|Any operating machine must obey
the two principal laws
of thermodynamics. The first law states that energy can be
converted from one form to another, but that it can't be created or
destroyed. The second law states that without any inputs, energy
naturally dissipates from a system. This is often restated in terms of
entropy, namely the degree of disorder in the system.
Because there is only a finite amount of energy in the universe, no matter how cleverly and efficiently a machine is built, it will always by subjected to these two cosmological Draconian laws. By the first law, energy inputs will be converted into other types of energy including heat; and by the second law, that heat is lost in the form of escaped energy. Eventually, the machine will cease to operate, since even if it were built to utilize all the energy in the universe, the loss of energy could not be recycled as a fuel input. Hence, no perpetual machine could be built.
Or could it? Perhaps if a machine was constructed upon a logical quagmire that offered a perpetual non-solution, then the machine would operate eternally.
Paradoxical logic such as Zeno's Paradox or Russell's Paradox present us with propositions that are both true and false, and hence offer a unique paradox. One of the most famous examples of paradoxical logic is the statement that "This statement is false". If that statement is in fact true, then we must say "This statement is true". But if that is the case, then the original statement "This statement is false" is really false. Thus, the original statement is both true and false; hence the paradox. If we were to continue with this line of reasoning, if "This statement is false" is false, then the statement should really be "This statement is true"; hence it reverts back to being true, and so forth.
What is happening here is that the original statement is first true, but then by analyzing the proposition in terms of that truth, a contradiction is forged, and hence the statement becomes false. The pointer to the content of the proposition becomes entangled with the content itself. Let us suppose that "Q" is the pointer to proposition P. Then: Q ==> P. Q will either be true or false. Here's what's happening with paradoxical statements:
Q first points to proposition P1: "This statement is false". If Q is true, then Q must also point to a proposition P2: "This statement is true". It's now pointing to two contradictory statements, P1 and P2.
If this were a dramatic rendition of the logical quandry, we would hear P1 tell Q that "you're pointing to the wrong statement". It's in effect ordering the pointer Q to point to something else: P2. But if the veracity of P2 is accepted, then P2 shouts back to Q to "reconnect with P1". And so forth.
In effect there is a perpetual motion created between P1 and P2, with pointer Q being the central pivot; P1 and P2 oscillate back and forth. This perpetual motion channels a logical energy between the pointer and the two contradictory propositions.
Now, if there was some way to build a machine based upon this paradoxical logic, it would become a perpetual motion machine. The idea is that the energy input would be represented by P1, and the energy loss by P2. The machine would in effect fake out the energy loss to "think" it was an energy input. Hence, P2 would become P1 as illustrated above. Then, after the "re-input" of energy in the form of P1, it would naturally go through it's dissipative state to become P2, which would become P1 after again being "faked out", and so forth. The machine would be designed in such a way to convert the energy input into a "faking out" mechanism which "converts" the energy loss into a re-input.
Note that P1 and P2 can't simply represent two different energy states such as measured by the luminescence of a light bulb. First, these wouldn't be paradoxical states, but at best "opposite" ones, one with the light on and one with it off. Second, the light bulb would flicker between P1 and P2, giving the illusion of temporary perpetual motion, but it would in fact be subjected to the Second Law of Thermodynamics and become a dissipative system where the bulb would eventually burn out. The only way a system could be a perpetual motion machine is for P1 to be an input, and P2 would be an output redirected back as an input into the system. The system would need sensors designed to be sensitive to a P2-input state.
If the system was built with a correct implementation of the logical paradox, where both ends of the paradox are represented by system inputs and outputs respectively, which alternatively became outputs and inputs respectively during the succeeding process cycle, and repetitively alternated ad nauseum, then it would have form a logical gateway to bypass the Laws of Thermodynamics. Think of this shortcut as a "wormhole" into the world of non-entropy! The perpetual time-cycle would create it's own time dilation to "slow down the clock" such that the observed rate of energy loss would dramatically decrease, and the rapid motion would create an energy that curved the surrounding space to close the "heat loss" valve altogether. And while this slow down and closure was occurring, the system would in effect be traveling through this wormhole!