In Our Time - Perpetual Motion

Episode Date: September 24, 2015

Melvyn Bragg and guests discuss the rise of the idea of perpetual motion and its decline, in the 19th Century, with the Laws of Thermodynamics. For hundreds of years, some of the greatest names in science thought there might be machines that could power themselves endlessly. Leonardo Da Vinci tested the idea of a constantly-spinning wheel and Robert Boyle tried to recirculate water from a draining flask. Gottfried Leibniz supported a friend, Orffyreus, who claimed he had built an ever-rotating wheel. An increasing number of scientists voiced their doubts about perpetual motion, from the time of Galileo, but none could prove it was impossible. For scientists, the designs were a way of exploring the laws of nature. Others claimed their inventions actually worked, and promised a limitless supply of energy. It was not until the 19th Century that the picture became clearer, with the experiments of James Joule and Robert Mayer on the links between heat and work, and the establishment of the First and Second Laws of Thermodynamics.With Ruth Gregory Professor of Mathematics and Physics at Durham UniversityFrank Close Professor Emeritus of Physics at the University of OxfordandSteven Bramwell Professor of Physics and former Professor of Chemistry at University College LondonProducer: Simon Tillotson.

Thank you for downloading this episode of In Our Time. For more details about In Our Time, and for our terms of use, please go to BBC.co.com. UK slash Radio 4. I hope you enjoy the program. Hello. Perpetual motion has intrigued some of the greatest names in science as they tried to invent machines that could power themselves endlessly. Leonardo da Vincius sketched a wheel to keep on turning. Robert Boyle worked on an apparently never-ending fountain.

They were designed to windmills, pumping bellows to drive their own sails, and water wheels recirculating their own mill streams. To scientists, the designs were a way of exploring the laws of nature. There were others, though, who claimed their inventions actually worked, promising and for free, a limitless supply of energy, supposedly another scientific miracle in the ages of discovery. Many doubted, among them Galileo, but none could prove perpetual motion was impossible. That had to wait for the 19th century and two of the most robust laws in science, the first and second laws of thermodynamics.

With me to discuss perpetual motion are Ruth Gregory, Professor of Mathematics and Physics at Durham University, Frank Close, Professor Emeritus of Physics at the University of Oxford, and Stephen Bramwell, Professor of Physics and Former Professor of Chemistry at University College London. Frank Close, what does scientists mean by perpetual motion? Well, the idea that you could have a machine that once it was operating could continue to run forever without needing any power to keep it going. That's the idea of perpetual motion. And if it was possible, it would be fantastic in all meanings of the word.

And to give an example of the problem, what's happening right now, I mean, people are listening to at this moment me speaking, and whatever the device they're using, the sound of my voice is propagating through the air to their ears, the sound energy coming out of their radio or their laptop. And where's that energy coming? from? Well, it's coming ultimately from the battery power in their radio or the electrical

power supply from the socket in the wall or maybe they've got a wind-up radio that they stored energy with. However you play it, energy that is being supplied to the radio or has been stored within the radio is being turned into sound energy. And that's an example of energy changing from one form to another. But you can't create energy out of nothing. That's the nature of the universe. So imagine that we didn't need the power in the radio to keep it working. You could throw the batteries away, you could unplug it from the power supply, and yet you could still hear me talking. That device would be creating sound energy out of nothing, and that would be a perpetual motion machine. It violates the first law of thermodynamics or the conservation of energy,

if you like. There were a great number of very clever people in their time, just as clever as anybody around, who with the knowledge they had available in the 12th century and so on and stuff, really tried and believed in this. Did they take their examples from, say, the moon going around the earth all the time? If the moon could do it, we could do it, sort of thing. Well, certainly, you know, at first sight, you might think, oh, the planets going around the sun or the moon going around the earth is an example of perpetual motion,

but perpetual means forever. There's no reason for people in the 12th century not to think it was forever. No, no, no, certainly not. I mean, in the 12th century, they didn't have the... insights into the nature of the laws of motion that only came much later. And the ideas of Aristotle, which probably enthused them into believing that perpetual motion might be possible, we now know those ideas were pretty much irrelevant to reality. So what they're talking about is not, it never does, does it really?

