On the Impossibility of World Rule through Thermodynamic Loopholes

This “e”-“paper” aims to deal with the controversial thesis purported by several leading figures and institutions in the international physics community (namely Mr Pigeon, Mr so-called “Pearson” and the “Pearson” hole of Mr “Pigeon”); namely that “…if we could get something for nothing then we could rule the world!”. Clearly this is nonsense. Or is it? Yes, it is.

First, for those symposiists whose memory needs refreshing, either due to having been asleep through A-level physics or through mistakenly not having taken it (a course of action which seems to have borne dire consequences such as doctorates from prestigious universities and well-paid jobs, but not necessarily both), here’s a reminder of how one assumes this process is supposed to work:

If we can put an amount of energy into an otherwise closed system and get out more energy than we put in, we will have made a net gain. We can then, presumably, repeat this process iteratively and amass an amount of energy which, over time, will tend to be infinite. Then we put this energy in a gun and shoot everyone! And we rule the world! Ahahahaha!

Actually I have implied this last stage of the process. A more credible endgame to this grand narrative would have the infinite amount of energy used to power some sort of machinery; say, for example, a facility dedicated to the automatic gathering of resources for, and construction of, death-robots. One might object that the construction of such a facility would be impractical; no matter, for our infinite amount of energy can first be used to construct a death-robot construction facility construction facility, which, as long as it is smaller than the death-robot construction facility, is a process which can be backwardsly iterated to give a death-robot construction facility construction facility construction facility, et cetera.

One might question the efficacy of such a course of action. However, it can easily be shown that, if the ratio of sizes of a death-robot (construction facility)^n to a death-robot (construction facility)^n+1 is consistently a positive real number smaller than one, then as n tends to infinite the size of the smallest construction facility tends to zero. Thus we can begin from an arbitrarily small construction facility, say, the size of a kidney bean, and proceed to a fully operational death-robot construction facility using only our infinite supply of energy. The design of this initial facility I leave as an exercise for the reader.

One may feel that this schema is a little baroque. There are surely more efficient ways to use your infinite supply of energy to conquer the world, and nitpickers may sneer at my under-analysis of the logistics of the above, let alone how it might be implemented within a single human lifetime. I merely include the above to give an example of the sort of cockamamie plan that crackpots such as Pigeon assume in their initial hypothesis. But, as several dissenting voices have pointed out (Baddiel, Skinner, 2001-), it’ll never work. And here’s why:

Reason 1: Assumptions as to Energy-Gathering Iteration

Pigeon and his ilk have assumed a constant energy gain from their quasi-mythical repeated process, but what if this is not the case? Indeed, given wear on the moving parts of such a device, it is more than likely that its efficiency will decrease with time. If, for example, the energy gathered were to decrease in accordance with a harmonic sequence then the sum would, although still tending to the infinite, surely reach the point of diminishing return rapidly. If one gathered an initial energy, E, and on the 200th iteration only gathered one two-hundredth of this initial yield, surely this could not be a reliable source of energy for the construction of construction facilities? The only way round this would be to use the energy for the construction of further energy-gathering devices, but even this seems far-fetched with a declining joule-per-iteration profit.

Worse still, what if the yield decreases exponentially? If the ratio between energy yield n and energy yield n+1 were constant, real and smaller than 1, the sum would tend towards a finite amount and be of no use at all! Pigeon has clearly made the assumption that in receiving “something for nothing” an infinite number of times, one will accrue an infinite amount of energy, with which one can then, in his words, “rule the world”. And he is wrong! Ahahaha, I win! But I shall continue.

Reason 2: Timeframe for Gathering of Energy

Let us assume that we have our energy-gathering machine; perhaps something of a misnomer, for if our machine is gathering energy it can be assumed that there will soon be no more energy in its locale for the gathering. No, let us call it an energy “creation” machine, which has somehow found a repeatable loophole in the laws of thermodynamics and is consistently capable of repeating a process which nets an energy profit of, say, 50 joules (as an arbitrary figure). Let us consider a useful amount of energy for ruling the world; a 1 kiloton bomb would be nice to begin with. This contains approximately 4e12 joules of energy. Thus, even if our process took a mere second, it would take us 2.5 years to accrue enough energy for this purpose. And, as anyone can tell you, one 1kT bomb does not a world-conqueror make! Of course, a process on an industrial scale could reap more than 50j/s, but experimental physics is a cruel mistress and we should not expect too much from her.

Reason 3: Storage and Re-Use of Energy

When dealing with large (or even quasi-infinite) amounts of energy, one assumes that they must be stored somewhere from time to time. How to achieve this? Clearly any inefficiency will result in a quasi-infinite amount of wasted energy, which will end up as useless heat. And nobody wants that in their back yard. Batteries are right out, as is compressed air, Archimedian screw-propelled tide-relocators, inverse hydro-electric reservoir-fillers or any of the other familiar energy storage solutions we have come to know and love.

Even a lossless form of energy storage such as a vortex of super-fluid such as helium near to absolute zero (note: I’m not making this up! Well, I am a bit) would lose energy as it were input or accessed. So how you like that, Pigeon?

I could go on but I find I am watching television. Perhaps I shall write to Science Shack.