Abstract
In this paper we rewrite the gravitational constant based on its relationship with the Planck length and based on this, we rewrite the Planck mass in a slightly different form (that gives exactly the same value). In this way we are able to quantize a series of end results in Newton and Einstein’s gravitation theories. The formulas will still give exactly the same values as before, but everything related to gravity will then come in quanta. This also gives some new insight; for example, the gravitational deflection of light can be written as only a function of the radius and the Planck length. Numerically this only has implications at the quantum scale; for macro objects the discrete steps are so tiny that they are close to impossible to notice. Hopefully this can give additional insight into how well or not so well (ad hoc) quantized Newton and Einstein’s gravitation is potentially linked with the quantum world.
Highlights
We suggest that Newton’s gravitational constant [1] could be written as a function of Planck’s reduced constant
Haug gravitational constant is known, or alternatively and more practically one can calibrate the Planck length based on empirical measurements of the gravitational constant
Gravitational acceleration field Gravitational time dilation Orbital time dilation Schwarzschild radius Newton bending of light Einstein bending of light Black holes g = GM r2
Summary
We suggest that Newton’s gravitational constant [1] could be written as a function of Planck’s reduced constant. Where is the reduced Planck’s constant, c is the well tested round-trip speed of light, and lp is the Planck length [2]. We could call this Planck’s form of the gravitational constant. Haug gravitational constant is known, or alternatively and more practically one can calibrate the Planck length based on empirical measurements of the gravitational constant. As shown by Haug [9], the Planck form of the gravitational constant enables us to rewrite the Planck length as l p2 c3. Using the gravitational constant in the Planck form, as well as the rewritten Planck units, we are able to modify a series of end results from Newton and Einstein’s gravitational theories to contain quantization as well
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