Where does an electron live?

The belief that a quantum particle such as the electron lives in spacetime is the last vestige of a mechanistic Newtonian view of the universe. In which space is absolute, time is absolute, and objects are embedded in space and time.

Special relativity took away the independent absolute status of space and of time, and gave us instead a four dimensional spacetime, in which classical material bodies and fields live. The geometry of spacetime is absolute and flat.

General relativity taught us that the geometry of spacetime is not absolute, but is determined by the classical bodies and fields which live in it. In turn, the geometry tells matter how to move. Also, it is a consequence of the Einstein hole argument that it is not possible to give an operational meaning to the point structure of the spacetime manifold, unless there overlies on it a non-trivial classical metric.

Quantum theory tells us that microscopic objects do not move on classical trajectories. However, the theory does retain classical spacetime, with its point structure. This latter retention however contradicts the Einstein hole argument. Because the metric undergoes quantum fluctuations, and is no longer classical. Therefore a quantum particle such as the electron cannot be said to live in a classical spacetime, except in an approximate roundabout sense.

Rather, a quantum particle lives in a complex space whose geometric symmetries are a union of the internal symmetries of the standard model (electroweak and color) and the Lorentz symmetry of the standard model. In such a space, the electron evolves dynamically, in a newly introduced absolute time, which is a feature of this complex space, not possessed by classical geometry.

When the elementary particles living in such a space form large scale entangled systems, they undergo a quantum-to-classical transition and are confined to 4D Lorentz invariant spacetime, which, because of the classical nature of the bodies which dominate it, acquires the classical geometry given by Einstein's general relativity.

A quantum particle such as the electron, which has not undergone the quantum-to-classical transition, continues to live in the original complex space. We incorrectly assume that the electron also lives in the emergent classical spacetime. However, this classical 4D spacetime is the domain only of classical objects and fields. Not of quantum systems.