Preprint Article Version 2 This version is not peer-reviewed

# Planck Mass Measured Totally Independent of Big G Utilizing McCulloch-HeisenbergNewtonian Equivalent Gravity

Version 1 : Received: 25 June 2018 / Approved: 25 June 2018 / Online: 25 June 2018 (14:00:37 CEST)
Version 2 : Received: 25 June 2018 / Approved: 26 June 2018 / Online: 26 June 2018 (14:45:54 CEST)

How to cite: Gaarder Haug, E. Planck Mass Measured Totally Independent of Big G Utilizing McCulloch-Heisenberg
Newtonian Equivalent Gravity. Preprints 2018, 2018060391 (doi: 10.20944/preprints201806.0391.v2). Gaarder Haug, E. Planck Mass Measured Totally Independent of Big G Utilizing McCulloch-HeisenbergNewtonian Equivalent Gravity. Preprints 2018, 2018060391 (doi: 10.20944/preprints201806.0391.v2).

## Abstract

In 2014, McCulloch showed, in a new and interesting way, how to derive a gravity theory
from Heisenberg's uncertainty principle that is equivalent to Newtonian gravity. McCulloch utilizes
the Planck mass in his derivation and obtains a gravitational constant of hbar*c/m_p^2. This is a composite constant, which is equivalent in value to Newton's gravitational constant. However, McCulloch has pointed out that his approach requires an assumption on the value of G, and that this involves some circular reasoning. This is in line with the view that the Planck mass is a derived constant
from Newton's gravitational constant, while big G is a universal fundamental constant. Here we will
show that we can go straight from the McCulloch derivation to measuring the Planck mass without
any knowledge of the gravitational constant. From this perspective, there are no circular problems
with his method. This means that we can measure the Planck mass without Newton's gravitational
constant, and shows that the McCulloch derivation is a theory of quantum gravity that stands on
its own. Even more importantly, we show that we can easily measure the Schwarzschild radius of
a mass without knowing its mass, or Newton's gravitational constant, or the Planck constant. The
very essence of gravity is linked to the Planck length and the speed of light, but here we will claim
that we do not need to know the Planck length itself. Our conclusion is that Newton's gravitational
constant is a universal constant, but it is a composite constant of the form G=l_p^2*c^3/hbar where the
Planck length and the speed of light are the keys to gravity. This could be an important step towards the development of a full theory of quantum gravity.

## Subject Areas

Heisenberg, Planck mass, McCulloch gravity, Newton, gravitational constant, Cavendish apparatus

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