Hydrodynamic limits of the nonlinear Schrödinger equation with the Chern-Simons gauge fields

<p style='text-indent:20px;'>We present two types of the hydrodynamic limit of the nonlinear Schrödinger-Chern-Simons (SCS) system. We consider two different scalings of the SCS system and show that each SCS system asymptotically converges towards the compressible and incompressible Euler system, coupled with the Chern-Simons equations and Poisson equation respectively, as the scaled Planck constant converges to 0. Our method is based on the modulated energy estimate. In the case of compressible limit, we observe that the classical theory of relative entropy method can be applied to show the hydrodynamic limit, with the additional quantum correction term. On the other hand, for the incompressible limit, we directly estimate the modulated energy to derive the desired asymptotic convergence.</p>

Measurements of the Planck Length from a Ball Clock without Knowledge of Newton’s Gravitational Constant G or the Planck Constant

We demonstrate how one can extract the Planck length from ball with a built-in stopwatch without knowledge of the Newtonian gravitational constant or the Planck constant. This could be of great importance since until recently it has been assumed the Planck length not can be found without knowledge of Newton’s gravitational constant. This method of measuring the Planck length should also be of great interest to not only physics researchers but also to physics teachers and students as it conveniently demonstrates that the Plank length is directly linked to gravitational phenomena, not only theoretically, but practically. To demonstrate that this is more than a theory we report 100 measurements of the Planck length using this simple approach. We will claim that, despite the mathematical and experimental simplicity, our findings could be of great importance in better understanding the Planck scale, as our findings strongly support the idea that to detect gravity is to detect the effects from the Planck scale indirectly.

Mass gap problem and Planck 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.

Reference standards-copies of mass unit: calibration 2020 using vacuum comparator CCL 1007

The article discusses the calibration results of reference standards-copies according to the State Primary Standard of the Mass Unit using the new CCL 1007 vacuum comparator and buoyancy artifacts. The authors provided historical data on the calibrations of copies of the International Prototype of the Kilogram (IPK) starting from 1892, including the Russian prototype № 12. The instability of the prototype of the kilogram No. 12 corresponds to international values and is assessed at 5 · 10–11 kg per year. Changes in the mass of copies are assessed in relation to the mass of the IPK, but it is impossible to determine to what extent it has changed. This was the reason for the adoption of a new value of the kilogram. Following the adoption at the 26th meeting of the General Conference on Weights and Measures (CGPM) held in Paris in November 2018, Planck constant was numerically established with absolute accuracy, and total uncer tainty of 1 · 10–8 kg was assigned to the mass of the IPK. Thus, the authors set the aim to preserve the numerical value of the total uncertainty of the reference standards-copies by reducing the transfer error of the State Primary Standard by 10 times. The article presents the calibration results of six reference standards-copies in relation to prototype No. 12 with the primary data processing using the method of least squares, and the uncertainty budget is provided. The calibration results of the reference standards-copies confirmed the accuracy increase of the transfer unit by 10 times in the range from 6 · 10–9 kg to 6 · 10–10 kg by the use of a vacuum comparator graduated 0.1 μg and buoyancy and sorption artifacts in direct measurements of air density. This has made it possible to compensate for the additional uncertainty attributed to the IPK based on the determination of the Planck constant value and to ensure the mass calibration of all accuracy grades preserving the entire hierarchical system of transferring the mass unit in the country.

Measurements of the Planck length from a Ball-Clock without Knowledge of Newton’s Gravitational Constant G or the Planck Constant

In this paper we show how one can extract the Planck length from ball with a built-in stopwatch with no knowledge of the Newtonian gravitational constant or the Planck constant. This is remarkable as until recently it has been assumed one cannot find the Planck length without knowledge of Newton’s gravitational constant. This method of measuring the Planck length should also be of great interest to not only physics researchers but also to physics teachers and students as it conveniently demonstrates that the Plank length is directly linked to gravitational phenomena, not only theoretically, but practically. To demonstrate that this is more than a theory we report 100 measurements of the Planck length using this simple approach. We will claim that, despite the mathematical and experimental simplicity, our findings could be of great importance in better understanding the Planck scale, as our findings strongly support the idea that to detect gravity is to detect the e↵ects from the Planck scale indirectly.

