Michael Berry’s Press release, Thursday 5 October 2000

IgNobel Prize 2000

Michael Berry, Physics Department, Bristol University (prize shared with Andrey Geim, Nijmegen University)

Levitation without Meditation

The flying frog was Andrey Geim’s experiment. I was told about it after giving a lecture on the physics of the levitron – a toy in which a magnetized spinning-top floats above a magnetized base. It seemed that the flying frog and the floating top ought to depend on similar physical principles, so I got in touch with Andrey. Then we worked together, to extend to the frog the explanation I had previously found for the levitron.

It is surprising at first to see the frog and the top suspended in midair, in apparent defiance of gravity. They are supported by the force of magnetism. For the frog, the force comes from an electromagnet (coil of wire in which a current is flowing); for the top, the source is a magnetized metal slab. These powerful magnets push upwards on the frog and the top, because they are magnets too (weak ones). The magnetic force exactly balances gravity, so the top and the frog are in equilibrium and can float – there is no net force on them. A slight difference is that the top is intrinsically magnetized – it is a permanent magnet – while the frog is intrinsically non-magnetic but becomes magnetized by the field of the electromagnet – this is ‘induced diamagnetism’. Most substances are diamagnetic, and Andrey was able to levitate a variety of objects, including drops of water and hazelnuts.

Magnetic levitation is not antigravity – gravity is not eliminated by the magnetic force, but counterbalanced by it. When you are standing, thedownward force of gravity is balanced by an upward force on the soles of your feet from the atoms in the ground, that stops you falling to the centre of the earth. But the force on your feet is a short-range force, so it only acts when your feet touch the ground. On the other hand, magnetism is a long- range force (like gravity), so the top and the frog can be suspended without touching anything.

(‘Touching’ is relative: on the finest scale, atoms are mostly empty space. Those short-range forces between the ground and your feet, acting over nanometres, are a consequence of electrostatics and quantum mechanics – so standing is a kind of ‘nanolevitation’.)

The magnetic field that holds up the frog is a few times stronger than the fields used medically, in magnetic resonance imaging. In principle, a person could be magnetically levitated too – like frogs, we are mostly water. The field would not have to be stronger, but would have to fill the much larger volume of a person, and that has not been achieved yet. I have no reason to believe such levitation would be a harmful or painful experience, but of course nobody can be sure of this. Nevertheless, I would enthusiastically volunteer to be the first levitatee.

To be levitated in this way could be an interesting experience. When we are standing, the force that holds us up acts only on our feet, and we feel the upward push. But with magnetic levitation the gravity-compensating force is approximately uniform over the whole body, like gravity itself, so magnetic levitation would be more like the weightlessness experienced by astronauts in space. But there is a difference: the diamagnetism of the body is not quite uniform – tissues, bone, blood, etc. have different magnetic properties – so we would feel slight pullings and pushes over the body. If the magnetic force on flesh is greater than that on bone, it would be as though we were held up by our flesh, with our bones hanging down – a bizarre reversal of the usual situation, and possibly the basis for an (expensive) type of face-lift. I know no other experience to compare this with, and so have no way to anticipate what it would feel like.

The tricky part of the physics is to understand why the equilibrium of the top and the frog is stable – that is, why the objects remain suspended. Most physicists would – mistakenly – expect the top and the frog to slip sideways out of the field, and fall (an analogy is the instability of a pencil balancing on its point). This wrong expectation is based on a theorem proved by Samuel Earnshaw in 1842: no stationary object can be held stably by magentism and gravity alone.

But the flotation is stable, notwithstanding Earnshaw’s theorem, because the top and the frog are not stationary. For the top this is obvious, because it is spinning – as it must be to prevent it from overturning and being attracted, rather than repelled, by the magnetized slab. In the case of the frog, the counterpart of spin is the circulation of electrons in the creature’s atoms. These are small effects, but they mean that Earnshaw’s theorem does not strictly apply, and this opens the possibility that the equlibrium could be stable.

Detailed calculations (involving the precise pattern of the magnetic field) show that there are very small regions – just a few millimetres in extent – where the frog and the top can be stable. The trick is to get the forces to balance in these regions – if you get it wrong, the top and frog will fall. Getting the balance right involves fine adjustments: of the strength of the magnetic field that holds up the frog, and of the weight of the top.

The theory of this sort of magnetic levitation was anticipated by other people. In 1960, Vladimirskii gave what amounts to the theory of the levitated top, but the spinning magnets he was thinking of were subatomic particles such as neutrons. And lectures given by Lord Kelvin in the 1850s give a strong hint that he had worked out the theory underlying the frog’s levitation – but he thought diamagentism was so weak that magnetic fields large enough to cause levitation could never be achieved.

Both Andrey and I spend most of our time on other physics. In his case this is the magnetism of solids; for me it is quantum theory and optics – see my home page:

More details can be found in the following papers:

Berry, M V, 1996, ‘Levitron physics’ Nontechnical account, issued as a leafletboxed with some levitrons

Berry, M V, 1996, ‘The LevitronTM: an adiabatic trap for spins’ Proc.Roy.Soc.Lond. A452, 1207 – 1220,.

