# Appendix to “The case against cold fusion experiments”: Extra bonus excess-heat-related systematic errors

## 1. Mismeasuring the input electrical power: “AC Burst Noise”

In the main article I talked about overestimating the heat actually created in the cell (CCS), or underestimating the amount of heat that can be explained by normal chemistry (UICC). An entirely different method of spuriously measuring excess heat is to underestimate the input power. I’m not sure exactly where this idea comes from originally, but it was mentioned by Richard Garwin when he played the token critic in the gushingly-pro-cold-fusion 2009 60 minutes TV segment.

A nice analysis of this topic is this webpage written by electrical engineer Barry Kort. I’ll summarize it briefly.

The input power at time t is the product of current through and voltage across the current driver, I(t)×V(t). This gives:

time-average power = DC power + AC power
DC power = (time-average current) × (time-average voltage)
AC power = Covariance of current and voltage

The question is whether cold fusion researchers are measuring AC power correctly.

If you have an ideal constant current source, then AC power is exactly zero. That was easy! …But unfortunately, ideal current sources do not exist!

The primary concern is high-speed response. The electrical load has fast dynamics because of bubbles. They gradually grow on the electrode, and then detach, suddenly changing the load impedance. Those fast dynamics, interacting with a real-world (not ideal) current driver, can create current fluctuations.

Michael McKubre, to his credit, at least acknowledges that mis-measuring AC power is a potential issue. But he seems to misunderstand it. He talks here about sampling I & V well above the Nyquist frequency of the intended current waveform. This, however, bears no relation to the Nyquist frequency of the load, which could be orders of magnitude higher.

Why does the AC power term increase, rather than decrease, the total power going to the cell? I actually don’t think this is literally always true. But I think it is almost always true for electrical loads that we would expect to see in practice. Why? There are a couple arguments at this link, to which I’ll add my own. (But it is really best to explore this with a pen and paper!) Picture your basic op-amp current driver as an adjustable voltage source with current feedback, and then think about the consequence of the voltage source having a finite slew rate. The way I see it, the key is that when load resistance is higher than average, it’s likelier to fluctuate downward than upward (reversion to the mean), and vice-versa. Thus when V is above its average value, fast resistance fluctuations will tend to bring current temporarily above its set-point, and conversely when V is below its average value, load fluctuations will tend to bring current temporarily below its set-point. Thus the covariance of current through and voltage across the current driver is (almost) guaranteed to be positive.

Is this a large enough effect to account for real cold fusion experimental results? I can’t find a great analysis, like with SPICE models of current drivers and load properties informed by the electrochemistry literature. So I’m uncertain. But this link does do some back-of-the-envelope calculations suggesting that yes it might be a big enough effect to matter.

Is this effect consistent with all the weird experimental signatures of excess heat? Sure! We’re now talking about detailed dynamics of exactly how bubbles detach from the surface at the nanosecond-to-microsecond timescale. Thus all the commentary in Section 3.2 about how deuterium loading and conditioning gradually alters the surface morphology and composition (and hence bubble nucleation, adhesion, and detaching dynamics) could also apply here.

Is this “The Explanation” for cold fusion excess heat? Absolutely 100% definitely not. One obvious example is that AC burst noise is not applicable to the genres of cold fusion excess heat experiments that have no input electrical power (gas loading, “heat after death”, etc.), whereas the CCS / UICC discussion in the main article is applicable to those. More generally, the CCS / UICC proposal has been validated in detail by Kirk Shanahan studying real cold fusion experimental data, and therefore is known to be a real problem, whereas AC burst noise is today merely a “possible additional problem that nobody has checked yet”.

## 2. Heat pumping

OK, let’s say we measured the electrical power going into the cell, and we measured the amount of heat exiting the cell, and we accounted for every possible error on each of those terms. Now we’re done, right? No, of course we’re not done! Why should it be so simple? There’s yet a third term in the energy balance equation: heat pumping.

Refrigerators and air conditioners are examples of heat pumps. They move heat from one place (which gets colder) to a different place (which gets hotter). You can’t just look at input power for this; for example, it’s perfectly possible for 1 watt of electrical power to make the cold side colder by 10 watts, and the hot side hotter by 11 watts.

Thanks to the Peltier effect, any electrical circuit is automatically a heat pump, as long as the current is flowing through more than one type of material or medium (which is always the case in an electrolysis setup).