We’ve just finished some work that shows that it is possible to conceive of models for the internal structure of particles. You can read the paper here: http://vixra.org/abs/1203.0086

Technically we have provided a non-local hidden-varible (NLHV) solution for fundamental particle structure. In plain language: we have produced a model of the inside of a particle (photon, electron, etc.) showing how the existence of internal structures could explain the behaviour of those particles, including the faster-than-light communication between entangled particles.

**What does this paper achieve?**

This paper is interesting in a conceptual way because it shows that it is not necessary to think of particles as zero-dimensional points. It is also potentially significant in a philosophical way because it refutes locality while still preserving an approximate form of locality and realism.

Refuting locality is not a big thing in itself because quantum mechanics does likewise. The novelty is in providing an explanation of the proposed underlying mechanisms, and the ability to explain why locality does exist for practical purposes. This could help explain the long-standing puzzle about locality.

A third area where the work may have significant implications is for the existing mathematical proofs (Bell-type inequalities) that deny certain classes of hidden-variable solutions. If our work stands up, then its provision of even a single example of a workable model of internal particle structure will falsify those mathematical attempts.

We don’t use the term ‘particle’, because it is too laden with the idea of zero-dimensional (0-D) point. We suggest that whole 0-D idea is the root of all the conceptual difficulties in fundamental physics. We use the term ‘particule’ for 3-D designs like ours.

**Background**

The Bell-type theorems are mathematical proofs that certain types of hidden variable solutions are incompatible with observed entanglement. In turn, entanglement refers to the ability of suitably prepared particles, e.g. pairs of photons, to influence each other instantly across a wide gap. So the empirical evidence is that faster-than-light (superluminal) communication can occur between particles at a distance.

The whole idea of entanglement has been enormously problematic in a conceptual sense. This is what Einstein referred to as ‘spooky action at a distance‘ and it still has not really been explained to complete satisfaction. Even more troublesome in a philosophical sense is that it implies that particles are affected by far-away effects, not only by their immediate neighbourhood: so the principle of locality also seems to fail.

Bell was the first to propose a mathematical proof that hidden-variables (HV) really could not cut it. But his proof only invalidated some types of HV solutions. Other proofs followed over the years by others, and recently it had been looking highly unlikely that any HV solution could exist: there was not much space left in which a solution could be hiding. The general feeling was that no kind of hidden-variable solution could now realistically be possible, so particles really ‘must’ be 0-D points, and if there was going to be a HV solution then it would have to be ‘counter-intuitive’. Indeed, the solution we propose in the cordus conjecture could easily be described in those terms.

**Related articles **

- Entanglement: en.wikipedia.org/wiki/Quantum_entanglement
- Locaility: http://en.wikipedia.org/wiki/Principle_of_locality

Norsen, T. (2011) *J.S. Bell’s Concept of Local Causality*. arxiv **0707.0401v3**, 1-19 DOI: arxiv.org/abs/0707.0401v3. Available from: http://arxiv.org/abs/0707.0401v3.

Marco, G., *Research on hidden variable theories: A review of recent progresses.* Physics Reports, 2005. **413**(6): p. 319-396. Available from: http://www.sciencedirect.com/science/article/pii/S037015730500147X.

Laudisa, F., *Non-Local Realistic Theories and the Scope of the Bell Theorem.* Foundations of Physics, 2008. **38**(12): p. 1110-1132.DOI: 10.1007/s10701-008-9255-8. Available from: http://dx.doi.org/10.1007/s10701-008-9255-8.