To derive the Planck length we start with the Schwarzschild radius (x=length; m=mass; G=Newton's constant; E=energy; c=light speed). (To find out how the Schwarzschild radius is derived, click here.)
We also need Heisenberg's Uncertainty Principle (p=momentum; x=position; h-bar=Planck's constant). (To find out how to derive the Uncertainty Principle, click here.) For our convenience we convert momentum (p) to energy (E) by multiplying both sides by light speed (c):
Divide both sides by E:
Multiply the above result by the Schwarzschild radius, then do some algebra to get the Planck length (x with a sub p):
To get the Planck time (t with a sub p), take the Schwarzschild radius and divide it by c:
Shall we call the above result the Schwarzschild time? We also need the other Heisenberg Uncertainty Principle, the one with energy (E) and time (t). Now do some more algebra to get the Planck time:
To get the Planck mass, set the Schwarzschild time equal to the Heisenberg time, then solve for E-squared:
Let's assume E is kinetic energy. Square it, make a substitution, do some more algebra, and get the Planck mass (m with a sub p):
John David Best has his web site Vida İnstitute. He put my articles page in 'Timeflow Theory' 'http://vidainstitute.org/?page_id=656'. Vida Institute is intersting site. And my web site is www.timeflow.org
ReplyDeleteIn your opinion, discovery of a planet is more exciting. Or, as I've presented in the attached article,
whether observing 'A very tiniest mass in the space, having completed its life, have been turning
into energy' would be more exciting or not ? It is my belief that, this observation will be the proof
of the General and the Special Theory of Relativity. This observation can be made only by NASA or
ESA. I hope that I will be able to see this consequence while I'm still alive. For further information,
please visit my web site www.timeflow.org . I will be indebted for your interest.
Sincerely
Salih KIRCALAR