Heisenberg's Uncertainty Principle
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BBC Sounds. Music, radio, podcasts. This is In Our Time from BBC Radio 4 and this is one of more than a thousand episodes you can find on BBC Sounds and on our website. If you scroll down the page for this edition, you'll find a reading list to go with it. I hope you enjoy the programme. Hello, at the age of 23, the German physics student Werner Heisenberg effectively created quantum mechanics for which he later won the Nobel Prize.

He made this breakthrough in a paper in 1925 when he worked backwards from what he observed of atoms and their particles and did away with the idea of continuous orbit, replacing this with equations. As we'll hear, this was momentous. And from this flowed what's known as his uncertainty principle. The idea that, for example, you can accurately measure the position of an atomic particle or its momentum, but not both.

With me to explain and discuss Heisenberg and his uncertainty principle are Fay Dauker, Professor of Theoretical Physics at Imperial College London, Harry Cliff, Research Fellow in Particle Physics at the University of Cambridge, and Frank Close, Professor Emeritus of Theoretical Physics and Fellow Emeritus at Exeter College at the University of Oxford. Frank, what was there in his background that suggested he was going to go in that direction?

Well, he was born in 1901 in Bavaria and his father was a teacher of classics and Greek. And I think that the young Werner was very interested in the ideas of Plato. He read Plato while he was hiking in the Bavarian mountains. And the reason I think that that was important for him is that later he made a remark about

which was that the smallest units of matter are not particles in an ordinary sense, but forms, ideas only expressed in mathematical language. So I think it was that classical background from his father that perhaps made him look that way. But he became interested, obviously, in maths and physics, and that was what he went to study as an undergraduate at Munich and then Göttingen from 1920 to 1923.

I think the seminal moment for him was in 1922, he went to a lecture given by Niels Bohr. Bohr was famous for having come up with the model of the atom as a miniature solar system with a nuclear sun in the middle and electrons like planets whirling around on the outside. And this piqued Heisenberg philosophically because nobody had seen these electrons orbiting around.

So what really made you believe that they were there? And so he spent a year then working with Bohr in Copenhagen, where Bohr was based. And I think it was during that year that the mathematical scheme that Heisenberg developed first began to mature based upon what you can see. Namely, the one thing we do know about atoms is that they emit light. They don't emit a whole rainbow, but they emit like a barcode of individual lines of

And why was that and how could you mathematically describe that? And in 1925, he came up with the equations that did that. And that is what we call now the birth of quantum mechanics.

Frank, can you tell us the essence of quantum theory before Heisenberg stepped into the picture? Well, quantum theory as such really began around 1900. Up to that time, nature appeared to be continuous. Light, there's a whole spectrum of light. Motion is a continuous thing. But the

that is how things are in the large-scale world, which we are aware of day to day and which the scientists up to that time have been examining. But Max Planck, a German physicist, had the insight that if he assumed that instead of continuous, nature was actually discrete, that's what the word quantum describes, there were certain things that could be explained that otherwise made no sense.

For example, he assumed that electromagnetic waves are not a sort of smooth legato wave, but more like a staccato bunch of what we call photons, particles. And by making that assumption, he was able to explain the way that hot bodies radiate light. Without that assumption, the classical theory of Maxwell just didn't work.

And then Einstein picked up on this idea and supposed that, indeed, these little particles of light...

as they crossed space and hit things. And with that, he was able to describe what happened when light hit metals and kicked electrons out, called the photoelectric effect. So these were the first two indications that if you assumed that nature was discrete on the small scale, things worked well. Then along comes Niels Bohr in 1913. Ernest Rutherford has discovered the exoplanet,

of the atomic nucleus. And the picture of the atom that emerges is pretty much one that is a good model today. As I mentioned earlier, the idea of a miniature solar system with the nucleus sun at the middle and the electrons, the planets whirling around on the outside, that was the sort of picture that emerged. The problem is that if you use the classical theory, the electrons whirling around would just spiral into the nucleus in a fraction of a second and we wouldn't be here.

So Bohr made the assumption that this discrete idea, this quantum idea, applied to electrons in atoms, that they couldn't go anywhere. They were like on rungs of a ladder that they could step down. And as you step from one rung to the next, a high-energy rung to a low-energy rung, the energy difference is radiated as light, and that is why you see a spectrum of lines, a barcode for the atoms. And that was Bohr's model. But again, it was all ad hoc.

And it worked, but it was a bit like imagining back in the 17th century...

People were aware that apples fall to earth or if you kick something, it moves. But the equations, the mechanics, Isaac Newton's laws of dynamics had not yet been written down. And it was a bit like that. The idea that nature is discrete on the very small scale was clearly true. But the equations of the quantum mechanics had not yet been written down. And that is what Heisenberg made the first step in doing. Thank you very much.

Can you set the scene for why Heisenberg in 1925, why his paper was so distinctive? So as Frank described, there was an ad hoc model of the atom, of atoms, but no internal dynamics to describe why the model had the structure that it does.

So Heisenberg steps in and makes a number of conceptual moves in 1925. So he takes on board the Bohrian structure of states that the electron in the atom can be in, and they are discrete. So you can number them, you can label them, one, two, three, four, and they are labeled by their energies. So there are higher energy states, lower energy states. So he takes that and doesn't change that particular...

particular idea. What he does change is that he denies the idea that the states correspond to the electron having particular orbits in space, that the electron is going around the nucleus at a fixed radius from the nucleus and with a fixed periodic rotation.

