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.

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.

The Newtonian Gravitational Constant G Interpreted as the Gravitational Inertia of Vacuum - G0. How to Arrange Twelve Precise Experimental Determinations of GZ in their Spread 500 ppm?

We have newly interpreted the Newtonian gravitational constant G as the gravitational inertia of vacuum G0. The source mass inserted into vacuum decreases this value G0 to GZ on the dependence of the atomic number Z of atoms in the source mass. This is the mechanism for the attraction of test masses through vacuum – the test mass follows the decrease of the gravitational inertia of vacuum towards the source mass. We have extracted the relationship GZ = G0 (1 – k Z) where k is the experimental constant from ten actual precise experimental determinations of GZ. This model was tested on two precise experimental values of GZ determined for GEARTH, and GBRASS. This model enables to predict values GZ for atoms, molecules and compositions of the studied source masses and to realize experimental verification with the existing experimental technology. The experimental GZ values are thus arranged into a system and the spread in these data is explained as the influence of atoms of the source masses on their surrounding via the decrease of the gravitational inertia of vacuum. We might achieve the accuracy of experimental values GZ with six significant figures for all configurations of source and test masses.

Testing weakest force with coldest spot

Ultra-cold atom experiment in space with microgravity allows for realization of dilute atomic-gas Bose-Einstein condensate (BEC) with macroscopically large occupation number and significantly long condensate lifetime, which allows for a precise measurement on the shape oscillation frequency by calibrating itself over numerous oscillation periods. In this paper, we propose to measure the Newtonian gravitational constant via ultra-cold atom BEC with shape oscillation, although it is experimentally challenging. We also make a preliminary perspective on constraining the modified Newtonian potential such as the power-law potential, Yukawa interaction, and fat graviton. A resolution of frequency measurement of $$(1-100)\,\mathrm {nHz}$$ ( 1 - 100 ) nHz at most for the occupation number $$10^9$$ 10 9 , just one order above experimentally achievable number $$N\sim 10^6{-}10^8$$ N ∼ 10 6 - 10 8 , is feasible to constrain the modified Newtonian potential with Yukawa interaction greatly beyond the current exclusion limits.

A cautionary tale in fitting galaxy rotation curves with Bayesian techniques

The application of Bayesian techniques to astronomical data is generally non-trivial because the fitting parameters can be strongly degenerated and the formal uncertainties are themselves uncertain. An example is provided by the contradictory claims over the presence or absence of a universal acceleration scale (g†) in galaxies based on Bayesian fits to rotation curves. To illustrate this we present an analysis in which the Newtonian gravitational constant GN is allowed to vary from galaxy to galaxy when fitting rotation curves from the SPARC database, in analogy to g† in the recently debated Bayesian analyses. When imposing flat priors on GN, we obtain a wide distribution of GN which, taken at face value, would rule out GN as a universal constant with high statistical confidence. However, imposing an empirically motivated log-normal prior returns a virtually constant GN with no sacrifice in fit quality. This implies that the inference of a variable GN (or g†) is the result of the combined effect of parameter degeneracies and unavoidable uncertainties in the error model. When these effects are taken into account, the SPARC data are consistent with a constant GN (and constant g†).

A Review and Revisit of Newton’s Law and Gravitational Constant Derivations

This paper is a review of, and complement to, my original papers previously published in Physics Essays [1] and ViXra [2]. While the derivations and results pertinent to this review are unchanged, a possible extension of the proposed model as it relates to the derivation of G and to G-experimental is explored and presented in the attached addendum. Herein, as proposed in my previous papers, is a theoretical model of Universal Gravitation based upon hypothetical mass/energy resonance waves, the intensities of which I propose to be casually analogous with those of electromagnetic waves. Using said model, I derive the expressed Newtonian law of gravitation from which an apparent Newtonian gravitational constant factors as a combination of other physical constants, yielding a primary G-value of 6.662936 x 10-11m3/kg s2, shown by extension to yield a secondary result that correlates well with the 2018 recommended value. A second resultant of the proposal is a demonstration that the quantum energy states of the hydrogen atom appear related to the length of these waves, shown equal to twice the ground state orbital radius in a Bohr hydrogen atom. Additionally determined, independently of any experimental G-value, are values for the Planck mass, length, and time.

Is Newtonian gravitational constant a quantized constant of microscopic quantum gravity?

Considering the Newtonian gravitational constant as a quantized constant of microscopic quantum gravity, an attempt is made to fit its value in a verifiable approach with reference to three large atomic gravitational constants pertaining to weak, strong and electromagnetic interactions linked with a quantum relation. Estimated value seems to be 865 ppm higher than the recommended value.

Precision measurement of the Newtonian gravitational constant

The Newtonian gravitational constant G, which is one of the most important fundamental physical constants in nature, plays a significant role in the fields of theoretical physics, geophysics, astrophysics and astronomy. Although G was the first physical constant to be introduced in the history of science, it is considered to be one of the most difficult to measure accurately so far. Over the past two decades, eleven precision measurements of the gravitational constant have been performed, and the latest recommended value for G published by the Committee on Data for Science and Technology (CODATA) is (6.674 08 ± 0.000 31) × 10−11 m3 kg−1 s−2 with a relative uncertainty of 47 parts per million. This uncertainty is the smallest compared with previous CODATA recommended values of G; however, it remains a relatively large uncertainty among other fundamental physical constants. In this paper we briefly review the history of the G measurement, and introduce eleven values of G adopted in CODATA 2014 after 2000 and our latest two values published in 2018 using two independent methods.