Is Condensed Matter Nuclear Science at a Critical Point?
In 2007 Edmund Storms’ book The Science of Low Energy Nuclear Reaction was published. This compilation of evidence and explanations about Cold Fusion lists 157 experiments from 1989 to 2004 where excess power in form of heat was generated. In other words: more energy came out than was put in. Figure 39 from the book is reproduced here (click to enlarge images). It shows that more than 100 experiments produced close to 0 Watt excess power. But in the upper limit two experiments produced ~100 Watt, one gave 144 Watt, and one 183 Watt.
Let’s test the hypothesis that excess power measurements are due to measurement error. The maximum measurement error in all 157 experiments was ±2 Watt. Using it as the overall error is gravely unfair to most experiments because most calorimeters used in these studies are accurate to less than 0.1 Watt. But we’ll do it anyway to develop our argument. 95% of all measurements should then be below 2 Watt. This conveniently sets the standard deviation (SD) to 1 Watt and power measurements can be interpreted as such.
In standard normal distributions almost all values lie within 3 SD. Yet, in physics SDs greater than, or equal to, 6 are often required to reduce the chance that a measurement is wrong to 1 in a billion. The average power produced in all 157 experiments is 12.7 Watt. The probability for 12.7 SDs is so increadibly small that the hypothesis can be rejected with astronomical certainty. (If someone has calculated the probability for the 183 Watt measurement, please let me know the result.)
Whenever, as in this case, distributions are extremely skewed it makes sense to test for a power-law distribution because they capture extreme events. Using Storms’ data, the left histogram shows 125 experiments with a power output equal to, or larger than, 0.5 Watt on double logarithmic axes. The frequency distribution is characterized by a power-law with a negative exponent of 1.15. Such a power-law is close to representing 1/f noise. Using precision measurements Kozima et al. have shown that power production in an individual excess heat experiment represents (a kind of) 1/f noise. That means that heat production occurs in bursts, most of which are small, but a few are large. This finding is now confirmed by Storms’ data on an aggregate scale. Most experiments generate little excess power, but a few generate a lot.
If true power-law signatures are found in complex systems in nature and society this is a true finding. Power-laws indicate scale invariance, the feature of a system to have the same property at different scales or resolutions. For example, there is no typical size of earthquakes or stock market quakes because sizes follow power-laws. In our case a power-law distribution of excess power outputs means that in 15 years no typical excess power output had been generated.
In non-equilibrium thermodynamics power-laws indicate that a system is at a critical point, undergoing a phase transition between order and chaos. The classical example is from statistical mechanics: at 768°C an iron permanent magnet is at its critical point between between order (ferromagnetism) and chaos (paramagnetism). I’m picking two theories where concepts of criticality are applied to natural and socio-economic systems. Bak theorizes that complex systems self-organize to be at critical transition points as an explanation of 1/f noise. Kauffman writes that order evolves at the “edge of chaos,” marked by power laws. Bettencourt et al. have shown that scientific fields as they evolve from discovery and invention to “normal science” undergo a universal phase transition from a small unconnected bunch of scientists to a large interconnected scientific community.
Let’s consider the 157 excess power measurements as a collective result of Condensed Matter Nuclear Science, the field formerly known as Cold Fusion, and let’s try to think of it in terms of a single socio-technical system. Is it fair to say that the distribution follows a power-law? If so, can one speak of a phase transition? A transition between what? What is chaos, what is order?