You three will know more than anybody to dismiss what people did centuries ago. Well, they hadn't made the discovery that you have now. So they were working on the knowledge available. And in that, they did amazing things. So this idea was going on. But scientists talked about motion of the first and the second kind. What do they mean by that? Well, the example I gave a moment of two ago,

which I said violates the conservation of energy. We now know that energy has many forms. Heat is an example of energy. And so the interplay of heat and motion, thermodynamics, that's the first law of thermodynamics. And that machine would be a perpetual motion machine of the first kind. It violates the first law. So what's the second law of thermodynamics?

Well, heat can be turned into work, but not with 100% efficiency. That, you know, you can boil some water and turn it into steam and drive a piston and drive a steam engine. But some of that heat will get lost, maybe in friction, maybe radiated out into the surroundings. And the second law of thermodynamics says, basically, you can't do it with 100% efficiency. that maybe 50% of the heat you're using will be turned into useful work and the other 50% gets lost to the environment. That's just the nature of the thing.

So a perpetual motion machine of the second kind which would violate the second law of thermodynamics would be a machine that has no losses at all, 100% efficient. Now I've got to go back and get to the laws of thermodynamics, there's a lot of hinterland to fill in. We'll start with Ruth Gregory. There are concepts that physicists use

which have a specific meaning in this discussion. One of them is work. Can you explain what you mean by that? Well, work's actually a very easy one to explain. I thought you were going to ask the difficult one, to be honest. So what we mean by work in physics is essentially the amount of energy that has to be expended or put in to change a system or to achieve a particular objective.

And that corresponds, I think, quite well to our intuitive notion of work. So the energy could be, as Frank has said, it could be mechanical, thermodynamics or electrical. But in physics, each of those corresponds to a slightly different as we would like to call formula. We like formula in physics. But I think work, you know, perhaps the easiest formula

that I think perhaps anyone can buy into for work is that we have this relation saying work is force times distance. So if you imagine pushing something, you know, it sometimes can be hard, you know, especially if the surface is quite rough. And so then you're doing work to actually move it. And so you're going to not argue with me, I hope, if I say that if you push it twice as far,

you'll feel you've done twice as much work. And that's indeed exactly what the physics formula tells us. Work is the force, the effort you have to push in, and the distance you go. What's going on when you think then? That's work. Sorry. Oh. What's going when you think?

Oh, right. Well, yes. That's probably the hardest work of all. Well, there's all sorts of different things going on there. Well, does that apply to thinking? I mean, it's things being pushed inside your head at the moment. So usually when you're thinking there's all sorts of synapses firing. There's a lot of electrical energy going on, you know, going on,

a lot of electrical energy being spent in your brain. So I suppose compared to some of the things like, you know, lifting weights, it's fairly small fry. But yes, it's still, it is still work. But it doesn't follow that formula that you express. No, no, that. So then there's a different thing. So, you know, in electricity.

Because we have, it's essentially, you're always somehow changing the energy of a state. And so it's how the energy is related to the particular constituents of the problem that you're looking at. So if you're moving something, it's the sort of friction force you have. If you're, if a, if current is running in a circuit, now you've got to think about the electromagnetic force. So inside the brain you're changing states all the time? Yes. And that's work? That is work.

Well, yes, it's work electrical energy. Well, we sort of that out. Now, a further concept that's important, the word in the second law of thermodynamics, is entropy. Indeed. Can you give us that? I shall try. Entropy is a little stickier one.

It's not, I think we have, although what I hope to convince you is we do have an intuitive notion of entropy. We often say that entropy is about how much disorder there is, in a system. And to an extent, that's true. But in physics, we define it via what we'd call a counting of states. So what does that mean? Well, it means how many different ways can you rearrange things so they look roughly the same? Now, a crowd is composed of individual people. They're different, but as far as we're concerned, it's a crowd. You could rearrange the people and it would still be a crowd. So that's the notion of entropy. What we are seeing is the crowd,

But there's lots of different ways of arranging the people in the crowd. But what does that lead to? So the second law of thermodynamics is states, technically states that in the entropy in any process, either increases or remains the same, and it only remains the same if you can undo the process. Now, why should entropy increase? Well, I think my analogy here is think of a bedroom

and think of a tidy bedroom. if you imagine the different states in a tidy bedroom, they're relatively few. Are there red socks on the right or left of the blue socks? So there's a certain number of ways a bedroom can be tidy, but there's a lot more ways a bedroom can be untidy as the sock on the bed, on the floor, on the chair, you know, somewhere. So that's why entropy is often thought of as disorder.

