Checking Temperature Effects

This will be most interesting as usual.

To: EMyrone@aol.com
Sent: 29/11/2014 19:48:00 GMT Standard Time
Subj: Re: Coding up Exact Solutions for the refraction theory

I will first check the temperature effects in the linearized theory, compared to the single frequency theory.

Horst

Am 29.11.2014 18:38, schrieb EMyrone

This would be of great interest, because it is the exact conservation of energy and momentum with the Planck distribution. Nothing else is assumed in the theory. In my opinion these equations are perfectly general and must be obeyed in any optical process involving reflection and refraction. A desk top these days is almost as powerful as the IBM 3084 of the eighties.

Sent: 29/11/2014 16:41:37 GMT Standard Time
Subj: Exact Solutions for the refraction theory

Eqs. (4) and (5) of note 279(8) are non-linear, transcendent equations. In principle they can be solved by a zero crossing (root finding) method. I will look if Maxima can handle more than one equation simultaneously for this. In the worst case this problem has to be coded by hand. I do not believe that a supercomputer is necessary, that should be handable on a desktop.

Horst

Am 29.11.2014 11:07, schrieb EMyrone

This note summarizes a scheme for comparison of experiment and theory using the linearized n photon monochromatic theory with conservation of energy and momentum. As shown yesterday by Horst Eckardt there are four possible solutions for the refracted frequency omega1 in terms of the incident frequency omega, and it is possible to produce refracted red shifts and blue shifts as observed experiemntally by Gareth Evans and Trevor Morris. In the first instance the refarctive index of olive oil can be used, n = 1.4665, to see if this is sufficient to produce red shifts. The angle theta3 appears to be unknown experimentally but it can be adjusted to try to produce a fit with data. I note that the frequencies in hertz sent over by Gareth are calculated from the wavelengths using the speed of light c as in Eq. (1). If this simple constant refractive index theory does not work then the complex refractive index must be used as described by Horst yesterday. The real and imaginary parts of the complex refractive index are given in Eqs. (10) and (11). The rigorous theory is given in Eqs. (4) and (5), using the Planck distribution. Can Maxima solve those equations? Probably not, a mainframe computer will probably be needed.


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