Berry, M V and Geim, A K, 1997, ‘Of flying frogs and levitrons’ Eur.J.Phys 18, 307-313.

Michael Berry, Bristol, October 2000

Joint Press release by Michael Berry and Andrey Geim:

The 2000 Ig Nobel Prize in Physics

shared by Andrey Geim and Michael Berry

The Physics of Flying Frogs

We are pleased to accept the Ig prize because we have always considered it a duty to make physics more understandable and bring it closer to nonscientists. We think the prize acknowledges our contribution in this direction.

Although some people tend to judge the quality of science by the seriousness of researchers doing it, there are lots of examples where good science has been fun – and science does not have to be boring to be good. The original idea of the founders of the Ig prize was exactly to support the above statement and, in the last years, Ig Nobel nominations have shown a clear tendency to follow this line. By accepting the Ig prize, we are supporting this tendency. We are glad to be associated with previous winners such as Alan Sokal and Len Fisher.

Our story is amusing on the surface, but also contains some unappreciated knowledge about magnetism. A careful observer usually finds this out very quickly. The flying frog aroused interest in magnetism in very different people – scientists and nonscientists – and their reaction was always enthusiastic. Therefore, we want to accept this prize also on behalf of the hundreds who wrote to us with their ideas and asking for details of themagnet setup. The enquiries came from engineers who wanted to use levitation for everything from waste recycling and materials processing to levitating sports shoes and jewellery in shop windows; from our physicist colleagues, some of whom admitted that after learning about the frog they finally understood some of their old results or artefacts; from chemists and biologists who did not want to wait for a space shuttle and realized they could do microgravity experiments in a magnet; from servicemen to pensioners and from prisoners to priests who wrote that they had no any science education but still wanted to learn about the magic of magnetism and use it. Sometimes, their ideas were bright and unexpected, sometimes goofy, sometimes ridiculous or even mad but always creative.

We want to thank all those schoolteachers and academics who asked us for the picture of the flying frog to teach magnetism in their classes. Even more rewarding were letters from children all over the world who asked for advice about school science projects they wanted to design for magnetic levitation or who just wanted to be sent a big magnet or who wrote “I am 9 years old and want to become a scientist”.

Levitation has been our scientific hobby for the last few years. It consumed a lot of our energy and required long working hours, especially to answer all those enquiries. Even so, we have never regretted this episode, and regard our efforts as vindicated by the public interest they have aroused.

Let there be more science with a smile!

Andrey Geim, Nijmegen, Michael Berry, Bristol, October 2000

How I Ended Up Levitating Frogs

Andrey Geim (University of Nijmegen, The Netherlands)

During the last century, magnetic fields proved to be a valuable scientific tool, which brought a wealth of new knowledge. [As a quick reference, let me mention the Nobel prizes in Physics of 1985 and 1998 given for the Quantum and Fractional Quantum Hall Effects. These discoveries would be impossible without high magnetic fields.] In the High Field Magnet Laboratory in Nijmegen, we have some of the most powerful magnets in the world and a significant part of our research here is concentrated around their use for studying various materials, trying to understand their properties and find new phenomena.

There is however one “but” regarding high magnetic fields: the very majority of phenomena studied in high fields also require the use of temperatures close to absolute zero (-273 C). It is commonly believed – and proven by time – that practically all high-field effects disappear under ambient conditions. For research in high fields, people routinely use special cryostats, which allow working at very low (liquid helium) temperatures. Unfortunately, it is not only a tedious procedure to prepare a low-temperature experiment but, more importantly, the temperature constraints create a barrier between this research and its potential applications.

My own research area – called mesoscopic physics or nanophysics – concerns studies of various small systems whose size is typically below one micrometer. The use of low temperatures is routine in this research. For many years, time after time I continued asking myself the same simple question: are there high-field phenomena similar to those found at low temperatures but which – despite the common belief – persist up to room temperature? Probably many other physicists wondered about this before, but my competitive advantage was the direct access to world-strongest magnetic fields (up to 30 Tesla). In 1996, I made yet another attempt in trying to answer this question in an experiment.

A somewhat obvious candidate to start with was water, one of the most pervasive substances on Earth. My interest in magnetic properties of water was further stimulated by a scientific paper describing a mysterious “Moses effect”: Japanese physicists discovered that water in a basin splits into two parts making a dry valley in the middle, when the basin is placed inside a strong magnetic field. The reason for the provocative title was clearly explained in the abstract but no attempt was made to explain the origin of the Moses effect. At that time, my colleagues and I decided that it was a hoax. Still, I wanted to try a high-field experiment with water, although nobody expected that anything marginally interesting could happen with water even in highest magnetic fields.

