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

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.

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Heisenberg, Bohr, Robertson, and the Uncertainty Principle

The Quantum Cookbook ◽

10.1093/oso/9780198827856.003.0008 ◽

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).

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AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s021988781250048x ◽

2012 ◽

Vol 09 (05) ◽

pp. 1250048 ◽

Cited By ~ 15

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.

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Fringes decorating anticaustics in ergodic wavefunctions

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1989.0082 ◽

1989 ◽

Vol 424 (1867) ◽

pp. 279-288 ◽

Cited By ~ 13

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 .

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Black-Body Radiation

An Introduction to Statistical Mechanics and Thermodynamics ◽

10.1093/oso/9780198853237.003.0025 ◽

2019 ◽

pp. 322-330

Author(s):

Robert H. Swendsen

Keyword(s):

Quantum Mechanics ◽

Energy Spectrum ◽

Electromagnetic Radiation ◽

Black Body ◽

Black Body Radiation ◽

Perfect Absorber ◽

Max Planck ◽

Planck’S Constant ◽

Light Waves ◽

Planck's Constant

A black body is a perfect absorber of electromagnetic radiation. The energy spectrum was correctly calculated by Max Planck under the assumption that the energy of light waves only came in discrete multiples of a constant (called Planck’s constant) times the frequency. This was perhaps the first achievement of quantum mechanics. The derivation is presented here. The purpose of the current chapter is to calculate the spectrum of radiation emanating from a black body. The calculation was originally carried out by Max Planck in 1900 and published the following year. This was before quantum mechanics had been invented, or perhaps it could be regarded the first step in its invention.

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