Laws of Physics

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Melvyn Bragg: Hello, since ancient times philosophers and physicists have tried to discover simple underlying principles that control the universe. In the 6th century BC, Thales declared "everything is water". Aristotle believed all of creation was forged from 4 elements, earth, air fire and water. Newton more successfully laid down the law of universal gravitation, and as we speak contemporary scientists are struggling to complete the task of string theory, the quest to find a single overarching equation that underpins all physics, and can perhaps explain the organisation of everything in existence .

But are the laws of physics really facts of life? Is what is true in physics, true in all areas of existence, is it even true in other areas of physics? With me is Mark Buchanan, author of a new book called "Ubiquity", which claims to identify universal principles that can underlie everything from an avalanche to a world war to a crash in the stock exchange to a forest fire.

We also joined by the physicist Frank Close, author of "Lucifer's Legacy - the meaning of assymetry" and by Nancy Cartwright, Professor of Philosophy at the LSE and author of "The Dappled World - a study of the boundaries of science".

Frank Close, some people claim that Aristotle held back science with his insistence on the 4 elements, earth, air, fire and water and this search for simplicity was rather damaging, would you agree with that?

Frank Close: Well I don't think it was damaging, it's certainly the case that intrigues me that 3000 years, science has progressed very successfully on the belief that there is some unity behind it all that we're trying to elucidate out of the complexity that we see around us, and although it's progressed that way successfully and I personally think that is the way forward, I've begun to ask myself a question quite often as to whether there really is a unity out there that we're walking towards, or whether we're trying to impose a unity for psychological reasons on something which is actually very complex.

Melvyn Bragg: When Newton was searching for his laws, was he searching for a source of truths of Nature or truths of the laws of physics d'you think?

Frank Close: Certainly Newton made a great advance in bringing together things that at first sight you'd never think were related at all, I mean to be able to realise that a falling apple is controlled by the same law of gravity as we now call it, to the way that the Moon goes round the Earth and the Earth round the Sun, was a tremendous insight, and I often wonder if the Earth had actually been covered by cloud, so that we'd never known of the stars and the Moon, whether Newton would've been able to do what he did whether science would have developed in a different way and order, and if we ever meet aliens from another planet, it would be nice to know if their science developed the same way as ours.

But Newton certainly was a great figure in the development of science, and I think it is simplistic but perhaps also arguably true that if you want to say where did modern science begin, it was with Newton.

Melvyn Bragg: Mark Buchanan, how would you define a law of physics?

Mark Buchanan: I think a law of physics generally is some pattern that is first observed somewhere in Nature whether at the sub atomic level or at the level of say ordinary materials, liquids and gases, that is so simple that it seems to cry out for some explanation. There are all kinds of patterns. There are extremely complex patterns that don't look much like meaningful patterns at all, and if you see a patterns like that, you generally don't try to make inferences about laws, underlying those patterns. However if you notice that you a gas into a box and measure the pressure and volume and temperature and always find that those 3 numbers fall on some extremely simple and orderly curve that follows a very simple equation, you can be pretty sure that there's some underlying order to that system, and so I think, what a law is in my mind is really an extremely simple and elegant way of describing some kind of order that we have recognised in Nature, and also that we have come to understand a little bit about where that order comes from in terms of deeper principles.

Melvyn Bragg: If a law such as Newton's first law of motion, every body perseveres in a state of rest, works in one area of physics, is it sensible to assume that it would working another area.

Mark Buchanan: Of yes and no I think for instance we no that Newton's laws apply to galaxies and stars and planets, and there's overwhelming evidence that that's true, we wouldn't just blindly take Newton's law and try to apply it to you know the behaviour of say pressures and volumes of a gas.

Melvyn Bragg: Nancy Cartwright, Newton's laws were worked out in a mathematical way through observation and abstract thinking, and they're about physics. He called them laws of Nature, and they really do seem to work in the real world.

What does that tell you?

Nancy Cartwright: Well...