So he just denies that. He says, forget that idea. As Frank said, that's not, he argues, that's not an observable thing. We cannot experimentally determine where the electron is inside the atom. So let's just say that...

that's not even speakable. We won't even speak about that. We just think of these states as being abstract states of the electron. So that's the first thing. He then centres a concept of the transition between these atomic states and

that he had already worked on with my collaborator Hendrik Kramers. So the transitions are not deterministic. You can't predict with certainty when or whether an electron in one state will transition to another particular state. There's just some probability for each possible transition. So he takes that and the intensities of the radiation that the atoms emit...

That was an experimentally determinable quantity that experimentalists were measuring in the lab. And the probabilities of these transitions translate exactly into the intensities of the radiation of those particular frequencies. So if you can calculate the probabilities of the transitions between these atomic states, then you can predict the intensities of the particular frequencies of light that would be emitted there.

So all of that was somehow already in the literature. But he takes that and he says, OK, I need to predict the actual energies of these atomic states and I need to predict the probabilities. How am I going to do that? And he works backwards. You said that in your introduction. That's exactly right. He works backwards from the form of the measured experimental outcomes of these intensities and these probabilities and these energies. And he asked, what would the position of the electron

have to be like in order to give me these particular results, these particular experimental results? And what he discovered was that it led him to a really startling proposal that the position of an electron in an atom is not given by a number. It's not here or there or here, but...

the position is represented by a completely new, unexpected mathematical entity called a matrix. This is something very abstract. It's not something that can be conceptualised as an actual place where the electron is in space. And he also postulated that

the matrix that corresponds to the position of an electron satisfies an equation of motion. So it's a dynamical thing. This is the quantum dynamics that Frank described that was needed, necessary to complete the quantum formalism to a fully fledged theory. And the equation of motion for this matrix position or position matrix was the analogue of Newton's second law. So in one way,

Heisenberg was being very revolutionary, saying that positions are not conceptualizable as being in space, three-dimensional space. They're these matrices. But on the other hand, the equation of motion that these matrices obey is just the normal, expected, familiar, 200-year-old Newtonian equation of motion for evolution of position. Thank you. Harry Cliff, can we just develop this paper, how it came about and...

Is he talking about practicalities here or thought experiments? What's going on? Well, there's a lovely story actually around the kind of key insight that leads to this paper, which is Heisenberg is in Göttingen working with Max Born at the time, but he suffers from terrible hay fever.

And he's driven mad by it. So he goes to one place he knows where there aren't any trees, which is this island called Helgeland off the German coast in the North Sea. So he retreats out there, stays in this lodging house, essentially, and is alone with his thoughts and the wind and the sea and bits of rock. And it relieves his hay fever. And there's this lovely description of he's sort of in the middle of the night. He's been doing these calculations and he has the kind of key realisation that Faye's been...

been describing. And there's this lovely quote from him where he says, I think gives a sense of what it's like to make a breakthrough like this. He said, at first I was deeply alarmed. I had the feeling that I had gone beyond the surface of things and was beginning to see a strangely beautiful interior and felt dizzy. So there's this real moment, I think, it's quite romanticized in the history of science about this breakthrough.

that he has. And as Faye said, the kind of algebra that he discovers or that he finds applies to these quantum transitions, he doesn't actually recognise as matrix algebra to begin with. He has these strange rules about how you multiply these different, what they're called amplitudes together according to particular rules.

And it's when he shares his paper with his colleagues, Born and Jordan, that I think it's Born who is, you know, a senior, more senior academic in Göttingen, who sort of in the back of his mind thinks, I recognize this strange algebraic law. I learned about this years ago. And it's the way matrices, these grids of numbers multiply together.

So he's almost sort of stumbled upon this algebra and actually then he's discovered that the maths already exist. But it's very unfamiliar to physicists at the time. And I think physicists really struggle to get their head around Heisenberg's approach because it's so abstract. And he uses a mathematical language that at the time is really unfamiliar to people. And it's actually just a year later, another German physicist called Erwin Schrodinger, who comes up with a different theory.

approach to the same problem, which is based, rather than on these strange mathematical objects called matrices, on something much more familiar, which is a wave. So Schrodinger has this wave description of, say, an electron around an atom. And a wave is something that's intuitively much easier to understand for physicists. They're very used to dealing with the algebra and the science of waves. So actually...

It's later realised that really Schrodinger's wave picture and Heisenberg's matrix mechanics are actually two different mathematical ways of ultimately describing the same thing. But there's a period where Schrodinger's approach is really adopted much more enthusiastically by the community because it's familiar. And this really irks Heisenberg and it becomes actually quite a sort of

a bad tempered sort of debate between Schrodinger and Heisenberg as to which picture is the correct one. Who wins? Well, in the end, actually, I mean, so what Schrodinger tries to say is that you can think of the electron as a physical wave. So when it when it sort of goes into one of these states around the atom, it's a sort of physical thing that adopts this strange wave like structure.

And what Heisenberg and others eventually show is that actually this isn't right, that the wave isn't really a physical thing. And it is later reinterpreted, I think, by Born, who says that actually this is not a physical wave. It's a mathematical object. And what this wave describes is not...

the sort of the physical nature of the electron, but it tells you the probability of finding the electron at a particular place in space. So in some ways, in a sense, conceptually, it's not so different from Heisenberg. Heisenberg has this wave representing this information as a grid of numbers, essentially. Schrodinger equally has this wave, but it's not a physical object. It's a mathematical description of the electron. So nothing is observed. Is everything a thought experiment then?

Well, I mean, no, things are observed. So these spectral lines that Frank talks about, these are the key bits of evidence about what's going on in the quantum realm. So what you do see in experiments are these particular frequencies of light that are absorbed and emitted as electrons transition. But you never see the wave that Schrodinger describes. And also, you know, Heisenberg's description is sort of, in a way, not visualizable at all. So...