The untidy bedroom is more disordered, higher entropy, and it's much easier to have. So you're saying entropy is inevitable, and it stands for disorder. So energy having been conserved with the first load dynamic, it's dissipated with the second law. No, I mean, the overall energy is actually conserved. But how do we decide, you know, normally our laws of nature actually tend to be the same, whether we go forwards or backwards in a process.

But if we, with entropy, the fact that nature wants to increase the entropy of a system, that kind of tells us which way we are flowing in that. in time. We shall come back to entropy. Steve, Steve Brownwell, can you go even further back and give us the early examples of these perpetual motion machines? People were doing this thinking it was possible. We have to remember that. Very clever people

thought this was possible. They say examples in nature and they took a lot of their inspiration from nature and this was going on all the time so they could do it as well. They could invent machines which should do it. Yes, so possibly the earliest recorded example is from the great Indian mathematician Bascaro from about 1150. And he drew diagrams of a wheel,

which became known as Baskara's wheel. This wheel had fixed to it tubes of liquid mercury. And if you look at the design, it looks as if the wheel is continually going to overbalance and therefore continually turn. It's possible that Baskara was sort of influenced by his Hindu religion in thinking of cyclical things. But in any case, this wheel of Bascara

was later picked up on by Islamic scholars and then kind of came to Western Europe in the sort of Renaissance period. And a lot of people actually tried to make these things and always discovered they stopped turning. They turn for a little while and then they stopped turning and the thing reaches equilibrium. Around the same time,

new sorts of perpetual motion machine were imagined. So we have Mark Anthony Zimmerer, who was a Renaissance scholar, a student of Aristotle, a philosopher of some repute. But he designed what looks to us as rather an outrageous machine, which is a windmill that powers some bellows and then it blows itself. So it's surely a very interesting.

efficient machine, but he wrote some quite detailed designs of this on paper. And then another example is, a famous example, is a description by Robert Flood. Now, Robert Flood was a scientist and also a mystic philosopher. He was a sort of crossover figure. And he drew a picture of a, and left some design of a water wheel that doesn't only grind the corn, but it also pumps the water back uphill. And actually he didn't believe it would work, but he was recording practice at the time. And there were scores even hundreds of these.

But then we come to the cusp of the change, which is the Enlightenment. And one of the great figures in the early Enlightenment was Robert Boyle, father of chemistry 1650s working in Octa and then Royal Society and so on. He, you've mentioned water, and water plays a big part in these machines, became obsessed by it. And he had this system of perpetual buckets. Can you tell us about this? Yes.

So Boyle, of course, one of the things he believed in really was the clockwork universe, that the idea that the universe was itself some kind of self-moving machine. And so his thoughts were never too far from a self-moving phenomena, which included perpetual motion of sorts. Today you find a lot of references to what's called Boyle's Flask, which is a flask that siphons water out of itself and then siphons it back into the same flask. Now, if you try that in the laboratory, it just doesn't work

because the siphon head actually has to be lower than the level of the water. So it always fails. And it's not entirely clear whether that really came from boil, but it kind of summarises the sort of things boil discussed and thought about in terms of water and hydrostatics, as it's called, but never far from his mind was the possibility of things moving. And they thought that water was a life of its own, it had a life force. Yes, absolutely.

And so ideas of life force or living force as well became important in that period. Living force was actually developed to start off with by the Dutch physicist Christian Hoykins, and it became called vis-viva or living force. And it's, roughly speaking, today, what we would call kinetic energy or energy of motion. So at that point, they were starting to get close to the modern conception of energy, and that's where it began.

But can we just take a little more time on these earlier things, Frank, before we close in with the back to the two laws of thermodynamics. What was going on was that nobody could disprove this. It was impossible to disprove this perpetual motion, So people kept experimenting with having a go. One of them actually built a big machine. Johann Bezler is also known as Orp Fierrez, have I got that right?

Can you tell us about him? Maybe. I mean, the point, as you say, is that they designed these machines but never actually succeeded in building them. And the example that Steve gave of the wheel that goes around because the weights miraculously were heavier on one side going down than on the other.

