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The Laws of Levitation

Writer's picture: Mishkat BhattacharyaMishkat Bhattacharya

Levitation may be defined as the state of countering gravity without making physical contact with the surroundings. It is a phenomenon which has fascinated humankind since ancient times. The literature of every civilization is sprinkled with levitation stories: the flying island of Laputa in Gulliver's Travels, the ascending moon goddess Chang-O in Chinese literature, and the legend of Trishanku, suspended between heaven and earth, from India.


But - in my opinion - the scientific story of levitation is equally fascinating. It is crucial for studies of fundamentally interesting systems (superfluids, anti-matter, Bose-Einstein condensates). It is also important for established applications (maglev, GPS) as well as emerging ones (quantum computing, nuclear fusion). And of course, it provides loads of fun (involving toys, Mobius strips, frogs, and various objets d'art).


Levitation science has played a central role in my career as physicist, and I would like to share some aspects of it in this post .


The Main Idea


The keystone to the physics of levitation is Earnshaw's theorem. In modern form, the theorem says no static electric fields can enforce stable equilibrium for a system of charged particles. Similar constraints apply to magnetic fields and magnets, and for gravitational fields and massive bodies. Practically all schemes for realizing levitation need to work around Earnshaw's theorem. Here are a few:


Levitating charged particles


One way to get around Earnshaw's theorem for charged particles - realizing static is a key word in its statement - is to use electric fields that change with time. The basic idea can be understood using a ball and a mechanical saddle. If the saddle is static, the ball escapes; if the saddle is rotated (fast enough, but not too fast!), the ball can be trapped. You may wonder why a bowl is simply not used instead of the saddle in the video - Earnshaw's theorem does not allow 'a bowl' for fields (i.e. it forbids the existence of a stable minimum in three-dimensional space - motion along at least one direction has to be unstable, in this case the direction in which the ball falls off the saddle).


The same idea can be used to levitate charged particles using time-varying electric fields. This work brought Nobel Prizes to Wolfgang Paul and Hans Dehmelt and later to David Wineland, for trapping ions. Paul traps - named after guess who - can even be made at home. Trapped ions provide one of the two major platforms for quantum computing (the other is superconducting circuits) - check out IonQ in case you feel like buying a trapped ion quantum computer!


Levitating neutral particles


A particle can be electrically neutral and still be levitated, if it is magnetic. But you can never get one magnet to levitate another in a static way - either using the repulsion of like poles or the attraction between unlike poles. Try it - in the end one magnet will flip over and get stuck to the other one!


However, if we rotate one of the magnets, levitation can happen, as realized in the ingenious Levitron toy. The same principle can be used to levitate and study Bose-Einstein condensates with magnetic atoms and neutrons. Nobel prizes were awarded for related work in 1997 and 2001.


Levitating with Light


Laser light consists of electric and magnetic waves, both of them varying in time. Should we expect levitation to occur in this case? I hope I have not made the conclusion sound trivial, because Art Ashkin was awarded part of the Nobel physics prize in 2018 for inventing the 'optical tweezer', which can levitate nanoparticles, molecules, and atoms using laser light. The mechanism of levitation is subtle, but simple enough to be implemented with a laser, a lens and a sharpie. Tell me, even if you are an expert, that it is not amazing to see the levitated particle being moved around by the laser!


With these few examples, I hope I have convinced you that levitation science is like a playground littered with toys. If you are interested in a more detailed exposition, here's a 2011 book on the science of levitation that in my opinion needs to be updated. What's next in this field of physics? Well, it would be nice to have a cheap and easy way to achieve personal levitation - maybe a simplified version of this.





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