In quantum mechanics spin can be described as that while rotating around the spin axis, the phase rotates "spin" times – in mathematics it’s called Conley (or Morse) index of topological singularity, it’s conservation can be also seen in argument principle in complex analysis.

So particles are at least topological singularities. I'll try to convince that this underestimated property can lead to explanations from that fermions are extremely common particles up to the 'coincidence' that the number of lepton/quark generations is ... the number of spatial dimensions.

I've made a simple demonstration which shows qualitative behavior of the phase while separation of topological singularities, like in particle decay or spontaneous creation of particle-antiparticle: http://demonstrations.wolfram.com/Se...Singularities/

The other reason to imagine particles as topological singularity or a combination of a few of them is very strong property of spin/charge conservation. Generally for these conservation properties it’s important that some ‘phase’ is well defined almost everywhere – for example when two atoms are getting closer, phases of their wavefunctions should have to synchronize before.

Looking form this perspective, phases can be imagined as a continuous field of nonzero length vectors – there is some nonzero vector in every point.

The problem is in the center of a singularity – the phase cannot be continuous there. A solution is that the length of vectors decreases to zero in such critical points. To explain it form physical point of view we can look at Higg’s mechanism – that energy is minimal not for zero vectors, but for vectors for example of given length.

So finally fields required to construct such topological singularities can be field of vectors with almost the same length everywhere but some neighborhoods of the singularities where they vanishes in continuous way.

These necessary out of energetic minimum vectors could explain (sum up to?) the mass of the particle.

Topological singularity for charge doesn’t have something like ‘spin axis’ – they can be ‘pointlike’ (like blurred Planck's scale balls).

Spins are much more complicated – they are kind of two-dimensional – singularity is ‘inside’ 2D plane orthogonal to the spin axis. Like the middle of a tornado – it’s rather ‘curvelike’.

The first ‘problem’ is the construction of 1/2 spin particles – after rotating around the singularity, the spin makes only half rotation – vector becomes opposite one.

So if we forget about arrows of vectors – use field of directions – spin 1/2 particles are allowed as in the demonstration – in fact they are the simplest ‘topological excitations’ of such fields … and most of our fundamental particles have 1/2 spin …

How directions – ‘vectors without arrows’ can be physical?

For example imagine stress tensor – symmetric matrix in each point –

we can diagonize it and imagine as an ellipsoid in each point – longest axis (dominant eigenvector) doesn’t choose ‘arrow’ – direction fields can be also natural in physics … and they naturally produce fermions …

It's emphasized axis - eigenvector for the smallest or largest or negative eigenvalue would have the strongest energetic preference to align in the same direction - it would create local time dimension and its rotation toward energy - creating gravity and GR related effects.

One of other three axises could create one type of singularity, and there still would remain enough degrees of freedom to create additional singularity - to combine spin and charge singularity in one particle - it could explain why there is 3*3 leptons/quarks types of particles.

Another ‘problem’ about spins is behavior while moving the plane in ‘spin axis’ direction – like looking on tornado restricted to higher and higher 2D horizontal planes - the field should change continuously, so the critical point should so. We see that conservation doesn’t allow it to just vanish – to do it, it has to meet with opposite spin.

This problem occurs also in standard quantum mechanics – for example there are e^(i phi) like terms in basic solutions for hydrogen atom – what happens with them ‘outside the atom’?

It strongly suggest that against intuition, spin is not ‘pointlike’ but rather curve-like – it’s a ‘curve along it’s spin axis’.

For example a couple of electrons could look like: a curve for spin up with the charge singularity somewhere in the middle, the same for spin down - connected in ending points, creating kind of loop.

Without the charges which somehow energetically ‘likes’ to connect with spin, the loop would annihilate and it’s momentums should create two photon-like excitations.

Two ‘spin curves’ could reconnect exchanging its parts, creating some complicated, dynamical structure of spin curves.

Maybe it’s why electrons like to pair in orbits of atoms, or as a stable Cooper pairs (reconnections should create viscosity…)

Bolzman distribution among trajectories gives something similar to QM, but without Wick’s rotation

http://www.thescienceforum.com/viewtopic.php?p=158008

In some way this model corresponds better to reality – in standard QM all energy levels of a well like made by a nucleus are stable, but in the real physics they want to get to the ground state (producing a photon). Without Wick’s rotation eigenfunctions are still stable, but the smallest fluctuation make them drop to the ground state. What this model misses is interference, but it can be added by some internal rotation of particles.

Anyway this simple model shows that there is no problem with connecting deterministic physics with squares appearing in QM. It suggests that maybe a classical field theory would be sufficient … when we understand what creation/annihilation operators really do – what particles are … the strongest conservation principle – of spin and charge suggests that they are just made of topological singularities… ?

What do you think about it?

I was said that this kind of ideas are considered, but I couldn’t find any concrete papers?

There started some discussion here:

http://groups.google.com/group/sci.p...817eec4df9bc6#