In some sense, you have to kind of give up on the idea of a mental picture of what's happening. And that's, I suppose, in some ways what's quite revolutionary about what Heisenberg is saying. He says you stick to what you can measure and you shouldn't concern yourselves with kind of an imagined picture of what's actually going on because it's only what you see in experiments that ultimately matters. Did previous theories in this area just fall away after this then? Did it displace, say, everything that Newton had said?

No, I mean, I think that there's sometimes a misunderstanding in the history of science that you have one picture of the world, there's a revolution and that overturns what was there before. But that's not really the way things happen. You kind of realise that actually there's a domain in which...

The old physics doesn't work, but it still works very well. So if you want to know about tennis balls going through the air, Newton's laws of motion are perfectly good for that. But in some ways, I suppose it's an extension of Newtonian mechanics and it now applies to the behaviour of things that are much smaller. When you zoom out, Newton's laws still work perfectly well, but they break down when you get down to the scale of atoms and molecules. I meant just to pick up on what Harry was saying there, that Newton's laws apply...

very, very well to things that are big and move around relatively slowly. By that, I mean slowly compared to the speed of light. And the two great revolutions of the early 20th century were that Einstein asked what happens if you go to very fast things and made the relativistic extension of Newton's laws. And now we've got the other extreme of very small things, which is the quantum extension of Newton's laws.

So Newton's laws are a limiting case of Einstein at slow speeds and Heisenberg at large scales. Can you sum up for listeners, he's talked of in the highest terms by you three and by other physicists at the time and since, what his breakthrough was, what he actually broke through and what was different after he'd done it in 1925?

One of the most remarkable things about his breakthrough was he was only 23 when he made it. I mean, that to me is one of the astonishing things. Harry just made the remark about Schrodinger. I'm not avoiding the question, but to put it in a bit of context, he came up with this set of matrices to describe the quantum world of the atom. It is pretty difficult to construct the matrices. And the fact that Schrodinger comes along a year later with this wave equation approach...

And the tools that you need mathematically to deal with that are called differential equations. And they're the things that all students have learned and are familiar with by the time you get to graduate school and meet these sort of ideas. So we get taught the Schrodinger wave approach. And actually, I think one tends to use that approach. There's only a few occasions I can think of where I actually use Heisenberg matrices.

And because the Schrodinger approach became so, not easy, but relatively speaking, convenient to use, that's why we tend to think of waves all the time. But that quickly gets you into these philosophical problems of waves in what and probabilities and does God play dice with the world and so on and so forth, which may be an artifact of the waves, which in Heisenberg's opinion, aren't really there anymore.

So that's avoiding your question slightly. So what is it that really has been done at this point? The equations of motion, the dynamics that apply to the micro world have been identified and you can now apply them to the micro world, which you could never do before.

And one of the first things which Heisenberg's approach discovers is that hydrogen, we talk of the hydrogen atom, the simplest thing, a single proton with a single electron whirling around the outside. But hydrogen tends to exist as a molecule of two hydrogen atoms together.

Two protons, each at atoms length apart, but sharing their two electrons, the electron swapping backwards and forwards, being exchanged between one hydrogen atom and the other. And Heisenberg's matrix approach turned out to have a very profound implication, which is this, that the electron is a lump of charge, but it also acts like a little magnet.

In the jargon we say it spins. It can spin up or spin down, like a North Pole up or a South Pole up. And this is the one place where Heisenberg's matrices really come to play, and one can illustrate them. A simple little column of just two numbers. If you think of a ground floor and a first floor, if the first floor is occupied, you put the 1 upstairs and the 0 downstairs. If the ground floor is occupied, the 1 goes downstairs and the 0 upstairs. Those are the two matrix systems

descriptions of an electron spinning up or down and the matrix approach of Heisenberg is perfect for this and he turns out to predict that there are two different forms of molecular hydrogen called ortho and para and his matrices predict that one of these should be three times more common than the other at room temperature.

And in 1929, these two forms are experimentally discovered and the abundance confirmed in line with what Heisenberg has predicted. And that is mentioned in the citation in his Nobel Prize by the Stockholm Nobel Academy. I think that that was the experimental proof.

that showed that this formalism that he'd created was able to predict things and explain things which had not previously been understood about something as fundamental as hydrogen.

Quickly then, people started applying these new techniques to electrons in all manner of stuff. Electrons in metals, electrons in insulators. Why do metals conduct? Why do insulators not conduct? These were questions you could not approach before. And suddenly, within the space of a few years, they were all falling into place thanks to this new quantum mechanics. And the final thing, I think, in 1928...

was that a Russian theorist called George Gamow applied quantum ideas to the atomic nucleus.

that one of the things that had been known since 1896 or so was that nuclei have a property called radioactivity. They emit this strange radiation, and one form is called alpha radioactivity. Gamow applied quantum mechanics to the atomic nucleus and explained how alpha radioactivity happens, previously something totally unexplained. Thank you. Fay, in what ways was his approach revolutionary?

It was both revolutionary, but also, I would say, completely embedded in its time. No breakthrough is made in isolation from everything else. Heisenberg was in constant communication with colleagues and embedded in his intellectual milieu. So these ideas of atomic states and transitions between states, they were already there.

