Progress in the Composite View of the Newton Gravitational Constant and Its Link to the Planck Scale

Abstract

The Newtonian gravity constant G plays a central role in gravitational theory. Researchers have, since at least the 1980s, tried to see if the Newton gravitational constant can be expressed or replaced with more fundamental units, such as the Planck units. However, it was already pointed out in 1987 that this led to a circular problem; namely, that one must know G to find the Planck units, and that it is therefore of little or no use to express G through the Planck units. This is a view repeated in the literature in recent years, and is held by the physics’ community. However, we will claim that the circular problem was solved a few years ago. In addition, when one expresses the mass from the Compton wavelength formula, this leads to the conclusion that the three universal constants of G, h, and c now can be replaced with only lp and c to predict observable gravitational phenomena. While there have been several review papers on the Newton gravitational constant, for example, about how to measure it, we have not found a single review paper on the composite view of the gravitational constant. This paper will review the history of, as well as recent progress in, the composite view of the gravitational constant. This should hopefully be a useful supplement in the ongoing research for understanding and discussion of Newton’s gravitational constant.

Newton Did Not Invent or Use the So-Called Newton’s Gravitational Constant; <i>G</i>, It Has Mainly Caused Confusion

“…However, here we will focus on expressing the gravity constant from the Planck units as this seems to lead to a significant step forward in understanding gravity. Some of these approaches are actually closely related when they are compared carefully; see [61]. In 2016 we [42] suggested this to express G as a composite constant of the form:…”

Potential Simplification of Charge and the Coulomb Force without Affecting Predictions

“…, which is simply the Planck length formula solved with respect to G. That is the composite view of G as recently discussed in detail by Haug [23]. However, now, as we can find p l independently of G, this no longer leads to a circular problem so we can replace G in a series of Planck-related electric properties and see that this leads to simpler and more intuitive formulas; see also [24].…”

Gravity Without Newton’s Gravitational Constant and No Knowledge of the Mass Size

“…To find Newton's gravitational constant in a Cavendish apparatus, we need to know the mass of the large lead balls first, in relation to their weight. In our view, the reason for this is that the embedded gravitational constant also contains the reduced Planck constant, G = l 2 p c 3 h ; see [26]. Mass in the form of kilogram is clearly related to the Planck constant.…”

“…There are several reasons to question whether or not Newton's gravitational constant is a composite constant [26], including the following points.…”