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

##plugins.themes.bootstrap3.article.main##

  •   Espen Gaarder Haug

Abstract




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.





Keywords: Planck length, Planck units, Newton’s gravitational constant, Planck constant, Compton wavelength

References

M. Planck. Natuerliche Masseinheiten. Der K¨oniglich Preussischen Akademie Der Wissenschaften, 1899.

M. Planck. Vorlesungen ¨uber die Theorie der W¨armestrahlung. Leipzig: J.A. Barth, p. 163, see also the English translation “The Theory of Radiation” (1959) Dover, 1906.

J. G. Stoney. On the physical units of nature. The Scientific Proceedings of the Royal Dublin Society, 3, 1883.

A. Einstein. N¨aherungsweise integration der feldgleichungen der gravitation. Sitzungsberichte der K¨oniglich Preussischen Akademie der Wissenschaften Berlin, 1916.

A. S. Eddington. Report On The Relativity Theory Of Gravitation. The Physical Society Of London, Fleetway Press, London, 1918.

P. W. Bridgman. Dimensional Analysis. New Haven: Yale University Press, 1931.

A. C. Mead. Possible Connection Between Gravitation and Fundamental Length Phys. Rev., 135(38), 1964. URL https://link.aps.org/doi/10.1103/PhysRev.135.B849.

T. Padmanabhan. Planck length as the lower bound to all physical length scales. General Relativity and Gravitation, 17, 1985. URL https://doi.org/10.1007/BF00760244.

S. Hossenfelder. Can we measure structures to a precision better than the Planck length? Classical and Quantum Gravity, 29, 2012. URL https://doi.org/10.1088/0264-9381/29/11/115011.

S. Hossenfelder. Minimal length scale scenarios for quantum gravity. Living Reviews in Relativity, 16, 2013. URL https://doi.org/10.12942/lrr-2013-2.

G. M. Obermair. Primordial Planck mass black holes (PPMBHS) as candidates for dark matter? Journal of Physics, Conference Series, 442, 2013. URL https://doi.org/10.1088/1742-6596/442/1/012066.

V. Faraoni. Three new roads to the Planck scale. American Journal of Physics, 85, 2017. URL https://aapt.scitation.org/doi/pdf/10.1119/1.4994804.

A. Unzicker. The Mathematical Reality: Why Space and Time Are an Illusion. Independently published, 2020.

E. G. Haug. Can the Planck length be found independent of big G ? Applied Physics Research, 9(6):58, 2017. URL https://doi.org/10.5539/apr.v9n6p58.

E. G. Haug. Finding the Planck length multiplied by the speed of light without any knowledge of G, c, or h, using a Newton force spring. Journal Physics Communication, 4:075001, 2020. URL https://doi.org/10.1088/2399-6528/ab9dd7.

E. G. Haug. Using a grandfather pendulum clock to measure the world’s shortest time interval, the Planck time (with zero knowledge of G). Journal of Applied Mathematics and Physics, 9:1076, 2021c.

A. H. Compton. A quantum theory of the scattering of xrays by light elements. Physical Review, 21(5):483, 1923. URL https://doi.org/10.1103/PhysRev.21.483.

G. Gr¨aff, H. Kalinowsky, and J. Traut. A direct determination of the proton electron mass ratio. Zeitschrift f¨ur Physik A Atoms and Nuclei, 297 (1), 1980. URL https://link.springer.com/article/10.1007/BF01414243.

R.S. Van-Dyck, F.L. Moore, D.L. Farnham, and P.B. Schwinberg. New measurement of the proton-electron mass ratio. International Journal of Mass Spectrometry and Ion Processes, 66(3), 1985. URL https://doi.org/10.1016/0168-1176(85)80006-9.

L.S. Levitt. The proton Compton wavelength as the ‘quantum’ of length. Experientia, 14:233, 1958. URL https://doi.org/10.1007/BF02159173.

