Sorry, but no. The Dirac equation is invariant under Lorentz transformations, so what’s local in one inertial reference frame is local in any other as well.
The Dirac equation is invariant, but there are a lot of problems with the concept of locality. For example, if you want to create localised one-particle states that remain local in any reference frame and form an orthonormal eigenbasis of the (one-particle subspace of) the Hilbert space, you will find it impossible.
The canonical solution in axiomatic QFT is to begin with local operations instead of localised particles. However, to see the problem, one has to question the notion of measurement and define it in a covariant manner, which may be a mess. See e.g.
I am sympathetic to the approach which is used by quantum gravitists, which uses extended Hamiltonian formalism and the Wheeler—DeWitt equation instead of the Schrödinger one. This approach doesn’t use time as special, however the phase space isn’t isomorphic to the state space on the classical level and similar thing holds on the quantum level for the Hilbert space, which makes the interpretation less obvious.
You’re missing my point. To make sense of the Dirac equation, you have to interpret it as a statement about field operators, so locality means (e.g.) that spacelike-separated operators commute. But that’s just a statement about expectation values of observables. MWI is supposed to be a comprehensive ontological interpretation, i.e. a theory of what is actually there in reality.
You seem to be saying that configurations (field configurations, particle configurations, it makes no difference for this argument) are what is actually there. But a “configuration” is spatially extended. Therefore, it requires a universal time coordinate. Everett worlds are always defined with respect to a particular time-slicing—a particular set of spacelike hypersurfaces. From a relativistic perspective, it looks as arbitrary as any “objective collapse” theory.
The moment you speak about configuration space as real, you have already adopted a preferred frame. That is the problem.
Sorry, but no. The Dirac equation is invariant under Lorentz transformations, so what’s local in one inertial reference frame is local in any other as well.
The Dirac equation is invariant, but there are a lot of problems with the concept of locality. For example, if you want to create localised one-particle states that remain local in any reference frame and form an orthonormal eigenbasis of the (one-particle subspace of) the Hilbert space, you will find it impossible.
The canonical solution in axiomatic QFT is to begin with local operations instead of localised particles. However, to see the problem, one has to question the notion of measurement and define it in a covariant manner, which may be a mess. See e.g.
http://prd.aps.org/abstract/PRD/v66/i2/e023510
I am sympathetic to the approach which is used by quantum gravitists, which uses extended Hamiltonian formalism and the Wheeler—DeWitt equation instead of the Schrödinger one. This approach doesn’t use time as special, however the phase space isn’t isomorphic to the state space on the classical level and similar thing holds on the quantum level for the Hilbert space, which makes the interpretation less obvious.
You’re missing my point. To make sense of the Dirac equation, you have to interpret it as a statement about field operators, so locality means (e.g.) that spacelike-separated operators commute. But that’s just a statement about expectation values of observables. MWI is supposed to be a comprehensive ontological interpretation, i.e. a theory of what is actually there in reality.
You seem to be saying that configurations (field configurations, particle configurations, it makes no difference for this argument) are what is actually there. But a “configuration” is spatially extended. Therefore, it requires a universal time coordinate. Everett worlds are always defined with respect to a particular time-slicing—a particular set of spacelike hypersurfaces. From a relativistic perspective, it looks as arbitrary as any “objective collapse” theory.