Melvyn Bragg: The laws of gravity put men on the moon that sort of thing?

Nancy Cartwright: It tells me that we could have a lot of confidence because we've had 200 years of using them or more. We came have a lot of confidence that when we run into systems which are very similar to the kinds that we've been studying that Newton's laws will continue to give very good, very precise, very accurate descriptions of new cases.

So it was one of the things that Mark mentioned, it was a great breakthrough of Newton's in contrast to the, in contrast to the previous Aristotelian physics. It was a plank in Newton's platform to say that heavenly bodies and Earthy bodies were the same, and would obey the same kind of laws. Previous to that, it was thought there was terrestrial mechanics and celestial mechanics and that there were different kinds of bodies that behaved in different ways, and Newton said, "No wherever you've got masses, they're going to behave in the same way, whether they are the masses of planets or the masses of cannonballs or as turns out later, the masses of molecules. So I think the success of Newton's laws over very very long period of detailed predictions that work out, provide us with very good reason to think that when we encounter systems which are like those systems that we've been looking at before, and which are in the kinds of environments in which we've looked at them before, we can expect to get to use Newton's laws to make very accurate predictions. It doesn't tell us I think, what we should expect when we encounter different kinds of systems.

Melvyn Bragg: Just a second Frank, do you think that fundamental rules can be found and applied right across physics physics then Nancy Cartwright?

Nancy Cartwright: I think we do not have sufficient evidence to put a lot of money in that programme! (giggles)

We've had... Franks said that there were these... this history of looking for unity and finding it in that science had been driven for 3000 years that way, but it is important to remember the history of science is the history of both successes and failures, and that's lot and lots of hunts for unity have failed and a few have succeeded and that as well as learning about some things that are unified, we've learned that - at different periods - that some things are disunified.

[If one invokes the monism derived from a single deity presumed to be the instigator of the universe, this is a bit of a problem for that concept, if we've discovered disunity, is that man's failings or does it show God (or nature) is not one singular unified thing. The lack of discovery of unity does not necessarily mean it isn't there, although the inability to tie the laws of the micro to the laws of the macro might be a fundamental disunity.

I think it is a problem of practical imposition, man will find some way of tying it together, purely out out of the drive to have laws that comply with what is observed, but what if there were two or more independent systems vying in competition with each other, is this the source of the God/Devil, Yin-Yang, Good-Evil, order-chaos duality? -LB]

Melvyn Bragg: Let's stick to the laws of physics for the moment.

Nancy Cartwright: Yes.

Melvyn Bragg: Because let's try and sort that out in the limited time available, you're saying it seems to me that the laws of physics as discovered even by Newton cannot be applied right across physics, that they refer to a special limited area of experience, knowledge and so on?

Nancy Cartwright: Yes. What I'm saying is that...

Melvyn Bragg: And what you're... yeah.

Nancy Cartwright: ... our evidence for them is that they apply in these limited experiences.

Melvyn Bragg: On the law of gravity for example you say, " that it has limitations", because we're talking about closed systems, I've read your book so could you just tell the listeners what you mean by that and why you think the law of gravity has limitations and what those are?

Nancy Cartwright: Yes, let me give a very controversial and striking example. Contrast dropping cannon balls off the leaning tower of Pisa, with an experiment that drops instead paper tissues off the leaning tower of Pisa. The first case when you drop the cannon ball, the cannon ball, the motion of the motion of the cannon ball is affected by the pull of the Earth.

In the second case the motion of the tissue let us imagine is affected by the pull of the Earth and the push of wind.

Now in the first case we have the law of motion, F=Ma, and...

Melvyn Bragg: Force equals mass, acceleration, right.

Nancy Cartwright: Force equals mass times acceleration, the basic law of motion very familiar from GCSE science, and it... can we apply this law to a study of the cannon ball? Yes we can because even though when I describe the cannon ball I said it's motion was affected by the pull of the Earth, and the pull of the Earth is not any of those words I said, it's not force it's, not mass, it's not acceleration

We know, because Newton taught us how to think of the pull of the Earth in terms of these more abstract concepts of physics. Newton taught us the law of gravity.

