There are more than 100 essays in the FQXi essay competition, covering the whole spectrum of craziness from practically mainstream to completely absurd. The point, of course, is to draw together and share lots of crazy ideas and get some discussion going as to which of them show promise for new approaches to old problems. It is counterproductive to dismiss any of them without first engaging with the discussion.

An essay I particularly liked was by Boris Semyonovich Dizhechko in which he argues for a Cartesian view of reality, in which matter and space are really the same thing. This philosophical viewpoint is quite attractive to those who try to explain macroscopic features such as spacetime as `emergent’ from aggregates of more elementary concepts. My view is rather similar, but with a relativistic slant: that is, I do not accept space as a fundamental concept, but insist on using spacetime instead.

The separation of spacetime into space and time is a property of the observer. It is then absolutely critical to maintain clarity as to which parts of a model are observer-independent and which are not. It is a main theme of this blog that this clarity is missing (and always has been) from all discussion of quantum mechanics. Wherever probability enters into quantum mechanics, one can take the view that the experiment is an “observer”, and that the uncertainty arises from an underlying observer-dependence. I have discussed many examples on this blog, including neutrino oscillations, kaon oscillations and others.

The central problem of quantum mechanics, as I see it, is that of interpretation of the spinor. In mainstream quantum mechanics, the spinor is a piece of magic that happens to work to make predictions. As such, I regard it in much the same light as any other piece of magic that claims to predict the future, such as horoscopes, crystal balls and tea-leaves. It may well be argued that quantum mechanics does a better job of prediction than these other methods, but the predictions are on different scales so cannot be directly compared. Either way, the spinor is still magic, and does not exist in the real universe.

It is of course true that a spinor (2-dimensional complex) cannot be embedded in Euclidean 3-space. But there is nothing to prevent it from embedding in 4-dimensional spacetime. There is therefore nothing to prevent us from regarding a fundamental spin 1/2 particle as a fundamental quantum of spacetime. Then the macroscopic structure of spacetime is built up from the local interactions of these spinors with each other. Everything in this blog is really just an elaboration of this idea, with some mathematics to describe space-time on different scales.

In particular, while spacetime on a macroscopic scale looks pretty rigid (as long as you don’t travel so fast that time dilation and Lorentz contraction start to kick in), on a microscopic scale it starts to look distinctly rubbery, or worse. At the smallest possible scales, spacetime effectively loses its structure altogether. But the elementary particles of which spacetime is made are still 4-dimensional objects, and therefore the local symmetry group in which the particle operates cannot be anything other than SL(4,R). This is not the symmetry group of the particle itself, which is obviously finite: it is the symmetry group of the spacetime environment in which the particle finds itself.

In other words, this group SL(4,R) contains within itself all the information required to describe the interactions of the particle with its environment, that is with other particles. Details can be found in many posts on this blog. For example, the measured value of the mass of an elementary particle contains too much information to be intrinsic to the particle, and instead lies in the group SL(4,R) that describes how the particle relates to its environment. Understanding mass therefore amounts to understanding this group, and how it actually models the relationship of a particle to its environment.