The only example of such a device which I know of that woodwork was one that Escher drew, and if it wasn't Escher that drew it, I'll claim it for myself, which the buckets on the right-hand side have got nine on to show that they weigh nine units. And then, of course, as they come up the other side, they've turned over and now only have six on, and so the wheel will go around because of that.

What do you mean, of course, they've turned over? You've left me behind. What do you mean, of course, if they've turned over, they've emptied the stuff out? They're only got the nine on. Yeah. It stuck to the wheel, and as it comes through the bottom and up the other side,

it's now turned over. it's got six on. So there's nine pulling down on one side, and that will work. I guarantee it. However, most things won't. Bessler is an example of somebody who indeed not only attempted to make a wheel that would continue to go forever, but claimed to have done so, and demonstrated the fact. But a bit like illusionists, you know, always something held back.

And what he did, he had this wheel, which he set in motion in a room in a castle. And on day one, people were shown this wheel turning around. And then he closed the room off. And then 14 days later, the room was opened up again, and people were invited to see the wheel still turning. And I used the phrase still turning, because, of course, psychologically, they thought it had been turning all the time, but there's no proof of that fact.

And that's what I call the illusion. Now, what he actually did, I've no idea. But I could imagine that if I was looking into this, I'd want to know, is there a tank of water on the roof, for example, that the water falling from the roof is powering this wheel, and you kept the wheel turning until the water had given out, you close off the room, two weeks later, there's enough rain has accumulated in the tank up top,

and you can get the wheel going again. So he kept things from people's view, and if his wheel indeed was working at all, it was probably being driven by some secret power source. Nobody has ever demonstrated a machine, and allowed every bits of the working pieces to be inspected when they claim to have made a perpetual motion machine. What data we're talking about here?

I think this is around the 17th century time. Ruth Gregory, so they're still doing it. These are amateur scientists as well as they're still, what is motivating them, century after century, to have this idea and then to attempt to build these machines? Well, I think that probably speaks to some fundamental human psychology. I think we all feel, you know, that this attraction of getting something for nothing. I mean, that, you know, there's some sort of, we see it, you know, in other sort of behaviour with the stock market, people, you know, coming up with dodgy share propositions.

I mean, there is this notion that if you could just make it work, then you would actually get something apparently for nothing. I think also to some extent it may be because when we are learning about new systems and new aspects of physics, we often our understanding is flawed and quite often these perpetual motion machines reflect this imperfect understanding. And so perhaps we're being also driven by a desire to, understand. Maybe quite often you can, in trying to solve a problem, you may take a slightly bizarre position simply, simply because it gives you a means of attacking the part you don't understand. Perhaps. Yes, I mean, perhaps to elaborate on that, I mean, I think as well as there being

some cranky inventors involved, there were also serious scientists involved. And I think ideas about perpetual motion played quite an important role in getting people to start thinking of mechanical analogies for nature and also to start thinking of machines in an abstract way, the sort of way that is ultimately useful for physics. And you can sort of see the germs of the discovery of the laws of thermodynamics in early discussions of perpetual motion. So they're kind of grappling towards a sort of abstract view of the world.

rather than thinking about the nuts and bolts and the crankshafts and the cogs, they're thinking of machines in more general terms. Was there over this period of time, or was there any progress? Were these machines getting better? Did they learn from the previous century's machine that that didn't quite work?

So they'd... Was there a handing on of information? Well, I mean, it seems as if, you know, I guess each time, if you know something doesn't work, of course you're going to try and refine the design. I think it's probably fair to say, although perhaps Steve can correct me on this, that by the 18th century

or that people were kind of losing hope, shall we say, with the mechanical types of perpetual motion. Absolutely. And people who sort of mechanists had pretty much decided that it wasn't possible by this point. But they were looking to other phenomena, particularly heat and electricity, and thinking, well, maybe it's possible there.