So that the pull...

Melvyn Bragg: We know about gravitational pull. Now what's the contrast with the paper hanky?

Nancy Cartwright: Well the contrast with the wind is that with the paper tissue is that we'd like to use the law of motion F... Force equals mass times acceleration. We know it's subject to the pull of the Earth, so we know that the pull of the Earth exerts the force of gravity, but what about the push of the wind?

Push of the wind isn't something that we have a law that tells us what it does.

So in order to bring the tissue, the behaviour of the tissue into and under the laws of physics we have to figure out some way to be able represent the push of the wind as a proper force in physics, and you're not allowed to do it just in an ad-hoc way, we actually have, in the case of the pull of gravity, we have a formula, and so the question is, whether or not the push of the wind can be brought into the domain of physics.

Melvyn Bragg: It seems to me what you're saying is that these laws work within closed systems. If you've got a closed system deep inside a thermos, inside a battery or you've got a clear almost controlled experiment, like cannonballs from Pisa, no messing, gravitational pull, bang, then you're okay.

If you've got systems outside that, then the laws of nature are almost contradict sometimes or interfere with the law of physics.

Nancy Cartwright: They interfere.

Melvyn Bragg: Frank Close, Frank Close what's your view on that?

Frank Close: I don't think it's that they interfere. What it is, is that the law of gravity is very simple to apply, when you've just got two bodies, like the Sun and the Earth. The moment yet a third body in there, the moon for example, you've got the Sun on the Earth, the Earth on the Moon, the Sun on the Moon, already at that level of three, it's almost impossible to solve.

And so you have to start making approximations, the moment you're dealing with the wind, it's getting extremely difficult that's why the weather forecasting is so difficult the basic underlying laws at the level of atoms and molecules and gravity and so forth we know. We can work them out an apply them to individual bits and pieces, but when you look at large systems where you've got lots of these things competing together, it becomes at the very least a problem for a computer to solve and even then it becomes very impractical.

\b Melvyn Bragg: Mark Buchanan, in your book "Ubiquity", it seems to me the book starts with these three scientists at the end of the 80s sprinkling grains of sand one at a time onto a table top, they did it through a computer because it would have taken a lot of time and dexterity to do it manually, and then what happened?

Mark Buchanan: What they discovered to just get it out in the open is a generic pattern of dynamics and change that occurs in the sandpile, but that also turns out to... well mathematical signatures of it show up in many other settings.

Now, one of the interesting things is if you did this experiment with droplets of water say on the top of a lake, you'd get very boring results, because you'd drop a drop in, the waves.. ripples would go away, and the lake would be a tiny, tiny bit higher and that, you could do that all day and you'd never find anything very interesting.

What's interesting about a pile of grains, is that it's an extremely... it's an irreversible situation, so you drop the grains, the pile builds up, each grain when you drop it, it falls it gets locked in place, and affect the silhouette of the top of the pile and when future grains get dropped on top they always get dropped on top of the setting that's already occurred, so every grain gets locked in place, and affects the whole future out of which this pile grows.

So, it's a very simple non -equilibrium or irreversible process, and so the reason people.. physicists are interested in it is it's so simple that one has a chance to hope to try to come to some deeper understanding of it. So anyway, what these three physicists found, is that as the pile grows, it ultimately reaches a steady state where as many grains on average fall off the edge of the table as you drop in from the top and it comes to be poised in a state of extreme unpredictability and instability, which is called the critical state . How this instability manifests itself is that when you drop the very next grain, you cannot only not predict the details of what's going to happen where the avalanche is going to be, and how it's going to progress, and where all the different grains are going to end up in the end, but you cannot even predict the rough magnitude of what's going to happen, so the grain may just fall and stick and trigger nothing at all, or it may trigger an avalanche involving ten or a hundred or a thousand or a million grains, and there's a particular mathematical rule known as a "power law ", which indicates that there is no sense in the idea of their being an average size or typical characteristic size for the avalanche that occurs.

