Matter and Quantum Conditions
The points within the primordial vacuum are indistinguishable from one another. The physical vacuum exhibits extension and the points within it are distinguishable from one another. This property of the physical vacuum is attributed to the presence of matter fields. The present approach to understanding physical phenomena indicates that the physical vacuum is not devoid of matter states, but is emergent from the primordial vacuum by virtue of the presence of matter states.
This state of affairs follows naturally from the necessity of quantum conditions. The manifestation of extension necessitates a conjugate property in accordance with the quantum conditions. If the property of extension has units of length then the conjugate property has units of momentum such that the product of the two has units of action. These properties are properties of quantum states of matter. The determination of location within the vacuum is a determination of a quantum state. This quantum state can be described by a wavefunction that is a function of the spacetime coordinates.
The quantum conditions follow naturally if the conjugate property is expressed using an operator on the wavefunctions that involves taking the derivative of the wavefunction with respect to the coordinates and multiplying by a factor with units of action. The quantum conditions are that the commutation of the momentum and position operators gives the factor with units of action.
As the two properties required for quantum conditions in the emergent spacetime points represent determinations of conjugate properties of quantum states, the uncertainty principle must apply to these determinations. As the spacetime vacuum exhibits extension due to the existence of matter, the uncertainty principle drives the virtual processes that maintain extension. These processes give rise to what is referred to as the vacuum energy.
The emergence of matter states is inherent in the emergence of spacetime points from the set of primordial vacuum points. This mechanism gives rise to the metric of matter as a functional of the matter fields and to the vacuum energy necessitated by the quantum conditions along with the uncertainty principle. The metric tensor describes the macroscopic character of the emergent spacetime, while the quantum conditions describe the quantum character of the emergent spacetime. Both the metric tensor and the wavefunction arise from the role that matter plays in the emergence of spacetime points from the primordial vacuum.