O. L. Trinhammer and H. G. Bohr. On proton charge radius definition. EPL, 128:21001, 2019. URL https://doi: 10.1209/0295-5075/128/21001.

E. Massam and G. Mana. Counting atoms. Nature Physics, 12:522, 2016. URL https://doi.org/10.1038/nphys3754.

P. Becker and H. Bettin. The Avogadro constant: determining the number of atoms in a single-crystal 28Si sphere. Phil. Trans. R. Soc. A, 369: 3925, 2011. URL https://doi:10.1098/rsta.2011.0222.

P. Becker. The new kilogram definition based on counting the atoms in a 28Si crystal. Contemporary Physics, 53:461, 2012. URL https://doi.org/10.1080/00107514.2012.746054.

I Newton. Philosophiae Naturalis Principia Mathematica. London, 1686.

H. Cavendish. Experiments to determine the density of the earth. Philosophical Transactions of the Royal Society of London, (part II), 88, 1798.

Bartl, G. et. al. A new 28Si single crystal: Counting the atoms for the new kilogram definition. Metrologica, 54:693, 2017. URL https://doi.org/10.1088/1681-7575/aa7820.

A. Cornu and J. B. Baille. D´etermination nouvelle de la constante de l’attraction et de la densit´e moyenne de la terre. C. R. Acad. Sci. Paris, 76, 1873.

C. V. Boys. On the Newtonian constant of gravitation. Nature, 5, 1894. URL https://doi.org/10.1038/050330a0.

R. Cross. Measuring the drag force on a falling ball. The Physics Teacher, 52(169), 2014. URL https://doi.org/10.1119/1.4865522.

E. G. Haug. The gravitational constant and the Planck units. A simplification of the quantum realm. Physics Essays, 29(4):558, 2016. URL https://doi.org/10.4006/0836-1398-29.4.558.

E. G. Haug. Collision space-time: Unified quantum gravity. Physics Essays, 33(1):46, 2020a. URL https://doi.org/10.4006/0836-1398-33.1.46.

K. Cahill. Tetrads, broken symmetries, and the gravitational constant. Zeitschrift F¨ur Physik C Particles and Fields, 23:353, 1984.

E. R. Cohen. Graviton Exchange and the Gravitational Constant in the book Gravitational Measurements, Metrology and Constants. Edited by Sabbata, V. and Gillies, G. T. and Melniko, V. N., Netherland, Kluwer

Academic Publishers, 1987.

M. E. McCulloch. Quantised inertia from relativity and the uncertainty principle. Europhysics Letters (EPL), 115(6):69001, 2016. URL https://doi.org/10.1209/0295-5075/115/69001.

E. G. Haug. Newton and Einstein’s gravity in a new perspective for Planck masses and smaller sized objects. International Journal of Astronomy and Astrophysics, 8, 2018. URL https://doi.org/10.4236/ijaa.2018.81002.

E. G. Haug. Demonstration that Newtonian gravity moves at the speed of light and not instantaneously (infinite speed) as thought! Journal of Physics Communication., 5(2):1, 2021. URL https://doi.org/10.1088/2399-6528/abe4c8.

E. G. Haug. Quantum Gravity Hidden in Newton Gravity And How To Unify It With Quantum Mechanics. in the book: The Origin of Gravity from the First Principles, Editor Volodymyr Krasnoholovets,

NOVA Publishing, New York, 2021b.

M. J. Duff, L. B. Okun, and G. Veneziano. Trialogue on the number of fundamental constants. Journal of High Energy Physics, 2002, 2002. URL https://doi.org/10.1088/1126-6708/2002/03/023.

J. Conlon. Why String Theory? CRC Press, 2015.

##plugins.themes.bootstrap3.article.details##

How to Cite
Haug, E. G. (2021). Measurements of the Planck Length from a Ball Clock without Knowledge of Newton’s Gravitational Constant G or the Planck Constant. European Journal of Applied Physics, 3(6), 15–20. https://doi.org/10.24018/ejphysics.2021.3.6.133