There's really a kind of democracy of scale at work in this problem, so the system treats avalanches of all sizes as being effectively equivalent.

Melvyn Bragg: I know this is... I don't think this is simplifying what you're doing but I want to just move to what I think is the centre of it, and then bring the other two in.

What we're talking about is the critical state, the critical state is where something happens to this sand. The critical state you also see in crashes of stock markets. Huge forest fires where there haven't been huge forest fires, and so on, world wars, the firs world war's a wonderful example of that, a man takes the wrong turning, a student kills two people, bang away we go for 4 years, and then make for the next 6 years, and so on and so forth.

No one thing that worries that I caught... one thing caught in the book, you talk of the special\b\ul organisationof the critical state but yet you also say, that you... the result of running these avalanches of sand through computer after computer to find a pattern was the result that there was no result, so I can't work out what the special organisation of the critical state is that applies to all these things, if after they've run it through again an again, they can't tell when an avalanche is going to occur, you say you can't tell when this big forest fire is going occur and so on and so forth, although there is a critical state condition around so I haven't quite got it.

Mark Buchanan: There is a very definite pattern that emerges in the system, and which is the signature of the critical state. However it doesn't emerge at the level of individual events. So you cannot predict what the next grain of sand is going to trigger, whether it's a small avalanche or intermediate size, or a large avalanche.

Melvyn Bragg: Or none at all?

Mark Buchanan: However, you can predict that if you do drop a million grains, and count up how many large avalanches, how many intermediate avalanches, how many small ones there are, and make a plot of those statistics, there's a very definite pattern that emerges at the level of many events and the statistics of those events.

Melvyn Bragg: How does that work with world wars, financial organisations and forest fires?

Mark Buchanan: Again, again...

Melvyn Bragg: How does that same system pull over to there, because the real experiment you've got is looking for earthquakes and that doesn't come off in your book.

Mark Buchanan: Er, well it does, there's...

Melvyn Bragg: Well it doesn't, the guys who turned up like waiting for the sort of second coming (laughter) for the earthquake, "with our best instruments in the world" you say, " never have so many instruments from so many geophysicists, been in one spot at the same time, they worked out the earth quake was going to happen, it was 12 years ago it still hasn't turned up.

Frank Close: Mark would say "Keep waiting".

Mark Buchanan: I'd say.. exactly... I agree with that completely, the trouble is that an earthquake it appears now from the mathematics is an event of the very same kind as one of these large avalanches triggered by a single grain.

Melvyn Bragg: Frank Close.

Frank Close: There's two different things here which I think have got a it confused up, there's power laws and there's critical states and these are quite different in my mind.

Power laws are much simpler to understand. if you throw a potato against a wall, and it breaks into lots of bits, and there'll be a lot of small pieces, there'll be a few large pieces, and what the power laws show you is that, if I compare those of 1mm size of those of 2mm size, there'll be half as many of the latter

and what happens in a single event is a source for much confusion amongst those not familiar with science -LB]

If I then compare the 2mm with the 4mm they'll be half as many of the 4mm and so on and so forth, and it doesn't matter how big you are, when you compare this big with twice as big you get the same ratio each time, that's the sort of power law.

Now when does this happen and when doesn't it happen? It happens when you're far away from anything that's quote "important in the problem". For example, the potato, there's two critical sizes, there's the size of the potato, you obviously can't get a bigger bit than that. At the other extreme you've got the very small molecules, that make up the potato, you can't get smaller than that.

As long as we're talking about bits of a potato that much bigger than molecules and much smaller than potatoes, these power laws happen. When things get interesting is when you get to the size of the molecules and then you start getting very detailed that happen which are inherently unpredictable, and that is when critical phenomena that Mark is referring to I think really come into their own.