Constraints on the spatial variation of Planck constant

Inspired by recently published researches, we present two protocols for setting an upper limit to the claimed variation of $$\hbar $$ ħ upon the position. The protocols, both within today state of art, involve the use of two delayed laser pulses driving an atom. The distinct positions of the laboratory, due to the Earth motion, affects $$\hbar $$ ħ and hence the atomic dynamics. The first protocol measures the difference in population of the atomic ground state while the second one the red-shift of the harmonics emitted by the atom in the two moments of the experiment. The protocols improve the reported upper limit of $$\varDelta \hbar /\hbar $$ Δ ħ / ħ . The theory shows that $$\hbar (\varvec{r})$$ ħ ( r ) induces a chaotic evolution to the atom. This form of Chaos is generated by a variation of a physical parameter and is one example of Parametric Chaos.

New hydrogen atom model and radiation absorption mechanism

Only Coulomb force is considered in Bohr model. It is found that electron in ground state hydrogen atom is also affected by Lorentz force of the same magnitude. Under the combined action of Coulomb force and Lorentz force, the radius of hydrogen atom is twice that of Bohr, and the rotation frequency of electron is half that of Bohr. The "half frequency" problem of Bohr's theory is solved, and the quantization result of the energy level of hydrogen atom is obtained by using the standing wave condition of quantum mechanics. The mechanism and details of photon absorption by hydrogen atom are analyzed and explained, and the physical meaning of Planck constant is explained.

Problem of the 8-th Experimental Physics Olympiad, Skopje, 8 May 2021 Determination of Planck Constant by LED

This is the problem of the 8th International Experimental Physics Olympiad (EPO8). The task of the EPO8 is to determine Planck constant ħh/2 using the given set-up with LED. If you have an idea how to do it, do it and send us the result; skip the reading of the detailed step by step instructions with increasing difficulties. We expect the participants to follow the suggested items – they are instructive for physics education in general. Only the reading of historical remarks given in the first section can be omitted during the Olympiad without loss of generality. Participants should try solving as much tasks as they can without paying attention to the age categories: give your best.

New hydrogen atom model and radiation absorption mechanism

Only Coulomb force is considered in Bohr model. It is found that electron in ground state hydrogen atom is also affected by Lorentz force of the same magnitude. Under the combined action of Coulomb force and Lorentz force, the radius of hydrogen atom is twice that of Bohr, and the rotation frequency of electron is half that of Bohr. The "half frequency" problem of Bohr's theory is solved, and the quantization result of the energy level of hydrogen atom is obtained by using the standing wave condition of quantum mechanics. The mechanism and details of photon absorption by hydrogen atom are analyzed and explained, and the physical meaning of Planck constant is explained.

Is the Devil in h?

This note is a part of my effort to rid quantum mechanics (QM) nonlocality. Quantum nonlocality is a two faced Janus: one face is a genuine quantum mechanical nonlocality (defined by the Lüders’ projection postulate). Another face is the nonlocality of the hidden variables model that was invented by Bell. This paper is devoted the deconstruction of the latter. The main casualty of Bell’s model is that it straightforwardly contradicts Heisenberg’s uncertainty and Bohr’s complementarity principles generally. Thus, we do not criticize the derivation or interpretation of the Bell inequality (as was done by numerous authors). Our critique is directed against the model as such. The original Einstein-Podolsky-Rosen (EPR) argument assumed the Heisenberg’s principle without questioning its validity. Hence, the arguments of EPR and Bell differ crucially, and it is necessary to establish the physical ground of the aforementioned principles. This is the quantum postulate: the existence of an indivisible quantum of action given by the Planck constant. Bell’s approach with hidden variables implicitly implies rejection of the quantum postulate, since the latter is the basis of the reference principles.