The Impossibility of Perpetual Motion Machines (Script) (Patreon)

Bad ideas come and go in physics. But there’s one bit of nonsense that is perhaps more persistent than all others: the perpetual motion machine. 

No working perpetual motion machine has ever been experiment verified. All break the laws of thermodynamics. In fact, we classify based on WHICH law of thermodynamics they break. We have perpetual motion machines of the first kind - they violate energy conservation - they  pump more energy out than they need to keep running. This includes most of the historical devices. Then there are machines of the second kind - they’re a bit more subtle in their wrongness because break the second law of thermodynamics - extracting energy by reversing entropy. Many modern “free-energy” devices fall into this category. Now the best modern designs are by you - answers to our recent challenge question, which we’ll get to at the end. But first let’s take a look at examples of what other people came up with - this’ll be a fun little journey through some pretty terrible science.

Designing a perpetual motion machine has a very long history and became quite the craze from the middle ages through the renaissance. The first well-documented design for a perpetual motion machine was from the 12th century. Bhāskara's wheel, named after the Indian mathematician, was embedded with tubes of mercury that would flow from back and forth as the wheel turned. Other types of over-balance wheels followed through to the  Renaissance and worked on the same principle. There were also designs that employed the magical-seeming lodestones – magnets. For example, this ramp in which a ball is pulled to the top by a magnet before falling through a hole and rolling to the bottom again. Then there are the self-pumping waterwheels or self-blowing windmills. 

None of these machines actually worked. In every case you can find a subtle bit of physics that the designers overlooked. The overbalance wheel pushes masses ou twards on one side, but that same at the same time increases the separation between those masses, so that moment of inertia is unchanged. A magnet strong enough to pull a ball up an incline would also prevent it from rolling back down again. Losses due to friction mean that water or wind driving a mill could never produce enough energy to fully complete the cycle. Close, but no perpetual lighting cigar.  

Now to be fair to the people working during the middle ages and Renaissance, the law of conservation of energy hadn’t been discovered yet. Thus the proliferation of first-type machines that could generate more energy than they used.

But absolute proof of their non-viability didn’t end the craze. Inventors just graduated to breaking the second law of thermodynamics instead. To review: the 2nd law states that entropy can never decrease over time – in other words, energy will tend to spread itself out as evenly as possible – to a state of maximum entropy. All machines work by riding this flow of energy as it redistributes itself. Machines of the second kind claim to be able to tap reservoirs of energy that are already evenly spread – effectively reversing the growth of entropy. Before we get to modern perpetual motion machines, let’s take a look at some actually interesting ideas that illustrate the limit of the second law.

First up, the Brownian Ratchet. It goes like this: a paddle wheel immersed in a gas is connected to a cog with a latch that only lets it turn in one direction. Individual gas particles are moving around with random – or Brownian motion. When one hits the wheel in one direction the cog turns, but in the other direction the rotation is blocked. Sounds … plausible. And it actually works. But ONLY if the chamber containing the cog is at a lower temperature. If it’s at the same temperature then the cog is as likely to be pushed back when the latch raises. Richard Feynman himself demonstrated this mathematically. This is  actually a specific example of a Maxwell’s demon device, an entropy-reversing thought  experiment that we’ve discussed before. 

With no energy or temperature gradient, no energy can be extracted. In fact there’s an absolute limit to the amount of energy that can be extracted based on a difference in temperature. That limit is defined by the most important – perhaps the only important perpetual motion system ever conceived: the Carnot cycle. In the early 19th century, Sadi Carnot described the most efficient possible engine – It’s a sequence of expansion and contraction of gas in a piston chamber that will provide the maximum possible energy as heat flows between reservoirs of different temperature. Critically, the Carnot cycle is reversible. Drive the piston in reverse with exactly the same amount of energy, and it’ll transfer energy from cold to hot. In principle a Carnot engine could extract energy from a temperature gradient and then pump it back in again, making it a candidate perpetual motion machine. But even in this most ideal case the ratio of energy in to energy out is exactly unity. No extra energy is extracted.

The Carnot cycle is, in principle, a perpetual motion process. But doesn’t break any laws of thermodynamics, so it’s not the first or second kind. In fact it’s the third kind. These are perpetual motion machines that do not attempt to generate energy – they just keep themselves running forever. Sounds OK, right? After all, Newton tells us, an object in motion tends to remain in motion unless acted on by an outside force . So remove all outside forces – remove all friction, all energy losses of any kind, and surely any machine can tick on forever.  Indeed there are ideal systems that, from pure classical principles should run forever. Like a perfect Carnot engine, or a frictionless wheel – with or without magnets and mercury tubes – or a planet orbiting a star.

