One topic that has always completely fascinated me is that of perpetual motion. Just the very idea of a machine or system running for indefinite time without an energy source is a completely crazy concept.
But can they really exist? Ultimately, no they cannot. A perpetual motion machine would disobey two of the most important laws governing our universe - the first two laws of thermodynamics.
1. Energy cannot be created or destroyed.
2. The entropy of a system cannot decrease.
Some of the first designs of perpetual motion machines were done by the Indian mathematician and astronomer, Bhaskara, II who invented the Bhaskara Wheel in 1150. The wheel consisted of curved or tilted spokes, each partially filled with mercury. Once in motion, the mercury would flow from one side of the spoke to another, thus forcing the wheel to continue motion, in constant dynamic equilibrium.
According to Newton's first law, motion itself is ultimately perpetual unless an outside or external force acts on the body in motion. When you really think about the type of environment that a perpetual motion machine would need to exist, Space seems much more viable on Earth with factors like air resistance and in sense gravity being significantly reduced. However, of course, energy created by the system would still not be able to be reverted 100% back into itself with sunlight and space dust and the gravitational pull from other planets taking affect. Energy will always dissipate in some form.
So in principal, I would say that perhaps things can in sense move forever - cosmologically some galaxies and planets have been moving forever. However, in terms of being able to extract energy or do work without reducing the energy available for more work, then no perpetual motion cannot exist.
One theory I often consider introduces the idea of harnessing black holes to implement a perpetual motion machine. When a black hole is formed from a compacting mass the last particle on the surface of the mass that reaches and crosses the Schwarzschild radius (Collapse of electrically neutral and non rotating body), R, violates the Schwarzschild metric - and so in turn every particle hereafter also proceeds with this violation. Each particle that then reaches a location r < R produces gravitational energy with it that is greater that the total energy equivalence. This very fact in itself can only happen in a perpetual motion machine. Finally, if the particle is allowed to approach and then eventually reach r = 0, an ultimate perpetual motion will be able to be created. Here, an unlimited and infinite amount of gravitation energy can be produced through the finite energy equivalence of the particle.
Who knows, maybe we just need a much better understanding of the celestial bodies in our cosmos? Maybe when us humans reach a type 2 or type 3 civilisation and our ability to capture the energy of our entire solar system or galaxy becomes far more enhanced we will then be able to understand how to literally create energy out of nothing and override all laws of thermodynamics.