But there's still no proof that it wouldn't work. We enter a brewer's son, a rich young man, who was a brilliant observational scientist son in Manchester, James Jewell in the 1840s. What did he do that mattered? That's right. So James Jule, you know, is one of the great figures of British science. He was an amateur scientist, a gentleman amateur,

as you say, born into a brewing family in Manchester. He grew up in Manchester in the 1830s, which was the sort of hub of the Industrial Revolution. This was a very exciting time in technological terms. There was a sort of euphoria around electricity and electrical engines. The first electric train ran in 1841, only a few years after Faraday's discovery of electromagnetic induction. And Jule was about 20 when he started getting really excited. by this and he started building electric motors and started asking some basic questions about heat and engines. All engines give out heat. He tried to quantify this and he did experiments

which gradually became more and more refined to try and work out the relationship between heat and what Ruth was talking about earlier work, you know, sort of the lifting of a weight. So when a weight falls, how much heat does that create heat? Now, this was a very radical program that he set himself at the time because in the early 19th century, heat was not thought of as anything to do with work. It was thought of as a substance, a substance called caloric. And the idea of converting heat into work would have been absurd to many people as converting, say, hydrogen into gravity or something like that.

They seem to be different things. and yet Jewell had this idea that heat and work were two aspects of the same thing, and we now know he was right. They're both forms of energy transfer or energy in motion. Let's explore this a bit more because we're getting very near the change, really, here with Jules, Frank Close. His experiments were resisted. Can you tell us how fine they were in the sense of how brilliant they were, really? Anyway, where you go, if you tell us all about him.

Well, I mean, it's interesting that Jule as a brewer, he was, in the first instance, motivated by making his business the most efficient. He didn't want to spend money primarily. And in the 19th century, we had this wonderful revolution that different ways of producing energy machines was becoming known. You've got steam power. You've got electrical power. And the question for Jule was which of these is best? And he started doing experiments to measure, as Steve, said, how much temperature change is there if I do this or that other mechanical or electrical

process. And he found that indeed if he compressed water and sending it through a sieve, that the temperature would increase. So he was doing work, we now know, squeezing the molecules of water together, which was causing them to jiggle faster, we now know, and jiggling faster means get hotter, we now know. So he measured the fact that there was a temperature rise when he did that. How did he measure it? The details of how he measured it, I don't know. But the fact that he was able to measure fractions of a degree

was one of the reasons why people didn't believe what he was doing. They said, you know, you can't do it that precisely. It was the fact that in the brewing industry, he had developed very precise means of measuring temperature changes that enabled him at that stage to do these fine detail, measurements that others couldn't. And then it was later when I think he did an experiment where

he dropped a weight and the motion of the weight then set a paddle wheel going and the paddle wheel through water in an insulated chamber he was able to measure a significant temperature rise and that I think convinced people. Indeed he was

showing that work can be turned into heat but more important he quantified it. He found the exchange rate if you like that how much work corresponds to how much heat. And from that, the idea that heat is indeed a form of energy and that you can convert, as Steve said, work into heat or heat into work, began. So this is the middle 19th century.

And I think it is at this stage that the ideas of energy and the conservation of energy and thermodynamics, heat and motion, all began to develop. I mean, the laws of motion have been known since the 17th century, 18th century and Isaac Newton. but the concepts of energy and conservation only really developed in the 19th century revolution around the time of dual.

When you say influence people, which people do you influence and how? Is he anything to do with the Royal Society? Is it the North acting as it so often did brilliantly independently at this stage? Is that a question or a statement? I just slipped into as I'm just back from a lot. It's a rust wearing off.

Oh, it's that second orthomidamics all that rust that's accumulating. He has to wear off again, right? What was the question again? No, it's a serious question. Is he working in association with the Royal Society at that time, London, with people have a more abstract turn of mind, and he's the great experimenter,

or is he working in that sense in isolation? He wasn't working totally in isolation. I think he worked with William Thompson and the combination of the two convinced people. Lord Kelvin. He knows more than I do. Yeah, I think what interesting thing is, So Jule wasn't the only scientist who sort of led this revolution.

There was Robert Mayer in Germany as well, who was a rather speculative thinker, unlike Jule, who was more of an experimentalist. And there were several other people. But what characterised them all was they were all very young people and they were all slightly outsiders. They were amateurs in a sense. And the truth was they got sort of great seats of learning. was still somewhat obsessed with Newtonian physics that had come from an earlier age.