Just eliminate ANY leakage of energy. But that’s not just an engineering challenge, it’s fundamentally impossible. In fact, quantum mechanics forbids it. Due to the intrinsic quantum randomness of all particles, as expressed by the Heisenberg uncertainty principle, everything moves. Internal parts always vibrate, guaranteeing some friction and internal heat. Even if that heat is recaptured, the outer walls of even the most carefully isolated system must radiate, slowly leaking energy. And then of course there’s the gravitational radiation that will slowly sap the “perpetual motion” of celestial systems. The best-case scenario for a perpetual motion machine of the third kind is a very, very slow wind-down to  stillness.

So let’s take a quick look at modern perpetual motion machines. Most look a lot like their ancient predecessors – often lots of wheels with lots of magnets, somehow powering their own motion and producing extra energy besides. These are often referred to as ov er-unity devices – the ratio of energy out to energy in is greater than one. That name was actually coined by the US patent office, which along with the UK, patent office and the French Academy of Science refuses to even review devices claiming over-unity energy production. Understandably - it eliminates 50% of their crank submissions.

Now the purveyors of over-unity devices typically do NOT claim to have created perpetual motion devices of the first kind. They have various explanations for how they don’t violate conservation of energy. However most end up shifting their device to the second kind of perpetual motion: they violate the 2nd law of thermodynamics by extracting energy where there is no energy gradient. One popular source of free energy is the zero-point energy of the quantum vacuum, and it’s the most fun to debunk.

I’m going to have to refer you to our entire playlist on the quantum vacuum for the physics, but the important point is that any energy of the vacuum is exactly the same everywhere. It has no energy gradient, so isn’t accessible as an energy source. Now it may be possible to create an energy gradient, for example with the Casimir effect in which plates are pulled together by lowering the zero-point energy between them. But doing so repeatedly in an engine cycle takes at least as much energy as it produces. At best you have a perpetual motion device of the third kind.

Most modern perpetual motion builders aren’t so technical. In fact the worst of them wouldn’t have physics or engineering chops to build a decent over-balance wheel. They rely more on pseudo-physics-speak - zero-point, mag-grav, plasma, torus vibrations sound fancy, but are typically less good at generating free energy than they are at directing you to their donate button or selling you a telluric field wellness crystal.

OK, enough with the nonsense . Let’s get to the challenge question, in which I asked YOU to come up with a perpetual motion machine based on the funky notion of negative mass. According to some interpretations, negative mass should be attracted to positive mass, but positive mass should be repelled by negative mass. The result is that a positive and negative mass should accelerate indefinitely, potentially powering an infinite energy device. But how to build one? Let’s see what you came up with.

Many of you hit on the most obvious and efficient approach: attaching the apples to a dynamo so they chase each other in circles, driving the generator. Here are some of the better designs. Nice adaption of the Bhāskara's wheel from Creepy Magician. Alex Taylor has an especially cool dynamo device in which the masses are contained in a magnetic field. He also does the full relativistic calculation for power – nice one Alex.

We have a rare non-dynamo device from Adrian Romeo, who uses cogs with negative and positive mass teeth. This post-it will be framed in the Smithsonian after the Romeo-engine solves humanity’s energy crisis. And the prize for most outlandish goes to Epsilon Centauri, whose machine requires an entire bubble universe with closed, pac-man borders, trapping the ever-accelerating apples.

If you saw your name and device just now, that means you’re a winner! You do get your pick from the Space Time store. Shoot us an email at pbspacetime@gmail.com and we’ll get your goodies to you. Feel free to check the store even if you didn’t win, or think you should’ve won, or didn’t get around to submitting but are pretty sure you would’ve won if you did. We all deserve merch. Link in the description. I’m also going to post some of the best solutions to this challenge on Instagram – check ‘em out at matt_of_earth.

And I leave you with wise words from someone who designed quite a few perpetual motion machines himself. Leonardo da Vinci. “Oh ye seekers after perpetual motion, how many vain chimeras have you pursued? Go and take your place with the alchemists. “ da Vinci was ahead of his time in some ways – he knew perpetual motion was bunk even before the laws of thermodynamics came along. But vain chimeras? Had only da Vinci known that his own perpetual motion machines could’ve score him such cool swag from Space Time.