Another aspect of his milieu was the movement in philosophy, which people call positivism or instrumentalism. And he would certainly have been aware of that, not least because that tradition is generally accepted to have had quite a lot of influence on Einstein in his development of special relativity. So he would have been very aware of those ideas that physics should deal only with observable quantities. So he was primed to accept

accept the strangeness of this new way of representing position. It was so embedded in people's consciousness that particles, bodies, every physical entity should have a position in space. It should have a position in space and move around in

But he was just ready to make the leap and say, no, we don't have to have such a picture. Harry, Harry Cliff, how did the uncertainty principle emerge then? So this is probably what Heisenberg is most associated with because it has his name attached to it. And it comes really from this matrix description of quantum mechanics and...

It comes ultimately mathematically from the way that matrices multiply with each other, which is different from ordinary numbers. If you take two ordinary numbers, say one and two, actually it's a bad example, but one and two is fine. One times two is two and two times one is also two. It doesn't matter which order you multiply them. You can switch them around and it's the same. With a matrix, that's not true.

So there are certain matrices that describe particular properties of an electron, for example. So you have a matrix that describes the position of the electron that Fay referred to. And also there's this corresponding quantity called the momentum, which is essentially related to how fast the electron is going, multiplied by its mass. And you have these two matrices. And...

The order that you multiply these matrices together matters. So if you can think of them in some ways as representing measuring either the position or the momentum of the electron. So it matters whether you measure the position first and then the momentum or the momentum first and then the position. And they give you different answers.

And from this mathematically, what that essentially, if you work through the consequence of this, you find that there is a limit to how well you can simultaneously know the position of a quantum particle and its momentum. And that is what the uncertainty principle states. What are the consequences of that, Frank? Profound in a word. That is how the universe is. I mean, as Harry said, there's a trade-off. You can...

If you know the position perfectly, you can't know anything about the momentum and vice versa. So there's a trade-off on what you can know on the average about both of them. I mean, I can give an example because people might be thinking, well, this is a bit odd. If you think of a wave on a pond and if I want to know the position, I just look at where the high spot on the ripple is.

But that tells me nothing at all about how fast the wave is moving. To get a measurement of its speed, I've got to watch some ripples pass me. And the more ripples that pass, the more precisely I will know the speed of that wave. But of course, the less I know about the position because there's been so many waves that have gone past and vice versa. If I want to measure the position precisely, I can't know anything at all about the speed. So that is an example that is familiar to

And now I'm getting into the area where I start sort of feeling I'm going in a whirlpool around some great black hole of ignorance or enlightenment. I can't be sure which. Waves are a very convenient model to understand why the uncertainty principle can apply to things. Is it the uncertainty principle that is fundamental and waves are a nice model that help us visualize it?

Or is it waves that are fundamental and the uncertainty principle is a consequence of that? Now, I'm in the first camp because I think that actually the moment you start inventing these waves, they're a very nice model and we think of them like that.

But the moment they start becoming too much reality, in quotes, you get into all of these horrible paradoxes about Schrodinger's cat and so forth, which is not for me. I mean, I'm out of the studio if we're going there. So that is the profound nature of it. Where it applies and what it matters...

Position and momentum are complementary. Energy and time is the other side of this. If you know at an instant where something is, you know nothing at all about its energy. If you know its energy precisely, you know nothing at all precisely about the time of the measurement.

And this surprisingly explains why CERN is so big. I mean, people often say, why do you need this huge accelerator device, 27 kilometers, to measure these things that are so small? Answer, blame Heisenberg. These things are so small, you need to have incredible precision in space to resolve them. And to get that precision, you have to have extremely high energy and vice versa.

There's a good joke to get some of this across maybe in a bit more easy, understandable way, which is, so Heisenberg is driving along in his motor car and he's stopped by a police officer who says, do you know how fast you were going, sir? He says, no, but I knew exactly where I was. So if you're a physicist, that's very funny. But I mean, I think one of the things we haven't really talked about, which I think is important about the uncertainty principle, is it says the thing that's really controversial about it is it makes the observer, the experimenter part of the system in a way. So it matters what you choose to measure in

determines what you will actually observe. So there's no longer this idea of an experiment as an objective thing that just looks at nature as it is. The choices you make in your observation determine the results you get. So if you choose to measure momentum or you choose to measure position, you will change the system fundamentally and change what you see.

And that is, I think, one of the most difficult ideas for people to accept when this is come up with in 1927. I think Fay alluded to this when he was saying about Heisenberg said nobody's seen these electrons in orbits. But he did a sort of thought experiment about what would you actually have to do to detect one of these electrons in an orbit? The answer is, well, you'd have to shine light on it and then the light would scatter back to you.

And of course, in the process, because an electron is such a tiny thing, the action of the light that went out hitting it has kicked it off somewhere else.

So you know where it was, but not where it is sort of thing. And this also perhaps gives an intuitive feeling for why it is that the uncertainty principle doesn't really concern us in our day-to-day affairs. It's absolutely the essence of the whole thing when you're down at the very small atomic scale where the little particles are so light and photons hit them and kick them all over the place. But by the time you get to macroscopic stuff like us...

the effects are so tiny, I can know precisely where Melvin is and I can know precisely that you're not moving at this moment because you're so wrapped by what is going on in the studio. But if I could somehow shrink you down to the size of the atom, I'd be able to know one of those but not both of them.

I was going to ask that. I'll turn to you, Farron. What value, I mean, this is a lumpenproletarian question, I hope you don't mind me asking it. What value does this have for most people? This discovery, people think we are better informed in order to do what? It's hard to overestimate the impact that quantum mechanics has had scientifically and technologically. It affects our daily lives. So from...

predictions of the abundances of the light elements produced in the first few minutes after the Big Bang through the standard model of particle physics that's tested and explored at CERN to the behaviour of semiconductor materials that are in the chips of all of our phones. So it has had

a huge impact on all of science, much technology that we all use. So you simply can't overestimate just how successful it has been. And yet, it's such an interesting situation whereby, I know I may drive Frank out of the studio in a moment, but I would claim that we cannot deduce, we cannot recover classical physics from quantum physics.