Earthquakes the rule there is, you can't predict when an earthquake will happen, but you know that there will be more earthquakes of size 5 on the Richter scale than of size 6, and in turn of size 7, they get rarer and rarer as you go bigger and bigger, but there's no inherent limit to the size of earthquakes, they just become rarer and rarer.

Melvyn Bragg: But isn't the basis of science predictability.

Franks Close: Er, yes and no, \b it depends what you mean by predictability...

Melvyn Bragg : Well if you do the same experiment again you get the same result, that's what I mean by predictability.

Franks Close: Oh in that case, er yes, I think the experiment here is that if you wait 50 years I can predict say that half of us will be dead.

And if we wait another 50 years, another half of people then will be dead, but when exactly we will die in that period, is inherently unpredictable. Now I regard that as science on statistical sense, not on a day to day sense.

Melvyn Bragg: I want to bring it back to the title of your book, you call it "Ubiquity" and we all know what that means, and you write "at the heart of our story, lies the discovery that networks of things of all kinds", I'm quoting, "atoms, molecules, species, people, and even ideas, have a marked tendency to\b\ul organisealong similar lines "

Now that's a big claim, and it's back to the idea that everything is water of Thales, and onto the Theory of Everything, which is being worked on.

Can you just say briefly what in your book would persuade us that that was the case.

[This is the distinction I make between a belief and knowledge or understanding. If one were to read Mark's book and be "persuaded" it was the case, one is merely believing Mark.

If one truly understands the reasoning behind his claim and sees it applies, one has knowledge that it is so or that it maybe so. One can be persuaded that the moon is made of cheese, that does mean the moon has to conform to your idea of it! -LB]

Mark Buchanan: Well there's two levels, I think of persuasion, the first level is that the mathematical form for the statistics of events, large events, intermediate events, small events, that conform to this pattern that Frank described called a "power law", it shows up in earthquakes, it shows up in forest fires, it shows up in the fluctuations of financial markets, if you look at how much prices change over say a day, over a week, it shows up in the statistics of the number of citations that scientific research papers receive, you find very few papers that receive a huge number of citations, very many that receive a few citations, and nevertheless over the whole range there's a terrifically simple mathematical formula which is the power law, and physicists only know of a few mechanisms that can give rise to power laws, and one of these is this notion of the critical state, and it seems to be the most widespread possible explanation for this particular kind of pattern.

There's a deeper answer and unfortunately it's a bit technical, but it goes into a concept which is known as universality, and it's called critical state universality.

The critical state was discovered originally not in the context of a sand pile, but in the context of what physicists call a "phase transition ", this is when a liquid turns into a vapour, and... or a magnet... if you heat it in a furnace eventually becomes not a magnet, it loses it's magnetic power, this is called... it changes from one phase of organisation to another phase of organisation. This is widespread in nature, many materials do it, and if you poise a material right on the boundary between two phases, then you find this critical state organisation and it turns out that extremely different substances that have no similarities in their molecular workings show exactly the same critical state behaviour, even down to the numbers, you know, several significant figures, describing the exact precise patterns in this critical state, and there is a deep theoretical reason why it tuns out that the details don't matter.

So it's very plausible that one can find the same kind of organisation welling up in systems such as the level of earthquakes or forest fires.

Melvyn Bragg: Frank Close, can you comment on that in terms of theories of everything and the present state of a theory which explains everything? First of all, do you think that, that theory is lurking around at the moment?

Frank Close: You keep hearing this, and I'm actually very sceptical, that when you look back in history, people have at various epochs thought that they had got a theory of everything, and what they really meant was "we've got a theory of everything, that we are currently aware of".

I think that Nature has a very sobering effect on us, which is it reminds us that we are not as clever as we think, that in the last century they thought that they had got an understanding of everything, that was then known, mechanics, electromagnetism, and so forth, there was a little problem on the background which was called "the black body radiation problem"and that led to Quantum Theory, which completely revolutionised science and developed the 20th century electronics industry and technology amongst other things.

