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Whenever we describe the position of an object, we actually mean the position relative to a frame of reference such as a wall, a table, the sun, etc. We are trying to understand the consequences of treating the reference frame as a quantum mechanical object itself. This has already been shown to lead to stronger conservation laws – valid in individual cases – and is thought to be an essential feature of quantum gravity. Carolina Moreira Ferrera, Ismael L. Paiva, Sandu Popescu and I introduced a new concept, in our paper networks of reference frames, where one frame is relative to another and so on, and showed that the way conservation laws work in such cases is somewhat paradoxical. This makes us rethink the nature of conserved quantities, and the way we describe the physical world.

In Quantum Mechanics, a cylinder can simultaneously rotate clockwise and anti-clockwise at the same time. This phenomenon, called superposition, is crucial for paradoxes like Schrödinger’s cat, and applications such as Quantum Computing. If we measure which way the cylinder rotates, we will find it to be clockwise or anti-clockwise. This gives us a paradox, as there is a law in physics which states that angular momentum (rotational mass * rotational speed) should be conserved. e.g. if the cylinder rotates clockwise, it shouldn’t flip to rotating anti-clockwise unless something physically stops it and sends it spinning the other way.

This paradox, involving the randomness at the heart of quantum mechanics, has troubled physicists since the dawn of quantum mechanics. Several solutions have been presented. However we have written a new paper which, we believe, solves the paradox. The change in angular momentum of the cylinder when it is measured is perfectly offset by a change in the device which prepared the rotating superposition in the first place.

This solution, inspired by a paper by Aharonov, Popescu and Rohrlich, says that this preparation device is also the frame of reference for the angle of rotation of the cylinder. Without such a frame, we would not be able to make the superposition of clockwise and anti-clockwise rotation in the first place.

Not only that, but we also show that the preparation can be arranged so that the preparation device is a finite object. In principle we can perform a laboratory experiment to test this, i.e. to show that the total angular momentum of the system and preparation device is conserved.

We can, we believe, rewrite the conservation laws in quantum mechanics, which so far only talked about conservation of the distribution over many repeated experiments of e.g. angular momentum. Now we say conservation applies for each individual outcome. We do have some remaining work to prove this holds in all cases: so far we only dealt with angular momentum on a circle. Pursuing this solution to the end should be fun, and lead to a better understanding of randomness, frames of reference, and conservation laws in physics.