It is not possible to take quantum physics as Heisenberg set it out and from that deduce, recover, have classical physics, the physics that describes the behaviour of macroscopic objects, the things in this room,

from that quantum world, from the rules of quantum theory as Heisenberg laid them down, because he was very clear that the theory is empty unless there's an observer. If there's an observer observing the system, then the theory, the quantum mechanical dynamics and the rules of prediction give you predictions about the results of observations that the observer makes on the system.

If there's no observer external to the system, then you cannot make any predictions. People call this the Heisenberg cut. It's necessary. You have to divide the world, the whole world, into two pieces. One, the quantum system, to which the quantum dynamics applies. There are quantum states. There are these matrices that correspond to, I won't say describe, they correspond to positions of particles here.

And all of that takes place in this abstract mathematical space, which is elsewhere. Then the rest of the world on the other side of the Heisenberg cut is the classical world, the world of observers, of experiments, of apparatuses.

and we can make definite statements about the outcomes of the measurements that we make. And there's this mysterious and absolutely not set out in any axiomatic way interaction between the two, of course. One of the heuristics of quantum theory is that when you...

interact with when you measure, when you observe the quantum system, then your decision about what to observe and what to measure, how you set up the apparatus determines what the possible outcomes of your experiment are going to be. But the actual interaction is not described by the theory. My students all say, oh yeah, well, what's a measurement? And I say, right question, wrong place.

Let me teach you the rules of quantum mechanics as laid down by Heisenberg. Sorry, when you say wrong place, you mean they should go and ask that in the philosophy department and not in the physics department? No, no, no. I mean wrong place and time. I said, come and ask me later. We have to get through this material. Come and talk to me later.

So it's the question that springs to everyone's mind when you first learn it, because it's central. The concept of measurement is central. Observation is central. And without it, Heisenberg's rules simply do not work. They're just empty. They don't say anything.

And so we're left with this puzzle. It's fascinating, a fascinating situation for us all to be in as theorists. We have this phenomenally successful theory. Einstein called it our most successful physical theory. I don't deny that. Don't disagree.

But on the other hand, it leaves us without any picture at all of a quantum system as it is in space. OK, Frank, you want to... I'm a Luddite physicist. To me, this is all very interesting, but I remember a cartoon I saw many years ago of somebody in an elevator who looked washed out and somebody said...

That smithers. He was doing great and then he started worrying about quantum mechanics. Strangely, the rules, if you apply them, they make predictions. I mean, that is indeed the test for me. If your theory makes a prediction that can be tested, an experiment either confirms or denies, then you know what you're doing. I'm also amazed that, as you alluded to, this

This last six months, I've benefited from magnetic resonance imaging, positron emission tomography. They are things that the quantum world has led to as tools that we now use in the macro world. So without quantum mechanics, a lot of the things we're taking for granted today would never have been invented. Whatever the philosophy behind it, I don't know.

Unfortunately, we have a limited time. We don't have the five hours I really deeply like at this moment. I really would. I'm joking. It's absolutely fascinating. For somebody who gave up physics at the age of 14, or was asked to give up physics at the age of 14 in order to take up Latin, imagine that. Harry, I'm going to switch now. We're talking about theories. But what about the man? One of the things about the man is that the politics of the 1930s

affected him and his position with regard to Germany. Yeah, so Heisenberg lived through a very turbulent period in German history. So when he's a young man just going into university, Germany is coming out of the humiliation of the First World War. There are armed groups on the street. And Heisenberg, I think, is dismayed by what's happened to his country. He is a sort of patriotic German. But then as you get into the 30s, the rise of Nazism...

anti-Semitism becomes increasingly prevalent in the academic world. And there are certain physicists, German physicist Philip Leonard is one example, Johannes Stark, who are deeply opposed to what they see as Jewish physics. So this is the sort of ideas proposed by Einstein around relativity, but also by extension quantum theory as well.

So, Heisenberg's reaction, I think, to this at first is his view is that somehow physics should be separate from politics, that actually politics is beneath the dignity of a sort of an academic aristocrat, that this is a sort of essentially the ultimate ivory tower, that he shouldn't have to deal with this. And his reaction to what's going on around him is, I think, quite...

He doesn't come out of it sort of smelling of roses. He's not an enthusiastic supporter of the Nazis, although when they do come to power, he does express some sympathy with some of the things they're trying to do, a sort of national revival, because he wants Germany to sort of be on the up. But at the same time, he does spend a lot of effort trying to prevent the dismissal of his Jewish colleagues from their university positions.

and also to persuade his colleagues not to leave Germany. And it's clear that in the 30s, his key objective is really to preserve German physics, so that when the Nazis go, there will be still physics of high quality in Germany. And that's his primary focus. But as a result, he does accommodate to a large extent with the regime that he finds himself living under. How does this affect his reputation in the world of physics?

Well, it's interesting because Heisenberg actually comes under quite virulent attack by people like Stark. So I think it's in 1937, Stark is writing articles in Nazi publications attacking Heisenberg as a sort of

You know, he's not Jewish himself, but saying he's a sort of supporter of Jewish physics. And this leads to an SS investigation into Heisenberg. So he's actually put under investigation by the SS. He becomes very desperate. He's interrogated in Berlin in the SS headquarters. He ends up writing to Himmler directly pleading his case. Eventually, he's exonerated after quite a sort of traumatic investigation, at which point he is kind of keen to prove his usefulness.

to the regime. And this extends into the Second World War when he becomes involved in the German nuclear research as well. So I think it definitely harms his reputation. He's given many opportunities actually to leave Germany. So he's offered positions in America, for example, at Columbia University. And many of his colleagues are perplexed as to why he refuses to leave Germany, given the sort of pressures he's come under personally. I think a lot of his colleagues view him quite critically for not having taken a more courageous stand against

what was going on in his country at the time. Faye, what is your continuing impact? So at the moment I'm working on a project on quantum field theory...

