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[Omega_0]

My personal view is, it is not possible to gain energy unless you disturb some kind of symmetry or the other. Emmy Noether's law is truly fundamental. But that law does not impose any restrictions on how the symmetry can be broken, which is a good thing.

I believe you can break the symmetry by changing the fundamental properties of the matter at atomic level. It cannot be done at gross level. Steorn has explored modulation of permeability of a ferrite material, causing unusual behavior. Something similar can be possible using a capacitor and modulating its Permittivity.

http://en.wikipedia.org/wiki/Permittivity#Classification_of_materials
http://en.wikipedia.org/wiki/Dielectric#Dielectric_relaxation

It may happen that the dielectric viscosity of the material in the capacitor is causing something unusual at high frequencies. We need an elaborate setup analogous to steorn's setup, but in electric domain, to intensionally modulate the permittivity for gain of energy. 

[teslaalset]

@All,

Please take a look at the attached theoretical writeup which gives a rigorous derivation of Pout/Pin problem we're discussing. As seen, theoretically, that ratio should be unity in all cases. It appear that @Omega_0's remark regarding the floating point errors as the cause for the observed discrepancies in the numerical integration with Excel hit the nail on the head. This rigorous theoretical derivation should provide a solid foundation when searching for the truth regarding the reported experimental OU.


P.S. @Omega_0, thanks a lot for providing that great link to Mathematica.

@Omnibus,
Nice overview. I think it's correct.

Regarding the numerical errors, I noticed following looking at your spreadsheets:
In the latest one you posted you used (per row) time fragments that correspond with 1/(360*800000) seconds (column A), while using 700000Hz as frequency in the 2*pi*f*t calculation (column D and E).
Each row represents 1 degree as shown (column C).
Showing the integration over 0 - T (corresponding with 360 degrees) demands not the integration over the results over 360 rows but 360 * 800000/700000 rows = 411.42857142857142857142857142857 rows.
Now in practice 411 or 412 rows will be used for the integration of one period.
I did not check in details on how you made the numerical integration over one period, but this may be the reason for your so called floating point errors.

I did not notice these floating point errors in my spread sheet model because I used time fragments that matches 1/360 of the time period of the actual frequency used in the 2*pi*f*t part of the formulas. Integration of one T period is done by using data of exactly 360 rows.

You may have to look at this.

[Omnibus]

@All,

Check this out. These are Excel files of three ways of calculating Pout/Pin. Two are theoretical, based on R = 9.9244Ohms, C = 991pF and f = 800kHz used in the experiment and the Vm = 14.92V observed. Notice that in all three data files what is processed is just one full period. I used 800kHz to be in agreement with @teslaalset's correct remark. Also, the phase angle is calculated separately in the theoretical spreadsheet to see it clearly. The first puzzling thing is that there is a discrepancy between the two theoretical ways of calculation. Could it be that Simpson's rule of integration isn't the right way to go or again we're haunted by the floating point errors? What good is Excel if that's the case? There may be a problem (not mathematical but of physical nature) in the theoretical derivation I posted yesterday. That derivation is a brute force approach. Anyway, I think we should look first into the discrepancy in the two theoretical approaches. Then we'll have to look very carefully into the experimental data. After all, what do we have -- just current and voltage (R is measured very precisely with the Keithley four point measurement). Should that be so difficult to measure correctly with the equipment at hand?

[Omnibus]

So, if we consider the theoretical calculation in the writeup I posted yesterday as the exact theoretical solution then, if there are indeed floating point errors in Excel, these errors are to the detriment of the observed OU effect -- the theoretical integration shows lower than unity Pout/Pin ratio which is lower than purportedly exact theoretical solution.

[teslaalset]

@All,

Check this out. These are Excel files of three ways of calculating Pout/Pin. Two are theoretical, based on R = 9.9244Ohms, C = 991pF and f = 800kHz used in the experiment and the Vm = 14.92V observed. Notice that in all three data files what is processed is just one full period. I used 800kHz to be in agreement with @teslaalset's correct remark. Also, the phase angle is calculated separately in the theoretical spreadsheet to see it clearly. The first puzzling thing is that there is a discrepancy between the two theoretical ways of calculation. Could it be that Simpson's rule of integration isn't the right way to go or again we're haunted by the floating point errors? What good is Excel if that's the case? There may be a problem (not mathematical but of physical nature) in the theoretical derivation I posted yesterday. That derivation is a brute force approach. Anyway, I think we should look first into the discrepancy in the two theoretical approaches. Then we'll have to look very carefully into the experimental data. After all, what do we have -- just current and voltage (R is measured very precisely with the Keithley four point measurement). Should that be so difficult to measure correctly with the equipment at hand?

@Omnibus,
I noticed that the use of the 'slope' function in Excel raises some questions.
When I replace the slope calculation by applying Pin=(K1004-K4)/(A1004-A4) and Pout=(L1004-L4)/(A1004-A4)
I get Pout/Pin = 1.00000 (theoretical_integration.xls).
So I took just delta(P)/delta(time) as replacement of the 'slope' function.

Doing the same for experimental_integration.xls gives me Pout/Pin=2.14 (!!)

update1
I made a mistake by extending the slope calculation by 1 extra row in the theoretical_integration.xls file. So 1004 should be replaced by 1003

update2
Using 1003 results in a Pout/Pin = 0.998131. So, the use of 1004 was correct, which makes sense overall.