The Planck Units are defined using three universal physical constants.....the reduced Planck constant ħ, the speed of light c, and the gravitational constant G. If ħ=c=1 then they become Planck Length = √G, Planck time= √G, and Planck mass = 1/√G.
For this blog posting just consider Newton's law of gravity. Which appears as part of general relativity in the weak field limit, and Schwarzchild geometry, such as in the solar system. (Basically any place but near a massive black hole.)
The potential of Newtonian gravity . V=-GM/r is supposed to have units of energy. But if the Planck units are used.
V= - G(1/√G)/√G = -√G/√G=1 ! Or the dimensions disappear! This is not supposed to happen unless all three base units are set equal to one all quantities should retain their units in the new system of measurement. So I propose the following modification to classical gravity when planck units are used.
When this is done and planck units are plugged in V=-(G/√G)/G= -√G/G=-1/√G The correct unit of measure for potential energy. Now I know it is not a trivial matter to modify such a well tested law of nature. However the concern I raise is such a simple and fundamental point of science it cannot be totally ignored.
- A Three Inch Equation: Gravity's Effect at the Smallest Length Scales.
- Planck's Variable of Motion and its Relationship to Planck's Constant
- Upgrading Newton's Universal Gravity Law
- Guest Post: Higgs? 126 GeV, Said The Four Colour Theorem
- A Simple Calculation That Shows Black Hole Firewalls Exist and How Hot They Are.