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Introduction to Tri-space
Welcome to the Tri-space Laboratory. Here, you can read about a multi-metric theory of space, time and matter, which was originally developed in 1997. This was motivated by my personal dissatisfaction with the level of understanding in theoretical physics, particularly nuclear and elementary particle physics, but also with the absence of foundations for quantum mechanics. The new theory appears to represent a mathematically simple, consistent and logically completable account of all of the laws of physics (see our Mission Statement).
Although it appears to complement Newtonian physics, special relativity is flawed by the requirement that physical length and historical time arise from the same metric, thus relating length and time intervals by √-1 (see The twin paradox). Quantum mechanics is based on a set of outrageously ad hoc rules and assumptions - yet it seems to make consistent but incomplete sense. Neither theory can encapsulate causality in time or the principles of classical thermodynamics; both are completely time reversible. These matters cannot be fixed after the metric structure of space and time has been over-simplified.
The multi-metric approach of 'Tri-space' (see figure on Page 2) is wholly consistent with the established laws of physics. The concept of an unsigned space-time metric is replaced by several signed metric spaces, defining 'energy' and making the physical dimensions specific to their functions (see Schrödinger's cat resolved). Quantisation occurs when these manifolds inter-connect, creating particles and sharing energy: history is made whenever the topology of connection changes. In between times, the amplitudes of inter-connection evolve and propagate - just like the corresponding wave function in quantum mechanics (see Space & time diagram).
But now material length is distinguished from distance in empty space, the one overlaying the other. This concept has enabled me to construct a theory of bonding for the liquid state, which can also be applied to glass and to the pairing of electrons in anisotropic crystalline lattices, describing a robust form of superconductivity. None of this is possible on a single, space-time manifold. The scope of my suggestion for quantum theory and condensed matter theory is summarised in Why Tri-space?
By connecting spaces with different metrics, using a 'wave function', various kinds of elementary particles can be described, with purely geometrical quantum numbers. By adding universal force laws, acting between the particles according to their wave functions, masses or quantum numbers, all of the forces of physics can be described.
Under How time works is a visualisation of the Tri-space description of how time works, in the case where a system of interacting particles is evolving. The process is inherently statistical and time-irreversible - like a perpetual game of dice.
Introduction page 2
My suggestion is that the classical metric itself is in fact composite - and I don't mean just rolled-up-small, extra dimensions. I mean a set of inter-connecting, signed, metric spaces, each of which provides a sub-set of nature's laws (see the figure). 'Tempospace' corresponds to time and empty space, which connects to the other spaces by a 'wave function' (ψ). Tempospace is global, but each connection projects into a separate instance of 'Real Space', giving local length in 3-dimensions. The space and time manifold is thus 8-dimensional, but it is divided into two 'complementary' metric spaces.
The Iceberg Diagram: Tempospace drives steady oscillations of Modal space and excess energy projects that wave function into Real space.
The Generic Equation of Connection, in the rest frame using ψ(t;rs) and Planck constant ħ with i2=-1 :-
driving energy = E0 = modal energy + spatial energy + potential energy
i ħδ/δtψ = E0ψ
= [Mc2 - ħ2/2μ
∂s2 + V(rs)]ψ
The left side describes the constant driving energy E0. M is the fixed mass; Mc2 is the corresponding energy (E0 and M are positive). The spatial energy resembles that in Schrödinger's equation in quantum mechanics and V(rs) describes the local potential energy. These must add up to a uniform value (but the 'effective mass' μ may not be uniform - as determined by the spatial metric: 2μ =M +(E0-V)/c2 = 2M+Es/c2 where Es is the spatial energy). All terms in a GEC are Lorentz scalars.
The GEC is 'scalable', for composite particles, because E0 can replace (part of) Mc2 at the next level of structure, which projects into a separate Real Space. A form of classical metric re-emerges as the resultant space and time, when the structure of matter has been resolved. But here history is inexplicably determined by matter and with instantaneous ('spooky') action at a distance when wave functions resolve. These are the main mysteries that haunt the theories of quantum mechanics and special relativity.
We can infer the properties of the underlying metrics from studying matter and the particles of nature, at all levels of structure and in all of its observable forms. I believe that one particular, multi-metric structure generates all of the forces and particles in nature, and that this should be understood by future students of physics (see Fundamentals of physics and Laws of the Multi-Metric and Full Multi-Metric Structure).
You will not yet find this multi-metric theory in any peer-reviewed journal (for the reasons described in Calling Organ Grinders). You can find more introductory material under Frequent Q&As and we offer some Free Articles. Your comments on this theory and my presentation of it are very welcome (to robertherrod@tri-space-lab.com).
Just one proviso - you must never use this theory to design or develop weapons of any kind. Further, the author accepts no responsibility for the correctness of the theory or any consequences of its application.
Robert Herrod
Örkelljunga, Sweden, November 2017 (last revised April 2026)