Assuming perpetual motion was possible, what influence would that have on society? Would the ready availability of energy help the current third-world? Would that even exist given how history would be different?
I'm going to modify the premise slightly, because perpetual motion is a real turn-off to a scientist.
If a new, plentiful energy source was found, what effect would it have on the world?
Firstly, a candidate for that plentiful energy source is Fusion. Consider weapons; when we had 'physical' energy storage like gravitational potential energy and elastic potential energy, the best we could do to throw stuff at people was archery, catapults and trebuchet. Guns are based on chemical potential energy instead, and provide a much greater energy density. Fission atomic weapons are many orders of magnitude more energetic, and Fusion weapons are orders of magnitude larger again. So working Fusion reactors could provide more energy than we have ever imagined possible.
Much of human history has been about resource constraints; having enough food, water and shelter without being eaten is the plight of all things, and our capacity to leverage the energy stored around us has led to our dominance, but we still face constraints:
Water: Although there is water on much of the surface of the Earth, we cannot use seawater without expensive desalination plants. The cost is dominated by the power required by the process, so nearly-free energy could permit us to liberate vast quantities of drinking water from seawater across the 3rd world.
Food: At present, our food effectively captured radiant energy from the existing fusion reactor in the Sun. By using intensive hydroponic techniques, we could have vertical farms vastly increasing the food grown per unit area. It is perhaps the only way to meet the food needs of an exponentially growing global population.
The deserts: There is a video somewhere of a 3d-printer making things out of the desert sand using only the sunlight and a massive fresnel lens. With cheap energy, we could construct vast sheltering structures in the desert, and carve out a habitat in which people could live. Beginning at the edges, they could populate some of the most empty regions of the Earth's surface.
Space: The current limitation on all of us getting our trip to space is the cost of accelerating 100kg of human to 7 km/s, and a lot of that is just the cost of the fuel. With electricity we can crack molecules apart and create many of the fuels we would use; water and energy will yield you cryogenically stored liquid hydrogen and oxygen, as used by Shuttle. By decimating the cost of such fuels, travel to space becomes far cheaper, and by extension the possibilities of constructing habitats in space open up.
Oil: Who needs gallons of liquid that have to be shipped about the globe, when you have free or nearly-free electricity? The political landscape of oil-rich nations would be utterly transformed.
So we have fed and watered the world, whose population is perhaps 30 billion people, using our free energy. There is a problem; all that energy goes somewhere. By using electrical energy to power e.g. a refrigerator, all the energy is eventually turned to heat. So all this plentiful energy will go to warming up the planet. Currently, our problem is that the sun is warming the planet and we are destroying the Earth's capacity to keep itself cool. We would eventually reach a point where we had obliterated the Earth's mechanisms to cope. All would not be lost, but we would have to construct our own mechanisms for keeping the Earth cool; raising its albedo by seeding more clouds, constructing vast parasols to shield the Earth as they orbit (creating some sort of light-shade cycle for people on the ground), living ever more shielded and indoor lives as our interventions increasingly mess up the ozone layer. We turn our planet into a space-ship; reliant on the systems we have created to maintain the conditions for life.
The rich would have left by this point. Having fought against the arrival of Fusion as it challenged every status quo and thus their positions atop the piles, some would be kings of the new world, others would have left for the Moon, Mars, Europa and eventually habitats.
The conditions for life down here are thoroughly dependent on the temperature, which is itself dependent on energy absorbed from the sun and from our own activities. We may manage to fix everything for the betterment of mankind, or we may just create new inequalities in which the rich are cool, indoor creatures and the poor are exposed to some unintended consequence.
If you think I'm overstating it by suggesting free energy would change everything, then find something you think wouldn't change and see whether it depends on some limitation of energy supply somewhere along the line. I think the arrival of Fusion is inevitable, the consequences are unimaginable, and the only questions are when it will happen, and what we will do with it.
If perpetual motion was possible, physics would break. The laws which would be broken would have terrible implications elsewhere. Such violations of these laws could open the door for other, unforeseeable things; like a creature which never needs to eat, photosynthesize, or look for chemicals. A world in which perpetual motion is possible would bear little resemblance to our own. (Such a universe may have never gotten around to making worlds! If the nebula which became our solar system had instances of particles with infinite energy, it may never have settled down to make the solar system.)
Assuming we had a wheel that went in circles no matter how much load we put into it, but it happened because the universe decided that it was time for it to be possible, you could expect everyone to exploit it. What would people do with infinite energy? Everything, I'm sure.
An infinite energy source would make things like railguns much more feasible. We could get things like Alcubierre Drives to easily work. Simply put, many, many more things would be much more possible than they are now. There are some things which may stay the same with our infinitely-turning wheel in existence.
Since the perpetual motion machine makes only mechanical energy, we'd still have to worry about things that require other forms of energy, like feeding ourselves. Power companies would worry more about transferring energy from our wheel to electricity, and then getting that everywhere.
Probably nothing would change. There are many energy sources like solar batteries or windmills that are not "perpetual motion" physically but could be viewed as such from the social point of view (Sun and winds are free to use). There are many other limiting factors:
- The amount of energy produced, as compared with the costs of making and operating the device. As any machine, it would probably run for a limited time only.
- The amount of power produced, as compared with size and weight of the device. Can it power a plane? A railway locomotive? You cannot use "free" windmill for that.
- Plain energy still cannot be easily converted into bread, mobile phones or shoes humans need. Even with free energy, the manufacturing costs will not drop to zero.
As a result, perpetual motion would be a useful technology comparable to electricity maybe. Same as electricity, it would have huge impact on society but is unlikely to solve the most of problems. Same effects on society are probably possible by discovering new advanced technologies that conform the physical laws.
Assuming that perpetual motion equals infinite free energy, The market for all kinds of fuels (fossil fuel, carbon fuel, wood as fuel, atomic fuel, etc.) would basically cease to exist, that is, if all these giant companies were somehow unable to hide and/or silence all knowledge about perpetual motion. Everybody could have their own perpetual motion machine generating "clean" energy, however, just because you are not polluting by way of chemicals and the byproducts of burning fuel, you can't completely overlook thermal pollution, as you will still be generating extra heat, because energy conversions are not 100% efficient and what doesn't get used up doing useful work turns into heat.
It is said that with great power comes great responsibility, well in this case, humankind would basically have infinite power at their fingertips, even the common man might accumulate extreme amounts of energy if he found a way to store it over time. Imagine if all that energy were somehow to be released at once... A person geared towards destruction could easily wreak havoc in the world. Maybe infinite energy is just too dangerous...