If the real world, at its base, is quantum, then should we not think with quantum logic?
Shahn Majid discusses how the notion of quantum symmetry coming out of modern ideas on space and time could provide clues to the workings of a truly quantum computer.
Have you ever sat through a really boring flow chart presentation and to pass the time found yourself wondering the following: See the way that flow chart arrow crosses that other flow chart arrow:
Does it matter whether the arrow ‘passes under’ the other arrow or ‘jumps over’ it?
If you are an engineer you could ponder the same question for a schematic for the wiring of a computer. In fact you could ponder the question when actually building a computer: does it matter if this wire connecting to that chip jumps over or under this other wire? If you thought it did matter, you would have discovered quantum computers as well as quantum symmetry!
Let me start with the symmetry. Truth, symmetry, beauty! The cornerstones of mathematics, some would argue of the very concept of knowledge. Surely, nothing could be deeper or more self-evident than the notion of symmetry — of finding patterns. But what if our usual conception of symmetry was not quite right? As scientists we should not be afraid to question even the most basic of assumptions. After all, Nature does not know or care what maths is in maths books, and maybe Nature is just a lot more imaginative than anything we have so far thought of.
Well, I do think that the usual notion of symmetry is not quite right and for reasons tied up with space and time, the topic of my multi-authored book On Space and Time. The point is that spacetime itself appears to be quantum. As part of that, we can expect that space is also typically quantum. Now, the notion of symmetry grew out of things like reflections or rotations of objects in space. Patterns are usually patterns in some space. This is by no means exclusive but at least for basic examples like these, the notion of symmetry therefore needs to be correspondingly quantum. We need a new concept, quantum symmetry.