The people who drove the sort of birth of thermodynamics, as I say, were mainly young people. As Frank said, Jewel developed a very strong relationship with William Thompson, Lord Kelvin, who was perhaps more of a conventional scientist in that sense. He was at the University of Glasgow. But quite a lot of the people in general were sort of amateurs and slightly outside us to the mainstream,

the sort of Royal Society in the mainstream actually dug their heels in a bit with Jule and people, and they took quite a bit of convincing, and it wasn't until later the ideas really started to become the mainstream. So it was a real kind of revolution. Ruth, back to you, I'm back to the first low of thermodynamics, which can I explore a bit further,

on the conservation of energy. Now, can you tell us precisely what that means and how effect... This came out of jewels and Maya and then we're getting there and in the second third of the 19th century it arrives. Now then, what is great about it?

And it changed the whole game. Yeah, well, right. So what it sort of arose out of was trying to make thermodynamics into a sort of quantitative physical science with these abstract but also real

quantities or definitions and it essentially encodes conservation of energy, but including heat. So the first law of thermodynamics tells us that if we do work on a system, then the amount of work we do will go into a sort of increase of the energy of the system and a component of heat, a sort of thermal exchange, if we are keeping our system at a constant temperature. So it's an energy balance equation, but what it does is it describes how heat contributes to that energy equation.

So in a simple system, it's just internal energy, but we may have other components. What's it conserving and why it's important that it's conserving what it is conserving? So, well, it means that the overall energy, energy is conserved. If we have a closed system, the overall energy is conserved because there's nowhere heat can go. But it's also telling us something about the different types of energy we can have. We can perform a mechanical process and expend energy. We can heat up things. We can

expend energy. And we can also change the internal energy of a system by maybe changing its state. So it is beginning to actually put a label on energy in its different forms. Frank. I mean, Steve mentioned how the caloric idea of heat had been around, and I think Jule, his work effectively did away with that and to sort of amplify what Ruth's just been saying, that if the heat in a body is a measure of how its little molecules are jiggling around, if they jiggle faster, the body is hotter.

Jiggling faster means they have more kinetic energy. So in heating the body up, in doing the work that Ruth was talking about on a body, you are transferring energy into the kinetic energy of the molecules. So they are moving faster, and that is what we recognise as heat. So that is the dynamics of how it's coming about.

It's how it works, yeah. So how did that change the game? I think it established what we might... Why could there be no more... of these machines sensibly proposed? Why no more perpetual motion machines? Well, the concepts of energy conservation were established, not just by these experiments,

but 300 years of experiments in a whole range of things. The idea, therefore, that you could create energy out of nothing was completely counter to that. Energy was always there. Energy was always there in one form or another, whether it is mechanical energy, chemical energy. So it's just a transformation of energy. energy we're talking about? It's transformations of energy.

And I think one point is that the idea of conservation of energy sort of spread like wildfire through all of science. So people like Helmholtz, the German scientist generalized it to talk about

physiological processes. And gradually it was very quickly elevated from something to do with buckets of water in Jules Back Garden in Manchester to a sort of cosmological principle. that was rapidly seen to govern everything that happens. So everything that happens in the world suddenly is seen in terms of energy conservation.

Like me dropping the pen under the table, that's governed by. Absolutely. Everything we do, you drop the pen, some of the energy comes out as noise, some of it comes out as heat, some of it goes into vibrations and molecules in the table. But we could in principle do measurements and then calculate the energy beforehand and do measurements and calculate the energy after you've dropped the pen and you discover they're the same. If instead of dropping a pen you'd dropped an egg and it had smashed,

then you'd have an example of what Ruth said at the very beginning. The smashed egg is like the crowd. The coherent egg before it started is the unlikely configuration. Let's go. Just for fun, Steve, what about the second law of things? them, I don't know. Go on, you're going to take, so there isn't much time, but you can do. Yeah, so, so, so there's a very important type of engine, which is the heat engine. An example is the steam engine or the car engine.

These take hot gases and they use the expansion of those gases in a piston to do work and drive the car. Now, what, as Ruth explained earlier, the second law of thermodynamics is, the law of increase of entropy. What that means, in practical terms, is that energy tends to convert into less useful forms. It goes away as heat. And so basically when, if you imagine a car piston doing one cycle, after that cycle is finished,

some of it, some of the energy has become work, but some has been irretrievably lost. Some has driven the car, but some has gone out of heat. It's like paying VAT. It's like if you, If you buy a television and then immediately sell it to somebody else, you lose money because of the VAT that you've had to pay. You don't get that back.

