universe

The scale of quantum mechanical effects in matter is set by Planck’s constant, \hbarℏ. This represents the quantisation scale for material objects. In this article, we present a simple argument why the quantisation scale for space, and hence for gravity, may not be equal to \hbarℏ. Indeed, assuming a single quantisation scale for both matter and geometry leads to the `worst prediction in physics’, namely, the huge difference between the observed and predicted vacuum energies. Conversely, assuming a different quantum of action for geometry, \beta \ll \hbarβ≪ℏ, allows us to recover the observed density of the Universe. Thus, by measuring its present-day expansion, we may in principle determine, empirically, the scale at which the geometric degrees of freedom should be quantised.

EFFECT OF MAXIMUM MOMENTUM ON QUANTUM MECHANICAL SCATTERING AND BOUND STATES

2013 ◽  
Vol 28 (15) ◽  
pp. 1350061 ◽  
Author(s):  
CHEE-LEONG CHING ◽  
RAJESH R. PARWANI
Keyword(s):  
Quantum Mechanics ◽  
Bound States ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Quantum Mechanical ◽  
Position Uncertainty ◽  
Exact Position ◽  
Usual Quantum ◽  
Quantum Mechanical Scattering ◽  
Mechanical Scattering

We construct the exact position representation for a deformed (non-relativistic) quantum mechanics which exhibits an intrinsic maximum momentum and use it to study problems such as a particle in a box and an asymmetric well. In particular, we show that unlike usual quantum mechanics, the present deformed case delays the formation of bound states in a finite potential well, a distinguishing feature that might be relevant for empirical investigations. We also contrast our results with the string-motivated type of deformed quantum mechanics which incorporates a minimum position uncertainty rather than a maximum momentum.

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