Metric Structure Diagrams

These diagrams (MSDs) can represent the metric structure within any collection of objects. They depict the form of metric separation, at each separate level of internal structure, which may determine the state of matter.

As depicted on Home page 2, Tempospace (T) drives steady oscillations of Modal space (M) or internal Tempospace (t) and excess energy projects that wave function into Real space - either external (RS) or internal (rs).

In the example above, a collection of (n) isolated particles (left) are combined together at a single level of structure (centre). This describes a simple solid state, where the particles all bind to each other.

The same diagram can describe a gas sample (where the particles are contained externally), but here there is no separation of metrics. Instead, the container causes 'metric alignment', so that the particles all share the same frame of connection (the Centre of Mass frame). An escaping particle would return to the state on the left, after the system is resolved.

Tempospace may separately connect to spatial modes of oscillation within either composite phase, describing sound quanta (called 'phonons'). Thus a collection of degenarate real space wave functions can support a boson 'field'. Applying electromagnetic theory, any enclosed region of real space must contain a photon field.

On the right is shown an example of multi-level separation, where objects 1 and 2 combine first: then object 3 combines at a separate level of structure, describing a more complicated composite object. In principle, any number of particles can combine at any number of levels, within a solid compsite.

Any change in the metric structure within condensed matter corresponds to an 'internal phase transition'. The order in which metric separation occurs is determined in general by the maximum binding energy that can be released. This principle is long established in quantum mechanics, when applying the Schrödinger Equation. But in the multi-metric theory, any tempodriver is associated with the full mass-energy of the driven particles, so it also determines the inertia within a bound system (including any contained fields).

GECs can be constructed (describing the 'Equation of State') according to the metric structure shown by the corresponding MSDs. This determines the form of the GECs, but not the particle properties or the potential energy terms. Internal angular momentum ('spin') is not shown on MSDs, but any component object can have spin and any internal real space can add an integer spin, corresponding to orbital angular momentum.

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Robert Herrod
Örkelljunga, Sweden, July 2021