Abstract
Here we derive Newton’s and Einstein’s gravitational results for any mass less than or equal to a Planck mass. All of the new formulas presented in this paper give the same numerical output as the traditional formulas. However, they have been rewritten in a way that gives a new perspective on the formulas when working with gravity at the level of the subatomic world. To rewrite the well-known formulas in this way could make it easier to understand the strengths and weaknesses in Newton’s and Einstein’s gravitation formulas at the subatomic scale, potentially opening them up for new important interpretations and extensions. For example, we suggest that the speed of gravity equal to that of light is actually embedded and hidden inside of Newton’s gravitational formula.
Highlights
In a recent paper, Haug [1] has rewritten many of Newton’s and Einstein’s gravitational results, without changing their output, into a quantized Planck form
We suggest that the speed of gravity equal to that of light is embedded and hidden inside of Newton’s gravitational formula
By making the gravitational constant a function form of the reduced Planck constant, one can rewrite many of the end results from Newton’s and Einstein’s gravitation in quantized form. This has been done recently for masses above or equal to the Planck mass. This framework has been extended to hold below Planck mass sized objects as well
Summary
Haug [1] has rewritten many of Newton’s and Einstein’s gravitational results, without changing their output, into a quantized Planck form. His results only hold down to the scale of Planck mass sized objects. Using the gravitational constant in the Planck form, as well as the mass formula relationship above, we can rewrite a series of mathematical end results from Newton’s and Einstein’s gravitational formulas without changing. Seeing well-known formulas in this new perspective seems to give new and additional insight that we believe can be useful
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