## Limiting Values in the Universe?

We have already played an algebra game with the fundamental constants of physics to get some interesting implications. Here, we play with some standard equations to generate approximations about what limits might actually exist in the universe.

Written 2000

Formatted 2010

### Let the Swartzchild radius equal the Heisenberg wavelength.

This conjecture is made of three parts:

First, escape velocity is the speed which will free an object from a spherical gravitational body. A black hole occurs when the escape velocity at the surface is equal to the speed of light. The radius at which this occurs is called the Schwartzchild radius. The formula for escape velocity, as drawn from a basic physics text, will be: V = sqrt(2Gm/R). Solving for radius (R) when velocity is the speed of light (c) gives: R = 2 Gm / c2.

Second: The energy contained in light is simply: E = h *nu, or E= hc/L where nu is the frequency, and L is the wavelength.

Third: The mass contained in energy occurs in the well known formula: E = mc2.

We ask, "What wavelength is its own Swartzchild radius?", implying that light of this frequency will fall into its own black hole. To do this we set R=L from the equations above. This eliminates all variables except for m, for which we solve. After that, we substitute back through the equations to get the other physical values.

 mass m = sqrt(hc/2G) 3.858x10-8 kg Energy E = mc2 3.467x109 joules frequency nu = E / h 5.233x1042 hz Wavelength L = c / nu 5.729x10-35 meters Time t = 1/nu 1.911x10-43 sec
Compare these values to the "fundamental units" we found in our simple algebra game. Compare these results to the Planck length and Planck time, also. How, then, did physicists determine the Planck length?

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