Fundamentals of physics

Composite objects and the Separation of Metrics

Two particles, a and b, combine under an attractive force. Initially, each is driven from Tempospace (T) and the connecting wave functions are projected into the corresponding Real Space (r). Both obey the equation of connection (the GEC) shown on Home page 2, depicted by the left side below.

The Tempospace connections combine to drive the modified system with a scalar `Tempodriver' t_a,b in the Centre of Mass frame. This drives both particles and projects a wave function into the relative real space (r_a,b), depicted by the right side. The combined object is also driven on external tempospace (T_a+b), with an external wave function projecting into r_a+b. The separation occurs because the spatial and temporal metrics are signed and complementary (meaning the virtual dimensions of one correspond to the real dimensions of the other - see The twin paradox), and there is a net binding energy.

Note that a tempodriver has only one real time dimension, so it cannot be boosted in isolation, and relative real space has only 3 real length dimensions. The virtual dimensions for all but one of the combined objects have disappeared. The above is similar to the description in quantum mechanics, but the concept of tempodrivers does not exist there - it is logically missing, so that time becomes ambiguous (see Schrödinger's cat resolved). The separation of metrics can be conveniently depicted by Metric Structure Diagrams, which are a more compact form of the figure shown above.

The GEC for the combined particles, in the relative real space r_a,b and with 1/_μa,b = 1/_μa + 1/_μb :

internal energy = Mc² = modal energy + spatial energy + potential energy
i ħ^δ/_δtψ = Mc²ψ = [m_ac²+m_bc² - ^ħ2/_2μa,b ∂_a,b² + V(r_a,b)]ψ

When a composite object disintegrates (due to excess spatial energy), this makes an 'entangled wave function' - still driven by a single connection to external tempospace. This introduces randomness into the combined wave function. Any external exchange of energy here will cause the spatial and temporal metrics to 'rejoin', so that the virtual dimensions re-appear allowing the components to have separate boosts again (left side in the figure) and leading to unpredictable, historical consequences.

These new physical principles clearly distinguish reality from the Platonic world of continuous mathematics, but without violating the laws of relativity or Newtonian mechanics.

Mass, length and time intervals

These arise from the three metric spaces, through the mechanism of the separation of metrics (click to view)

Inertial mass (M) is determined by the frequency (f) with which modal space resonates, when driven by tempospace (M=hf/c² in the GEC). But composite objects also have characteristic masses, corresponding to solutions of the separated form of the GEC, giving the same expression.

Length is determined by the relative position wave functions of composite objects (such as r_a,b above). Length intervals project into external tempospace, when composite objects are driven. This occurs because, when complementary metric spaces are connected by a wave function, the real dimensions of one overlay the virtual dimensions of the other.

Time intervals are determined by changes in the driving phase, when massive particles are projected by the GEC. This becomes observable when transitions within known particles cause macroscopic changes to a display: transitions always occur in proportion to the driven phase angle. So time is universally scaled by the modal resonant frequencies corresponding to the elementary particles, and it also depends on the attractive forces holding them together.

Heat, work and action

These quantities also arise from the multi-metric, through application of the GEC (click to view)

The relative position wave function, in the real space between bound particles, can itself be harmonically driven, causing them to oscillate about some mean separation, describing a 'phonon'. This kind of motion provides the major component of heat, but it can also include usable kinetic energy (if it has an observable phase angle). Heat (Q) is incoherent spatial motion of the (many) particles bound into macroscopic objects. It has no motion vectors, since wave functions can oscillate in all available directions simultaneously. Since phonons have no conserved quantum numbers, their tempodrivers can coalesce, describing the transition to thermodynamic equilibrium.

Where a tempodriven object moves relative to other, separately driven objects, there is free kinetic energy (T). This is associated with measurable, vector, relative velocity. Thus heat is associated with real space, but work (meaning free kinetic energy) is associated with tempospace.

Action in tri-space corresponds to the total phase change (of external tempospace), within any closed system in a fixed time interval. The rate of change of action (called the `Lagrangian') is thus the total driven frequency and the system evolves in a way that makes the total action stationary. Connections of tri-space can thus be described by Lagrangian density functions) (using more advanced maths).

Mass-energy and heat are driven in the local rest frame, making a positive contribution to the Lagrangian. Then relative motion between externally-driven objects reduces their net contribution by T, (according to the Lorentz transformation law - see The twin paradox) so that the net Lagrangian is ∑Mc²+Q+V-T where V represents potential energy. No other theory can distinguish between heat Q and work T at the fundamental level.

Quantisation by the multi-metric

Tri-space causes all forms of quantisation in nature according to the `Zeroth Law' (click to view)

When N distinct, metric spaces are connected by a steady wave function, there must occur (N-1) distinct quantisations. This is because tempospace drives the wave function into every other available space, causing it to project with a definite energy to satisfy the boundary conditions in each one.

For example, atomic electrons are driven from tempospace into modal space (first quantisation), and then the wave function must project consistently into real space (second quantisation) - see the GEC on Home page 2. Further examples include the excitations of oscillator modes in matter ('phonons'), where the lattice allows tempospace to connect to real space directly (single quantisation).

Some conclusions

No system containig multiple connections to external Tempospace can be described by a single wave function (unless they are identical) - see the diagram.

Another conclusion arising partly from this page is that special relativity, quantum mechanics and thermodynamics can all be derived from the tri-space description of nature. But tri-space cannot be derived from any or all of those other theories, so it must be a new, fundamental theory of physics.

The quantisation law, taken together with a generalised exchange symmetry principle for identical particles, can replace all of the foundation rules of quantum field theory (click to view).

The tempo-driver exchange symmetry for identical objects must be odd for fermions or even for bosons. (A Fermion is a particle with half-integer internal angular momentum: Bosons have integer internal angular momentum.) This must match the product of the wave function exchange symmetries from all of the connected metric spaces.

For example, electrons are fermions, so any multi-electron wave function must have net odd exchange symmetry for any pair. We assume that whole elementary particles are all even in modal space, but hadron isospin must extend this concept. (Isospin is a symmetry of hadrons, where for example protons are exchanged with neutrons within a nuclear orbital.)

Robert Herrod
Örkelljunga, Sweden, May 2021 (last revised May 2025)