And so it's a bit like a tax on energy. So how does this stymie perpetual motion machines? Yeah, so it doesn't, so this is perpetual motion machines of a second sort, of the second type, are ones that try and convert heat entire. into work. So for example, I mean, there's actually a good practical example from the 1860s when the American government got interested in a ship that purportedly extracted heat from the ocean and used it to drive the ship.

So it never needed any fuel, just took heat from the ocean. Now, this actually breaks the second law. And because... And so the ship stopped. So the ship stopped. And they did actually build it. It didn't work. And so what engineers came to realize

is that by applying the second law, there's a fundamental limit on the efficiency of heat engines. And so it's not just about how good an engineer you are. You will ultimately run up against a fundamental limit given by the laws of physics, the second law of thermodynamics. So we've got these two laws with stop perpetual motion machines.

It doesn't stop them being invented because of eternal optimism. The law of eternal optimism never goes away. But it really does stop them being taken seriously and sets off a whole range of developments in physics which are more unimaginable, and that's also true. Were these laws ever challenged, Frank? Or are they there forever?

Well, that actually is a very good question about the nature of scientific inquiry and knowledge. I mean, it's like the terms and conditions, read them very carefully in nature's list. And occasionally we find this fine print that we've been applying what we thought were universal laws outside their range of validity. For example, the appearance of Einstein's theory of relativity

because we've been applying Newton outside his range of validity. When you come to the world of atomic physics and quantum physics, then you can apparently violate the conservation of energy for very short times. It's Heisenberg's uncertainty principle, that energy can be, quote, borrowed as long as it's paid back in an unimaginably short period of time. So in the quantum world, we know that it's possible to avoid the conservation of energy. In the macroscopic world, however, it is to all practical purposes, to the best experiments we have done in 300 years can serve forever.

There may be loopholes in quantum gravity, a theory which we do not yet have. So there may be terms and conditions in nature's laws that we don't yet know of that allow energy to be violated. but in the absence of that at the moment, it would seem to be that if you can find them, go ahead, but we're not aware where they are. Ruth Greggia, do you want to take this up? Yes, I think it's also worth pointing out

that in the context of 20th century physics, we actually have another reason why we really do believe in conservation of energy, at least again if we read the terms and conditions carefully enough, because, you know, following on from Einstein, we actually have a mathematical theorem, Nurtus theorem, that tells us relates conservation of energy to underlying symmetries of nature. So...

What does that mean? Well, in that... So a theorem, you know, NERA approved this theorem, which, you know, in mathematics is as close as we come to the truth, which says that if you have a... So what is a symmetry?

A symmetry is where you do something and it doesn't change. So if you imagine ice skating on an enormous lake where you have no point of reference. If you move, you can't really tell that you've moved other than keeping a memory of having moved. So that's an example of a symmetry.

And of course, ice skates have very little friction. If you start to move, you will keep moving. And there you have a conservation, the conservation of momentum or this energy of motion. So that's an example linking this. And NERTA managed to link conservation of energy to a symmetry in nature. And so this is why we as physicists

actually believe that energy is, you know, conserved except in the quantum world, of course, we have special, you know, little get-out clauses. I mean, if I can maybe pick up a little bit on Nertes theorem. I mean, so energy conservation, I think, faced a sort of mini-crisis with Einstein in that Einstein proved essentially that mass and energy are interconvertible.

and more or less the same thing. Is that his famous theorem? That's his famous theorem equals MC squared, energy equals mass times speed of light squared. Now, the question then arose that was, so was energy still conserved or was mass energy conserved? And this question was taken up by the great German mathematician David Hilbert. And he turned to this young Jewish German lady, Eminertr, who managed to prove this amazing theorem. And it showed something very, I mean, Ruth's going to explain the details better than I can, but my understanding of it really is that it really arises from the constancy in time of the laws of physics.

So if we do the same experiment next week as we do today, we get roughly the same result with an experimental error. The fact the laws of physics don't change with time give rise to conservation of energy. Frank, which of course begs the question of whether the laws of physics are constant in time, and you could imagine that they are not. Physicists get things wrong. They've got things wrong about the right brothers, didn't I? They've got things wrong about the right brother.