So one of the things that I think we've alluded to already is that the principles of quantum mechanics, which were essentially discovered in 1925 by Heisenberg and then separately in a sort of different form by Schrödinger, those principles were very swiftly formalized and then it was realized that they could be applied to

to any physical system whatsoever, so long as the classical form of the theory obeyed Newton's laws. You could do this process which people call quantization. So you take the classical form of the theory, Newton's laws,

and you turn the handle almost, Heisenberg-Schrodinger handle, and you produce the quantum theory. And that this was so universal that there wasn't, I think people thought at the time, there's no limit to what we can apply this to. It's so universal we can apply it to any system at all. And one of the systems that people applied it to was field theory. So electromagnetism was a field theory.

the fields of Faraday and Maxwell. And so quantum field theory is a quantum theory that is completely in accord with those axioms that were essentially laid out by Heisenberg in 1925. So I'm doing a project on quantum field theory, and we say the word Heisenberg probably about 20 times a day. So there's the Heisenberg operators, there's the Heisenberg equation, there's the Heisenberg picture.

Although, on the other hand, my research area is quantum gravity. So I would like to understand how quantum matter can be compatible with our understanding of space-time as Einstein laid it out in General Relativity. Gravity does not fit...

into this paradigm. You cannot take general relativity, turn the Heisenberg-Schrodinger handle and produce a quantum theory for gravity that works. And the reason is that the theory of gravity that we have, our best theory of gravity, is a theory of space-time itself.

So in order for there to be a quantum theory of gravity, there has to be a quantum theory of space-time. So space-time itself must be part of the quantum system. And that raises this issue which I've mentioned, that in order for the Heisenberg-Schrodinger rules to apply, you need something outside the system to do the observing. But if your system is space-time itself...

then kind of by definition, there's nothing outside it because everything that happens happens in space and time. So how could you make that work? So the struggles in producing a theory of quantum gravity are as much conceptual as they are technical concepts.

And this idea of the necessity of there being an observer and hanging everything, all your meaning on the results of measurements and observations is actually a barrier now to making progress in quantum gravity, in my view. Finally, Frank, what Faye was just saying, the universe, why are we here at all?

I don't mean here today, I mean the whole thing she's saying. And it has been suggested semi-seriously or maybe even seriously that the universe's existence is itself an example of Heisenberg's uncertainty principle. The idea that you can overdraw the energy accounts by a small amount for a small amount of time so long as the product of the two is constrained by this quantum uncertainty.

And one of the surprising things is that the universe itself, because there's a lot of gravity around, when you're in a gravitational field, you have negative potential energy. There's a lot of positive energy around in all of our MC squared and so forth. It is possible that the sum total energy of the whole gravitational universe is nothing.

In which case, Heisenberg says you can borrow that nothing forever. And so the universe could be a quantum fluctuation satisfying Heisenberg's uncertainty principle. The problem, or a problem with that is, so where was that encoded?

Who or what encoded that principle that enabled a universe to erupt out of nothing with a total energy balance which Heisenberg, millennia, eons later, would formulate? Answers on a postcard.

Well, thank you all very much. That was exhilarating. Thanks, Frank. Frank Close, Faye Dauker and Harry Cliff and our studio engineer, Never Mysterian. Next week, uprising in Algeria in 1871 against the rule of France when that country was reeling from the parish commune and the loss of Alsace-Lorraine to the new Germany. That's a McCranley rebuilt. 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. That was terrific. I'm afraid I'm going to ask you to do some more. When you were asking about how the Heisenberg uncertainty principle gets used, I know that you're always loving these amazingly small things or huge numbers and the things that you keep totting around.

In particle physics all the time, this complementarity between energy uncertainty and time uncertainty is key. I mean, time uncertainty, most of the particles that we find are unstable. They live for 10 to the minus 24 seconds. That's the time it takes light to cross one-tenth the size of an atomic nucleus, that small amount of time. But Heisenberg tells us that if you try to measure the mass of that particle...

its MC squared, its energy, will be uncertain because of the

limited time. And we can measure that uncertainty in energy, and that's the way that we do it. At CERN, they discovered the Z boson years ago by tuning the beams to start making it, and the beams were showing nothing. Then gradually they built up to a peak and then down the other side, so there was a spread in the energy. And from Heisenberg, that spread in energy was interpreted as the lifetime of the particle. So we can measure times of that

minute amount by using Heisenberg and I think it's fair to say those are the smallest measures of time that we actually do measure in practice and it's using Heisenberg to do it. Harry?

I mean, one of the things we didn't talk about, I think, is I don't know if we emphasised enough how revolutionary the new quantum mechanics was, because, you know, there's the sort of famous debates between Bohr and Einstein and also Einstein and Heisenberg. So, I mean, Einstein really reacted very strongly against Heisenberg's sort of really pragmatic. We only worry about what you can measure.