Just at that time, my former PhD student Dr Humberto Carmona came for a visit from the University of Nottingham (UK) where he worked as a postdoctoral researcher for Professor Peter Main. Together with Humberto and Professor Jan Kees Maan (Nijmegen), we gave the Moses effect a first try, simply pouring water into a vertical 20 Tesla magnet. To our surprise, the water did not splash on the floor as everyone expected but stuck inside the magnet, when the field was on. It took us ten minutes of calculations to understand that the reason for this intriguing observation (as well as for the Moses effect) was feeble magnetism called diamagnetism.

Diamagnetism is a universal property of all materials, which arises due to changes introduced by magnetic field in the motion of electrons around nuclei. Forces associated with diamagnetism are so weak that it is never on people’ minds. Such things as water or, say, a frog or an apple are – certainly in public’s perception – completely nonmagnetic. Even scientists routinely working with strongest magnetic fields perceive them as virtually nonmagnetic. The magnetism of water is a billion times weaker than, say, of a paper clip made from iron. One billion (1,000,000,000) is such a large number that, for a scientists, it is hard to accept that a magnetic field of 10 Tesla – which is only 100 times stronger than the field of a fridge magnet – is strong enough to lift “nonmagnetic” substances. It does require to be confronted with such counter-intuitive observations as the flying frog to appreciate the strength of diamagnetism and … never forget about it afterwards.

When next day we wanted to share our new experiences about levitating water – as well as many other unlikely objects such as pieces of wood, plastic, cheese, pizza, etc. – with colleagues and students in the department, everyone took it for a joke. Of course, they all knew about diamagnetism but thought it was so negligible that it could be seen only in very elaborate experiments and, certainly, could not cancel the force of gravity. However, seeing is believing: For the whole of the following week we were busy doing levitation demonstrations to a continuous stream of visitors.

During that week, it had become obvious to us that the magnetic levitation of “nonmagnetic” things excites genuine interest, and people simply love this new scientific demonstration of diamagnetism. Furthermore, we learned that we were not the first to discover diamagnetic levitation. In 1991, two French physicists from Grenoble (Eric Beaugnon and Robert Tournier) published a report in Nature about diamagnetic levitation of several organic substances and graphite. Somewhat later, we found out that the French discovery was also a rediscovery. In 1939, Werner Braunbeck already levitated small beads of bismuth and graphite (these materials exhibit strongest diamagnetism). These levitation reports, however, remained largely unknown even among the very narrow circle of specialists. For example, we met people working in the same building as the French group who first learned about the levitation from us. This may be hard to believe but, unfortunately, it is a rather common experience in our era of extremely specialised science.

With this in mind, we decided that it was sort of our public duty to change the reigning perception about diamagnetism and try to make the levitation common knowledge. Such a task, rather unusual for physicists, required not only formulas, graphics and scientific explanations – what scientists normally do – but finding a clear symbol for the effect. After many unsuccessful attempts, we came to the frog, which turned out to be a lucky choice.

To our surprise, even with the flying frog at hand, it was not easy to persuade people – and especially physicists – in the reality of diamagnetic levitation: on first seeing photographs and movies of flying water and frogs, many of them thought they were a joke, despite the accompanying explanations. For example, when the photograph of a levitating frog first appeared in April’s issue of Physics World in 1997, many colleagues congratulated us with a funny April fool’s joke. However, pictures and movies of the flying frog have gradually helped to spread the knowledge, and the media played a crucial role in this.

Applying the strongest magnetic fields possible is not enough to make a frog fly. In our experience, it was very easy to make water stick in a magnet but very hard to make a water ball or a frog to actually hover in mid-air. In fact, there is another crucial element in the physics of flying frogs, which allows them to fly rather than just being lifted. Indeed, everyone has seen a piece of iron attracted to a fridge magnet but no one saw the iron hovering in air. I entirely ignored this point until it was explained to me by Michael Berry, who is one of today’s leading theorists studying mathematical quantum physics. His theory of flying frogs explains why we needed to adjust magnetic fields with an accuracy of a few percent to levitate things, and why “non-magnetic” frogs can be levitated but a strongly magnetic paper clip cannot.

The subtlety and beauty of the physics behind the free magnetic flight of “non-magnetic” things, which Michael explained, gave the flying frog another dimension, appealing to many scientists in the same manner as a good game of chess causes admiration of masters. An American colleague told me that he used the picture of flying frog in his classes asking first-year students to explain why the frog could fly. The right answer is “everything is diamagnetic”. A couple of years later, the same students following a more advanced course in physics had to encounter exactly the same question but now they needed to explain how the frogs could fly while magnetic iron cannot. In a story Levitation without Meditation, Michael explains how.

All this happened four year ago but the story drags on. In the ensuing years, I have spent uncountable number of hours sending photographs on requests of academics, schoolteachers and journalists; helping visitors from various countries and disciplines to use Nijmegen’s magnets for their experiments to mimic low-gravity conditions; replying to pupils who wanted to use levitation for their school science projects; answering an infinite number of enquiries from engineers who wanted to develop new technologies based on levitation; as well as declining participation in numerous patents for supposedly new means of transportation, medical cure, etc. and not replying to claimants of new theories of Big Bang, UFO, the Universe, God, etc.

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