That's a wonderful... I just slipped out. Two wrongs don't make a right, though. So physics is always provisional in the sense that we operate on what we understand at this present time, being aware that one discovery, if it is absolutely clear-cut, makes us have to revise things. Perhaps to pick up on the Wright brothers, yes, there was physicists at the time of the Wright brothers, early 20th century, who thought that flight was impossible and indeed wrote learned papers on it, while these Wright Brothers planes were buzzing overhead. They were still having academic conferences. But on the other hand, I think these laws of thermodynamics are among, as you said right at the start, are among the most robust laws within some caveats. because they affect all of science. And, you know, if the laws of thermodynamics were to fall in some spectacular way,

all of science would have to be reinvented in some way. So it's really, I think it's generally considered as highly unlikely that the laws of thermodynamics are going to be, fall any time soon, if you're doing. We would really have to radically change our notion of physics and description of the world in a way, that it's hard to imagine would not overturn pretty much everything that we have done. Now, maybe, of course. And one thing to note, actually, is, you know, if you look back at the fossil record,

it shows the laws of physics were probably the same a billion years ago as they are today. Well, we'll do a billion years ago next time we all meet again. Thank you very much. Thanks to Ruth Gregory, Frank Close, and Steve Bramwell. Next week we'll be talking about Alexander the Great, about 3 or 400 BC. Thanks for listening. And the In Our Time podcast gets... some extra time now with a few minutes of bonus material from Melvin and his guests.

The Wright Brothers got it wrong. I mean, you can't throw a left curveball like that in. I think Lord Kelvin was very, very anti-flight for some reason. Actually, mentioning Kelvin, the example of energy conservation, of course, was used in the 19th century to solve the paradox of the sun, because the sun given chemical... It looks like it's giving out energy. That's right. Chemical energy would not explain how the sun had lasted long enough to be consistent with evolution timescales.

And then, of course, the discovery of nuclear energy solved the conundrum. Yeah, yes. Should have perhaps mentioned Clausius and Rudolf Clausius, you know, made these very famous, concise statement of the laws of thermodynamics. You know, the energy of the university is constant. The entropy of the universe tends to maximum, in 1865. and that's what everyone remembers. The energy of the universe constantly and I think Clauses, he did the world of great service

in distilling it down to such a simple statement that people could understand. I was saying to Steve beforehand, there's the pithy statement of the laws, which is that you can never win, you can only break even, that's the first one. You can't even break even, you can only lose, except at absolute zero.

That's the second one. And the third law is you can never reach absolute zero. Well, we'll get on to that sometimes. I wanted Maxwell's demon. Oh, yeah. You're all full of Maxwell's demons. He never came up. Yeah.

And what's about Marshall's demon? So he's, it's such a whimsical little picture, but it's absolutely charming. This is a great... Again, it was trying to understand whether, and exploring whether these ideas of, as Frank kept talking about, you know, heat and the excite, you know, their little molecules moving.

It's trying to sort of see whether this, what we call this statistical picture because it's all talking about broad averages of the crowd, whether that was really true. And so he sort of imagined that maybe there were two rooms with a gate in between

and the little demon keeps an eye out on the molecules and says, here's a fast one coming, I'm going to let it through and then the slow ones, he won't let through. If you persistently do that, one room will get hotter

and the other room will get covered. and that is apparently in violation, but certainly it looks like that is decreasing the entropy if we count the different ways of organising the crowds in each room. On the other hand, what, as always, when you find an apparent violation of these laws of thermodynamics or apparent perpetual motion machine, what you've usually done is there is a part of the system that you've forgotten about. And in this case it's the demon, the demon, but has to do work, has to figure out which molecules are going fast, which slow. And if you include, you imagine what physical way could a demon decide that, you will find that that costs.

It costs you. These are great examples for actually deepening the understanding. Yes, absolutely. Because if I was asked, is there any use at all to worrying about perpetual motion, I would say, great for students. If I send the students away and say, write me an essay on the first law of thermodynamics, big deal. Go and do a research project on a perpetual motion machine and if you can't do it, explain why, much more interesting. I think we're about to be interrupted by Simon Taylor's not before time.

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