Authors: Espen Gaarder Haug
n 2014, McCulloch showed, in a new and interesting way, how to derive a gravity theory from Heisenberg’s uncertainty principle that is equivalent to Newton gravity. McCulloch utilizes the Planck mass in his derivation and gets a gravitational constant of hc/m_p^2 . This is a composite constant, which is equivalent in value to Newton’s gravitational constant. However, McCulloch has pointed 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. Therefore, from this perspective, there are no circular problems with his method. This means that we can measure the Planck mass totally independent of Newton’s gravitational constant, and shows that the McCulloch derivation is a theory of quantum gravity that stands on its own, with no need for input from Newton. This also strongly points towards the idea that Newton’s gravitational constant should be seen as a composite constant. Based on this perspective, for the first time since it was theoretically introduced 119 years ago, the Planck units can be measured completely independent of any knowledge of Newton’s gravitational constant. This could be an important step towards the development of a full theory of quantum gravity.
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