In the 1930s at last one had if you like, the equation of everything on a T-shirt, we now call it the Dirac equation which describes the way that electrons behave in atoms, that equation in principle underpins everything in chemistry, biology, life, but nobody's solved it.

Melvyn Bragg: What about now?

Frank Close: At the moment, we are again at one of these states where all the phenomena that we've seen and know, we are getting very exciting feelings that there is a unity to them that we are analogous if you like to the 1930s to being able to write an equation not quite on a T-shirt, let alone to be able to solve it, whichin principle might describe everything that there is, whether it does or not, is for experiment to decide, and I think that exciting though this is, ubiquitous as it is, it is indeed the experiments that will be performed in about 5 years from now at CERN that are going to go to extremes, the first moments after the big bang if you like simulated in the lab, to see if it really was like that, or whether we only just think it was like that, because if it turns out that those experiments show that there's something out there that we haven't dreamt of yet, we will have to take that on board, and revise everything.

Melvyn Bragg: Nancy Cartwright, do you think that this search for a Theory of Everything a solution or a cluster of facts written in "Ubiquity" which make for a solution. D'you think that that is some kind of religious impulse, as much as anything else?

Nancy Cartwright: I think that Frank thinks that, and I'm not very clear about the psychological motivations that drive us. I know that it's something that has come again and again throughout the history of humanity, we've looked for unity, we never achieve it, butI don't think it's the only metaphysical or religious drive we have. I think that there is the exactly counter drive, that ... well there's the simple way that people think in terms of intellectual history, it's between the enlightenment and romanticism, and in a sense the enlightenment stood for unity, unity of ... all people are the same, and romanticism has been a movement that says, "pay attention to the differences pay attention to Nature which is highly varied", and I think \b we have both drives,

I'm very fond of... the reason I call my book "The Dappled World" is because I'm often confronted with this aesthetic or religious ideal of unity, and told that if one gives that up one's giving up the whole beauty and excitement of physics, and I myself, have always had a totally different aesthetic, the one of Gerard Manley Hopkins, who says, you know his poem "Pied Beauty" - "Glory be to God for dappled things".

Melvyn Bragg: "Glory be to God for dappled things". Yeah.

I want to come back to this idea of ubiquity to end on though. Mark Buchanan you do suggest in your book, that human history maybe governed by the same underlying principles as govern the fluctuations in this pile of sand.

Let's go back to this intriguing pile of sand. Could you briefly tell us you make that leap?

Mark Buchanan: Okay well again, it's through this mathematical pattern which is the power law, which is a very special kind of pattern that you don't find arising very easily in Nature, at least on our earlier understanding. Now it seems to be emerging in many different cases at many levels. It turns out that there is some statistics on ... it's not easy to get a mathematical handle on history of course, but if you try to do so, you can look at for example, the statistics of the wars that have occurred over the past 5 centuries, and there's a guy from the University of Kentucky named Jack Levy who's done this and he finds a quite accurate power law for.. if you take the grimmest of all statistics, which is the number of casualties, just to get some measure on the size of the conflict, then if you look over 5 centuries, wars follow exactly the same statistical pattern as do earthquakes.

So even though it may shock our sensibilities to believe that the political fabric could somehow be following a pattern that is quite similar the way stresses and strains build up in the Earth's crust, perhaps they also build up in the fabric of international relations, certainly the mathematics, suggests that that is a possibility, and all I really want to suggest is that one ought to take on board the idea that is a theoretical possibility and instead of trying to interpret these complex systems in terms of older ideas from physics, be they cycles or simple linear progressions, we ought to start to think about, the kinds of mathematical patterns of change that arise in the more complicated systems that physicists are looking at, such as the pile of grains.

Melvyn Bragg: Well thank you all very much indeed it was er... I hope people were enlightened as I think I am a little bit, thank you very much. Next week I'll be discussing the Tudors that burst from the Medieval world via those invaders from Wales that set it off, with John Guy and Christine Carpenter.