Laws of the Tri-space Theory

The laws associated with multi-metric theory (Tri-space) correspond somewhat with the thermodynamic laws, so I have numbered them as such. These laws relate to the basic multi-metric structure and function; they do not depend on the elementary particles and forces of nature.

Tri-space consists of a group of signed, metric spaces, which connect themselves together spontaneously, with a 'wave function', when energy is available. The 'Zeroth Law' describes the origin and nature of the quantisation of wave functions; it is described in Fundamentals of Physics. This law is unique to multi-metric theory (any link with the existence of temperature is purely circumstantial).

The 'First Law' was introduced on Home page 2 and extended to multi-particle systems in Fundamentals of Physics. To describe any particle or form of matter, Tempospace drives steady oscillations of Modal space, or internal Tempospace, and excess energy projects that wave function into Real space - either external (with four dimensions) or internal (with three or fewer dimensions), as described in e.g. Metric Structure Diagrams. Applying Born's Rule from quantum mechanics, any steady wave function is normalised in the corresponding Real space. It follows from the zeroth law that all such objects are quantised.

This is always expressed by a General Equation of Connection (GEC), equating the driving frequency energy with the sum of the energies from every driven space, plus any interaction energy (this sum can be called the 'full Hamiltonian'). It also relates inertial mass (equal to E₀/c²) to the driven frequency. The GEC corresponds to a Lorentz invariant form of the relevant equation of state. This implies total energy conservation and it includes the equivalence (in energy content) of heat and work.

The 'Second Law' concerns the nature of transitions, in the multi-metric. It is a universal law corresponding to Fermi's Golden Rule of quantum mechanics, applied in the real space corresponding to the centre of mass of the interacting objects.

The rate of transition, from any definite, initial, physical state of projection to any other state, which is accessible under the acting forces (i.e. allowed), is determined only by the Hamiltonian applied between the final and initial states (the 'matrix element') and the spatial density of final states per unit energy:-

Planck const. * transition rate = 4π² * absolute square of matrix element *
spatial density of final states per unit energy * no. of final spin states

One can use just a 'difference Hamiltonian', expressing the differences between the states (which may be tiny compared to their rest mass energy). The law is time reversible, but the wave function may be collapsed already into a pure input state, or it may collapse due to a subsequent inelastic process, making the transition definite (see Schrödinger's cat resolved). The same law is used to determine the rate at which elementary particles are created or destroyed in fundamental processes, such as those described in quantum field theory.

The 'Third Law' concerns the nature of causal time and how history is made. It is described in How time works and by the diagram in Space & time diagram. This law is also unique to the multi-metric theory (quantum theory cannot describe elapsed time, whilst classical mechanics is purely deterministic):-

Free object wave functions always expand into their external real spaces of projection,
between re-connection events, describing the causal arrow of time AND
Excess spatial energy expands into internal real spaces,
describing the thermodynamic arrow of time.

These are just mathematical consequences of the first and second laws above, but with profound physical implications. These follow because, when spaces with complementary metrics are connected by a wave function, the real dimensions of one overlay the virtual dimensions of the other. This causes the corresponding object to make inherently unpredictable displacements in the space of the driving metric, at subsequent events.

This law tells us not only that heat always flows from hot to cold, but also how it does so, allowing the calculation of thermal conductivity in any kind of matter (which is not possible using quantum mechanics).

One consequence, of applying these laws to dynamical systems, is that each (separately driven) sub-system settles into the lowest accessible state of internal energy (the 'ground state'). I term this effect 'Schrödinger's Law', because it is assumed or required when applying the Schrödinger equation (or any GEC) to matter.

That's all of the basic laws. The elementary particles and forces of nature (except gravity) must be determined by the structure and functions of Modal space, and the ways that it can be connected to the spatial and temporal metrics. Gravitation corresponds to a curvature of external tempospace, in proportion to the total frequency it is driving per unit volume. This is described by Einstein's general theory of relativity and it involves no kind of quantisation.

Robert Herrod
Örkelljunga, Sweden, January 2023