Hi Joe, you'll remember that I had a bit of a problem deciding on the speed of gravity being either h = c^2 / b^2 or barh = c^2 / b^2
b being the speed of gravity. All I had to do was divide the mass in E = mb^2 by 2pi but being a bear of little brain this confused me.
Then your post got me thinking about dimensionless numbers again. C^2 / b^2 is dimensionless and I want to work in nothing but those numbers. Remember that for the speed of gravity we get something very close to c^3 Now, I wanted a dimensionless number for particle masses and the obvious choice is the reduced Planck mass. I divide any mass particle by that; or multiply by the reciprocal. Just to see what would happen i multiplied C^2 by the reciprocal and then worked out what the planck mass would have to be, to give me the speed of gravity of about 2.92E 25 The reduced planck mass is approximately 4.34E-9 = Sqrt(barh c / 8pi G )
Just with a pocket calculator and only working to a few decimal places I get a Planck mass of sqrt(barh c / 15.92pi G)
Remember that when we are talking about the planck mass particle, we are talking about a micro black hole. We take the Compton wavelength and make that equal to the Schwarzschild radius,
h / mc = 2Gm / c^2
Its mass is proportionate and not yet settled, it's in the ball park for expressing masses as dimensionless though.