And, you know, Einstein really wanted to hang on to this idea of a mental picture of what was going on, which Heisenberg sort of approached tonight. But also this fact of the universe being probabilistic and not being deterministic. I mean, we did we did talk about it, I think, but maybe that sort of should be emphasized a bit and just how radical that was. It's a complete break with, you know, how you think about the world in the 19th century, where if you know the positions of all the atoms in this room and how fast they're going, you can predict things.

arbitrarily far in the future what's going to happen and quantum mechanics says no you're not allowed to know that you can only say what the probability of certain outcomes is in the future who says that's the only thing you can say well i mean that's what that's the sort of fundamental to quantum mechanics so now you know when you if even if you know everything you can know about a system because of the uncertainty principle because of quantum mechanic the laws of quantum mechanics you

All you can say from this position in time is that there are certain possible outcomes and we can assign probabilities to those outcomes, but we can't say which outcome we're going to arrive at. And that is the sort of, I suppose, the philosophical, the really big change that comes in with quantum mechanics. To know what's going to happen to one particle in the future of the universe, you've got to know two things precisely, both where it is now and how fast it is moving now.

And Heisenberg says you can't know both of those. And so that's the uncertainty that you're bringing in. So in principle... Does he say you can't know both of those together or you can't know both of those at all? You can't know both of them to perfect precision. There's a trade-off. And the amount of trade-off is controlled by the size of the discrete quantum. And in fact, if you know, say, the...

the position of an electron exactly, you know nothing about its momentum at all. So you lose all information about how fast it's going and correspondingly the other way around. So if you know exactly how fast it's going, you have no idea where it is.

Well, I think Frank sort of talked about this, this idea of a wave. So if you can, a wave, imagine a wave on the surface of a pond that goes on forever, that mathematically has a well-defined momentum. So you can express that as a pure state of momentum effect. So you know the momentum of that wave perfectly, but a wave that's infinite in extent has no position. It's everywhere. So you can't say where it is. Equally, if you want to localize that wave,

One of the ways you can do it is by adding up lots of different waves with different frequencies in such a way that the peaks and troughs add up and cancel out that you get, and you end up with a spike at one location. So you've got now a location, but that's made up of a huge number of different waves with different frequencies, and you don't know what the momentum is anymore. So that's a sort of, I don't know how intuitive that is, but that's one way of thinking about what's going on. The listeners invite them now, let's draw a wave on a piece of paper. It's a series of dots. So please put down the first dot.

And what's the wavelength of that wave? No idea at all. Put some more dots in and I can now begin to get an idea of what the wavelength is. But you spread those dots over a range. So there's a trade-off between position and wavelength. That's much better than what I said, actually. What you said is the mathematical realisation of that. It's called Fourier analysis. It's got a long history back into the centuries. Wow.

What Harry and Frank are describing is indeed the mathematical reasons for the theorem which we call the uncertainty principle, the uncertainty relation principle.

But what's really revolutionary about it is that it doesn't refer to the position or the momentum of the particle in itself, because that you have to deny. So what's really revolutionary is that you say it doesn't have a position, it doesn't have a momentum, and this is just an uncertainty which expresses itself. Experimentally, it happens.

It takes the form of statistical uncertainty about sequences of measurements. You do many, many repeated measurements of the same thing over and over on an identically prepared quantum system. And the uncertainty relation relates to the statistics of those measurements. It doesn't say, actually, in the axiomatic formulation, it doesn't say anything about...

about the position or the momentum of the particle. That's what's so fascinating about the 1927 paper about the uncertainty relational, uncertainty principle. Heisenberg is having this debate with himself in print on the page. So he's debating Schrodinger. So as Harry said, there was this...

this discussion, debate, argument between Heisenberg and Schrodinger at the time. And you can see that in the 1927 paper. He's responding to Schrodinger in print in the paper, but he's also responding and debating with himself. And he's trying to hold true to this idea that you should not ever talk about particles having a position and a momentum. But then he uses that picture to describe this so-called Heisenberg microscope argument

whereby you imagine that the particle does have a position, you're trying to locate it by shining light on it, blah, blah. But that whole Heisenberg microscope argument relies on you having this picture of it having a position in momentum, which you're supposed to deny. So it's simply, he's struggling, and you can see it, it's totally fascinating, struggling with himself about...

wanting not to talk about position and momentum and space, but then needing to talk about position and momentum and space in order to give people a heuristic way of understanding the uncertainty relation. I think that's really what I was alluding to when we had this debate during the programme when I said I'm a Luddite physicist, that if I start asking myself questions

trying to understand what's really going on there, I end up in a fog. If I use the rules that have been developed, they work. And in that sense, I'm in the latter camp. Like an engineer, I will use the rules and let others worry about why they are. And I think also it was interesting what you said about Heisenberg's debate, the gap between the micro world and the Heisenberg cut.

Whether you look at Heisenberg or Schrodinger and waves and things, you end up, there's a problem. Is the Heisenberg cut or it is the Schrodinger's cat? Whichever way you look at it, there's this dichotomy. How do you get from the quantum world to the macro world? So I take what you say perfectly, Frank, and I, in your lab, I completely agree that as a practical matter,

the rules of quantum theory work for making predictions about the results of your experiment. But what's practical depends on what you're trying to do. So if you're trying to find a theory of quantum gravity in which the whole universe is quantum, then as a practical matter...

the rules of quantum theory as laid down by Heisenberg will not work. They cannot because there's no external observer. So you have to, you're forced as a practical matter to

If you can think of trying to find a theory of quantum gravity as a practical matter, as a practical matter, as a working scientist, you have to go beyond it. I'm an experimental physicist. I'm feeling slightly out of my depth here, to be honest. But I mean, one thing I was going to ask Faye about this, actually. So with quantum gravity, as I understand it, my very limited understanding, you're talking about effects that only really manifest themselves at extremely high energies, extremely short distances in terms of... So as the question is,

in terms of the practical things you would observe in an experiment, what is a theory of quantum gravity actually trying to solve? Because at the moment, as far as I... As I said, you're much more expert than me. But as far as I know, there aren't really any experimental inconsistencies with the two theories we have for the universe at the moment, quantum mechanics and general relativity. They cover everything we've ever seen perfectly well. And it's more a sort of... We're worrying about things that might happen and in very extreme conditions that we haven't yet observed. So, I mean...

