Since the scalar product is the only internal structure of a Hilbert space, all vectors of norm 1 are equivalent, in the sense that they form a perfect sphere in the Hilbert space, on which every vector looks the same. The state vector of the univers
e contains no information that distinguishes it from other state vectors of the same Hilbert space. If the state vector is considered as the only fundamental entity, the world is completely structureless. The illusion of interacting subsystems is due to a bad choice of factorization (i.e. decomposition into subsystems) of the Hilbert space. There is always a more appropriate factorization available in which subsystems dont interact and nothing happens at all. This factorization absorbs the time evolution of the state vector in a trivial way. The Many Worlds Interpretation is therefore rather a No World Interpretation. A state vector gets the property of representing a structure only with respect to an external observer who measures the state according to a specific factorization and basis.
Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields.
Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a non-vanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops.