I suppose if we're going to take that practical approach that Frank takes to quantum gravity, what are the problems? Why do we need such a theory? Is it more philosophical and kind of we would like a quantum theory of gravity because we think...

these two things should be reconciled. But what's the actual practical problem we're trying to address? I'm on Fay's side here. This is exactly analogous to what Einstein was worrying about in 1900, about what happens if he lived in the light wave. And by doing those thought experiments, found the contradictions and moved forward. And likewise, the questions about imagining what happens if you do an experiment where you're making quantum black holes fluctuate out,

At least you can imagine that. Although we can't do it in the laboratory, we can imagine that and we can show that quantum theory as at present formulated and generativity cannot live together and something has to give. Is that a fair statement? Yes, absolutely. But I think there's more than just a...

an intellectual problem there of trying to bring together two theories which at the moment are in contradiction in certain extreme regimes. So for example, what people call the standard model of cosmology today is a very simple model, but there are parameters in the model that thus far are just phenomenological parameters. You just choose them to fit the data. And

Two things about those parameters. One is that there's starting to be real tension between our observations and the standard model. So there's something called the Hubble tension, which is measurements of the Hubble constant or Hubble parameter today.

from late-time measurements of observations of, for example, supernovae and early-time measurements of, for example, the cosmic microwave background radiation. So those two measurements of this Hubble parameter today are in tension. And some people, increasing number of people, believe that that tension is irreversible.

It's a real tension. It's something which we can now say, yes, there's definitely a discrepancy between the model and our observation. So that's the first thing. The second thing is some of those parameters are very strange. So, for example, at the Big Bang, the hot, dense state that the universe began in, we believe, space is very, very, very, very, very, very, very flat, right?

You would expect it on dimensional grounds to be very curved, that everything is of the scale of what people call the Planck scale, that there is curvature on the Planck scale in time, but in space, it's super, super, super flat. As far as we know, it's consistent with being perfectly flat.

but there's a bound on how much curvature there can be in space. It's very strange. And that is what people call a fine-tuning problem. Why should it be so flat then? So those initial conditions of the universe, so there's the dynamics of the universe, we believe it's general relativity and other classical theories, but the initial conditions are unexplained. Why is the world, the universe, the way it is? Why did the cosmos start out the way it did?

And we expect, we believe, we hope that a theory of quantum gravity would tell us why the universe started out the way it did, because in some sense it would tell us what happened before the Big Bang. So what led up to the Big Bang? That would be the deep quantum regime in which there's no classical space-time at all. We would have the full quantum theory of space-time, which probably looks like nothing that we have now.

and that would then give us those initial conditions. So it is a scientific problem today, not just an intellectual exercise that may bear fruit in the future. The fact that we can ask such questions, actually, is the result of the things that Heisenberg did and have been developed from that. I mean, the fact that such questions can be asked and answered

tackled scientifically today are a legacy of the things that Heisenberg did in 1925 and grew from it. And also, actually, moving away from science into technology, the big breakthroughs people are expecting technologically, a lot of them are quantum-related, so quantum computing, which has become...

you know, increasingly a kind of growth area. Like a lot of my PhD students who work in experimental physics are now going off to, one of my old students is now writing software for quantum computers as his job. And this has become an area that's, you know, potentially going to have revolutionary impacts on the way we live, particularly coupled with AI and other developments. You have quantum sensing. So, you know, the future, I think, is going to be quantum as well. So the legacy of Heisenberg isn't just quantum.

It's also now, well, it has had a huge technological impact already, but it's going to continue to do so in the future as well. Thank you very, very much. On time, here comes our producer, Simon. In Our Time with Melvyn Bragg is produced by Simon Tillotson.

Hello, I'm Greg Jenner. I'm the host of You're Dead to Me on BBC Sounds. We are the comedy show that takes history seriously. And we are back for a seventh series where, as ever, I'm joined by brilliant comedians and historians to discuss global history. And we're doing Catherine the Great of Russia with David Mitchell, the history of Kung Fu with Phil Wang. We're doing the Bloomsbury Group for our 100th episode with Susie Ruffell. And we're finishing with a Mozart spectacular with the BBC Concert Orchestra. So that's series seven of You're Dead to Me, plus our back catalogue. Listen and subscribe on BBC Sounds.

Yoga is more than just exercise. It's the spiritual practice that millions swear by.

And in 2017, Miranda, a university tutor from London, joins a yoga school that promises profound transformation. It felt a really safe and welcoming space. After the yoga classes, I felt amazing. But soon, that calm, welcoming atmosphere leads to something far darker, a journey that leads to allegations of grooming, trafficking and exploitation across international borders.

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You just get sucked in so gradually.

And it's done so skillfully that you don't realize. And it's like this, the secret that's there. I wanted to believe that, you know, that...

Whatever they were doing, even if it seemed gross to me, was for some spiritual reason that I couldn't yet understand. Revealing the hidden secrets of a global yoga network. I feel that I have no other choice. The only thing I can do is to speak about this and to put my reputation and everything else on the line. I want truth and justice.

And for other people to not be hurt, for things to be different in the future. To bring it into the light and almost alchemise some of that evil stuff that went on and take back the power. World of Secrets, Season 6, The Bad Guru. Listen wherever you get your podcasts.